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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
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 Leaf Spring Typical deflection behavior:
Typical Leaf Spring Typical Path behavior on deflection
Motion Ratio Analysis
Motion Ratio Analysis
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
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
[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]
The end! Thank You

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Suspension Lecture