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MEEN 442 SolidWorks
Computer Aided Engineering Journal




         Completed by: Eric Halfmann

            Texas A&M University

                Summer 2011

               August 8, 2011
Journal Abstract
The purpose of this journal is to present my computer aided engineering (CAE) skills. My ability
to utilize engineering software (in this case SolidWorks) in the aid of design, manufacturing, and
sales will be illustrated. These three aspects are important to any engineer and will greatly
enhance my ability to successfully communicate my work and design to customers and
manufacturing personnel. The following journal will show my wide range of SolidWorks graphic
skills through the presentation of many different assignments that cover the use of all the
different features that SolidWorks has to offer. Engineering drawings per ASME standards will
be developed for some of these parts and some basic Finite Element Analysis will be performed
on one of the shafts for the Planetary Gear Reducer. Finally, my ability to utilize SolidWorks as
a computer aided engineering software and not just a graphics tool will be presented with the
design and design analysis of a Planetary Gearbox for a 1 HP 3600 rpm NEMA C Face Motor.




                                                1
Table of Contents

Journal Abstract………………………………………………………………………………………………………………………….. 1
Table of Contents………………………………………………………………………………………………………………………… 2
List of Figures…………………………………………………………………………………………………………………………. 3
List of Tables………………………………………………………………………………………………………………………….. 4
1. Planetary Gearbox Design Project……………………………………………………………………………………..                 5
       Abstract…………………………………………………………………………………………………………………………… 5
       Nomenclature…………………………………………………………………………………………………………………6
       1.1 Introduction…………………………………………………………………………………………………………….. 8
       1.2 Design Concept……………………………………………………………………………………………………….. 8
       1.3 Gear Design……………………………………………………………………………………………………………… 9
       1.4 Shaft Force and Stress Analysis……………………………………………………………………………….. 13
       1.5 Bearing Design…………………………………………………………………………………………………………. 16
       1.6 SolidWorks Modelling……………………………………………………………………………………………… 17
       1.7 SolidWorks FEA……………………………………………………………………………………………………….. 20
       1.8 Future Work…………………………………………………………………………………………………………….. 24
       1.9 Conclusion……………………………………………………………………………………………………………….. 25
       1.10 References ……………………………………………………………………………………………………………. 25
2. Vases………………………………………………………………………………………………………………………………….. 26
3. Google House…………………………………………………………………………………………………………………….. 28
4. Guide Rod Assembly Plates………………………………………………………………………………………………… 29
5. Guide Rod Assembly…………………………………………………………………………………………………………… 30
6. Rotating Crank Assembly……………………………………………………………………………………………………. 31
7. Basic Gearbox Assembly…………………………………………………………………………………………………….. 31
8. Basic Gearbox 2D Engineering Drawings…………………………………………………………………………….. 32
9. Surface Truck……………………………………………………………………………………………………………………… 36
10. Basic Finite Element Analysis (FEA) Using SolidWorks Simulation………………………………………..37
Appendix 1: Free Body Diagrams and Hand Calculations of Planetary Gearbox……..………………... 38
Appendix 2: Engineering Drawings of Planetary Gearbox Components…………………………………….. 44




                                              2
List of Figures

Figure 1: 3D Image of Proposed Planetary Gearbox Design……………………………………………………….. 9
Figure 2: Basic Figure of gear meshes and associated forces……………………………………………………… 12
Figure 3: Forces on Carrier Arm…………………………………………………………………………………………………. 15
Figure 4: Stage 1 and Stage 2 Gear Assemblies…………………………………………………………………………… 17
Figure 5: Stage 1 and Stage 2 Gear Assemblies…………………………………………………………………………… 17
Figure 6: Side Image of all gears assembled………………………………………………………………………………… 18
Figure 7: Gear Assembly with housing…………………………………………………………………………………………. 19
Figure 8: Complete Gearbox Assembly……………………………………………………………………………………….. 19
Figure 9: Bending Stress FEA of Input Shaft…………………………………………………………………………………. 20
Figure 10: Torsional FEA Analysis of the Input Shaft……………………………………………………………………. 21
Figure 11: Stage 1 Carrier Shaft Torque FEA Analysis……………………………………………………………………. 21
Figure 12: Stage 2 Carrier shaft torque analysis……………………………………………………………………………. 22
Figure 13: FEA Analysis showing the shear stresses in the carrier arm………………………………………… 22
Figure 14: Bending Stresses on Stage 1 Carrier Arm……………………………………………………………………… 23
Figure 15: Stage 2 Carrier Arm Shear and Bending FEA Analysis…………………………………………………… 23
Figure 16: Planet Shaft shear stress FEA……………………………………………………………………………………….24
Figure 17: "Round Top" vase and"Round Front" vase…………………………………………………………………. 26
Figure 18: "Mahogany Heavy" vase and "Twisted Carbon Fiber" vase………………………………………. 27
Figure 19: "Porcelain Petite" vase………………………………………………………………………………………………. 27
Figure 20: Original Google Maps image and New image with 3D model of house on the image… 28
Figure 21: 2 different angles presenting the 3D model of the house and its features……………….. 28
Figure 22: Left front and Right back isometric views of original plate……………………………………….. 29
Figure 23: Left front and Right back isometric views of Modified Plate…………………………………….. 29
Figure 24: 3D unexploded and exploded views of the Guide Rod Assembly………………………………. 30
Figure 25: Modified Guide Rod Assembly mounted on plate……………………………………………………… 30
Figure 26: Exploded View of Modified Guide Rod Assembly mounted on plate…………………………. 30
Figure 27: Crank assembly at 3 different rotated positions and rotation direction is shown………. 31
Figure 28: Isometric View of Gearbox Assembly with and without housing sides removed……….. 31
Figure 29: Exploded View of the Basic Gearbox Assembly…………………………………………………………. 32
Figure 30: Two Isometric views of the surface truck…………………………………………………………………… 36
Figure 31: Front and Rear Views of the surface truck model……………………………………………………… 36
Figure 32: Side View of truck and Side View with doors colored gray………………………………………… 36
Figure 33: Bending stress FEA of Shaft……………………………………………………………………………………….. 37
Figure 34: Deflection results of shaft FEA analysis……………………………………………………………………… 37




                                                  3
List of Tables

Planetary Gearbox Project Design Tables:
Table 1: Gear Ratios……………………………………………………………………………………………………………………… 10
Table 2: Gear Train Sizes………………………………………………………………………………………………………………. 10
Table 3: Forces on the Gears……………………………………………………………………………………………………….. 11
Table 4: Gear Stress Analysis Values……………………………………………………………………………………………. 13
Table 5: Input/Output Shaft Materials and Basic Dimensions……………………………………………………… 13
Table 6: Stresses in Gearbox Shafts……………………………………………………………………………………………… 14
Table 7: Allowable Stresses in Shafts……………………………………………………………………………………………. 14
Table 8: Keyway Design……………………………………………………………………………………………………………….. 15
Table 9: Initial Carrier Arm Stress Analysis……………………………………………………………………………………. 16
Table 10: Adjusted Carrier Arm Stress Analysis…………………………………………………………………………….. 16
Table 11: Bearing Design……………………………………………………………………………………………………………….16




                                                 4
2-Stage Planetary Gearbox Design

Texas A&M University
MEEN 442 Design Project
Completed by: Eric Halfmann
To: Mr. Randall Tucker
July 29th, 2011




                                               Abstract

A planetary gearbox is a device, like any other gearbox, used to transmit power from the motor to the
application and to adjust the speed and torque available from the motor. Planetary gear drives are able
to transmit high torques at high speeds and are used in many different applications. The following
paper describes the design of a 2-stage Planetary Speed Reducer with an overall gear ratio of 10:1 for a
1 HP 3600 rpm NEMA C Face motor. All equations for the stress and force analysis of the design are
given and a minimum safety factor of 2 is used to ensure that the proposed design is a successful design
that will hold up to the forces and torques in the system. In addition, a 3D SolidWorks model of the
gearbox is created. Using this model, the gearbox design can be effectively communicated and
illustrated as well as used to ensure the design functions correctly. Finite Element Analysis performed
on the SolidWorks model was verified by the analytical calculations and further proves that the
proposed design is adequate and will operate without failure. Finally, the SolidWorks model makes
creating engineering drawings more time efficient and puts the gearbox design in a format that is ready
to be manufactured. The following paper describes and illustrates a successful 2-stage planetary
gearbox design for a 1 HP NEMA C Face motor operating at 3600 rpms.




                                                   5
Nomenclature

b = gear thickness
d = shaft diameter
m = module
n = overall gear ratio for that particular stage
p = number of planet gears
r = radius of shaft
t = thickness of carrier arm
usp= sun/planet gear ratio
v = poisson’s number
A = cross sectional area on shaft
CG = Gradient Factor
CL = Load Factor
CR = Reliability Factor
CS = Surface Factor
CT = Temperature Factor
Crsp = Sun/planet Contact Ratio
Crrp = Ring/planet Contact Ratio
Creq = Required load rating capacity for bearing
D = Diameter of Gear
E = Modulus of Elasticity
F = force
Fe = force on the bearing
FBD = Free Body Diagram
Fp = Tangential forces
Fc = Torque producing forces on carrier arm
H = diameter of hole in the carrier arm
I = moment of Inertia
J = polar moment of Inertia
Ka = bearing shock loading factor
     = Factor for division for load between teeth
     = Load distribution factor for bending
     = Factor for the division of load between teeth
      = Load distribution factor for surface pressure
Kr = bearing reliability factor
KT = Stress Concentration Factor
L = distance from support to location of force
Lkey = length of the keyway
LR = Life of bearing corresponding to rated capacity
M = moment which is force*distance
N = number of teeth in Gear
Pm = power motor
R = Radius of Gear
           = Factor of safety
Sn = Allowable stress
Su = Ultimate strength of material
Sy = Yield strength of material

                                                        6
= allowable stress value
T = Torque
W = width of carrier arm
   = Form factor for bending stress
    = Stress Cycle Factor for bending stress
   = Reliability Factor
   = Helix angle factor for bending
   = Contact Ratio Factor for bending
   = Temperature Factor
   = Form factor for Hertzian pressure
    = Material Factor for surface pressure
   =Stress cycle factor for surface pressure
     = Hardness ratio factors for pitting resistance
    = Contact Ratio Factor for surface pressure
  = bending deflection
σ = basic moment bending stress
    = Gear Bending Stress
    = Gear Surface Pressure
    = torsional stress on shaft
   = shear stress on planet gear shaft
α = pressure angle (Here is 20 deg)
ω = angular velocity

Subscripts:
in = input to Stage
out = output of Stage
r = Ring Gear in Stage
s= Sun Gear in Stage
p= Planet Gear in Stage




                                                       7
1.1 Introduction

Motors are used to produce the energy needed for many mechanical systems to function as desired.
However, sometimes the motor doesn’t provide the required torque and/or speed, the needed
flexibility to adjust operating conditions, or provide the capabilities to be directly coupled to the
application. In these instances, gearboxes are used to bridge the gap between the motor and the
application and to increase or decrease the amount of output torque at the expense of decreasing or
increasing the operating speed. Gearboxes are commonly used in all types of vehicles to transmit the
power from the motor to the wheels of the vehicle. A particular style of gear system called a Planetary
Gear Drive is often used in vehicle transmissions as well as many other applications. The planetary gear
system is able to transmit high torques and operate at high speeds. One reason for this is because the
evenly spaced planetary gears help to keep the overall forces acting on the system symmetric and thus
sum up to zero. In other words, there are essentially no other forces acting on the shafts of the gearbox
except the torque at the input and output of each stage. This makes the planetary gearbox an attractive
solution to many gearbox needs as well as its compact and efficient design.

The design project for the MEEN 442 Summer 2011 course is to design a planetary gearbox with a 10:1
gear reduction for a 1 HP 3600 rpm NEMA C face motor similar to the one found in reference [5]. The
following text will provide the details for the design of a 2-stage planetary gearbox. The paper will
discuss the basic design concept for the gearbox, provide all necessary equations used for the design,
illustrate the use of some basic finite element analysis done using SolidWorks, and show multiple figures
and engineering drawings of the gearbox design produced using the SolidWorks 3D engineering
software. All free body diagrams (FBD) and hand calculations are provided in Appendix 1. However, the
engineering analysis software MatLab was used to do the majority of the stress analysis calculations.
This was done so that design parameters such as ring gear and shaft sizes could be altered and then the
corresponding design calculations could be easily and quickly reproduced. This made the design process
much more efficient.

                                          1.2 Design Concept

The design requirements provided no dimensional requirements and it was left up to the students to fill
in the blanks. It is assumed that only 1 gearbox will be manufactured, so readily available parts and
simple features will be used to design the gearbox to reduce the manufacturing costs of the gearbox.
Metric dimensions were chosen for the design of this project so that the common force, distance, and
weight units of newtons, meters, and kilograms used in many engineering texts could easily be used
with minimal unit conversions needed. A module value of 1 (m=1) was chosen for simplicity so that the
number of teeth for the gear equaled the pitch diameter of the gear in millimeters. It was also chosen
to design a planetary gearbox where the ring gear is stationary, the sun gear is the input, and the carrier
shaft is the output. In the design of this gearbox, it was decided that gearbox radial size was more
important than the overall weight of the system. This led to using a 2-stage design concept which
allowed for much smaller ring gears to be used to meet the 10:1 reduction. However, this adds a whole
other set of gears, but these gears will be much smaller so the weight difference could be comparable.
Due to the number of gears in a 2-stage system, the planetary gears for each system were given the
same pitch diameter so that the actual number of different gears in the system would be reduced.
According to the NEMA C Face dimensions in [6] and the common “56” frame used for these motors like
the one in [5], the diameter of the “56” frame is 6-5/8 inches. This led to a maximum ring gear pitch
diameter of 160mm (~6.3in) to be chosen so the overall radial size of the gearbox would be comparable


                                                     8
to that of the motor. All other components such as the shafts, keys, keyways, etc. were designed to
work with this basic design concept.

In addition, the housing for the gearbox is a half-shell design so that symmetry can be used to
manufacture the main housing piece. This also makes assembly, accessing, and performing
maintenance on the gearbox easy. Figure 1 is a 3D image of the planetary gearbox which will be
described in this paper.




                Figure 1: 3D Image of proposed planetary gearbox design with top of housing removed



                                               1.3 Gear Design

1.3.1 Gear Ratio Design:

To begin the design of the gearbox, the overall size for the Stage 1 ring gear needs to be determined. As
mentioned earlier, the ring gear pitch diameter chosen for Stage 1 is 160 mm. With the ring gear pitch
diameter determined, equations 1 and 2 given in [3] are used to determine the gear sizes for the sun
and planet gears. The initial design statement gave us the output power of the motor. This power is
converted to watts and then the input torque to the motor is given in equation 3 and the output torque
for that stage is give in equation 4 from the Juvinal Design Book [1]. The values for the gear reductions
and the gear sizes are given in Tables 1 and 2.

