Power Steering

1. Power Steering ABE 435 October 21, 2005

2. AckermanGeometry δo δi • Basic layout for passenger cars, trucks, and ag tractors • δo= outer steering angle and δi = inner steering angle • R= turn radius • L= wheelbase and t=distance between tires Center of Gravity L Turn Center R δi δo Figure 1.1. Pivoting Spindle t (Gillespie, 1992)

3. α V t Fy Cornering Stiffness and Lateral Force of a Single Tire • Lateral force (Fy) is the force produced by the tire due to the slip angle. • The cornering stiffness (Cα) is the rate of change of the lateral force with the slip angle. Figure 1.2. Fy acts at a distance (t) from the wheel center known as the pneumatic trail (1) (Milliken, et. al., 2002)

4. Slip Angles • The slip angle (α) is the angle at which a tire rolls and is determined by the following equations: α (2) V t Fy (3) W = weight on tires C α= Cornering Stiffness g = acceleration of gravity V = vehicle velocity Figure 1.2. Repeated (Gillespie, 1992)

5. δi L R δi δo Steering angle • The steering angle (δ) is also known as the Ackerman angle and is the average of the front wheel angles • For low speeds it is: • For high speeds it is: δo (4) Center of Gravity (5) αf=front slip angle αr=rear slip angle Figure 1.1. Repeated t (Gillespie, 1992)

6. Three Wheel Figure 1.3. Three wheel vehicle with turn radius and steering angle shown • Easier to determine steer angle • Turn center is the intersection of just two lines R δ

7. Both axles pivot Figure 1.5. Both axles pivot with turn radius and steering angle shown • Only two lines determine steering angle and turning radius • Can have a shorter turning radius R δ

8. Articulated • Can have shorter turning radius • Allows front and back axle to be solid Figure 1.6. Articulated vehicle with turn radius and steering angle shown

9. α V t Fy Aligning Torque of a Single Tire • Aligning Torque (Mz) is the resultant moment about the center of the wheel due to the lateral force. (6) Mz Figure 1.7. Top view of a tire showing the aligning torque. (Milliken, et. al., 2002)

10. Camber Angle • Camber angle (Φ) is the angle between the wheel center and the vertical. • It can also be referred to as inclination angle (γ). Φ Figure 1.8. Camber angle (Milliken, et. al., 2002)

11. Camber Thrust • Camber thrust (FYc) is due to the wheel rolling at the camber angle • The thrust occurs at small distance (tc) from the wheel center • A camber torque is then produced (MZc) Mzc tc Fyc Figure 1.9. Camber thrust and torque (Milliken, et. al., 2002)

12. Camber on Ag Tractor Pivot Axis Φ Figure 1.10. Camber angle on an actual tractor

13. Wheel Caster Pivot Axis • The axle is placed some distance behind the pivot axis • Promotes stability • Steering becomes more difficult Figure 1.11. Wheel caster creating stability (Milliken, et. al., 2002)

14. Neutral Steer • No change in the steer angle is necessary as speed changes • The steer angle will then be equal to the Ackerman angle. • Front and rear slip angles are equal (Gillespie, 1992)

15. Understeer • The steered wheels must be steered to a greater angle than the rear wheels • The steer angle on a constant radius turn is increased by the understeer gradient (K) times the lateral acceleration. α V t ay (7) Figure 1.2. Repeated (Gillespie, 1992)

16. Understeer Gradient • If we set equation 6 equal to equation 2 we can see that K*ay is equal to the difference in front and rear slip angles. • Substituting equations 3 and 4 in for the slip angles yields: (8) Since (9) (Gillespie, 1992)

17. Characteristic Speed • The characteristic speed is a way to quantify understeer. • Speed at which the steer angle is twice the Ackerman angle. (10) (Gillespie, 1992)

18. Oversteer • The vehicle is such that the steering wheel must be turned so that the steering angle decreases as speed is increased • The steering angle is decreased by the understeer gradient times the lateral acceleration, meaning the understeer gradient is negative • Front steer angle is less than rear steer angle (Gillespie, 1992)

19. Critical Speed • The critical speed is the speed where an oversteer vehicle is no longer directionally stable. (11) Note: K is negative in oversteer case (Gillespie, 1992)

20. Lateral Acceleration Gain • Lateral acceleration gain is the ratio of lateral acceleration to the steering angle. • Helps to quantify the performance of the system by telling us how much lateral acceleration is achieved per degree of steer angle (12) (Gillespie, 1992)

21. ExampleProblem • A car has a weight of 1850 lb front axle and 1550 lb on the rear with a wheelbase of 105 inches. The tires have the cornering stiffness values given below:

22. Determine the steer angle if the minimum turn radius is 75 ft: • We just use equation 1. rad. Or 6.68 deg

23. Basic System Components • Steering Valve • Cylinder/Actuator • Filter • Reservoir • Steering Pump • Relief Valve • Can be built into pump

24. Pump • Driven by direct or indirect coupling with the engine or electric motor • The type depends on pressure and displacement requirements, permissible noise levels, and circuit type

25. Actuators • There are three types of actuators • Rack and pinion • Cylinder • Vane • The possible travel of the actuator is limited by the steering geometry

