1. Lecture 2- Suspension Systems Professor Mike Blundell Phd, MSc, BSc (Hons), FIMechE, CEng Bergamo University Italy 12 th -14 th June 2012

2. Contents Suspension Design Process Suspension Types Modelling Suspension Systems Measurements and Simulated Outputs

3. Suspension Design Process Activities Wheel Load Variation Body Isolation Handling Load Control Compliant Wheel Plane Control Kinematics Wheel Plane Control Compliant Loading Environment Investigation Design Strategies Set Design Targets Verify Proposed Designs Wheel load variation - A classic case of static indeterminacy Front wheel drive hatchback cornering pose 3

4. Body Isolation –Ride Model Proving Ground or Shaker Rig Isolation and Comfort Loss of Tyre/Ground Contact 4

5. Body Isolation – A Classical Quarter Vehicle Ride Model Predict Sprung Mass (Body) and Unsprung Mass (Wheel) Natural Frequencies Transmissibility Time (s) X Z m k c z zgzg Vehicle Body or Sprung Mass Suspension Spring and Damper Ground Input Body Response 5

6. Handling Load Control The simplest possible representation of a vehicle manoeuvring in the ground plane (bicycle model) Weight transfer Tyre lateral force characteristics as a function of tyre load GRF O1O1 X1X1 Y1Y1 O 2 G 2 Y2Y2 X2X2 V x2 FyFy FyFy V y2  z2 6

7. Handling Load Control (Continued) Side forces calculated for a 0.1 rads/s ramped input to 0.01 rads beginning at 0.3s Front axle side force Rear axle side force 7

8. Graphical Representation of Front Suspension Configurations in ADAMS/Chassis Provided courtesy of MSC.Software Hotchkiss SLA (Perch) SLA (Torsion Bar) Twin I-Beam SLA (Coil) McPherson Strut 8

9. Graphical Representation of Rear Suspension Configurations in ADAMS/Chassis 9 Provided courtesy of MSC.Software 4 Link Panhard4 Link Watts Central Link Quardalink (Strut) Semi Trailing Arm Twist Beam

10. Double Wishbone Suspension System 10 Upper Ball Joint (Bushes on Rear) Wheel Knuckle (Stub Axle) (Kingpin) Road Wheel Lower Ball Joint (Bushes on Rear) Track Rod End Upper Wishbone (Control Arm) Upper Bushes (Mounts) Damper Spring Lower Bushes (Mounts) Lower Wishbone (Control Arm) Connection to Rack (Body on Rear) Track Rod (Tie Rod on Rear)

11. McPherson Strut Suspension System 11 Lower Bushes (Mounts) Spring Damper Upper Mount Wheel Knuckle (Stub Axle) (Kingpin) Road Wheel Lower Ball Joint Track Rod End Connection to Rack Track Rod Lower Wishbone (Control Arm)

12. Double Wishbone Suspension Modelled with Bushes 12 Modelled with Bushes Modelled with Joints Bushes Universal Spherical Revolute Translational Motion In-Plane Motion Revolute Spherical Revolute Universal Motion Spherical Revolute Translational In-Plane

13. Coventry University Formula Student Car 13 Body Mount Spherical Spring Damper Bell Crank Revolute Universal Push Rod Modelling of push rod and bell crank mechanism in student race car

14. Suspension Analysis Data Requirements Kinematic or Quasi-static vertical rebound to bump analysis Co-ordinates of suspension linkage connections Bush stiffnesses (If this effects the movement) Spring stiffness ( If suspension wheel rate is to be calculated) Static or Quasi-static durability analysis Co-ordinates of suspension linkage connections Bush stiffnesses Spring stiffness Bump and rebound stops Component flexibility (some suspensions) Dynamic durability or vibration analysis Co-ordinates of suspension linkage connections Mass and inertial properties Bush stiffnesses Bush damping coefficients Spring stiffness Damper properties Bump and rebound stops Component flexibility (some suspensions)