     (1)
     (2)
     (3)
     (4)




                                                        9
Table 1: Gear Ratios
                                                         Input Output
                                        Overall            10    1
                                        Stage 1             3    1
                                        Stage 2           3.33   1

                                    Overall RPM           3600      360
                                    Stage 1 RPM           3600      1200
                                    Stage 2 RPM           1200      360

                                Overall Torque (N*m)      1.98      19.8
                                   Stage 1 (N*m)          1.98      5.94
                                   Stage 2 (N*m)          5.94      19.8


                                        Table 2: Gear Train Sizes
                             Diameters (mm)        Stage 1       Stage 2
                             Ring Gear                160           140
                             Sun Gear                 80             60
                             Planet Gear              40             40

                             Number of Teeth       Stage 1     Stage 2
                             Ring Gear                160         140
                             Sun Gear                 80           60
                             Planet Gear              40           40
                                    Width for All Gears: b = 10mm

1.3.2 Gear Force and Stress Analysis:

With the gear sizes determined, then the force and stress analysis can be performed on the gears. All
FBDs associated with this section are shown in Appendix 1. The equations and process for determining
the stresses can be found in references [3] and [2]. To begin determining the forces on the system, a
FBD for the carrier/output shaft, the planet gear, sun gear, and ring gears are drawn. Using the FBD’s
and equations 5-7 from [3], we were able to determine the tangential forces, Fp, on the gear teeth and
the torque producing force, Fc, on the carrier arms. The forces are shown in Table 3.

     (5)
     (6)                                                     or
     (7)




                                                   10
Table 3: Forces on the Gears
                                    Stage 1: Forces
                                   Tangential Force             16.5 N
                                   Carrier Force                 33 N
                                    Stage 2: Forces
                                   Tangential Force             49.5 N
                                   Carrier Force                 99 N


With the forces on the gears determined, then the stress analysis can be performed. According to [1]
and [2], the surface pressure and the bending stress are the two critical stress analysis procedures that
need to be performed on the gears. The following equations used for this analysis are from reference
[3] because in [3] they had already derived the changes needed for the different gear meshes, especially
the internal gear mesh which required different derivation for its contact ratio. Reference [3] uses the
Swedish gear standards, but when compared to the procedures in [1] and [2] the stress analysis seems
to be identical. A check was made with a few of the different equations and the values calculated were
the same, so it is assumed the stress analysis in [3] is adequate for American standards.

For the sun/planet gear mesh, equations 8-12 are used to determine the surface pressure on the gears.
In equation 8,                are assumed to be 1 and 1.3 as used in [3]. Equations 13-16 are used to
calculate the bending stress in the gears. Here is 1 and                  are given the same value as
              which is suggested in [3].

     (8)


     (9)                  √                                 √


     (10)                                               √
                                                                                   **All values from the presented
                                                                                   calculations in this paper are
                                                                                   logged in the Tables.
     (11)                                               √



     (12)                                               √


     (13)


     (14)

     (15)



                                                   11
Sun/Planet Mesh
                                                         Fc               Ring/Planet Mesh




                                                       Planet        Fp
                                           Fp
                                                       Gear

                           Sun Gear                                   Ring
                                                                      Gear


                            Figure 2: Figure of gear meshes and the associated forces

For the ring/planet gear mesh, the same equations that were used for the sun/planet gear mesh are
used here except with a small change in the contact pressure calculations. This change is mainly a slight
difference in calculating the contact ratio between the planet and ring gear which is given in equations
16 and 17.

     (16)


     (17)                  √                                          √



With the stresses determined, the maximum allowable stress had to be calculated to determine
whether the stresses found in the previous equations would be acceptable or not. The following
equations, 18 and 19, for determining the maximum allowable stresses are from [2]. The values for the
allowable stress factors given in equations 18 and 19 are given in reference [2]. The material used for
the allowable stress is assumed Grade 1 steel as given in Tables 14-3 and 14-6 in reference [2] and a
safety factor of 2 is used as suggested by [1]. Table 4 shows the allowable stresses and the calculated
bending and surface stresses found using the equations described. Observing the values in Table 4
verifies that the stresses in the gears do not exceed the allowable surface and bending stresses and thus
the proposed design will be satisfactory for the gearbox specifications desired in this project.

Also, the catalog torque limits can be observed to come to this same conclusion. According to
www.qtcgears.com, the allowable torque for the planet gear is 14.7Nm, and the allowable torques for
similar sun gears for stage 1 and stage 2 are 33.9Nm and 24.2Nm respectively. For the specified
gearbox, these torques are not exceeded and thus the chosen gears are satisfactory.

     (18)
     (19)




                                                       12
Table 4: Gear Stress Analysis Values
                        Stage 1: Sun/Planet Gear Mesh                           Stage 2: Sun/Planet Gear Mesh
               Surface Pressure                 115.7 N/mm^2                 Surface Pressure 229.24 N/mm^2
               Bending Stress                   2.7 N/mm^2                   Bending Stress     8.24 N/mm^2
                        Stage 1: Ring/Planet Gear Mesh                         Stage 2: Ring/Planet Gear Mesh
               Surface Pressure                 56.14 N/mm^2                 Surface Pressure 94.7 N/mm^2
               Bending Stress                   2.5 N/mm^2                   Bending Stress     7.55 N/mm^2
                   Allowable Stress Values
               Allowable Surface Presssure      390.7 N/mm^2
               Allowable Bending Stress         103.3 N/mm^2

                                             1.4 Shaft Force and Stress Analysis

    1.4.1 Input/Output Shaft Analysis:

    The planetary gear design is a unique gear design that allows for high torques to be transmitted because
    the major forces in the system are only seen on the gears. Since the forces on the gears cancel each
    other by having equal spaced planet gears, the only forces that the shafts see are forces due to the
    weight of the system. However, the shafts will still experience the total torque transmitted by the gears.
    Thus, the critical part for designing the shafts is the torsional stress limit. This is illustrated in the
    attached free body diagrams. The proposed shaft dimensions and material properties for the shafts are
    documented in Table 5.

                                      Table 5: Input/Output Shaft Materials and Basic Dimensions
                                                               Stage 1
               Length   Min. Dia. Max. Dia. Material     Density    Mass* Modulus of Elasticity Su, Ultimate Strength Sy, Yield Strength
Input Shaft    91mm      15mm      17mm 1020 HR Steel 7.7e3 Kg/m2 0.1325 kg   207e9 Pa                 455e6 Pa            290e6 Pa
   Carrier     53mm      15mm      17mm 1020 HR Steel 7.7e3 Kg/m3 0.3437 kg   207e9 Pa                 455e6 Pa            290e6 Pa
Planet Shaft   34 mm     10 mm     12mm 1020 HR Steel 7.7e3 Kg/m4 0.0219 kg   207e9 Pa                 455e6 Pa            290e6 Pa
                                                                 Stage 2
               Length Min. Dia. Max. Dia. Material     Density    Mass* Modulus of Elasticity Su, Ultimate Strength Sy, Yield Strength
   Carrier     53 mm     17mm    20mm 1020 HR Steel 7.7e3 Kg/m3 0.378 kg    207e9 Pa                 455e6 Pa            290e6 Pa
Planet Shaft 34 mm       10 mm   12mm 1020 HR Steel 7.7e3 Kg/m4 0.0219 kg   207e9 Pa                 455e6 Pa            290e6 Pa
*Mass is taken from SolidWorks


    To calculate the static torsional stress in the shaft, equations 20 and 22 from [1] are used where the KT
    value in both equations 20 and 23 is the stress concentration factors due to the shoulders on the shafts
    and the grooves for retaining rings. Also, the calculations for the basic torsional stress and bending
    stress are done using the minimum shaft diameter since each shaft has a step change in its size. The
    input shaft initially has the common 5/8 in. diameter shaft to easily couple with the motor, but then the
    shaft diameter is adjusted to allow for the bearing and a shoulder to hold the gear in place. In equation
    21 the torsional fatigue strength for infinite life and 99.9% reliability is calculated and in Table 7 a safety
    factor of 2 is incorporated. In this equation Sn’=0.5Su for steel for the lack of better data and the rest of
    the strength factors are found on pg. 303 of [1] the Juvinal Design book. Equations 20 and 23 utilize the
    stress concentration factor values taken from [1].

           (20)
           (21)

                                                                   13
(22)

Along with the torsional stresses, the bending stresses and deflections of the shafts without bearings
can be calculated to determine if the bending stresses or deflections are a critical design parameter. As
mentioned before, the only bending forces on the shaft is the weight of the shaft itself so it does not
appear to be very critical. However, the bending stresses and deflections are easily calculated with
equations 23-25 and equation 26 is used to calculate the shear stress in the planet gear shaft. The
fatigue strength for bending can be calculated using equation 21 and the appropriate values for the
factors.

     (23)
     (24)
     (25)
     (26)

The values for the torsional and bending stresses and the deflections can be seen in Table 6. The output
shaft is the shaft part of the “carrier”. The stresses seen in Table 6 do not exceed the allowable stresses
shown in Table 7, so the proposed shaft design is satisfactory for the required specifications. As shown
in Table 5, the minimum diameter for the output shaft had to be increased to 17mm so that the
torsional stresses in the shaft would be less than the allowable stress.

                                  Table 6: Stresses in Gearbox Shafts
                                                Stage 1
                         Torsional Stress Bending Stress Deflection at L/2 Shear Stress
            Input Shaft 3.58 N/mm2        0.2356 N/mm2     7.9e-5 mm              -
            Ouput Shaft 10.75 N/mm2        0.178 N/mm3     4.07e-5 mm             -
            Planet Shaft        -                -               -         0.5602 N/mm2
                                                 Stage 2
                           Torsional Stress Bending Stress Deflection at L/2 Shear Stress
            Ouput Shaft      24.6 N/mm2      0.135 N/mm3     7.9e-5 mm              -
            Planet Shaft           -               -               -         1.6807 N/mm2


                             Table 7: Allowable Stresses in Shaft (SF = 2)
                                                 Stage 1
                                 Torsional                  26.8 N/mm2
                                 Bending                    46.2 N/mm2
                                                 Stage 2
                                 Torsional                 26.8 N/mm2
                                 Bending                   46.2 N/mm2
                                  1020 HR Yield Strength = 290 N/mm^2



                                                    14
1.4.2 Keyway Design Analysis:

With the size of the shafts determined based off of stress design including stress concentration factors
and a safety factor, then the keyways need to be designed. The following equations, 27 and 28, from [1]
are used for the keyway design. Table 8 shows the keyway specifications and it shows that the
allowable torques are not exceeded by the torque values being transmitted by the gearbox from the
specified 1 HP motor and a 10:1 gear reduction.

     (27)
     (28)

                                        Table 8: Keyway Design
                                                Stage 1
                                     Key Length in            27 mm
                                   Key Length Carrier         27 mm
                                  Allowable Torque in       127.7 N/m
                                 Allowable Torque out       127.7 N/m
                                                Stage 2
                                   Key Length Carrier         30mm
                                  Torque allowed out        185.9 N/m
                               Key Square = 5x5mm from SolidWorks Gear

1.4.3 Carrier Arm Stress Analysis:

                                                                 Shear Stress

                                            Fc

                                                               Bending Stress




                                        Figure 3: Forces on Carrier Arms

In section 6, it is shown that the carrier arm design utilizes a bearing that is inset into the arm. This
design allows for the carrier force, Fc, to act directly onto the hole inside of the arm. This means that
the stresses in the arm will act like a tensile force acting on the inside of the hole and thus for this part
the stress analysis needs to incorporate a stress concentration factor. The equation for this tensile
stress analysis is given in equation 29 from [1] and the stress concentration factor is given by KT as well.
Equation 23 is used to calculate the bending stress for this part as well. Table 9 shows the stresses in
the carrier arm based off of the original proposed design for the carrier arm. The stress values in Table 9
for Stage 2 exceed the yield strength of 1020 HR steel given in Table 5. This suggests that the design of
the Stage 2 carrier arm needs to be adjusted so that the stress in the arm does not exceed the material
yield strength. The two options for this are to either make the carrier arm a full disk or to increase the

                                                      15
width and thickness of the carrier arm. It was chosen to adjust the geometry of just the Stage 2 carrier
arm to have a width of 40 mm instead of the width of 30 mm initially used which is still used for Stage 1.
Both carrier arms still incorporate a thickness of 7 mm. Table 10 shows the new bending stress value of
2.068 MPa which is well under the yield strength for 1020 HR steel given in Table 5.

     (29)


                               Table 9: Initial Carrier Arm Stress Analysis
                                          Tensile                Bending
                     Stage 1     0.754 N/mm^2 (0.754MPa) 1.84 N/mm^2 (1.84 MPa)
                     Stage 2     2.263 N/mm^2 (0.226 MPa) 4.29 N/mm^2 (4.29 Mpa)

                          Table 10: Adjusted Carrier Arm Stress Analysis
                                           Tensile                Bending
                     Stage 1      0.754 N/mm^2 (0.754MPa) 1.84 N/mm^2 (1.84 MPa)
                     Stage 2            0.97 N/mm^2       2.068 N/mm^2 (2.07 Mpa)

                                              1.5 Bearing Design

With the keyway design done, then the FBD for the overall gearbox needs to be evaluated and then
radial loads on the bearings determined. With the radial load, we can calculate the bearings required
for the application. To determine the bearing required for 90e6 revolution life and 99% percent
reliability, equation 30 from [1] is used. The following values for the constants are: Ka = 1.3 for ball
bearing, Kr = 0.2 for 99% reliability, and Lr = 90e6 revolutions for use with Table 14.2 in [1]. Design is
assumed for machines for 8-hour service every working day, so L = revolutions for 20-30 thousand hours
at 3600 rpms as given in [1]. For the FBD we need to know the total weight of the gearbox design.
However, the ring gear and housing supports the weight of all of the gears, so essentially the bearings
will only be supporting the weight of the shafts. The weight of the shafts is shown in Table 5 and these
values are approximate and taken from SolidWorks.
      (30)

                                              Table 11: Bearing Design
                                                  Required Capacity
                                      Input Bearing (17mm bore)           21.3 N
                                     Middle Bearing (17mm bore)           15.4 N
                                      Output Bearing (20mm bore)          10.7 N
                                      Planet Bearing (10mm bore)          752 N
                                     Bearing Capacity for Xlt (ExtraLight)*
                                              10 mm Bore                 1.02 kN
                                              17 mm Bore                 1.32 kN
                                              20 mm Bore                 2.25 kN
                                             *Capacities from Table 14.2 in [1]
                                     Bearing Capacity from Solidworks Calculator*
                                       10 mm Bore - 15 mm OD            1.1 kN
                                       17 mm Bore - 23 mm OD            1.9 kN
                                        20mm Bore - 27mm OD             2.5 kN
                                             *Capacity for 99% reliability




                                                           16
Table 11 provides the bearing capacity calculation values. The required bearing capacity for each
bearing is given at the top of Table 11. The bearing capacity for extra-light bearings as given in Table
14.2 of [1] is shown in Table 11 as well. These values were compared to the SolidWorks bearing capacity
calculator values for the actual bearings created using the SolidWorks toolbox. When observing the
values in Table 11, the bearing capacity numbers from [1] are real similar to the calculated numbers
given from the Solidworks calculator and these capacities for the bearings exceed the required
capacities given from equation 30 and are thus acceptable.

                                    1.6 SolidWorks Model of Gearbox

The gearbox design is built as a 3D model using the SolidWorks engineering software. This section will
highlight the 3D model of the gearbox and illustrate additional features of the design as well as address
SolidWorks tools used to make the 3D part.

