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An investigation of structural integrity of chassis mounted platform subjected
1.
INTERNATIONALMechanical Engineering and
Technology (IJMET), ISSN 0976 – International Journal of JOURNAL OF MECHANICAL ENGINEERING 6340(Print), ISSN 0976 – 6359(Online) Volume 4, Issue 1, January - February (2013) © IAEME AND TECHNOLOGY (IJMET) ISSN 0976 – 6340 (Print) ISSN 0976 – 6359 (Online) Volume 4, Issue 1, January- February (2013), pp. 115-122 IJMET © IAEME: www.iaeme.com/ijmet.asp Journal Impact Factor (2012): 3.8071 (Calculated by GISI) www.jifactor.com ©IAEME AN INVESTIGATION OF STRUCTURAL INTEGRITY OF CHASSIS MOUNTED PLATFORM SUBJECTED TO CONCENTRATED LOAD DURING BRAKING Prof.Dr. Matani A.G1 Prof.Deulgaonkar V.R2 Prof.Dr. Kallurkar S.P3 1 (Mechanical Engineering, Govt. College of Engineering, Amravati, Sant Gadge Baba Amravati university, Amravati, India, ashokgm333@rediffmail.com) 2 (Mechanical Engineering, Govt. College of Engineering, Amravati, Sant Gadge Baba Amravati university, Amravati, India, vikasdeulgaonkar@gmail.com) 3 (Mechanical Engineering, D.Y Patil College of Engineering, University of Pune, Pune , India, drkallurkar@yahoo.co.in ) ABSTRACT The present work deals with the investigation of strength of a specialized chassis mounted platform/structure designed to carry concentrated load. This work deals with the mathematics behind braking through shear and bending diagrams analysis processes. The perceptible loading case in the present analysis comprises braking load and its effect on the platform/structure by usage of simple shear force & bending moment diagrams. These diagrams reveal the distribution of shearing force during braking for typical Indian truck. Present analysis accentuates on the design stage aspects of the platform as this research is a step in doctoral study. Effect of load during braking for an atypical type of combination of longitudinal and cross members in platform/frame design is formulated. This paper provides a new technique for computation of strength using shear and bending diagrams. Peculiarity of this analysis is the usage of combined section modulus of three members for computation of stress. Keywords: Braking condition, horizontal load, shear stress, Structural strength shear force and bending moment diagram. 115
2.
International Journal of
Mechanical Engineering and Technology (IJMET), ISSN 0976 – 6340(Print), ISSN 0976 – 6359(Online) Volume 4, Issue 1, January - February (2013) © IAEME 1. INTRODUCTION The safe and reliable use of a road vehicle necessitates the continual adjustment of its speed and distance in response to change in traffic conditions. Braking system in every vehicle plays a vital role in fulfilling this requirement. Design of the braking system which makes an efficient use as possible of the finite amount of traction available between the tire and the road over the entire operational range is of prime importance. A detailed torque characteristics study of small disk brake using magnetic fluid is carried out by Hyung S.B et.al. The torque characteristic of small disk brake by a magnetic body force is studied through the relation between magnetic field intensity and rotational disk velocity [2]. Dynamic stability of vehicle is evaluated using real time dynamic stability control system, a different approach to estimate the vehicle velocity by Li L et.al, [3]. Chul-Goo Kang analyzed design parameters of the braking system in the development of new high speed train. He proposed a hardware-in-loop system for the braking system of a Korean high-speed train [4]. Gyu Ha Kim et.al used a virtual proving ground approach for obtaining the dynamic stress or strain distribution. Realistic boundary conditions of tire/road surface interactions are implemented by using the virtual proving ground approach [5]. 