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Spring Rates, Wheel Rates, Motion Ratios and Roll Stiffness Appendix 1 ME 470 Vehicle Structural Design Dr. Richard Hathaway, P.E., Professor Mechanical and Aeronautical Engineering

Spring Rate Calculations ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Spring Rate Calculations ,[object Object],[object Object]

Spring Rate Calculations ,[object Object],L = Bar Length d = Bar Diameter r = lever arm length Let the deflection at the end =  L r d 

Spring Rate Calculations ,[object Object],L r d  Then the deflection rate at the free end is found Since T = F x r &

Spring Rate Calculations ,[object Object],L r d  The deflection rate at the wheel can now be found through analysis of the motion ratio

Spring Rate Calculations ,[object Object],[object Object],L = Bar Length d = Bar Diameter r = lever arm length

Typical Leaf Spring Typical deflection behavior:

Typical Leaf Spring Typical Path behavior on deflection

Motion Ratio Analysis ,[object Object],[object Object]

[object Object],[object Object],Motion Ratio Analysis Figure 1

[object Object],Motion Ratio Analysis

[object Object],[object Object],Motion Ratio Analysis Figure 2

[object Object],[object Object],[object Object],Motion Ratio Analysis

Suspension Roll Stiffness ,[object Object],[object Object],[object Object],Note: t is equal to the wheel track if the wheel rates are used

[object Object],[object Object],Suspension Roll Stiffness

[object Object],[object Object],Suspension Roll Stiffness K = Individual wheel rate (N/m) t = track width (m)

[object Object],Suspension Roll Stiffness T = track width (in) K = Individual Wheel Rate (lb/in)

[object Object],Suspension Roll Stiffness K  F = Front Roll Stiffness K  R = Rear Roll Stiffness K  (devices) = Stabilizer etc contributions

Lateral Spring Center Position

[object Object],Lateral Spring Center Position Which reduces to

[object Object],[object Object],Lateral Spring Center Position

Roll Stiffness (Asymmetric Chassis) ,[object Object],[object Object],[object Object]

Roll Stiffness (Asymmetric Chassis) ,[object Object],Then by substitution becomes,

[object Object],[object Object],[object Object],[object Object],Roll Stiffness

[object Object],Roll Stiffness Asymmetric Setup: LR w = 200 lb/in RR w = 175 lb/in Asymmetric Setup: LR w = 200 lb/in RR w = 150 lb/in Note: Avg = 175 lb/in Track = 68 inches

[object Object],[object Object],Suspension Roll Stiffness k t = tire stiffness (N/m) t r = rear track width k  ax = Rotational stiffness (N-m/deg) k s = spring stiffness (N/m) t s = rear spring spacing k  b = Rear stabilizer bar (N-m/deg) k  r susp = Rotational stiffness (N-m/deg)

[object Object],[object Object],Suspension Roll Stiffness  a = Axle roll angle  c = Chassis roll angle

[object Object],[object Object],Suspension Roll Stiffness ,[object Object],mr = motion ratio

[object Object],Suspension Roll Stiffness

Anti-Roll (Stabilizer) Bar Analysis

Anti Roll Bar Analysis ,[object Object], The deflection rate at the wheel can now be found through analysis of the motion ratio previously defined. L r d

Anti Roll Bar Analysis ,[object Object],r 1 = length of the attachment arm r 2 = the pivot to attachment length ,[object Object]

Anti Roll Bar Analysis ,[object Object],[object Object]

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