1.6.1 Gear Assembly
                                                                   Retaining Ring Grooves




           Keyway




                                              Keyway                                        Keyway

                      Figure 4: Left is Stage 1 gear assembly and Right is Stage 2 Gear Assembly


                                          Planet Shaft with ring
                                          groove and key way




                      Figure 5: Left is Stage 1 Gear Assembly and Right is Stage 2 Gear Assembly




                                                         17
Bearing 17mm bore                                           Bearing 20mm bore




                                                                                     Planet Bearing
                                                                                     10mm bore

                                                      Bearing 17mm bore

                                        Figure 6: Side Image of Gear Assembly

Figures 4-5 are the assembly of the gearbox without the housing around the gears. The sun and ring
gears were built using the SolidWorks Toolbox utilities feature. This feature has commonly available
mechanical parts such as gears, bolts, bearings, retaining rings, nuts, etc. already built in the SolidWorks
program and all the user has to do is specify certain dimensions. For the gears, only the pitch diameter,
module, pitch angle, gear width, hub dimensions, and whether a keyway is needed has to be specified
and then SolidWorks builds the part. This feature is also used to build the bearings, retaining rings, and
bolts used in this assembly. The bearings are noted in Figure 6. The SolidWorks Toolbox also has an
automatic grooving feature which automatically constructs the grooves for common retaining rings, and
this tool was used for all retaining ring grooves. Many manufacturers for mechanical parts provide 3D
drawings for available parts that they sell. The planet gears for the assembly were taken from
www.qtcgears.com and then assembled in the gearbox. The benefit to using common and readily
available parts is that the overall price to manufacture a gearbox is greatly reduced. As mentioned in
the earlier design portion of this paper, the material for the gears is steel and the material for the shafts
is 1020 HR steel. These materials were chosen for their low cost and for being readily available.

1.6.2 Gearbox Housing

The housing for the gearbox is chosen to be built out of 6061 aluminum due to its low cost, easy
manufacturability, and it being readily available. The total amount of force transmitted to the housing is
the sum of all the carrier forces, Fc. There are currently no analytical design calculations performed to
ensure the proposed housing design will hold up to the total amount of force transmitted to the
housing. The following housing design is to propose a geometric design concept that will work for
housing the planetary gear system designed in this paper.

The design concept chosen for the housing is a shell type of housing. This design concept provides easy
accessibility and assembly for the planetary gearbox. It also utilizes symmetry for each half of the
housing so it will be cheaper to manufacture the housing components with only the addition of a few
bolt holes in the top shell. The housing is designed to secure the bearings in place and the shells attach
by a flange style connection. To secure the middle bearing in place, an additional column was built
which bolts internally onto the main housing shell and a flange style connector to secure the bearing in
place on the column. This adjustment was made as an additional part so alignment onto the stage 1
carrier shaft would be easier and adjustable if need be. For the planetary gearbox design to function

                                                         18
properly, the ring gear has to be stationary and is thus designed to be bolted straight to the housing.
Figures 7 and 8 are different 3D views of the gearbox assembly housing.
                                                                                             Middle Bearing Support

                                                                                                                 Gasket




        Figure 7: Left image is bottom shell of housing and Right is bottom shell with gear assembly mounted in it




  Input Shaft Cover




       Input Shaft
                                           Output Shaft
                                                                                                              Gearbox Feet


 Figure 8: Left is Gearbox assembly with input shaft cover and right is 3D image of gearbox assembly with all components



There are a few features about the gearbox assembly housing that need to be pointed out. All of the
bolts used in the assembly are M4 threaded bolts with varying lengths. This was done to reduce the
number of tap dies needed to make the holes, the number of tools needed to assemble the gearbox,
and the number of different bolting components since it is assumed that only 1 of these gearboxes will
be manufactured. Figure 8 also shows a shaft cover/connecting piece mounted onto the gearbox. This
piece is added to cover the input shaft of the gearbox and the output shaft of the motor during
operation. This increases the safety of the gearbox for nearby workers or other equipment. This cover
is designed to align directly to a 56 frame NEMA C Face motor. This will also help with the rigidity of the
entire system when mounted to the motor. There were also feet added to the housing assembly. These
feet will allow for stability of the gearbox and make the gearbox easy to secure to a mounting location.

1.6.3 Engineering Drawings

In addition to building a 3D model of the proposed planetary gearbox design in SolidWorks, engineering
drawings are produced in SolidWorks which will aid in the manufacturing of the various components.


                                                           19
These drawings include all necessary data needed to manufacture each component and are organized
based off of ASME standards as directed by the 2010 SolidWorks book [7]. The tolerances for the shafts
and holes are based off of H9/d9 and D9/h9 fits for the hole and shaft basis as described in the 27th
Edition Machinery’s Handbook [8]. These fits are free running fits intended for higher running speeds.
The fit for a 15mm and 17mm shafts was not given, so the tolerance for the 16mm shaft from [8] is used
for both of these shaft sizes in the attached drawings since it is the closest. The tolerance for the
location of the bearings on its related shaft or inset on the carrier uses the location fit H7/h6 from [8]. If
the actual size is not in [8] then the next closest size in [8] will be used. This provides a snug fit for the
bearings and allows for the bearings to be freely assembled and disassembled. Drawings for the
gearbox design can be found in Appendix 2.

                                1.7 SolidWorks Finite Element Analysis

SolidWorks is a powerful engineering analysis tool in addition to a 3D graphic software. In this section,
multiple finite element analysis (FEA) studies will be done on a few of the components in the gearbox.
All FEA tools should be used with skepticism and should always be verified with analytical calculations
when possible. Analytical calculations only work for really basic geometries and typically involve
multiple assumptions in order for the basic analysis equations to be accurate and simple. Because of
this, the FEA stresses in the gearbox components are expected to be different from the hand
calculations and will probably be higher than the analytical calculations due to the additional features
such as retaining ring grooves and keyways. To verify the FEA analysis from SolidWorks, the stress
values of the components well away from the applied loads and additional features will be compared to
the analytical values. In this section we will observe the FEA analysis of stresses in the input shaft,
planet shaft, and carrier components. All loads applied in the FEA analysis are the same values as the
forces and torques shown in Tables 1 and 3.

1.7.1 Bending Stress of Input Shaft

As observed in the analytical calculations, the bending stress in the shafts was not a critical design issue
because the only force on each shaft is the weight of the shaft. So only the bending stress of the input
shaft is studied for comparison with the analytical calculation values in Table 6. Here the weight of the
shaft is given in Table 5 and this produces a force of 1.3N. The FEA analysis is shown below in Figure 9.
Figure 9 shows 3 different stress values obtained in the FEA analysis. The highest stresses are expected
to be at the end of the shaft where the shaft is fixed. Figure 9 shows that this is the case and that
stresses a little over a diameter away from the end are about 0.256 N/mm^2. This is similar to the 0.236
N/mm^2 obtained by equation 23 and located in Table 6.
                                                                          Applied Vertical Load


           0.256 N/mm^2: (*Compare to
           0.236 N/mm^2 in Table 6)




                                    Figure 9: Bending Stress FEA of Input Shaft


                                                       20
1.7.2 Torsional FEA Analysis of Shaft Components

Here we will study the torsional stresses in the input shaft, stage 1 carrier shaft, and stage 2 carrier
shaft. Figure 10 shows the FEA for the input shaft, and in this study the torque was applied around the
face of the shaft over the area of the keyway and then the keyway on the other end was the fixed
geometry. The stress values closer to the center of the shaft and on each side of the shoulder are used
to compare with the values in Table 6. As shown in Figure 10, the analytical calculations predict a stress
value of 3.58 N/mm^2 which is pretty similar to the values of 3.86N/mm^2 and 4.37N/mm^2. Thus the
FEA analysis is assumed to be accurate and the input shaft is sufficient for this design.



                          4.37 N/mm^2 (*compare
                          to 3.58 N/mm^2 in Table 6)




                                                  3.86 N/mm^2 (*compare
                                                  to 3.58 N/mm^2 in Table 6)

                                Figure 10: Torsional FEA Analysis of the Input Shaft

Figures 11 and 12 are the torsional analysis of the Stage 1 and Stage 2 carrier components. Here the
carrier arm feature is held fixed while the torsional load is applied to the face of the shaft in the area of
the keyway. Figure 11 shows that the stress values obtained by the FEA a distance away from the
keyway are very similar to the analytical value for stress in Table 6. This value is expected to be close to
the analytical value since it is located away from the applied load and any unique features. The stresses
increase as you get closer to the keyway and the area where the torque is applied which is expected.
The stress values given by the FEA analysis are still within the acceptable range and are verified by how
similar they are to the analytical values.


                    10.1N/mm^2 (*compare to
                    10.75N/mm^2 in Table 6)




                                                       17.4N/mm^2 (*compare to
                                                       10.75N/mm^2 in Table 6)

                                Figure 11: Stage 1 Carrier Shaft Torque FEA Analysis


                                                         21
Figure 12 is the torsional analysis for the Stage 2 carrier shaft. Here similar results are found to what
was found in Figure 11. The torsional stress values closer to the carrier arm feature is very similar to the
analytical calculations, which verifies the FEA analysis, and as you get closer to the area where the
torque was applied and the keyway feature, the stress values increase. The FEA analysis verifies that the
stress values are still within the acceptable range.




              20.9N/mm^2 (*compare to
              24.6N/mm^2 in Table 6)




                                                                         34.2N/mm^2 (*compare to
                                                                         24.6N/mm^2 in Table 6)


                                   Figure 12: Stage 2 Carrier shaft torque analysis

1.7.3 Carrier Arm Shear and Bending Stresses

In this section the carrier arm shear and bending stresses produced by the carrier force, as shown in
Figure 3 and given in Table 3, will be studied. The stress values given by the FEA analysis will be
compared to the values in Table 10. Figures 13 and 14 are the FEA analysis for the shear and bending of
the Stage 1 carrier arm. Figure 13 shows that the FEA analysis only predicts 0.3N/mm^2 shear stress
while the analytical calculations predict 0.75N/mm^2. The discrepancy in the values is that the
analytical calculations assume the 15mm hole the bearing sits in goes all the way through the arm but in
reality there is still the small lip with a 11mm diameter hole which will decrease the stress values.




                     0.3N/mm^2 (*compare to
                     0.75N/mm^2 in Table 10)




                        Figure 13: FEA Analysis showing the shear stresses in the carrier arm



                                                         22
Figure 14 shows that the predicted bending stresses obtained in the FEA Analysis are very similar to
what was obtained analytically.




                                                             1.42N/mm^2 (*compare to
                                                             1.84N/mm^2 in Table 10)


                                Figure 14: Bending Stresses on Stage 1 Carrier Arm

Figure 15 is the FEA analysis for the shear and bending stresses in the Stage 2 carrier arm. In this figure
both the shear stresses due to the load and the bending stresses are noted. Figure 15, similar to the
Stage 1 Carrier analysis, shows that the stresses in the Stage 2 Carrier arm due to the carrier force, Fc,
are satisfactory for this design and that the FEA analysis and the analytical calculations are very similar
thus verifying their accuracy.



      0.48N/mm^2 (*compare to
      0.97N/mm^2 in Table 10)




                                                                         2.24N/mm^2 (*compare to
                                                                         2.07N/mm^2 in Table 10)



                           Figure 15: Stage 2 Carrier Arm Shear and Bending FEA Analysis

1.7.4 Planet Shaft Shear FEA

The final FEA analysis performed is the shear stress analysis of the planet gear shaft due to the carrier
force. The stress values produced by the FEA analysis will be compared to the shear stress value in
Table 6 for the stage 2 planet shaft since this stage is where the planet shaft will experience the highest

                                                        23
carrier force of 99N. Figure 16 shows that near the location where the shear force is applied, the stress
values are similar to that of the analytical calculations. The stress values increase as you get closer to
the fixed end. The fixed geometry is not a good representation of the actual design since the section
with the key would be supported by the gear. The higher stresses closer to the fixed end are actually
bending stresses due to the way the FEA analysis was done with the fixed geometry. This suggests that
the FEA analysis should be performed with a different fixture and with a different load applied to better
resemble the load applied to the area the bearing occupies and for the fixture to cover the area inside of
the gear.




              1.06N/mm^2 (*compare to
              1.7N/mm^2 in Table 6)




                                                   3.6N/mm^2 (*compare to
                                                   1.7N/mm^2 in Table 6)




                                     Figure 16: Planet Shaft shear stress FEA

This section successfully verified the accuracy of both the analytical calculations and the FEA analysis
predictions. This increases the confidence that each of these components are correctly designed for this
gearbox design and will operate correctly.

                                              1.8 Future Work

This paper described a fully designed gear system including shaft and bearing analysis. However, to
have a fully designed gearbox suitable for operation, there is additional design analysis that needs to be
performed. A vibration study needs to be performed to identify the natural frequencies of the gearbox
and to ensure the system is not running at any of the critical speeds. If a system operates at one of its
natural frequencies, then the vibrations of the system will be large and can continue to increase causing
major damage to the system which could lead to a catastrophic failure.

Further work needs to be done on the lubrication and sealing of the gearbox. It is assumed that the
gearbox will be oil lubricated and the type of lubricant can be easily determined from lubrication text
and the speed and torque of the system. Gearboxes of this type are commonly oil lubricated and the
gearbox is partially filled with oil, so as the gears rotate they will continue to be lubricated by passing
through the oil. With this type of lubrication, additional holes will need to be added onto the gearbox to
allow for draining and filling the oil. Also, a pressure relief cap or hole will need to be designated so the

                                                       24
pressure added to the gearbox on startup can escape the housing. Finally, additional stress analysis
needs to be performed on the housing to ensure that its current geometrical design and chosen material
will hold up to the forces and torques of the system.

A final minor design adjustment needs to be made on the planet gear shaft and the carrier arm. The
current design makes the retaining rings have an extremely tight fit that might not work in real life.
Some minor adjustments need to be made to ensure the retaining rings comfortably fit in their grooves.

                                              1.9 Conclusion

A 2-stage planetary gearbox was successfully designed for a 1 HP NEMA C Face motor operating at 3600
rpms. The 2-stage gearbox design ensures that the gearbox will fit in any radial space that the driving
motor will fit and still obtains the desired 10:1 reduction required out of the gearbox. All necessary
design calculations were utilized to design the individual components and to ensure the successful
functionality of the gearbox design. These calculations verified the FEA done on a few of the
components which greatly increases the confidence that this design will function properly. In addition
to fully designing the 2-stage planetary gear system through design analysis, SolidWorks was used to
build a 3D model of the gearbox. The SolidWorks model made it possible to ensure the gearbox design
functioned properly, provided the graphics needed to effectively communicate the design to customers,
and puts the gearbox design in a format that can easily be manufactured through the engineering
drawings and the SolidWorks parts. This paper provided a successful and complete design of a Planetary
Gear Reducer for a 1 HP NEMA C Face motor operating at 3600 rpms, and with a little more design
analysis (as mentioned in Section 8) this gearbox will be ready to be manufactured and tested.