15. Use of Virtual Test Rig to Analyse a Half Vehicle Suspension Model 15 Superimposed animation frames giving visual indication of wheel envelope Provided courtesy of MSC.Software

16. Input of Vertical Motion at the Wheel Centre 16  J  I In-Plane Motion Time (s) Rebound 100 -100 0.25 Bump Movement (mm) Bump 1.0 0.5 0.75

17. Geometric and Instant Steer Axes of a Suspension System 17 Geometric Steer Axis Instant Steer Axis

18. Bump Movement, Wheel Recession and Half Track Change 18  BM = DZ(WC,FG)  HTC = DY(WC,FG)  WR = DX(WC,FG) Wheel Change Marker (WC) BM HTC Fixed Ground Marker (FG) z y z x WR FG WC

19. Half Track Change (HTC) A measure of how much the contact patch moves in and out relative to the vehicle body at bump movement Double Wishbone Mc Pherson Influence in Vehicle Dynamics Full Track Change effect Beneficial on the outside wheel Limits of bodywork  BM = DZ(WC,FG)  HTC = DY(WC,FG)

20. Wheel Recession (WR) A measure of fore-aft movement as the wheel moves between Bump and Rebound Influence in Vehicle Dynamics Ride Comfort Increased component durability WR= DX (WC, FG) Double Wishbone Mc Pherson

21. Calculation of Camber Angle and Steer Angle 21      = (180/  ) ATAN (DZ(WC,SA)/DY(SA,WC)) z y WC SA  =(180/  ) ATAN (DX(WC,SA)/DY(SA,WC)) x SA

22. Camber angle (  ) γ = (180/π) ATAN (DY(WC,SA)/DZ(SA,WC)) As the vehicle rolls it’s needed to attempt and keep the tyre flat on the road and avoid opposite camber thrust the tyres running on their edges Double Wishbone Mc Pherson 0% Camber Rollover compensation 100% Camber Rollover compensation

23. Bump (Roll) Steer (δ) As the suspension moves between bump and rebound small amounts of steer (toe) change may be introduced due to suspension geometry. It can be desirable to add to an understeer characteristic Double Wishbone Mc Pherson δ = (180/π) ATAN (DY(WC,WB)/DX(WC,WB)) Gradient Shopping cars 4-5 o /m Sport cars >10 o /m

24. Calculation of Castor Angle and Suspension Trail 24   = (180/  ) ATAN (DX(UB,LB)/DZ(UB,LB)) TR = DX(WB,LB) + DZ(LB,WB) * DX(UB,LB) / DZ(UB,LB) Upper Ball Joint Marker (UB) Lower Ball Joint Marker (LB) Wheel Base Marker (WB) TR Intersection of Steering Axis with Ground x z

25. Castor Angle (φ) and Suspension Trail (TR) Castor angle adds to the self-centering with the Pneumatic Trail φ = (180/π) ATAN(DX(UB,LB)/DZ(UB,LB)) TR = DX (WB, LB) +DZ (LB, WB)*DX (UB, LB)/DZ (UB, LB) Castor Angle change Double Wishbone Mc Pherson Suspension (Mechanical) Trail Typical Value 35-50mm

26. Calculation of Steering Axis Inclination and Ground Level Offset 26  = (180/  ) ATAN (DY(LB,UB)/DZ(UB,LB)) GO = DY(WB,LB) - DZ(LB,WB) * (DY(LB,UB) / DZ(UB,LB)) Intersection of Steering Axis with Ground z  UB GO y Wheel Base Marker (WB)

27. Steering Axis Inclination (θ) and Ground level Offset (GO) GO offset minimises scrubbing of the tyre during steering when stationary. Alternative method of tweaking GO is by using rims with offset.

