The Influence of Roll and Weight Transfer on Vehicle Handling

Transcription

1 The Influence of Roll and Weight Transfer on Vehicle Handling Christopher R. Carlson April 20, 2004 D D L ynamic esign aboratory.

2 Motivation Design decisions related to vehicle roll directly influence the stability of the vehicle at the limits (If you get it wrong, you will probably end up sliding off of the road) Stanford University The Influence of Roll and Weight Transfer on Vehicle Handling - 2 Dynamic Design Lab

3 Goal of this Talk Introduce useful models for understanding vehicle roll behavior. All models are wrong, some are useful Primarily static model insights today Stanford University The Influence of Roll and Weight Transfer on Vehicle Handling - 3 Dynamic Design Lab

4 Overview What is a sway bar (stabilizer bar)? Simple models of vehicle roll and assumptions Review approach Work through the dynamics and algebra of roll Interpret the mathematical results Summarize key points covered Stanford University The Influence of Roll and Weight Transfer on Vehicle Handling - 4 Dynamic Design Lab

5 Stabilizer Bars F=Kθ θ Essentially roll bars are torsional springs Stanford University The Influence of Roll and Weight Transfer on Vehicle Handling - 5 Dynamic Design Lab

6 Stabilizer Bars II φ S f Stabilizer bars attach to the suspension and chassis and provide forces through torsion Stanford University The Influence of Roll and Weight Transfer on Vehicle Handling - 6 Dynamic Design Lab

7 { { Modeling Roll h 1 { h r h CG hf { Roll Axis Roll Centers The roll axis connects the front and rear roll centers For small angles, this is not a bad assumption Stanford University The Influence of Roll and Weight Transfer on Vehicle Handling - 7 Dynamic Design Lab

8 Modeling Roll II S r S f F sir F rr F sor F sif F sof } M h sr r F rf } h f F yir F yor F yif F yof M sf F zir F zor F zif F zof tr Rear Axle FBD φ tf Front Axle FBD ma y F sif F sir mg F sof F sor F rf F rr M sf M rf Sprung Mass FBD } h 1 Stanford University The Influence of Roll and Weight Transfer on Vehicle Handling - 8 Dynamic Design Lab

9 Approach Solve for the roll angle in terms of lateral acceleration Solve for the weight transfer on each axle Interpret the effect of this weight transfer on handling Discuss how springs and roll bars are used to tune vehicle behavior Stanford University The Influence of Roll and Weight Transfer on Vehicle Handling - 9 Dynamic Design Lab

10 Sum the moments about the roll center φ ma y F sif F sir mg F sof F sor F rf F rr M sf M rf Sprung Mass FBD } h 1 ΣM = mgh 1 sin(φ) + (F sif F sof ) S f 2 cos(φ) + (F sir F sor ) S r 2 cos(φ) (M sf + M sr ) = ma y h 1 cos(φ) Stanford University The Influence of Roll and Weight Transfer on Vehicle Handling - 10 Dynamic Design Lab

11 What are typical roll angles? Some very loose guidelines RollRate Application 1 5 Race Cars 3 4 Sports Cars 5 Sport Sedan 7 Pretty soft 8 Late 60 s early 70 s Even in the extreme, the roll angles are small in the sense of linearization Stanford University The Influence of Roll and Weight Transfer on Vehicle Handling - 11 Dynamic Design Lab

12 Assume Small Roll Angle Once again, ΣM = mgh1 sin(φ) + (F sif F sof ) S f 2 cos(φ) Assume small roll angle, + (F sir Fsor) S r 2 cos(φ) (M sf + M sr ) = ma y h 1 cos(φ) ma y h 1 = mgh 1 φ + (F sif F sof ) S f 2 + (F sir F sor ) S r 2 (M sf + M sr ) The inside and outside forces may be written in terms of the roll angle Stanford University The Influence of Roll and Weight Transfer on Vehicle Handling - 12 Dynamic Design Lab

13 Spring forces φ x S f F sof = F sfs + K sf x Stanford University The Influence of Roll and Weight Transfer on Vehicle Handling - 13 Dynamic Design Lab

14 Spring forces For the front and rear F sof = F sfs + K sf x = F sfs K sfs f φ F sif = F sfs 1 2 K sfs f φ 1 ( ) Fsof F 2 sif Sf = 1 ( 2 1 ) 2 2 K sfs f φ S f = 1 2 K sfs 2 f φ 1 2 (F sor F sir ) S f = 1 2 K srs 2 f φ Stanford University The Influence of Roll and Weight Transfer on Vehicle Handling - 14 Dynamic Design Lab

15 Stabilizer Bar Forces Stabilizer bars may be modeled as torsional springs Remember that the vehicle body is rigid. The roll angle, φ, is the same front and rear M sf = K stabf φ M sr = K stabr φ You will visit this assumption again in a future lab (it is a good one) Stanford University The Influence of Roll and Weight Transfer on Vehicle Handling - 15 Dynamic Design Lab