                                             1.10 References

[1]Juvinall, R.C., and Marshek, K., Fundamentals of Machine Component Design 4th Edition, John Wiley &
Sons 2006, Print

[2]Budynas, R.G., and Nisbett, J.K., Mechanical Engineering Design 8th Edition, McGraw Hill Companies
Inc, 2008 Pring

[3] Roos, F., and Spiegelberg, C., “Relations between size and gear ratio in spur and planetary gear
trains,” Department of Machine Design, Royal Institute of Technology, Stockholm 2004 ISSN 1400-1179

[4]Palazzolo, A., “Dr. Alan Palazzolo’s MEEN 617 Vibration Course Notes,” Texas A&M University, 2010

[5] http://www.grainger.com/Grainger/DAYTON-General-Purpose-Motor-5K673

[6] http://www.electricmotorservice.net/nemachart.pdf

[7] Planchard, D.C., and Planchard, P.P., Engineering Design with SolidWorks 2010, SDC Publications
2010

[8] Oberg, E., Jones, F.D., Horton, H.L., and Ryffel, H., Machinery’s Handbook 27th Edition, Industrial Press
Inc, 2004


                                                     25
2. Vases
In this assignment multiple different vases were built as 3D models in SolidWorks. Here
multiple different features such as lofting, revolving, extruding, sweeping, etc. were used to
build the vases. The vases were all given materials that suit their particular features and the
images of these vases were rendered using the Photoworks add in. The following figures are
the 5 vases created.




    Figure 17: LEFT: "Round Top" vase with green glass; RIGHT: "Round Front" vase with clear glass and patterned back




                                                           26
Figure 18: LEFT: "Mahogany Heavy" vase and RIGHT: "Twisted Carbon Fiber" vase




                      Figure 19: "Porcelain Petite" vase




                                     27
3. Google House:
In this homework, a house was found using google maps and then a 3D graphic of the house
was built up off of the google map image. By using surrounding objects, a very close scale for
the house could be obtained and then an accurate 3D model of the house could be built. All
features of the house including doors, windows, etc. were built and materials were applied to
these components. The following figures present this assignment.




      Figure 20: LEFT: Original Google Maps image; RIGHT: New image with 3D model of house built on the image




                 Figure 21: 2 different angles presenting the 3D model of the house and its features




                                                         28
4. Guide Rod Assembly Plates:
Here the plates for the Guide Rod Assembly in the Solidworks Tutorial book, reference [7] of
the gearbox design report, were built. This was done following along in the book and utilized
many additional features such as the hole wizard. The figures below show the original plate
from the book and a modified plate.




                     Figure 22: Left front and Right back isometric views of original plate




                     Figure 23: Left front and Right back isometric views of Modified Plate




                                                      29
5. Guide Rod Assembly:
Here the complete Guide Rod assembly was built and assembled as instructed by the
SolidWorks tutorial book. Many features, such as mirroring, linear pattering, and the hole
wizard, were utilized to aid in the building and assembling of the Guide Rod. The original guide
rod assembly as instructed by the book was made, and then it was altered to make a new guide
rod assembly that has different dimensional sizes.




                   Figure 24: 3D unexploded and exploded views of the Guide Rod Assembly




                          Figure 25: Modified Guide Rod Assembly mounted on plate




                  Figure 26: Exploded View of Modified Guide Rod Assembly mounted on plate



                                                    30
6. Rotating Crank Assembly:
Here a basic rotating crank assembly model was built and assembled in SolidWorks. It was built
and assembled so that the crank assembly would operate correctly. To illustrate the operation
of the crank, 3 different views of the assembly are shown with the crank in 3 different positions
rotating clockwise.




              Figure 27: Crank assembly at 3 different rotated positions and rotation direction is shown




7. Basic Gearbox Assembly:
In this assignment, a very basic gearbox was modeled. Two identical gears were created using
the SolidWorks Toolbox and then the shafts and the housing were built so that they could be
assembled together. The goal of the assignment was to learn how to add new parts to an
assembly and then construct the housing around the assembly.



                                                      Output Shaft




     Input Shaft



       Figure 28: LEFT: Isometric View of Gearbox Assembly; RIGHT: Isometric View with housing sides removed




                                                         31
Figure 29: Exploded View of the Basic Gearbox Assembly




8. Basic Gearbox 2D Engineering Drawings
2D engineering drawings of the shafts and housing of the basic gearbox is made. The drawings
were made per ASME Y14.5 as instructed by the SolidWorks book. The un-dimensioned
tolerance block was filled out, a logo was added, and an assembly drawing with a bill of
materials is made to detail the assembly. The engineering drawings are on the following pages.




                                                  32
33
34
35
9. Surface Truck Model:
The truck model shown below is a truck built using only “Surface Features.” Surface features
are important when modeling complex features such as the surfaces on a computer mouse and
these surface models make manufacturing complex features much easier. Here the truck
modeled includes headlights, taillights, windows, doors, tires, and wheels. This assignment
highlights the abilities of surface features and how unique surfaces can be built.




                             Figure 30: Two Isometric views of the surface truck




                          Figure 31: Front and Rear Views of the surface truck model




                 Figure 32: LEFT: Side View of truck; RIGHT: Side View with doors colored gray




                                                      36
10. Basic Finite Element Analysis (FEA) using SolidWorks Simulations
Here a basic bending stress FEA study was done using the input shaft of the Planetary Gearbox
designed in the design project. A bending stress study was performed and the force in the
study is 1.4N from the weight of the shaft. The following equation is the basic bending stress
equation where M = 1.4*moment arm.



SolidWorks also has a beam calculator feature which does basic analytical beam calculations.
The stress value from this calculator is verified with the equation above and the stress and
deflection values are 0.14 N/mm2 and 0.000034mm.

The figures below show the FEA study results from SolidWorks and their comparable analytical
values. The accuracy of the FEA study is verified.


                       0.155 N/mm2 compared to the value
                       obtained analytically of 0.14 N/mm2




                                        Figure 33: Bending stress FEA of Shaft



                                                                                        Fixed end



              Deflection of 0.000051mm compared to
              the analytical value of 0.000034mm




                                  Figure 34: Deflection results of shaft FEA analysis



                                                             37
Appendix 1: Free Body Diagrams and Hand Calculations for Project




                                            38
39
40
41
42
43
Appendix 2: Engineering Drawings of Gearbox Components for Planetary Gearbox




                                    44
27
                          48
                                                                                                                                         1.600
                               60

                                                                                                                                                                               R3.050
                                                                                                                                                   2.500
                                      93

                                                                                                                  R0.500
                                                                                                                                                                   R1
                                                                                                                                                     DETAIL A
                                                                                                                                                    SCALE 2 : 1
                                                                                          B27.8 - 3DM1 - 15
                                                                                          (External Retaining Ring Groove)




                                                                                                                                                             R1
                                       2.420
     B
                                                                                                       A
                                                                               4.755
                                                            DETAIL B
                                                           SCALE 2 : 1



                                                                                                                                                            Eric Halfmann
                                                                                 UNLESS OTHERWISE SPECIFIED:                      NAME     DATE

                                                                                 DIMENSIONS ARE IN MILLIMETERS DRAWN
                                                                                 TOLERANCES:
                                                                                 ANGULAR: MACH 0 30'           CHECKED                            TITLE:
                                                                                 ONE PLACE DECIMAL      0.5


                                                                                                                                                            Input Shaft
                                                                                                               ENG APPR.
                                                                                 TWO PLACE DECIMAL 0.15
                                                                                                                      MFG APPR.



SolidWorks Student Edition.
    PROPRIETARY AND CONFIDENTIAL
 THE INFORMATION CONTAINED IN THIS
                                                                                 INTERPRET GEOMETRIC
                                                                                 TOLERANCING PER: ASME Y14.5
                                                                                 MATERIAL
                                                                                                                      Q.A.
                                                                                                                      COMMENTS:
                                                                                                                                                  SIZE DWG. NO.                           REV

                                                                                                                                                  A
                                                                                            1020 HR Steel

For Academic Use Only.
 DRAWING IS THE SOLE PROPERTY OF
 <INSERT COMPANY NAME HERE>. ANY                                                                                                                           InputShaft_Stage1_Drawing
 REPRODUCTION IN PART OR AS A WHOLE                                              FINISH
 WITHOUT THE WRITTEN PERMISSION OF         NEXT ASSY                 USED ON                 Machined
 <INSERT COMPANY NAME HERE> IS
 PROHIBITED.                                           APPLICATION                   DO NOT SCALE DRAWING                                         SCALE: 1:1 WEIGHT:               SHEET 1 OF 2
            5                                             4                                             3                                   2                                  1
14.950
                              14.907


                                                                                                                                    38
                              17.000
                              16.989

                                                                                                                                                                         R4.265
                                                                                            2.785                                   34
                              15.825
                              15.782
                                                                                           R0.500

                                                                           2.071                                                    DETAIL D
                                                                                                                                   SCALE 2 : 1

                                   5
                                                                                                                     D


        C
                                              DETAIL C
                                             SCALE 2 : 1




                                                                                                                                             Eric Halfmann
                                                                           UNLESS OTHERWISE SPECIFIED:               NAME   DATE

                                                                           DIMENSIONS ARE IN MILLIMETERS DRAWN
                                                                           TOLERANCES:
                                                                           ANGULAR: MACH 0 30'           CHECKED                   TITLE:
                                                                           ONE PLACE DECIMAL      0.5


                                                                                                                                             Input Shaft
                                                                                                         ENG APPR.
                                                                           TWO PLACE DECIMAL 0.15
                                                                                                         MFG APPR.



SolidWorks Student Edition.
    PROPRIETARY AND CONFIDENTIAL
 THE INFORMATION CONTAINED IN THIS
                                                                           INTERPRET GEOMETRIC
                                                                           TOLERANCING PER: ASME Y14.5
                                                                           MATERIAL
                                                                                                         Q.A.
                                                                                                         COMMENTS:
                                                                                                                                    SIZE DWG. NO.                          REV

                                                                                                                                    A
                                                                                    1020 HR Steel

For Academic Use Only.
 DRAWING IS THE SOLE PROPERTY OF
 <INSERT COMPANY NAME HERE>. ANY                                                                                                            InputShaft_Stage1_Drawing
 REPRODUCTION IN PART OR AS A WHOLE                                        FINISH
 WITHOUT THE WRITTEN PERMISSION OF     NEXT ASSY                 USED ON              Machined
 <INSERT COMPANY NAME HERE> IS
 PROHIBITED.                                       APPLICATION                 DO NOT SCALE DRAWING                                 SCALE: 1:1 WEIGHT:              SHEET 2 OF 2
            5                                         4                                      3                               2                                  1
15.018
                                                           15.000



R15
                                                                11

                       DETAIL A
                      SCALE 2 : 1.5                                                                                                      7




                                                60
                                                                                                                                                                53
      120.00°
                                                                                                                                                         20

                                                                       30



                                                                                                                                                                          R1

                                    51.340
  A


                                                                                                                                                    Eric Halfmann
                                                                                 UNLESS OTHERWISE SPECIFIED:               NAME   DATE

                                                                                 DIMENSIONS ARE IN MILLIMETERS DRAWN
                                                                                 TOLERANCES:
                                                                                 ANGULAR: MACH 0 30'           CHECKED                   TITLE:
                                                                                 ONE PLACE DECIMAL      0.5


                                                                                                                                             Stage 1 Carrier
                                                                                                               ENG APPR.
                                                                                 TWO PLACE DECIMAL 0.15
                                                                                                               MFG APPR.



      SolidWorks Student Edition.
          PROPRIETARY AND CONFIDENTIAL
       THE INFORMATION CONTAINED IN THIS
                                                                                 INTERPRET GEOMETRIC
                                                                                 TOLERANCING PER: ASME Y14.5
                                                                                 MATERIAL
                                                                                                               Q.A.
                                                                                                               COMMENTS:
                                                                                                                                         SIZE DWG. NO.                          REV

                                                                                                                                         A
                                                                                          1020 HR Steel

      For Academic Use Only.
       DRAWING IS THE SOLE PROPERTY OF
       <INSERT COMPANY NAME HERE>. ANY
                                                                                 FINISH
                                                                                                                                                  Carrier_Stage1_Drawing
       REPRODUCTION IN PART OR AS A WHOLE
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                  5                                         4                                      3                               2                                 1
R3.050

             5                                                     5                                                                                         27

                                                                                                                                                                                 B27.8M - 3DM1-15
                                                                                                                                                                                 (External Retaining Ring Groove)




                                                                                                                                                                                     R0.500
 7.475                                                                                                                                DETAIL B                    2.100
R                          DETAIL C                         17.000
 7.455                                                      16.989                                                                   SCALE 2 : 1
                          SCALE 2 : 1.5




                                                                                                                 6.500
                                                                                                                 B27.7M - 3DM1-15                                                                          B
                                           C
                                                                                                                 (Internal Retaining Ring Groove)

                                                                                    18

                                                                                                                                                                    D
                                                                                                                 0.500
                                                                                        DETAIL D
                                                                                       SCALE 2 : 1.5

                                                                                                                                                                        Eric Halfmann
                                                                                   UNLESS OTHERWISE SPECIFIED:                          NAME        DATE

                                                                                   DIMENSIONS ARE IN MILLIMETERS DRAWN
                                                                                   TOLERANCES:
                                                                                   ANGULAR: MACH 0 30'           CHECKED                                   TITLE:
                                                                                   ONE PLACE DECIMAL      0.5


                                                                                                                                                              Stage 1 Carrier
                                                                                                                 ENG APPR.
                                                                                   TWO PLACE DECIMAL 0.15
                                                                                                                    MFG APPR.



    SolidWorks Student Edition.
            PROPRIETARY AND CONFIDENTIAL
         THE INFORMATION CONTAINED IN THIS
                                                                                   INTERPRET GEOMETRIC
                                                                                   TOLERANCING PER: ASME Y14.5
                                                                                   MATERIAL
                                                                                                                    Q.A.
                                                                                                                    COMMENTS:
                                                                                                                                                           SIZE DWG. NO.                              REV

                                                                                                                                                           A
                                                                                            1020 HR Steel

    For Academic Use Only.
         DRAWING IS THE SOLE PROPERTY OF
         <INSERT COMPANY NAME HERE>. ANY
                                                                                   FINISH
                                                                                                                                                                    Carrier_Stage1_Drawing
         REPRODUCTION IN PART OR AS A WHOLE
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         <INSERT COMPANY NAME HERE> IS
         PROHIBITED.                                       APPLICATION                 DO NOT SCALE DRAWING                                                SCALE: 1:4 WEIGHT:                SHEET 2 OF 2
                    5                                         4                                      3                                               2                                   1
R0.500



            54
                                              R2

  7                  20                        R1


                                                                                              5                           2.350
                                                                                                   DETAIL C
                                                                                                  SCALE 2 : 1.5



        50 30                                90.00°

                                                                            15.018
                                                                            15.000
                             C          A


                                                                                11
                             40                                                                                     8.475
                                                                                                                   R                                                   20.000
                                                                                                                    8.455
                                                                                                                                          DETAIL A                     19.987
                                                                                                                                         SCALE 2 : 1.5


                                                                                                                                                         Eric Halfmann
                                                                                     UNLESS OTHERWISE SPECIFIED:                  NAME   DATE

R20                                                                                  DIMENSIONS ARE IN MILLIMETERS DRAWN
                                                                                     TOLERANCES:
                                                                                     ANGULAR: MACH 0 30'           CHECKED                      TITLE:
                                                                                     ONE PLACE DECIMAL      0.5


                                                                                                                                                   Stage 2 Carrier
                                                                                                                   ENG APPR.
                                                                                     TWO PLACE DECIMAL 0.15
                                                                                                                   MFG APPR.