26. Cylinders • Between the steered wheels • Always double acting • Can be one or two cylinders • Recommended that the stroke to bore ratio be between 5 and 8 (Whittren)

27. Hydrostatic Steering Valve • Consists of two sections • Fluid control • Fluid metering • Contains the following • Linear spool (A) • Drive link (B) • Rotor and stator set (C) • Manifold (D) • Commutator ring (E) • Commutator (F) • Input shaft (G) • Torsion bar (H) E D A G F C H B

28. Steering Valve Characteristics • Usually six way • Commonly spool valves • Closed Center, Open Center, or Critical Center • Must provide an appropriate flow gain • Must be sized to achieve suitable pressure losses at maximum flow • No float or lash • No internal leakage to or from the cylinder • Must not be sticky

29. Valve Flows • The flow to the load from the valve can be calculated as: (1) • The flow from the supply to the valve can be calculated as: (2) QL=flow to the load from the valve A1=larger valve orifice QS=flow to the valve from the supply A2=smaller valve orifice Cd=discharge coefficient ρ=fluid density PS=pressure at the supply PL=pressure at the load (Merritt, 1967)

30. Flow Gain • Flow gain is the ratio of flow increment to valve travel at a given pressure drop (Wittren, 1975) • It is determined by the following equation: (3) QL=flow from the valve to the load Xv=displacement from null position

31. Flow Gain Lands ground to change area gradient

32. Open Center Valve Flow • The following equation represents the flow to the load for an open center valve: (10) • If PL and xv are taken to be 0 then, the leakage flow is: (11) U=Underlap of valve (Merritt, 1967)

33. Open Center Flow Gain • In the null position, the flow gain can be determined by (Merritt, pg. 97): (12) The variables are the same as defined in the previous slide. (Merritt, 1967)

34. Pressure Sensitivity • Pressure sensitivity is an indication of the effect of spool movement on pressure • It is given by the following equation from Merritt: (4)

35. Open Center Pressure Sensitivity • In the null position, the open center pressure sensitivity is: (13) U = underlap (Merritt, 1967)

36. Open Center System • Fixed Displacement Pump • Continuously supplies flow to the steering valve • Gear or Vane • Simple and economical • Works the best on smaller vehicles

37. Open Center Circuit, Non-Reversing Metering Section • Non-Reversing-Cylinder ports are blocked in neutral valve position, the operator must steer the wheel back to straight

38. Open Center Circuit, Reversing • Reversing – Wheels automatically return to straight

39. Open Center Circuit, Power Beyond • Any flow not used by steering goes to secondary function • Good for lawn and garden equipment and utility vehicles Auxiliary Port

40. Open Center Demand Circuit • Contains closed center load sensing valve and open center auxiliary circuit valve • When vehicle is steered, steering valve lets pressure to priority demand valve, increasing pressure at priority valve causes flow to shift • Uses fixed displacement pump

41. Closed Center System • Pump-variable delivery, constant pressure • Commonly an axial piston pump with variable swash plate • A compensator controls output flow maintaining constant pressure at the steering unit • Usually high pressure systems • Possible to share the pump with other hydraulic functions • Must have a priority valve for the steering system

42. Closed Center Circuit, Non-Reversing • Variable displacement pump • All valve ports blocked when vehicle is not being steered • Amount of flow dependent on steering speed and displacement of steering valve

43. Closed Center Circuit with priority valve • With steering priority valve • Variable volume, pressure compensating pump • Priority valve ensures adequate flow to steering valve

44. Closed Center Load Sensing Circuit • A special load sensing valve is used to operate the actuator • Load variations in the steering circuit do not affect axle response or steering rate • Only the flow required by the steering circuit is sent to it • Priority valve ensures the steering circuit has adequate flow and pressure

45. Arrangements • Steering valve and metering unit as one linked to steering wheel • Metering unit at steering wheel, steering valve remote linked

46. Design Calculations-Hydraguide • Calculate Kingpin Torque • Determine Cylinder Force • Calculate Cylinder Area • Determine Cylinder Stroke • Calculate Swept Volume • Calculate Displacement • Calculate Minimum Pump Flow • Decide if pressure is suitable • Select Relief Valve Setting (Parker, 2000)

47. Kingpin Torque (Tk) • First determine the coefficient of friction (μ) using the chart. E (in) is the Kingpin offset and B (in) is the nominal tire width Figure 3.10. Coefficient of Friction Chart and Kingpin Diagram (Parker) (Parker, 2000)

48. Kingpin Torque • Information about the tire is needed. If we assume a uniform tire pressure then the following equation can be used. (1) W=Weight on steered axle (lbs) Io=Polar moment of inertia of tire print A=area of tire print μ.= Friction Coefficient E= Kingpin Offset (Parker, 2000)

49. Kingpin Torque • If the pressure distribution is known then the radius of gyration (k) can be computed. The following relationship can be applied. (2) • If there is no information available about the tire print, then a circular tire print can be assumed using the nominal tire width as the diameter (3) (Parker, 2000)

50. Calculate Approximate Cylinder Force (Fc) (4) Fc= Cylinder Force (lbs) R = Minimum Radius Arm TK= Kingpin Torque Figure 3.11 Geometry Diagram (Parker) (Parker, 2000)