16 Roll Moment Equation From before, ma y h 1 = mgh 1 φ + (F sif F sof ) S f 2 + (F sir F sor ) S r 2 (M sf + M sr ) Now, ( ma y h 1 = mgφ K stabf + 1 ) 2 K sfsf 2 φ ma y h 1 = ( ) K φf + K φr mgh 1 φ = ( ) K φ mgh 1 φ ( K stabr + 1 ) 2 K srsr 2 φ Stanford University The Influence of Roll and Weight Transfer on Vehicle Handling - 16 Dynamic Design Lab

17 Solving for Roll Angle The roll angle depends upon stiffnesses, mass and lateral acceleration ma y h 1 = ( ) K φ mgh 1 φ mh φ = 1 a y K φ mgh 1 In other notation φ = wh 1 K φ wh 1 ( V 2 Rg ) Stanford University The Influence of Roll and Weight Transfer on Vehicle Handling - 17 Dynamic Design Lab

18 Weight Transfer S f F sif F sof F zif F rf } h f F yif M sf F yof F zof tf Front Axle FBD Now that we have the roll angle, we can figure out the weight transfer terms on the axle diagrams Stanford University The Influence of Roll and Weight Transfer on Vehicle Handling - 18 Dynamic Design Lab

19 Weight Transfer II Sum the moments about the front roll center ΣM = M sf + S f 2 F sof S f 2 F sif + tf 2 F zif tf 2 F xof + h f F yif + h f F yo ( 1 ( ) ) w f K φf φ t f Fzof F 2 zif + h f g a y = 0 ( ) w f K φf φ t f Fzf + hf g a y = 0 F zf = 1 ( ) w f K t φf φ + h f f g a y, and similarly for the rear F zr = 1 ( ) w r K t φr φ + h r r g a y Stanford University The Influence of Roll and Weight Transfer on Vehicle Handling - 19 Dynamic Design Lab

20 Weight Transfer III Now plug in our expression for φ to savor the meaning of all of this math. F zf = 1 t f = 1 t f ( ) w f K φf φ + h f g a y ( K φf h 1 K φf + K φr mgh 1 + h f ) ma y Remember the expression for roll angle is φ = mh 1 K φf + K φr mgh 1 a y Stanford University The Influence of Roll and Weight Transfer on Vehicle Handling - 20 Dynamic Design Lab

21 What happens when when K φ increases? If K φ increases, then for the same lateral acceleration the roll angle will be smaller. If the roll angle decreases, then F zf decreases, ie, the weight transfer is less. Race cars are often tuned to minimize load transfer (load transfer affects peak side force, more on that later.) Stanford University The Influence of Roll and Weight Transfer on Vehicle Handling - 21 Dynamic Design Lab

22 What happens when when K φf increases? Is F zf with K φf scaled by (a > 1) > F zf 1 t f ( h ak 1 φf + h ak φf + K φr mgh f ma y (>?) 1 ( ) 1 h K 1 φf + h K φf + K φr mgh f ma y 1 t f a 1 (>?) ak φf + K φr mgh 1 K φf + K φr mgh1 ) a(k φr mgh1)(>?)(k φr mgh 1 ) F zf increases, and F zr decreases Stanford University The Influence of Roll and Weight Transfer on Vehicle Handling - 22 Dynamic Design Lab

23 The major points Increasing the roll stiffness on both the front and rear axles decreases weight transfer Increasing roll stiffness on only one axle increases the load transfer on that axle and decreases it on the other This load transfer stuff really is critical for designing cars which behave well at the limits Stanford University The Influence of Roll and Weight Transfer on Vehicle Handling - 23 Dynamic Design Lab

24 Tires 8000 Latera Force Vs Slip Angle 6000 Force [N] Slip Angle [%] As you know, tires are nonlinear near the peak of the curve Since this curve is concave down, load transfer reduces your peak side forces Stanford University The Influence of Roll and Weight Transfer on Vehicle Handling - 24 Dynamic Design Lab

25 General Design Rules Increasing the front roll stiffness will tend to make the vehicle more understeering At the limits it is generally considered safer to understeer rather than oversteer Increasing the rear roll stiffness will tend to make the vehicle more oversteering This is ok as long as overall the vehicle is still understeering Stanford University The Influence of Roll and Weight Transfer on Vehicle Handling - 25 Dynamic Design Lab

26 This is just the beginning Depending on how the suspension is designed, vehicle roll will often steer the vehicle Roll also effects camber which also affects the force-slip curves The force-slip curves also depend upon normal load directly... Stanford University The Influence of Roll and Weight Transfer on Vehicle Handling - 26 Dynamic Design Lab

27 Summary Simple models show how vehicle roll directly effects limit handling performance Adding roll stiffness to the front tends to makes the vehicle more understeering Adding roll stiffness to the rear tends to make the vehicle more oversteering Increasing roll stiffness in general tends to increase peak attainable side forces Stanford University The Influence of Roll and Weight Transfer on Vehicle Handling - 27 Dynamic Design Lab

28 El fin Questions? Stanford University The Influence of Roll and Weight Transfer on Vehicle Handling - 28 Dynamic Design Lab

29 Minute Sheet Please take a minute to fill out my Minute Sheet Stanford University The Influence of Roll and Weight Transfer on Vehicle Handling - 29 Dynamic Design Lab