 SolidWorks Student Edition.
         PROPRIETARY AND CONFIDENTIAL
      THE INFORMATION CONTAINED IN THIS
                                                                                     INTERPRET GEOMETRIC
                                                                                     TOLERANCING PER: ASME Y14.5
                                                                                     MATERIAL
                                                                                                                   Q.A.
                                                                                                                   COMMENTS:
                                                                                                                                                SIZE DWG. NO.                     REV

                                                                                                                                                A
                                                                                              1020 HR Steel

 For Academic Use Only.
      DRAWING IS THE SOLE PROPERTY OF
      <INSERT COMPANY NAME HERE>. ANY
                                                                                     FINISH
                                                                                                                                                      Carrier_Stage2_Drawing
      REPRODUCTION IN PART OR AS A WHOLE
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                 5                                         4                                           3                                  2                            1
6.500
                                                                                                                                       0.500


                                                                                                                                                                     18



                                                                                                                                                 B27.7 - 3DM1 - 15
                                                                                                                                                 (Internal Retaining Ring Groove)


                                                                                                                                             DETAIL E
                                                                                                                                           SCALE 2 : 1.5                                          E


                                                                                                  30
                                                                                                                                                                           D


                                                                                                                                                R3.050




                                             2.500                                                          DETAIL D
                                                                                                           SCALE 2 : 1
                                                                                                   B27.8 - 3DM1 -15
                                                                                                   (External Retaining Ring Groove)




                                                                                                                                                             Eric Halfmann
                                                                          UNLESS OTHERWISE SPECIFIED:                         NAME       DATE

                                                                          DIMENSIONS ARE IN MILLIMETERS DRAWN
                                                                          TOLERANCES:
                                                                          ANGULAR: MACH 0 30'           CHECKED                                  TITLE:
                                                                          ONE PLACE DECIMAL      0.5


                                                                                                                                                    Stage 2 Carrier
                                                                                                        ENG APPR.
                                                                          TWO PLACE DECIMAL 0.15
                                                                                                          MFG APPR.



SolidWorks Student Edition.
    PROPRIETARY AND CONFIDENTIAL
 THE INFORMATION CONTAINED IN THIS
                                                                          INTERPRET GEOMETRIC
                                                                          TOLERANCING PER: ASME Y14.5
                                                                          MATERIAL
                                                                                                          Q.A.
                                                                                                          COMMENTS:
                                                                                                                                                 SIZE DWG. NO.                                 REV

                                                                                                                                                 A
                                                                                   1020 HR Steel

For Academic Use Only.
 DRAWING IS THE SOLE PROPERTY OF
 <INSERT COMPANY NAME HERE>. ANY
                                                                          FINISH
                                                                                                                                                       Carrier_Stage2_Drawing
 REPRODUCTION IN PART OR AS A WHOLE
 WITHOUT THE WRITTEN PERMISSION OF    NEXT ASSY                 USED ON              Machined
 <INSERT COMPANY NAME HERE> IS
 PROHIBITED.                                      APPLICATION                 DO NOT SCALE DRAWING                                               SCALE: 1:4 WEIGHT:                     SHEET 2 OF 2
            5                                        4                                      3                                             2                                         1
Meen 442 Journal Final Pdf V2
Meen 442 Journal Final Pdf V2
Meen 442 Journal Final Pdf V2
Meen 442 Journal Final Pdf V2
Meen 442 Journal Final Pdf V2
Meen 442 Journal Final Pdf V2
Meen 442 Journal Final Pdf V2
Meen 442 Journal Final Pdf V2
Meen 442 Journal Final Pdf V2
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Meen 442 Journal Final Pdf V2

