Transverse Weight Transfer and Engine Torque Reactions

1. Transverse Weight Transferand Engine Torque Reactions Dr. Richard Hathaway, P.E. Professor Mechanical and Aeronautical Engineering

2. WEIGHT TRANSFER Weight Transfer The forces that enable a road vehicle to accelerate, corner and stop all act at the road surface. The center of gravity, which is located considerably above the road surface, and which is acted upon by the accelerations resulting from the lateral and longitudinal forces at the tire footprints, generates a moment which transfers weight. As asymmetric weight results in differing traction limits, a vehicles handling is affected by the “dynamic weight distribution”.

3. WEIGHT TRANSFER Weight transfers between the Center of Gravity and the road surface through a variety of paths. SUSPENSION GEOMETRY Front: Location of instant centers Rear: Instant centers or Panhard bar SUSPENSION SPRINGS Front: Coils, leafs or Torsion bars Anti-roll bars Rear: Coils, leafs or Torsion bars

4. Weight transfer (cont). SHOCK ABSORBERS During transient maneuvers Primarily Corner entry and exit Where and how you balance the weight transfer between the Springs, Geometry, Dampers determines how well the car will handle. WEIGHT TRANSFER

5. Weight Transfer Control Devices Dampers (Shock Absorbers) Along with the springs, transfer the weight of the rolling component of the vehicle. Determine how the weight is transferred to and from the individual wheels while the chassis is rolling. Springs Along with the shocks, transfer the weight of the rolling component of the car to the road surface. The springs and shocks share this with the shock control larger during initial stage of entry/exit.

6. Roll Centers/Instant Centers The roll centers/instant centers transfer the NON-ROLLING forces to the road surface. The height of the roll centers and the instant center placement determines how much of the weight transfer at either end (F & R) goes through the springs/shocks (rolling) and how much through the geometry (non-rolling). With low roll centers the springs and shocks transfer the majority of the weight. With high roll centers the location of the instant centers and panhard bar take care of the majority of the weight transfer. Weight Transfer Control Devices

7. Roll Centers and Instant Centers

8. Transverse Weight Transfer

9. Transverse Weight Transfer Transverse weight transfer occurs because the driveshaft torque (Td) reacts between the frame mounted engine and the axle. The engine, which is a part of the sprung weight, produces the torque through the transmission. The rear axle has to resist that torque at the rear tire patch. Transverse weight transfer adds cross weight under acceleration and removes cross weight during deceleration. The magnitude of the transverse weight shift is a function of the instantaneous engine torque and the roll stiffness (K?).

10. Transverse Weight Transfer

11. Front Axle Transverse Reaction Torque (TFS): Rear Axle Transverse Reaction Torque (TRS): Transverse Weight Shift (Wy): Transverse Weight Transfer

12. Transverse Weight Shift (cont.) since Transverse weight shift in terms of drive shaft torque is reduced to: Transverse Weight Transfer

13. Transverse Weight Shift (cont.) If other than 1:1 transmission ratio is engaged: Transverse Weight Transfer

14. Transverse Weight Transfer (cont.) Considering Transverse weight transfer in terms of engine torque If we consider transverse weight transfer in terms of tractive force (Fx) Recall, this occurs only with dependent rear suspension Hotchkiss type and others using frame mounted engine and a drive shaft torque reacting directly with the road surface through a beam type axle. Transverse Weight Transfer

15. Engine Torque reactions (cont.) It is important to understand how this transverse reaction influences the acceleration potential of the vehicle. If the vehicle has an open (non-limited slip) differential the vehicle torque on each axle shaft is equivalent. That is each axle shaft delivers equal torque to each of the rear tires. Since equal torque is delivered that torque that each axle shaft receives is the torque that can be delivered to the most litely loaded tire. Transverse Weight Transfer

16. Acceleration Limits Starting with Newton’s Law Therefore Fx for the most lightly loaded tire is derived as follows Or continuing

17. Acceleration Limits Starting with the previous equation Therefore Fx for both drive tires of the vehicle is Factoring out Fx

18. Acceleration Limits The maximum tractive force that can be obtained with an open differential with a dependent type drive axle is

19. Acceleration Limits The maximum acceleration in g’s that can be obtained with an open differential with a dependent type drive axle is

20. Engine Torque reactions (cont.) Considering Transverse weight transfer in terms of roll angles and including tire stiffness characteristics The rotational stiffness of the rear axle (k? ax) due to the tire stiffness is The rotational stiffness of the rear springs and rear stabilizer bar are Transverse Weight Transfer

21. Engine Torque reactions (cont.) The moment produced on the rear axle due to the tire stiffness is The moment produced on the rear axle due to the springs and anti-roll bar is Transverse Weight Transfer

22. Engine Torque reactions (cont.) If no stabilizer bar is present the front suspension springs and the tire stiffness can be combined as a series system of springs to determine an equivalent ride rate. Transverse Weight Transfer

23. Engine Torque reactions (cont.) Combining chassis roll rate with the tire contribution The front suspension acts to produce a restoring moment in the chassis based on the total front roll rate. Transverse Weight Transfer

24. Drive shaft torque results in a negative torque applied to the axle and an equal but opposite torque applied to the chassis through the engine mounts. Solving for ?A Similarly the chassis reactions must equal zero. By substitution and solving for ?C Transverse Weight Transfer

25. The increase in right front wheel load is as follows The increase in Left rear wheel load is as follows Transverse Weight Transfer

26. Rear Axle Torque Reactions Forces at the tire footprints during acceleration result in a torque reaction equal and opposite that tries to rotate the drive axle. The drive axle must be constrained under acceleration (and deceleration) from the associated torques. Linkage systems and/or leaf springs can be used to constrain the resultant torques. Linkage system may result in vertical forces at the tire footprint that improve tractive forces.

27. Three link Rear Suspension forrear axle Torque management

28. Three Link Rear Suspension Solving for forces in the X direction. Solving for forces in the Z direction. Solving for moments about the tire footprint.

29. Substitution of previous equations results in the following equation. Substituting equations 4 and 5 into equation 2 results in equations 6 and 7. Three Link Rear Suspension

30. therefore The above equation describes the relationship between the vertical load acting through the tire footprint, due the tractive force, and the tractive force itself. From figure one the following equations can be derived. Three Link Rear Suspension

31. Race car rear suspension utilizing a Torque Arm with Leaf Springs

32. Torque Arm with Leaf Springs

33. Torque Arm with Leaf Springs

34. Torque Arm with Leaf Springs

35. Race car rear suspension utilizing a Torque Arm with Coil Springs

36. Torque Arm Analysis

37. Torque Arm Analysis

38. Torque Arm Analysis

39. Torque Arm Analysis

40. Torque Arm Analysis

41. Rear Roll Center Location

42. The end! Thank You