2. BRAKING MECHANISM MATHEMATICS Braking performance equation is obtained from Newton’s Second Law applied in horizontal direction. Applying the Newton’s Law to a light truck loaded with a container, we get an equation as that relates all the forces exerted during braking. The vehicle weight W is subjected to a linear deceleration, which is balanced by the total action of front & rear axle braking force Fxf & Fxr, aerodynamic drag Da, and the sine component of weight all considered in horizontal direction. െ Dx ൌ െFxf െ Fxr െ Da െ Wsinθ ------ (1) -ve sign is to account for linear deceleration. For present case linear deceleration is presumed considering the adhesion between tire and ground. The braking efficiency or the maximum retarding force F, applied by the brakes at the wheels relies on the friction coefficient between the tire and the road surface and the component of weight of the vehicle on the wheel. These terms are interrelated as : F ൌ µW------ (2) This shows that the braking efficiency is highly affected by the coefficient of friction. Considering all the on road possibilities, braking efficiency of 50% is hypothesized. The component of vehicle weight including the laden weight in the container generates a moment around the centre of gravity of the vehicle. The total weight in present research is so arranged that it is distributed at six locations on the platform. All these locations are referred to as ISO corner locations. Total weight of twelve tones is distributed variably at front, middle and rear ISO coroners. At two front and two rear ISO corners a total load of six tone is applied 1.5 tone at each. A load of six tone is applied at the two mid ISO corners, three tone each on each side. By considering a braking efficiency of 50%, a horizontal force in addition to vertical 116
3.
International Journal of
Mechanical Engineering and Technology (IJMET), ISSN 0976 – 6340(Print), ISSN 0976 – 6359(Online) Volume 4, Issue 1, January - February (2013) © IAEME one acts at each ISO corner. The magnitude of each load is half the load that acts at each ISO corner. This horizontal force is shear force that induces a shear stress at each ISO corner location. The magnitude of this stress is estimated using shear force and bending moment diagrams. The section properties of the individual members i.e. vehicle chassis, main longitudinal member and square cross member is evaluated in [18]. The combined section modulus values of the unsymmetrical section are calculated for estimating the stress during braking condition. 3. ESTIMATION OF SHEAR FORCE, BENDING MOMENT AND STRENGTH OF THE STRUCTURE During braking a horizontal load acts on the platform. This load acts in addition to the load in stationary condition. So, for this case the resultant bending moment is combination of horizontal and vertical bending moment. The support reaction calculations are done as below. ΣFy = RA + RD = 140 KN ΣMa = Ra x 0 + 35 x 0.7 + 70 x 3.55 – RD x 5.6 + 35 x 7.4 RD = 95 KN (upward) RA = 140 – RD = 45 KN (upward) During braking a horizontal force of magnitude equal to half of vertical loads magnitude at respective ISO corner. This is taken into account by considering a moment around the centroidal axis of outer longitudinal member. A sample calculation of shear force and bending moments in transverse direction to outer longitudinal member is shown in table 1.The calculations for shear force and bending moment are tabulated below TABLE 1: Shear force and Bending Moment Sample calculations Point Shear force calculation (S.F) Bending Moment calculation (B.M) S.F Just LHS S.F Just RHS B.M Just LHS B.M Just RHS (KN) (KN) (KN-m) (KN-m) A 0 45 0 0 B 45 10 31.5 31.5 C 10 -60 60 60 D -60 35 -63 -63 E 35 0 0 0 The shear force and bending moment diagrams for both concentrated load and concentrated load with moment around each load point is shown in fig1 and fig.2 117
4.