  • 1. MEEN 442 SolidWorks Computer Aided Engineering Journal Completed by: Eric Halfmann Texas A&M University Summer 2011 August 8, 2011
  • 2. Journal Abstract The purpose of this journal is to present my computer aided engineering (CAE) skills. My ability to utilize engineering software (in this case SolidWorks) in the aid of design, manufacturing, and sales will be illustrated. These three aspects are important to any engineer and will greatly enhance my ability to successfully communicate my work and design to customers and manufacturing personnel. The following journal will show my wide range of SolidWorks graphic skills through the presentation of many different assignments that cover the use of all the different features that SolidWorks has to offer. Engineering drawings per ASME standards will be developed for some of these parts and some basic Finite Element Analysis will be performed on one of the shafts for the Planetary Gear Reducer. Finally, my ability to utilize SolidWorks as a computer aided engineering software and not just a graphics tool will be presented with the design and design analysis of a Planetary Gearbox for a 1 HP 3600 rpm NEMA C Face Motor. 1
  • 3. Table of Contents Journal Abstract………………………………………………………………………………………………………………………….. 1 Table of Contents………………………………………………………………………………………………………………………… 2 List of Figures…………………………………………………………………………………………………………………………. 3 List of Tables………………………………………………………………………………………………………………………….. 4 1. Planetary Gearbox Design Project…………………………………………………………………………………….. 5 Abstract…………………………………………………………………………………………………………………………… 5 Nomenclature…………………………………………………………………………………………………………………6 1.1 Introduction…………………………………………………………………………………………………………….. 8 1.2 Design Concept……………………………………………………………………………………………………….. 8 1.3 Gear Design……………………………………………………………………………………………………………… 9 1.4 Shaft Force and Stress Analysis……………………………………………………………………………….. 13 1.5 Bearing Design…………………………………………………………………………………………………………. 16 1.6 SolidWorks Modelling……………………………………………………………………………………………… 17 1.7 SolidWorks FEA……………………………………………………………………………………………………….. 20 1.8 Future Work…………………………………………………………………………………………………………….. 24 1.9 Conclusion……………………………………………………………………………………………………………….. 25 1.10 References ……………………………………………………………………………………………………………. 25 2. Vases………………………………………………………………………………………………………………………………….. 26 3. Google House…………………………………………………………………………………………………………………….. 28 4. Guide Rod Assembly Plates………………………………………………………………………………………………… 29 5. Guide Rod Assembly…………………………………………………………………………………………………………… 30 6. Rotating Crank Assembly……………………………………………………………………………………………………. 31 7. Basic Gearbox Assembly…………………………………………………………………………………………………….. 31 8. Basic Gearbox 2D Engineering Drawings…………………………………………………………………………….. 32 9. Surface Truck……………………………………………………………………………………………………………………… 36 10. Basic Finite Element Analysis (FEA) Using SolidWorks Simulation………………………………………..37 Appendix 1: Free Body Diagrams and Hand Calculations of Planetary Gearbox……..………………... 38 Appendix 2: Engineering Drawings of Planetary Gearbox Components…………………………………….. 44 2
  • 4. List of Figures Figure 1: 3D Image of Proposed Planetary Gearbox Design……………………………………………………….. 9 Figure 2: Basic Figure of gear meshes and associated forces……………………………………………………… 12 Figure 3: Forces on Carrier Arm…………………………………………………………………………………………………. 15 Figure 4: Stage 1 and Stage 2 Gear Assemblies…………………………………………………………………………… 17 Figure 5: Stage 1 and Stage 2 Gear Assemblies…………………………………………………………………………… 17 Figure 6: Side Image of all gears assembled………………………………………………………………………………… 18 Figure 7: Gear Assembly with housing…………………………………………………………………………………………. 19 Figure 8: Complete Gearbox Assembly……………………………………………………………………………………….. 19 Figure 9: Bending Stress FEA of Input Shaft…………………………………………………………………………………. 20 Figure 10: Torsional FEA Analysis of the Input Shaft……………………………………………………………………. 21 Figure 11: Stage 1 Carrier Shaft Torque FEA Analysis……………………………………………………………………. 21 Figure 12: Stage 2 Carrier shaft torque analysis……………………………………………………………………………. 22 Figure 13: FEA Analysis showing the shear stresses in the carrier arm………………………………………… 22 Figure 14: Bending Stresses on Stage 1 Carrier Arm……………………………………………………………………… 23 Figure 15: Stage 2 Carrier Arm Shear and Bending FEA Analysis…………………………………………………… 23 Figure 16: Planet Shaft shear stress FEA……………………………………………………………………………………….24 Figure 17: "Round Top" vase and"Round Front" vase…………………………………………………………………. 26 Figure 18: "Mahogany Heavy" vase and "Twisted Carbon Fiber" vase………………………………………. 27 Figure 19: "Porcelain Petite" vase………………………………………………………………………………………………. 27 Figure 20: Original Google Maps image and New image with 3D model of house on the image… 28 Figure 21: 2 different angles presenting the 3D model of the house and its features……………….. 28 Figure 22: Left front and Right back isometric views of original plate……………………………………….. 29 Figure 23: Left front and Right back isometric views of Modified Plate…………………………………….. 29 Figure 24: 3D unexploded and exploded views of the Guide Rod Assembly………………………………. 30 Figure 25: Modified Guide Rod Assembly mounted on plate……………………………………………………… 30 Figure 26: Exploded View of Modified Guide Rod Assembly mounted on plate…………………………. 30 Figure 27: Crank assembly at 3 different rotated positions and rotation direction is shown………. 31 Figure 28: Isometric View of Gearbox Assembly with and without housing sides removed……….. 31 Figure 29: Exploded View of the Basic Gearbox Assembly…………………………………………………………. 32 Figure 30: Two Isometric views of the surface truck…………………………………………………………………… 36 Figure 31: Front and Rear Views of the surface truck model……………………………………………………… 36 Figure 32: Side View of truck and Side View with doors colored gray………………………………………… 36 Figure 33: Bending stress FEA of Shaft……………………………………………………………………………………….. 37 Figure 34: Deflection results of shaft FEA analysis……………………………………………………………………… 37 3
  • 5. List of Tables Planetary Gearbox Project Design Tables: Table 1: Gear Ratios……………………………………………………………………………………………………………………… 10 Table 2: Gear Train Sizes………………………………………………………………………………………………………………. 10 Table 3: Forces on the Gears……………………………………………………………………………………………………….. 11 Table 4: Gear Stress Analysis Values……………………………………………………………………………………………. 13 Table 5: Input/Output Shaft Materials and Basic Dimensions……………………………………………………… 13 Table 6: Stresses in Gearbox Shafts……………………………………………………………………………………………… 14 Table 7: Allowable Stresses in Shafts……………………………………………………………………………………………. 14 Table 8: Keyway Design……………………………………………………………………………………………………………….. 15 Table 9: Initial Carrier Arm Stress Analysis……………………………………………………………………………………. 16 Table 10: Adjusted Carrier Arm Stress Analysis…………………………………………………………………………….. 16 Table 11: Bearing Design……………………………………………………………………………………………………………….16 4
  • 6. 2-Stage Planetary Gearbox Design Texas A&M University MEEN 442 Design Project Completed by: Eric Halfmann To: Mr. Randall Tucker July 29th, 2011 Abstract A planetary gearbox is a device, like any other gearbox, used to transmit power from the motor to the application and to adjust the speed and torque available from the motor. Planetary gear drives are able to transmit high torques at high speeds and are used in many different applications. The following paper describes the design of a 2-stage Planetary Speed Reducer with an overall gear ratio of 10:1 for a 1 HP 3600 rpm NEMA C Face motor. All equations for the stress and force analysis of the design are given and a minimum safety factor of 2 is used to ensure that the proposed design is a successful design that will hold up to the forces and torques in the system. In addition, a 3D SolidWorks model of the gearbox is created. Using this model, the gearbox design can be effectively communicated and illustrated as well as used to ensure the design functions correctly. Finite Element Analysis performed on the SolidWorks model was verified by the analytical calculations and further proves that the proposed design is adequate and will operate without failure. Finally, the SolidWorks model makes creating engineering drawings more time efficient and puts the gearbox design in a format that is ready to be manufactured. The following paper describes and illustrates a successful 2-stage planetary gearbox design for a 1 HP NEMA C Face motor operating at 3600 rpms. 5
  • 7. Nomenclature b = gear thickness d = shaft diameter m = module n = overall gear ratio for that particular stage p = number of planet gears r = radius of shaft t = thickness of carrier arm usp= sun/planet gear ratio v = poisson’s number A = cross sectional area on shaft CG = Gradient Factor CL = Load Factor CR = Reliability Factor CS = Surface Factor CT = Temperature Factor Crsp = Sun/planet Contact Ratio Crrp = Ring/planet Contact Ratio Creq = Required load rating capacity for bearing D = Diameter of Gear E = Modulus of Elasticity F = force Fe = force on the bearing FBD = Free Body Diagram Fp = Tangential forces Fc = Torque producing forces on carrier arm H = diameter of hole in the carrier arm I = moment of Inertia J = polar moment of Inertia Ka = bearing shock loading factor = Factor for division for load between teeth = Load distribution factor for bending = Factor for the division of load between teeth = Load distribution factor for surface pressure Kr = bearing reliability factor KT = Stress Concentration Factor L = distance from support to location of force Lkey = length of the keyway LR = Life of bearing corresponding to rated capacity M = moment which is force*distance N = number of teeth in Gear Pm = power motor R = Radius of Gear = Factor of safety Sn = Allowable stress Su = Ultimate strength of material Sy = Yield strength of material 6
  • 8. = allowable stress value T = Torque W = width of carrier arm = Form factor for bending stress = Stress Cycle Factor for bending stress = Reliability Factor = Helix angle factor for bending = Contact Ratio Factor for bending = Temperature Factor = Form factor for Hertzian pressure = Material Factor for surface pressure =Stress cycle factor for surface pressure = Hardness ratio factors for pitting resistance = Contact Ratio Factor for surface pressure = bending deflection σ = basic moment bending stress = Gear Bending Stress = Gear Surface Pressure = torsional stress on shaft = shear stress on planet gear shaft α = pressure angle (Here is 20 deg) ω = angular velocity Subscripts: in = input to Stage out = output of Stage r = Ring Gear in Stage s= Sun Gear in Stage p= Planet Gear in Stage 7
  • 9. 1.1 Introduction Motors are used to produce the energy needed for many mechanical systems to function as desired. However, sometimes the motor doesn’t provide the required torque and/or speed, the needed flexibility to adjust operating conditions, or provide the capabilities to be directly coupled to the application. In these instances, gearboxes are used to bridge the gap between the motor and the application and to increase or decrease the amount of output torque at the expense of decreasing or increasing the operating speed. Gearboxes are commonly used in all types of vehicles to transmit the power from the motor to the wheels of the vehicle. A particular style of gear system called a Planetary Gear Drive is often used in vehicle transmissions as well as many other applications. The planetary gear system is able to transmit high torques and operate at high speeds. One reason for this is because the evenly spaced planetary gears help to keep the overall forces acting on the system symmetric and thus sum up to zero. In other words, there are essentially no other forces acting on the shafts of the gearbox except the torque at the input and output of each stage. This makes the planetary gearbox an attractive solution to many gearbox needs as well as its compact and efficient design. The design project for the MEEN 442 Summer 2011 course is to design a planetary gearbox with a 10:1 gear reduction for a 1 HP 3600 rpm NEMA C face motor similar to the one found in reference [5]. The following text will provide the details for the design of a 2-stage planetary gearbox. The paper will discuss the basic design concept for the gearbox, provide all necessary equations used for the design, illustrate the use of some basic finite element analysis done using SolidWorks, and show multiple figures and engineering drawings of the gearbox design produced using the SolidWorks 3D engineering software. All free body diagrams (FBD) and hand calculations are provided in Appendix 1. However, the engineering analysis software MatLab was used to do the majority of the stress analysis calculations. This was done so that design parameters such as ring gear and shaft sizes could be altered and then the corresponding design calculations could be easily and quickly reproduced. This made the design process much more efficient. 1.2 Design Concept The design requirements provided no dimensional requirements and it was left up to the students to fill in the blanks. It is assumed that only 1 gearbox will be manufactured, so readily available parts and simple features will be used to design the gearbox to reduce the manufacturing costs of the gearbox. Metric dimensions were chosen for the design of this project so that the common force, distance, and weight units of newtons, meters, and kilograms used in many engineering texts could easily be used with minimal unit conversions needed. A module value of 1 (m=1) was chosen for simplicity so that the number of teeth for the gear equaled the pitch diameter of the gear in millimeters. It was also chosen to design a planetary gearbox where the ring gear is stationary, the sun gear is the input, and the carrier shaft is the output. In the design of this gearbox, it was decided that gearbox radial size was more important than the overall weight of the system. This led to using a 2-stage design concept which allowed for much smaller ring gears to be used to meet the 10:1 reduction. However, this adds a whole other set of gears, but these gears will be much smaller so the weight difference could be comparable. Due to the number of gears in a 2-stage system, the planetary gears for each system were given the same pitch diameter so that the actual number of different gears in the system would be reduced. According to the NEMA C Face dimensions in [6] and the common “56” frame used for these motors like the one in [5], the diameter of the “56” frame is 6-5/8 inches. This led to a maximum ring gear pitch diameter of 160mm (~6.3in) to be chosen so the overall radial size of the gearbox would be comparable 8
  • 10. to that of the motor. All other components such as the shafts, keys, keyways, etc. were designed to work with this basic design concept. In addition, the housing for the gearbox is a half-shell design so that symmetry can be used to manufacture the main housing piece. This also makes assembly, accessing, and performing maintenance on the gearbox easy. Figure 1 is a 3D image of the planetary gearbox which will be described in this paper. Figure 1: 3D Image of proposed planetary gearbox design with top of housing removed 1.3 Gear Design 1.3.1 Gear Ratio Design: To begin the design of the gearbox, the overall size for the Stage 1 ring gear needs to be determined. As mentioned earlier, the ring gear pitch diameter chosen for Stage 1 is 160 mm. With the ring gear pitch diameter determined, equations 1 and 2 given in [3] are used to determine the gear sizes for the sun and planet gears. The initial design statement gave us the output power of the motor. This power is converted to watts and then the input torque to the motor is given in equation 3 and the output torque for that stage is give in equation 4 from the Juvinal Design Book [1]. The values for the gear reductions and the gear sizes are given in Tables 1 and 2. (1) (2) (3) (4) 9
  • 11. Table 1: Gear Ratios Input Output Overall 10 1 Stage 1 3 1 Stage 2 3.33 1 Overall RPM 3600 360 Stage 1 RPM 3600 1200 Stage 2 RPM 1200 360 Overall Torque (N*m) 1.98 19.8 Stage 1 (N*m) 1.98 5.94 Stage 2 (N*m) 5.94 19.8 Table 2: Gear Train Sizes Diameters (mm) Stage 1 Stage 2 Ring Gear 160 140 Sun Gear 80 60 Planet Gear 40 40 Number of Teeth Stage 1 Stage 2 Ring Gear 160 140 Sun Gear 80 60 Planet Gear 40 40 Width for All Gears: b = 10mm 1.3.2 Gear Force and Stress Analysis: With the gear sizes determined, then the force and stress analysis can be performed on the gears. All FBDs associated with this section are shown in Appendix 1. The equations and process for determining the stresses can be found in references [3] and [2]. To begin determining the forces on the system, a FBD for the carrier/output shaft, the planet gear, sun gear, and ring gears are drawn. Using the FBD’s and equations 5-7 from [3], we were able to determine the tangential forces, Fp, on the gear teeth and the torque producing force, Fc, on the carrier arms. The forces are shown in Table 3. (5) (6) or (7) 10
  • 12. Table 3: Forces on the Gears Stage 1: Forces Tangential Force 16.5 N Carrier Force 33 N Stage 2: Forces Tangential Force 49.5 N Carrier Force 99 N With the forces on the gears determined, then the stress analysis can be performed. According to [1] and [2], the surface pressure and the bending stress are the two critical stress analysis procedures that need to be performed on the gears. The following equations used for this analysis are from reference [3] because in [3] they had already derived the changes needed for the different gear meshes, especially the internal gear mesh which required different derivation for its contact ratio. Reference [3] uses the Swedish gear standards, but when compared to the procedures in [1] and [2] the stress analysis seems to be identical. A check was made with a few of the different equations and the values calculated were the same, so it is assumed the stress analysis in [3] is adequate for American standards. For the sun/planet gear mesh, equations 8-12 are used to determine the surface pressure on the gears. In equation 8, are assumed to be 1 and 1.3 as used in [3]. Equations 13-16 are used to calculate the bending stress in the gears. Here is 1 and are given the same value as which is suggested in [3]. (8) (9) √ √ (10) √ **All values from the presented calculations in this paper are logged in the Tables. (11) √ (12) √ (13) (14) (15) 11
  • 13. Sun/Planet Mesh Fc Ring/Planet Mesh Planet Fp Fp Gear Sun Gear Ring Gear Figure 2: Figure of gear meshes and the associated forces For the ring/planet gear mesh, the same equations that were used for the sun/planet gear mesh are used here except with a small change in the contact pressure calculations. This change is mainly a slight difference in calculating the contact ratio between the planet and ring gear which is given in equations 16 and 17. (16) (17) √ √ With the stresses determined, the maximum allowable stress had to be calculated to determine whether the stresses found in the previous equations would be acceptable or not. The following equations, 18 and 19, for determining the maximum allowable stresses are from [2]. The values for the allowable stress factors given in equations 18 and 19 are given in reference [2]. The material used for the allowable stress is assumed Grade 1 steel as given in Tables 14-3 and 14-6 in reference [2] and a safety factor of 2 is used as suggested by [1]. Table 4 shows the allowable stresses and the calculated bending and surface stresses found using the equations described. Observing the values in Table 4 verifies that the stresses in the gears do not exceed the allowable surface and bending stresses and thus the proposed design will be satisfactory for the gearbox specifications desired in this project. Also, the catalog torque limits can be observed to come to this same conclusion. According to www.qtcgears.com, the allowable torque for the planet gear is 14.7Nm, and the allowable torques for similar sun gears for stage 1 and stage 2 are 33.9Nm and 24.2Nm respectively. For the specified gearbox, these torques are not exceeded and thus the chosen gears are satisfactory. (18) (19) 12