28. Steering Axis Inclination (θ) and Ground level Offset (GO) (continued) When braking on split m u surface vehicle tends to yaw due to higher braking forces on the high m u side. Using negative ground level offset can compensate the effect. θ = (180/π) ATAN(DY(LB,UB)/DZ(UB,LB)) GO =DY (WB, LB)-DZ (LB, WB)*(DY (LB, UB)/DZ (UB, LB)) Double Wishbone Mc Pherson GO typical Value 10mm Front right wheel

29. Instant Centre and Roll Centre Positions Double Wishbone Suspension 29 Centre Line y Wheel Base (WB) Roll Centre Height Instant Centre Roll Centre z A B C D Double Wishbone Suspension McPherson Strut Suspension B Instant Centre Roll Centre Height Roll Centre Centre Line Wheel Base (WB) y z A C D

30. Position of Instant Centre Construction Points on Wheel Centre YZ Plane 30 Z X Y WC A D C B

31. Height of Roll Centre (RC) RC is the corresponding point of lateral force application on the vehicle sprung mass and relative to its distance from the Vehicle’s CM is the applied roll torque. Mc Pherson Double Wishbone

32. Calculation of Wheel Rate (Equivalent Spring Acting at the Wheel Centre) 32 ww VEHICLE BODY Equivalent spring acting at the wheel centre ls lw Fw ss Fs ks kw Fw ww kw A

33. Wheel Rate The “equivalent” spring acting between wheel centre and the vehicle body Wheel rate can be set so as to be softer during initial bump and stiffer during increased bump travel for better ride comfort and roll control Double Wishbone Mc Pherson

34. 34 Case Study – Suspension Kinematics

35. 35 Modelling Bushes

36. 36 Modelling Bushes

37. Data Input – Joint, Linear Bush, Non-Linear Bush 37

38. 38 Comparison of Suspension Outputs

39. 39 Suspension Durability Static Analysis Single Suspension System Model, Range of Load Cases (3G Bump, 2G Rebound, 1G Braking, ….) Dynamic Analysis using Road Load Data Single Suspension System Model, Quarter or Full Vehicle Model Full Virtual Modelling and Analysis for Durability Full Vehicle Model with Transient Dynamics Physical Tyre Model Required Road/ Terrain model (Laser scanned)

40. Suspension Durability Analysis LOADCASE Fx (N) Fy (N) Fz (N) 3G Bump 11180 2G Rebound -7460 0.75G Cornering 4290 5880 (Outer Wheel) 0.75G Cornering -1180 1620 (Inner Wheel) 1G Braking 5530 5530 0.35G Reverse -2150 3330 Braking Kerb Impact 9270 4120 Pothole Braking 15900 12360 Fy Lateral loads Fx Longitudina l loads Fz Vertical loads Garrett, T. K., (1953) Automobile dynamic loads some factors applicable to design, Automobile Engineer, February.

41. 41 Weight Transfer-Braking F Fz = F SFz + F B = + F Rz = F RFz – F B = - F Fx =  F Fz F Fx =  F Fz X Z F Fz = F SFz + F B F Rz = F SRz – F B F Fx F Rx mg cm mA x a L b h Hand calculations can be performed To establish loads for braking or cornering

42. Case Study - Pothole Braking Case Ramping loads on over 1 second (Quasi-static) Allows animation (visual check) Load path through damper not modelled Unless static equivalent force included

43. Typical Results

44. Animation

45. 45 Simple starting point Dynamic Analysis Road Bump Strike Tyre stiffness and damping Tyre can lift off Jack Part Quarter Vehicle Body Part Body connects to Ground by Translational Joint Quarter Vehicle Model

46. 46 Road Profile X Z 10 m/s GRF x y. 7. 1. 5. 6. 8. 9. 3. 4. 2 1000 20010000200 150 Point 1 2 3 4 5 6 7 8 9 Distance x (mm) 0 1000 1200 1400 1600 1800 2000 2200 12200 Time x (s) 0 0.10 0.12 0.14 0.16 0.18 0.20 0.22 1.22 Height y (mm) 0 0 75 150 150 150 75 0 0

47. Animation

48. 48 Quarter Model Results Time = 0 sec Time = 0.18 sec Time = 0.14 sec