International Journal of
Mechanical Engineering and Technology (IJMET), ISSN 0976 – 6340(Print), ISSN 0976 – 6359(Online) Volume 4, Issue 1, January - February (2013) © IAEME Fig.1: Shear Force and Bending Moment Diagram for Concentrated Load 118
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International Journal of
Mechanical Engineering and Technology (IJMET), ISSN 0976 – 6340(Print), ISSN 0976 – 6359(Online) Volume 4, Issue 1, January - February (2013) © IAEME Fig.2. Shear force and Bending moment diagram for braking condition 119
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International Journal of
Mechanical Engineering and Technology (IJMET), ISSN 0976 – 6340(Print), ISSN 0976 – 6359(Online) Volume 4, Issue 1, January - February (2013) © IAEME 3.1 Stress in the longitudinal member The resultant bending moment is the vector sum of the maximum bending moments at the mid ISO corner. So the resultant bending moment is given as ܯൌ ඥሺ53.6ሻ2 ሺ60ሻ2 M = 80.45470776 KN-m. Using this value of bending moment we further compute stress using the fundamental ெ bending equation as : ݂ ൌ --- (3). Inputting the values of maximum bending moment and section modulus computed in (3), we get the stress magnitude at braking. 80.45470776 fሺbrakingሻ ൌ 965241.9618 fሺbrakingሻ ൌ 83.351MPa also as the section being unsymmetrical, the stress induced during braking is evaluated from both sides. 80.45470776 fሺbrakingሻ ൌ 641454.3918 fሺbrakingሻ ൌ 125.425 MPa 4. CONCLUSION For the design process of specialized platforms/structures mounted on chassis of truck or heavy vehicles intended for carrying containers a new method is attempted with the extension of classical method of stress computation. Estimation of load & stress in accordance with the static and braking load is done with the aid of classical shear force and bending moment method for dynamic condition of the vehicle. The stress computed by this technique is well within permissible limits of yield strength of the material. Furthermore this method can be extended for estimation of shear stress at the load location during braking. This method provides a prior approximation of stress and stress distribution in at this variable loading condition. This method is not accurate as it gives values of stress and strain only at load location and not at the other locations on the platform. This technique also limits its application in x and z directions for evaluation of stress and strain values in these directions cannot be computed. REFERENCES [1] Bum Suk Kim, Maksym Spiryagin, Bong Soo Kim, Hong Hee Yoo, Analysis of the effects of main design parameters variation on the vibration characteristics of vehicle sub frame, Journal of Mechanical Science and Technology 23(2009) 960-963. [2] Hyung-Sub Bae and Myeong-Kwan Park, A Study of Torque characteristics of small disk brake using magnetic fluid, Journal of Mechanical Science and Technology 25(2)(2011) 349-355. 120
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International Journal of
Mechanical Engineering and Technology (IJMET), ISSN 0976 – 6340(Print), ISSN 0976 – 6359(Online) Volume 4, Issue 1, January - February (2013) © IAEME [3] L. Li, J. Song, L. Kong, Q. Huang, Vehicle velocity estimation for real-time dynamic stability control, International Journal of Automotive Technology 2009 Vol.10 No.6 675-685. [4] Chul-Goo Kang, Analysis of Braking System of the Korean High-Speed train using real time simulations, Journal of mechanical science and technology 21 (2007) 1048-1057. [5] Gyu Ha Kim, Kyu Zong Cho, In Bum Chyun, Gi Seob Choi, Dynamic stress analysis of vehicle frame using a non linear finite element method, KSME International Journal (2003) Vol.17 No.10, 1450-1457. [6] Lee, H.C., Reliability indexed sensor fusion and its application to vehicle velocity estimation, (2006) ASME, 128, 236-243. [7] Choi,S.J., Rark,J.W., and Jeon, K.K., Extreme driving characteristics estimation for ESP equipped passenger car, International Journal of Automotive