  • 14. Table 4: Gear Stress Analysis Values Stage 1: Sun/Planet Gear Mesh Stage 2: Sun/Planet Gear Mesh Surface Pressure 115.7 N/mm^2 Surface Pressure 229.24 N/mm^2 Bending Stress 2.7 N/mm^2 Bending Stress 8.24 N/mm^2 Stage 1: Ring/Planet Gear Mesh Stage 2: Ring/Planet Gear Mesh Surface Pressure 56.14 N/mm^2 Surface Pressure 94.7 N/mm^2 Bending Stress 2.5 N/mm^2 Bending Stress 7.55 N/mm^2 Allowable Stress Values Allowable Surface Presssure 390.7 N/mm^2 Allowable Bending Stress 103.3 N/mm^2 1.4 Shaft Force and Stress Analysis 1.4.1 Input/Output Shaft Analysis: The planetary gear design is a unique gear design that allows for high torques to be transmitted because the major forces in the system are only seen on the gears. Since the forces on the gears cancel each other by having equal spaced planet gears, the only forces that the shafts see are forces due to the weight of the system. However, the shafts will still experience the total torque transmitted by the gears. Thus, the critical part for designing the shafts is the torsional stress limit. This is illustrated in the attached free body diagrams. The proposed shaft dimensions and material properties for the shafts are documented in Table 5. Table 5: Input/Output Shaft Materials and Basic Dimensions Stage 1 Length Min. Dia. Max. Dia. Material Density Mass* Modulus of Elasticity Su, Ultimate Strength Sy, Yield Strength Input Shaft 91mm 15mm 17mm 1020 HR Steel 7.7e3 Kg/m2 0.1325 kg 207e9 Pa 455e6 Pa 290e6 Pa Carrier 53mm 15mm 17mm 1020 HR Steel 7.7e3 Kg/m3 0.3437 kg 207e9 Pa 455e6 Pa 290e6 Pa Planet Shaft 34 mm 10 mm 12mm 1020 HR Steel 7.7e3 Kg/m4 0.0219 kg 207e9 Pa 455e6 Pa 290e6 Pa Stage 2 Length Min. Dia. Max. Dia. Material Density Mass* Modulus of Elasticity Su, Ultimate Strength Sy, Yield Strength Carrier 53 mm 17mm 20mm 1020 HR Steel 7.7e3 Kg/m3 0.378 kg 207e9 Pa 455e6 Pa 290e6 Pa Planet Shaft 34 mm 10 mm 12mm 1020 HR Steel 7.7e3 Kg/m4 0.0219 kg 207e9 Pa 455e6 Pa 290e6 Pa *Mass is taken from SolidWorks To calculate the static torsional stress in the shaft, equations 20 and 22 from [1] are used where the KT value in both equations 20 and 23 is the stress concentration factors due to the shoulders on the shafts and the grooves for retaining rings. Also, the calculations for the basic torsional stress and bending stress are done using the minimum shaft diameter since each shaft has a step change in its size. The input shaft initially has the common 5/8 in. diameter shaft to easily couple with the motor, but then the shaft diameter is adjusted to allow for the bearing and a shoulder to hold the gear in place. In equation 21 the torsional fatigue strength for infinite life and 99.9% reliability is calculated and in Table 7 a safety factor of 2 is incorporated. In this equation Sn’=0.5Su for steel for the lack of better data and the rest of the strength factors are found on pg. 303 of [1] the Juvinal Design book. Equations 20 and 23 utilize the stress concentration factor values taken from [1]. (20) (21) 13
  • 15. (22) Along with the torsional stresses, the bending stresses and deflections of the shafts without bearings can be calculated to determine if the bending stresses or deflections are a critical design parameter. As mentioned before, the only bending forces on the shaft is the weight of the shaft itself so it does not appear to be very critical. However, the bending stresses and deflections are easily calculated with equations 23-25 and equation 26 is used to calculate the shear stress in the planet gear shaft. The fatigue strength for bending can be calculated using equation 21 and the appropriate values for the factors. (23) (24) (25) (26) The values for the torsional and bending stresses and the deflections can be seen in Table 6. The output shaft is the shaft part of the “carrier”. The stresses seen in Table 6 do not exceed the allowable stresses shown in Table 7, so the proposed shaft design is satisfactory for the required specifications. As shown in Table 5, the minimum diameter for the output shaft had to be increased to 17mm so that the torsional stresses in the shaft would be less than the allowable stress. Table 6: Stresses in Gearbox Shafts Stage 1 Torsional Stress Bending Stress Deflection at L/2 Shear Stress Input Shaft 3.58 N/mm2 0.2356 N/mm2 7.9e-5 mm - Ouput Shaft 10.75 N/mm2 0.178 N/mm3 4.07e-5 mm - Planet Shaft - - - 0.5602 N/mm2 Stage 2 Torsional Stress Bending Stress Deflection at L/2 Shear Stress Ouput Shaft 24.6 N/mm2 0.135 N/mm3 7.9e-5 mm - Planet Shaft - - - 1.6807 N/mm2 Table 7: Allowable Stresses in Shaft (SF = 2) Stage 1 Torsional 26.8 N/mm2 Bending 46.2 N/mm2 Stage 2 Torsional 26.8 N/mm2 Bending 46.2 N/mm2 1020 HR Yield Strength = 290 N/mm^2 14
  • 16. 1.4.2 Keyway Design Analysis: With the size of the shafts determined based off of stress design including stress concentration factors and a safety factor, then the keyways need to be designed. The following equations, 27 and 28, from [1] are used for the keyway design. Table 8 shows the keyway specifications and it shows that the allowable torques are not exceeded by the torque values being transmitted by the gearbox from the specified 1 HP motor and a 10:1 gear reduction. (27) (28) Table 8: Keyway Design Stage 1 Key Length in 27 mm Key Length Carrier 27 mm Allowable Torque in 127.7 N/m Allowable Torque out 127.7 N/m Stage 2 Key Length Carrier 30mm Torque allowed out 185.9 N/m Key Square = 5x5mm from SolidWorks Gear 1.4.3 Carrier Arm Stress Analysis: Shear Stress Fc Bending Stress Figure 3: Forces on Carrier Arms In section 6, it is shown that the carrier arm design utilizes a bearing that is inset into the arm. This design allows for the carrier force, Fc, to act directly onto the hole inside of the arm. This means that the stresses in the arm will act like a tensile force acting on the inside of the hole and thus for this part the stress analysis needs to incorporate a stress concentration factor. The equation for this tensile stress analysis is given in equation 29 from [1] and the stress concentration factor is given by KT as well. Equation 23 is used to calculate the bending stress for this part as well. Table 9 shows the stresses in the carrier arm based off of the original proposed design for the carrier arm. The stress values in Table 9 for Stage 2 exceed the yield strength of 1020 HR steel given in Table 5. This suggests that the design of the Stage 2 carrier arm needs to be adjusted so that the stress in the arm does not exceed the material yield strength. The two options for this are to either make the carrier arm a full disk or to increase the 15
  • 17. width and thickness of the carrier arm. It was chosen to adjust the geometry of just the Stage 2 carrier arm to have a width of 40 mm instead of the width of 30 mm initially used which is still used for Stage 1. Both carrier arms still incorporate a thickness of 7 mm. Table 10 shows the new bending stress value of 2.068 MPa which is well under the yield strength for 1020 HR steel given in Table 5. (29) Table 9: Initial Carrier Arm Stress Analysis Tensile Bending Stage 1 0.754 N/mm^2 (0.754MPa) 1.84 N/mm^2 (1.84 MPa) Stage 2 2.263 N/mm^2 (0.226 MPa) 4.29 N/mm^2 (4.29 Mpa) Table 10: Adjusted Carrier Arm Stress Analysis Tensile Bending Stage 1 0.754 N/mm^2 (0.754MPa) 1.84 N/mm^2 (1.84 MPa) Stage 2 0.97 N/mm^2 2.068 N/mm^2 (2.07 Mpa) 1.5 Bearing Design With the keyway design done, then the FBD for the overall gearbox needs to be evaluated and then radial loads on the bearings determined. With the radial load, we can calculate the bearings required for the application. To determine the bearing required for 90e6 revolution life and 99% percent reliability, equation 30 from [1] is used. The following values for the constants are: Ka = 1.3 for ball bearing, Kr = 0.2 for 99% reliability, and Lr = 90e6 revolutions for use with Table 14.2 in [1]. Design is assumed for machines for 8-hour service every working day, so L = revolutions for 20-30 thousand hours at 3600 rpms as given in [1]. For the FBD we need to know the total weight of the gearbox design. However, the ring gear and housing supports the weight of all of the gears, so essentially the bearings will only be supporting the weight of the shafts. The weight of the shafts is shown in Table 5 and these values are approximate and taken from SolidWorks. (30) Table 11: Bearing Design Required Capacity Input Bearing (17mm bore) 21.3 N Middle Bearing (17mm bore) 15.4 N Output Bearing (20mm bore) 10.7 N Planet Bearing (10mm bore) 752 N Bearing Capacity for Xlt (ExtraLight)* 10 mm Bore 1.02 kN 17 mm Bore 1.32 kN 20 mm Bore 2.25 kN *Capacities from Table 14.2 in [1] Bearing Capacity from Solidworks Calculator* 10 mm Bore - 15 mm OD 1.1 kN 17 mm Bore - 23 mm OD 1.9 kN 20mm Bore - 27mm OD 2.5 kN *Capacity for 99% reliability 16
  • 18. Table 11 provides the bearing capacity calculation values. The required bearing capacity for each bearing is given at the top of Table 11. The bearing capacity for extra-light bearings as given in Table 14.2 of [1] is shown in Table 11 as well. These values were compared to the SolidWorks bearing capacity calculator values for the actual bearings created using the SolidWorks toolbox. When observing the values in Table 11, the bearing capacity numbers from [1] are real similar to the calculated numbers given from the Solidworks calculator and these capacities for the bearings exceed the required capacities given from equation 30 and are thus acceptable. 1.6 SolidWorks Model of Gearbox The gearbox design is built as a 3D model using the SolidWorks engineering software. This section will highlight the 3D model of the gearbox and illustrate additional features of the design as well as address SolidWorks tools used to make the 3D part. 1.6.1 Gear Assembly Retaining Ring Grooves Keyway Keyway Keyway Figure 4: Left is Stage 1 gear assembly and Right is Stage 2 Gear Assembly Planet Shaft with ring groove and key way Figure 5: Left is Stage 1 Gear Assembly and Right is Stage 2 Gear Assembly 17
  • 19. Bearing 17mm bore Bearing 20mm bore Planet Bearing 10mm bore Bearing 17mm bore Figure 6: Side Image of Gear Assembly Figures 4-5 are the assembly of the gearbox without the housing around the gears. The sun and ring gears were built using the SolidWorks Toolbox utilities feature. This feature has commonly available mechanical parts such as gears, bolts, bearings, retaining rings, nuts, etc. already built in the SolidWorks program and all the user has to do is specify certain dimensions. For the gears, only the pitch diameter, module, pitch angle, gear width, hub dimensions, and whether a keyway is needed has to be specified and then SolidWorks builds the part. This feature is also used to build the bearings, retaining rings, and bolts used in this assembly. The bearings are noted in Figure 6. The SolidWorks Toolbox also has an automatic grooving feature which automatically constructs the grooves for common retaining rings, and this tool was used for all retaining ring grooves. Many manufacturers for mechanical parts provide 3D drawings for available parts that they sell. The planet gears for the assembly were taken from www.qtcgears.com and then assembled in the gearbox. The benefit to using common and readily available parts is that the overall price to manufacture a gearbox is greatly reduced. As mentioned in the earlier design portion of this paper, the material for the gears is steel and the material for the shafts is 1020 HR steel. These materials were chosen for their low cost and for being readily available. 1.6.2 Gearbox Housing The housing for the gearbox is chosen to be built out of 6061 aluminum due to its low cost, easy manufacturability, and it being readily available. The total amount of force transmitted to the housing is the sum of all the carrier forces, Fc. There are currently no analytical design calculations performed to ensure the proposed housing design will hold up to the total amount of force transmitted to the housing. The following housing design is to propose a geometric design concept that will work for housing the planetary gear system designed in this paper. The design concept chosen for the housing is a shell type of housing. This design concept provides easy accessibility and assembly for the planetary gearbox. It also utilizes symmetry for each half of the housing so it will be cheaper to manufacture the housing components with only the addition of a few bolt holes in the top shell. The housing is designed to secure the bearings in place and the shells attach by a flange style connection. To secure the middle bearing in place, an additional column was built which bolts internally onto the main housing shell and a flange style connector to secure the bearing in place on the column. This adjustment was made as an additional part so alignment onto the stage 1 carrier shaft would be easier and adjustable if need be. For the planetary gearbox design to function 18
  • 20. properly, the ring gear has to be stationary and is thus designed to be bolted straight to the housing. Figures 7 and 8 are different 3D views of the gearbox assembly housing. Middle Bearing Support Gasket Figure 7: Left image is bottom shell of housing and Right is bottom shell with gear assembly mounted in it Input Shaft Cover Input Shaft Output Shaft Gearbox Feet Figure 8: Left is Gearbox assembly with input shaft cover and right is 3D image of gearbox assembly with all components There are a few features about the gearbox assembly housing that need to be pointed out. All of the bolts used in the assembly are M4 threaded bolts with varying lengths. This was done to reduce the number of tap dies needed to make the holes, the number of tools needed to assemble the gearbox, and the number of different bolting components since it is assumed that only 1 of these gearboxes will be manufactured. Figure 8 also shows a shaft cover/connecting piece mounted onto the gearbox. This piece is added to cover the input shaft of the gearbox and the output shaft of the motor during operation. This increases the safety of the gearbox for nearby workers or other equipment. This cover is designed to align directly to a 56 frame NEMA C Face motor. This will also help with the rigidity of the entire system when mounted to the motor. There were also feet added to the housing assembly. These feet will allow for stability of the gearbox and make the gearbox easy to secure to a mounting location. 1.6.3 Engineering Drawings In addition to building a 3D model of the proposed planetary gearbox design in SolidWorks, engineering drawings are produced in SolidWorks which will aid in the manufacturing of the various components. 19
  • 21. These drawings include all necessary data needed to manufacture each component and are organized based off of ASME standards as directed by the 2010 SolidWorks book [7]. The tolerances for the shafts and holes are based off of H9/d9 and D9/h9 fits for the hole and shaft basis as described in the 27th Edition Machinery’s Handbook [8]. These fits are free running fits intended for higher running speeds. The fit for a 15mm and 17mm shafts was not given, so the tolerance for the 16mm shaft from [8] is used for both of these shaft sizes in the attached drawings since it is the closest. The tolerance for the location of the bearings on its related shaft or inset on the carrier uses the location fit H7/h6 from [8]. If the actual size is not in [8] then the next closest size in [8] will be used. This provides a snug fit for the bearings and allows for the bearings to be freely assembled and disassembled. Drawings for the gearbox design can be found in Appendix 2. 1.7 SolidWorks Finite Element Analysis SolidWorks is a powerful engineering analysis tool in addition to a 3D graphic software. In this section, multiple finite element analysis (FEA) studies will be done on a few of the components in the gearbox. All FEA tools should be used with skepticism and should always be verified with analytical calculations when possible. Analytical calculations only work for really basic geometries and typically involve multiple assumptions in order for the basic analysis equations to be accurate and simple. Because of this, the FEA stresses in the gearbox components are expected to be different from the hand calculations and will probably be higher than the analytical calculations due to the additional features such as retaining ring grooves and keyways. To verify the FEA analysis from SolidWorks, the stress values of the components well away from the applied loads and additional features will be compared to the analytical values. In this section we will observe the FEA analysis of stresses in the input shaft, planet shaft, and carrier components. All loads applied in the FEA analysis are the same values as the forces and torques shown in Tables 1 and 3. 1.7.1 Bending Stress of Input Shaft As observed in the analytical calculations, the bending stress in the shafts was not a critical design issue because the only force on each shaft is the weight of the shaft. So only the bending stress of the input shaft is studied for comparison with the analytical calculation values in Table 6. Here the weight of the shaft is given in Table 5 and this produces a force of 1.3N. The FEA analysis is shown below in Figure 9. Figure 9 shows 3 different stress values obtained in the FEA analysis. The highest stresses are expected to be at the end of the shaft where the shaft is fixed. Figure 9 shows that this is the case and that stresses a little over a diameter away from the end are about 0.256 N/mm^2. This is similar to the 0.236 N/mm^2 obtained by equation 23 and located in Table 6. Applied Vertical Load 0.256 N/mm^2: (*Compare to 0.236 N/mm^2 in Table 6) Figure 9: Bending Stress FEA of Input Shaft 20
  • 22. 1.7.2 Torsional FEA Analysis of Shaft Components Here we will study the torsional stresses in the input shaft, stage 1 carrier shaft, and stage 2 carrier shaft. Figure 10 shows the FEA for the input shaft, and in this study the torque was applied around the face of the shaft over the area of the keyway and then the keyway on the other end was the fixed geometry. The stress values closer to the center of the shaft and on each side of the shoulder are used to compare with the values in Table 6. As shown in Figure 10, the analytical calculations predict a stress value of 3.58 N/mm^2 which is pretty similar to the values of 3.86N/mm^2 and 4.37N/mm^2. Thus the FEA analysis is assumed to be accurate and the input shaft is sufficient for this design. 4.37 N/mm^2 (*compare to 3.58 N/mm^2 in Table 6) 3.86 N/mm^2 (*compare to 3.58 N/mm^2 in Table 6) Figure 10: Torsional FEA Analysis of the Input Shaft Figures 11 and 12 are the torsional analysis of the Stage 1 and Stage 2 carrier components. Here the carrier arm feature is held fixed while the torsional load is applied to the face of the shaft in the area of the keyway. Figure 11 shows that the stress values obtained by the FEA a distance away from the keyway are very similar to the analytical value for stress in Table 6. This value is expected to be close to the analytical value since it is located away from the applied load and any unique features. The stresses increase as you get closer to the keyway and the area where the torque is applied which is expected. The stress values given by the FEA analysis are still within the acceptable range and are verified by how similar they are to the analytical values. 10.1N/mm^2 (*compare to 10.75N/mm^2 in Table 6) 17.4N/mm^2 (*compare to 10.75N/mm^2 in Table 6) Figure 11: Stage 1 Carrier Shaft Torque FEA Analysis 21