Technology 7,7 (2006) 816-819. [8] Kato, I.,Terumichi, Y., Adachi, M. and Sogabe,K., Dynamics of track/wheel systems on high speed vehicles, Journal of Mechanical Science and technology (2005) Vol. 19, No. 1, 328-335. [9] Schiehlen,W., Recent developments in multi-body dynamics, Journal of Mechanical science and technology (2005) Vol.19 No.1 227-236. [10] Dugoff,H., Francher, P.S. and Segal,L., An analysis of tire traction properties and their influence on vehicle dynamic performance (1970) SAE Paper No. 700377 [11] Ilki Moon., Kyongsu Yi., Vehicle tests of a longitudinal control law for application to stop-and-go cruise control, KSME International Journal (2002) Vol.16 No.9 1166-1174. [12] Cho, D., and Hedrick, J.K., Automotive Power train modeling for control, ASME transactions on dynamic system, measurements and control (1989), Vol.111. [13] Choi, S., and Devlin, P., Throttle and brake combined control for intelligent vehicle highway systems, (1995) SAE paper No. 951897. [14] Kunsoo Huh, Kyungyoung Jhang, Jaeeung Oh, Joonyoung Kim and Jaehee Hong, Development of a simulation tool for the cornering performance analysis of 6WD/6WS vehicles, KSME International Journal (1999) Vol.13No.3 211-220. [15] Bakker, E., Pacejka, H.B and Linder, L., A new tire model with an application in vehicle dynamics studies (1989) SAE 890087. [16] Dhandapani N.V., Dr. Mohan Kumar G., Dr. Debanath K.K., Static analysis of off- highway vehicle chassis support for the effect of various stress distributions, International Journal of Advanced Research in Technology (2012) Vol.2 Issue 1, 1-8. [17] Seong –Wan Park, Load Limits based on Rutting in pavement foundations, KSCE Journal of Civil Engineering (2004) Vol.8 No.1 23-28. [19] Deulgaonkar V.R., Dr. Matani A.G., Dr. Kallurkar S.P., Advanced Mathematical Analysis for chassis integrated platform designed for unconventional loading by using simple technique for static load, International Journal of Engineering and Innovative technology(2012), Volume 1 Issue 3 ISSN 2277-3754. [20] Prof.Deulgaonkar V.R., Prof. Dr. Kallurkar S.P., Prof. Dr. Matani A.G., Mathematical Analysis of Section properties of Platform Integrated with Vehicle chassis, International Journal of scientific and research publications (2012), Volume 2, Issue 1, ISSN 2250-3153 [21] Crolla D.A, Automotive engineering power train, chassis system and vehicle body (Butterworth-Heinemann, 2009). [22] Timoshenko S.P., Goodier J.N., Theory of Elasticity, third edition (New Delhi, Tata Mc-Graw Hill Edition 2010) 121
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Mechanical Engineering and Technology (IJMET), ISSN 0976 – 6340(Print), ISSN 0976 – 6359(Online) Volume 4, Issue 1, January - February (2013) © IAEME [23] Dr. S. K. Doifode and Dr. A. G. Matani, “Advanced Environment Protection Techniques by Industries: Potential For Corporate Social Responsibility Activities” International Journal of Civil Engineering & Technology (IJCIET), Volume 4, Issue 1, 2013, pp. 45 - 51, Published by IAEME. [24] Onyelowe, Ken C. and Agunwamba, J.C., “Conformal Mapping And Swartz-Christophel Transformation Of The Critical Normal Stress Distribution Of Footing On Slope” International Journal of Civil Engineering & Technology (IJCIET), Volume 3, Issue 1, 2012, pp. 128 - 135, Published by IAEME. [25] Dr. A. G. Matani, “Curricula Challenges of Technical and Management Education Institutions” International Journal of Management (IJM), Volume 4, Issue 1, 2013, pp. 56 - 60, Published by IAEME. [26] Dr. A. G. Matani, “Effective Energy Conservation Techniques in Industries” International Journal of Mechanical Engineering & Technology (IJMET), Volume 4, Issue 1, 2013, pp. 74 - 78, Published by IAEME. [27] Manjeet Singh and Dr. Satyendra Singh, “Estimation Of Stress Intensity Factor of a Central Cracked Plate” International Journal of Mechanical Engineering & Technology (IJMET), Volume 3, Issue 2, 2012, pp. 310 - 316, Published by IAEME 122
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