  • 23. Figure 12 is the torsional analysis for the Stage 2 carrier shaft. Here similar results are found to what was found in Figure 11. The torsional stress values closer to the carrier arm feature is very similar to the analytical calculations, which verifies the FEA analysis, and as you get closer to the area where the torque was applied and the keyway feature, the stress values increase. The FEA analysis verifies that the stress values are still within the acceptable range. 20.9N/mm^2 (*compare to 24.6N/mm^2 in Table 6) 34.2N/mm^2 (*compare to 24.6N/mm^2 in Table 6) Figure 12: Stage 2 Carrier shaft torque analysis 1.7.3 Carrier Arm Shear and Bending Stresses In this section the carrier arm shear and bending stresses produced by the carrier force, as shown in Figure 3 and given in Table 3, will be studied. The stress values given by the FEA analysis will be compared to the values in Table 10. Figures 13 and 14 are the FEA analysis for the shear and bending of the Stage 1 carrier arm. Figure 13 shows that the FEA analysis only predicts 0.3N/mm^2 shear stress while the analytical calculations predict 0.75N/mm^2. The discrepancy in the values is that the analytical calculations assume the 15mm hole the bearing sits in goes all the way through the arm but in reality there is still the small lip with a 11mm diameter hole which will decrease the stress values. 0.3N/mm^2 (*compare to 0.75N/mm^2 in Table 10) Figure 13: FEA Analysis showing the shear stresses in the carrier arm 22
  • 24. Figure 14 shows that the predicted bending stresses obtained in the FEA Analysis are very similar to what was obtained analytically. 1.42N/mm^2 (*compare to 1.84N/mm^2 in Table 10) Figure 14: Bending Stresses on Stage 1 Carrier Arm Figure 15 is the FEA analysis for the shear and bending stresses in the Stage 2 carrier arm. In this figure both the shear stresses due to the load and the bending stresses are noted. Figure 15, similar to the Stage 1 Carrier analysis, shows that the stresses in the Stage 2 Carrier arm due to the carrier force, Fc, are satisfactory for this design and that the FEA analysis and the analytical calculations are very similar thus verifying their accuracy. 0.48N/mm^2 (*compare to 0.97N/mm^2 in Table 10) 2.24N/mm^2 (*compare to 2.07N/mm^2 in Table 10) Figure 15: Stage 2 Carrier Arm Shear and Bending FEA Analysis 1.7.4 Planet Shaft Shear FEA The final FEA analysis performed is the shear stress analysis of the planet gear shaft due to the carrier force. The stress values produced by the FEA analysis will be compared to the shear stress value in Table 6 for the stage 2 planet shaft since this stage is where the planet shaft will experience the highest 23
  • 25. carrier force of 99N. Figure 16 shows that near the location where the shear force is applied, the stress values are similar to that of the analytical calculations. The stress values increase as you get closer to the fixed end. The fixed geometry is not a good representation of the actual design since the section with the key would be supported by the gear. The higher stresses closer to the fixed end are actually bending stresses due to the way the FEA analysis was done with the fixed geometry. This suggests that the FEA analysis should be performed with a different fixture and with a different load applied to better resemble the load applied to the area the bearing occupies and for the fixture to cover the area inside of the gear. 1.06N/mm^2 (*compare to 1.7N/mm^2 in Table 6) 3.6N/mm^2 (*compare to 1.7N/mm^2 in Table 6) Figure 16: Planet Shaft shear stress FEA This section successfully verified the accuracy of both the analytical calculations and the FEA analysis predictions. This increases the confidence that each of these components are correctly designed for this gearbox design and will operate correctly. 1.8 Future Work This paper described a fully designed gear system including shaft and bearing analysis. However, to have a fully designed gearbox suitable for operation, there is additional design analysis that needs to be performed. A vibration study needs to be performed to identify the natural frequencies of the gearbox and to ensure the system is not running at any of the critical speeds. If a system operates at one of its natural frequencies, then the vibrations of the system will be large and can continue to increase causing major damage to the system which could lead to a catastrophic failure. Further work needs to be done on the lubrication and sealing of the gearbox. It is assumed that the gearbox will be oil lubricated and the type of lubricant can be easily determined from lubrication text and the speed and torque of the system. Gearboxes of this type are commonly oil lubricated and the gearbox is partially filled with oil, so as the gears rotate they will continue to be lubricated by passing through the oil. With this type of lubrication, additional holes will need to be added onto the gearbox to allow for draining and filling the oil. Also, a pressure relief cap or hole will need to be designated so the 24
  • 26. pressure added to the gearbox on startup can escape the housing. Finally, additional stress analysis needs to be performed on the housing to ensure that its current geometrical design and chosen material will hold up to the forces and torques of the system. A final minor design adjustment needs to be made on the planet gear shaft and the carrier arm. The current design makes the retaining rings have an extremely tight fit that might not work in real life. Some minor adjustments need to be made to ensure the retaining rings comfortably fit in their grooves. 1.9 Conclusion A 2-stage planetary gearbox was successfully designed for a 1 HP NEMA C Face motor operating at 3600 rpms. The 2-stage gearbox design ensures that the gearbox will fit in any radial space that the driving motor will fit and still obtains the desired 10:1 reduction required out of the gearbox. All necessary design calculations were utilized to design the individual components and to ensure the successful functionality of the gearbox design. These calculations verified the FEA done on a few of the components which greatly increases the confidence that this design will function properly. In addition to fully designing the 2-stage planetary gear system through design analysis, SolidWorks was used to build a 3D model of the gearbox. The SolidWorks model made it possible to ensure the gearbox design functioned properly, provided the graphics needed to effectively communicate the design to customers, and puts the gearbox design in a format that can easily be manufactured through the engineering drawings and the SolidWorks parts. This paper provided a successful and complete design of a Planetary Gear Reducer for a 1 HP NEMA C Face motor operating at 3600 rpms, and with a little more design analysis (as mentioned in Section 8) this gearbox will be ready to be manufactured and tested. 1.10 References [1]Juvinall, R.C., and Marshek, K., Fundamentals of Machine Component Design 4th Edition, John Wiley & Sons 2006, Print [2]Budynas, R.G., and Nisbett, J.K., Mechanical Engineering Design 8th Edition, McGraw Hill Companies Inc, 2008 Pring [3] Roos, F., and Spiegelberg, C., “Relations between size and gear ratio in spur and planetary gear trains,” Department of Machine Design, Royal Institute of Technology, Stockholm 2004 ISSN 1400-1179 [4]Palazzolo, A., “Dr. Alan Palazzolo’s MEEN 617 Vibration Course Notes,” Texas A&M University, 2010 [5] http://www.grainger.com/Grainger/DAYTON-General-Purpose-Motor-5K673 [6] http://www.electricmotorservice.net/nemachart.pdf [7] Planchard, D.C., and Planchard, P.P., Engineering Design with SolidWorks 2010, SDC Publications 2010 [8] Oberg, E., Jones, F.D., Horton, H.L., and Ryffel, H., Machinery’s Handbook 27th Edition, Industrial Press Inc, 2004 25
  • 27. 2. Vases In this assignment multiple different vases were built as 3D models in SolidWorks. Here multiple different features such as lofting, revolving, extruding, sweeping, etc. were used to build the vases. The vases were all given materials that suit their particular features and the images of these vases were rendered using the Photoworks add in. The following figures are the 5 vases created. Figure 17: LEFT: "Round Top" vase with green glass; RIGHT: "Round Front" vase with clear glass and patterned back 26
  • 28. Figure 18: LEFT: "Mahogany Heavy" vase and RIGHT: "Twisted Carbon Fiber" vase Figure 19: "Porcelain Petite" vase 27
  • 29. 3. Google House: In this homework, a house was found using google maps and then a 3D graphic of the house was built up off of the google map image. By using surrounding objects, a very close scale for the house could be obtained and then an accurate 3D model of the house could be built. All features of the house including doors, windows, etc. were built and materials were applied to these components. The following figures present this assignment. Figure 20: LEFT: Original Google Maps image; RIGHT: New image with 3D model of house built on the image Figure 21: 2 different angles presenting the 3D model of the house and its features 28
  • 30. 4. Guide Rod Assembly Plates: Here the plates for the Guide Rod Assembly in the Solidworks Tutorial book, reference [7] of the gearbox design report, were built. This was done following along in the book and utilized many additional features such as the hole wizard. The figures below show the original plate from the book and a modified plate. Figure 22: Left front and Right back isometric views of original plate Figure 23: Left front and Right back isometric views of Modified Plate 29
  • 31. 5. Guide Rod Assembly: Here the complete Guide Rod assembly was built and assembled as instructed by the SolidWorks tutorial book. Many features, such as mirroring, linear pattering, and the hole wizard, were utilized to aid in the building and assembling of the Guide Rod. The original guide rod assembly as instructed by the book was made, and then it was altered to make a new guide rod assembly that has different dimensional sizes. Figure 24: 3D unexploded and exploded views of the Guide Rod Assembly Figure 25: Modified Guide Rod Assembly mounted on plate Figure 26: Exploded View of Modified Guide Rod Assembly mounted on plate 30
  • 32. 6. Rotating Crank Assembly: Here a basic rotating crank assembly model was built and assembled in SolidWorks. It was built and assembled so that the crank assembly would operate correctly. To illustrate the operation of the crank, 3 different views of the assembly are shown with the crank in 3 different positions rotating clockwise. Figure 27: Crank assembly at 3 different rotated positions and rotation direction is shown 7. Basic Gearbox Assembly: In this assignment, a very basic gearbox was modeled. Two identical gears were created using the SolidWorks Toolbox and then the shafts and the housing were built so that they could be assembled together. The goal of the assignment was to learn how to add new parts to an assembly and then construct the housing around the assembly. Output Shaft Input Shaft Figure 28: LEFT: Isometric View of Gearbox Assembly; RIGHT: Isometric View with housing sides removed 31
  • 33. Figure 29: Exploded View of the Basic Gearbox Assembly 8. Basic Gearbox 2D Engineering Drawings 2D engineering drawings of the shafts and housing of the basic gearbox is made. The drawings were made per ASME Y14.5 as instructed by the SolidWorks book. The un-dimensioned tolerance block was filled out, a logo was added, and an assembly drawing with a bill of materials is made to detail the assembly. The engineering drawings are on the following pages. 32
  • 34. 33
  • 35. 34
  • 36. 35
  • 37. 9. Surface Truck Model: The truck model shown below is a truck built using only “Surface Features.” Surface features are important when modeling complex features such as the surfaces on a computer mouse and these surface models make manufacturing complex features much easier. Here the truck modeled includes headlights, taillights, windows, doors, tires, and wheels. This assignment highlights the abilities of surface features and how unique surfaces can be built. Figure 30: Two Isometric views of the surface truck Figure 31: Front and Rear Views of the surface truck model Figure 32: LEFT: Side View of truck; RIGHT: Side View with doors colored gray 36
  • 38. 10. Basic Finite Element Analysis (FEA) using SolidWorks Simulations Here a basic bending stress FEA study was done using the input shaft of the Planetary Gearbox designed in the design project. A bending stress study was performed and the force in the study is 1.4N from the weight of the shaft. The following equation is the basic bending stress equation where M = 1.4*moment arm. SolidWorks also has a beam calculator feature which does basic analytical beam calculations. The stress value from this calculator is verified with the equation above and the stress and deflection values are 0.14 N/mm2 and 0.000034mm. The figures below show the FEA study results from SolidWorks and their comparable analytical values. The accuracy of the FEA study is verified. 0.155 N/mm2 compared to the value obtained analytically of 0.14 N/mm2 Figure 33: Bending stress FEA of Shaft Fixed end Deflection of 0.000051mm compared to the analytical value of 0.000034mm Figure 34: Deflection results of shaft FEA analysis 37
  • 39. Appendix 1: Free Body Diagrams and Hand Calculations for Project 38
  • 40. 39
  • 41. 40
  • 42. 41
  • 43. 42
  • 44. 43
  • 45. Appendix 2: Engineering Drawings of Gearbox Components for Planetary Gearbox 44
  • 46. 27 48 1.600 60 R3.050 2.500 93 R0.500 R1 DETAIL A SCALE 2 : 1 B27.8 - 3DM1 - 15 (External Retaining Ring Groove) R1 2.420 B A 4.755 DETAIL B SCALE 2 : 1 Eric Halfmann UNLESS OTHERWISE SPECIFIED: NAME DATE DIMENSIONS ARE IN MILLIMETERS DRAWN TOLERANCES: ANGULAR: MACH 0 30' CHECKED TITLE: ONE PLACE DECIMAL 0.5 Input Shaft ENG APPR. TWO PLACE DECIMAL 0.15 MFG APPR. SolidWorks Student Edition. PROPRIETARY AND CONFIDENTIAL THE INFORMATION CONTAINED IN THIS INTERPRET GEOMETRIC TOLERANCING PER: ASME Y14.5 MATERIAL Q.A. COMMENTS: SIZE DWG. NO. REV A 1020 HR Steel For Academic Use Only. DRAWING IS THE SOLE PROPERTY OF <INSERT COMPANY NAME HERE>. ANY InputShaft_Stage1_Drawing REPRODUCTION IN PART OR AS A WHOLE FINISH WITHOUT THE WRITTEN PERMISSION OF NEXT ASSY USED ON Machined <INSERT COMPANY NAME HERE> IS PROHIBITED. APPLICATION DO NOT SCALE DRAWING SCALE: 1:1 WEIGHT: SHEET 1 OF 2 5 4 3 2 1
  • 47. 14.950 14.907 38 17.000 16.989 R4.265 2.785 34 15.825 15.782 R0.500 2.071 DETAIL D SCALE 2 : 1 5 D C DETAIL C SCALE 2 : 1 Eric Halfmann UNLESS OTHERWISE SPECIFIED: NAME DATE DIMENSIONS ARE IN MILLIMETERS DRAWN TOLERANCES: ANGULAR: MACH 0 30' CHECKED TITLE: ONE PLACE DECIMAL 0.5 Input Shaft ENG APPR. TWO PLACE DECIMAL 0.15 MFG APPR. SolidWorks Student Edition. PROPRIETARY AND CONFIDENTIAL THE INFORMATION CONTAINED IN THIS INTERPRET GEOMETRIC TOLERANCING PER: ASME Y14.5 MATERIAL Q.A. COMMENTS: SIZE DWG. NO. REV A 1020 HR Steel For Academic Use Only. DRAWING IS THE SOLE PROPERTY OF <INSERT COMPANY NAME HERE>. ANY InputShaft_Stage1_Drawing REPRODUCTION IN PART OR AS A WHOLE FINISH WITHOUT THE WRITTEN PERMISSION OF NEXT ASSY USED ON Machined <INSERT COMPANY NAME HERE> IS PROHIBITED. APPLICATION DO NOT SCALE DRAWING SCALE: 1:1 WEIGHT: SHEET 2 OF 2 5 4 3 2 1
  • 48. 15.018 15.000 R15 11 DETAIL A SCALE 2 : 1.5 7 60 53 120.00° 20 30 R1 51.340 A Eric Halfmann UNLESS OTHERWISE SPECIFIED: NAME DATE DIMENSIONS ARE IN MILLIMETERS DRAWN TOLERANCES: ANGULAR: MACH 0 30' CHECKED TITLE: ONE PLACE DECIMAL 0.5 Stage 1 Carrier ENG APPR. TWO PLACE DECIMAL 0.15 MFG APPR. SolidWorks Student Edition. PROPRIETARY AND CONFIDENTIAL THE INFORMATION CONTAINED IN THIS INTERPRET GEOMETRIC TOLERANCING PER: ASME Y14.5 MATERIAL Q.A. COMMENTS: SIZE DWG. NO. REV A 1020 HR Steel For Academic Use Only. DRAWING IS THE SOLE PROPERTY OF <INSERT COMPANY NAME HERE>. ANY FINISH Carrier_Stage1_Drawing REPRODUCTION IN PART OR AS A WHOLE WITHOUT THE WRITTEN PERMISSION OF NEXT ASSY USED ON Machined <INSERT COMPANY NAME HERE> IS PROHIBITED. APPLICATION DO NOT SCALE DRAWING SCALE: 1:4 WEIGHT: SHEET 1 OF 2 5 4 3 2 1
  • 49. R3.050 5 5 27 B27.8M - 3DM1-15 (External Retaining Ring Groove) R0.500 7.475 DETAIL B 2.100 R DETAIL C 17.000 7.455 16.989 SCALE 2 : 1 SCALE 2 : 1.5 6.500 B27.7M - 3DM1-15 B C (Internal Retaining Ring Groove) 18 D 0.500 DETAIL D SCALE 2 : 1.5 Eric Halfmann UNLESS OTHERWISE SPECIFIED: NAME DATE DIMENSIONS ARE IN MILLIMETERS DRAWN TOLERANCES: ANGULAR: MACH 0 30' CHECKED TITLE: ONE PLACE DECIMAL 0.5 Stage 1 Carrier ENG APPR. TWO PLACE DECIMAL 0.15 MFG APPR. SolidWorks Student Edition. PROPRIETARY AND CONFIDENTIAL THE INFORMATION CONTAINED IN THIS INTERPRET GEOMETRIC TOLERANCING PER: ASME Y14.5 MATERIAL Q.A. COMMENTS: SIZE DWG. NO. REV A 1020 HR Steel For Academic Use Only. DRAWING IS THE SOLE PROPERTY OF <INSERT COMPANY NAME HERE>. ANY FINISH Carrier_Stage1_Drawing REPRODUCTION IN PART OR AS A WHOLE WITHOUT THE WRITTEN PERMISSION OF NEXT ASSY USED ON Machined <INSERT COMPANY NAME HERE> IS PROHIBITED. APPLICATION DO NOT SCALE DRAWING SCALE: 1:4 WEIGHT: SHEET 2 OF 2 5 4 3 2 1
  • 50. R0.500 54 R2 7 20 R1 5 2.350 DETAIL C SCALE 2 : 1.5 50 30 90.00° 15.018 15.000 C A 11 40 8.475 R 20.000 8.455 DETAIL A 19.987 SCALE 2 : 1.5 Eric Halfmann UNLESS OTHERWISE SPECIFIED: NAME DATE R20 DIMENSIONS ARE IN MILLIMETERS DRAWN TOLERANCES: ANGULAR: MACH 0 30' CHECKED TITLE: ONE PLACE DECIMAL 0.5 Stage 2 Carrier ENG APPR. TWO PLACE DECIMAL 0.15 MFG APPR. SolidWorks Student Edition. PROPRIETARY AND CONFIDENTIAL THE INFORMATION CONTAINED IN THIS INTERPRET GEOMETRIC TOLERANCING PER: ASME Y14.5 MATERIAL Q.A. COMMENTS: SIZE DWG. NO. REV A 1020 HR Steel For Academic Use Only. DRAWING IS THE SOLE PROPERTY OF <INSERT COMPANY NAME HERE>. ANY FINISH Carrier_Stage2_Drawing REPRODUCTION IN PART OR AS A WHOLE WITHOUT THE WRITTEN PERMISSION OF NEXT ASSY USED ON Machined <INSERT COMPANY NAME HERE> IS PROHIBITED. APPLICATION DO NOT SCALE DRAWING SCALE: 1:4 WEIGHT: SHEET 1 OF 2 5 4 3 2 1
  • 51. 6.500 0.500 18 B27.7 - 3DM1 - 15 (Internal Retaining Ring Groove) DETAIL E SCALE 2 : 1.5 E 30 D R3.050 2.500 DETAIL D SCALE 2 : 1 B27.8 - 3DM1 -15 (External Retaining Ring Groove) Eric Halfmann UNLESS OTHERWISE SPECIFIED: NAME DATE DIMENSIONS ARE IN MILLIMETERS DRAWN TOLERANCES: ANGULAR: MACH 0 30' CHECKED TITLE: ONE PLACE DECIMAL 0.5 Stage 2 Carrier ENG APPR. TWO PLACE DECIMAL 0.15 MFG APPR. SolidWorks Student Edition. PROPRIETARY AND CONFIDENTIAL THE INFORMATION CONTAINED IN THIS INTERPRET GEOMETRIC TOLERANCING PER: ASME Y14.5 MATERIAL Q.A. COMMENTS: SIZE DWG. NO. REV A 1020 HR Steel For Academic Use Only. DRAWING IS THE SOLE PROPERTY OF <INSERT COMPANY NAME HERE>. ANY FINISH Carrier_Stage2_Drawing REPRODUCTION IN PART OR AS A WHOLE WITHOUT THE WRITTEN PERMISSION OF NEXT ASSY USED ON Machined <INSERT COMPANY NAME HERE> IS PROHIBITED. APPLICATION DO NOT SCALE DRAWING SCALE: 1:4 WEIGHT: SHEET 2 OF 2 5 4 3 2 1