#### Transcript Power Steering

Power Steering ABE 435 October 21, 2005 Ackerman Geometry δo 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 L δi Center of Gravity Turn Center R δi t δo Figure 1.1. Pivoting Spindle (Gillespie, 1992) 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 α angle. C V Fy Fy (1) t Figure 1.2. Fy acts at a distance (t) from the wheel center known as the pneumatic trail (Milliken, et. al., 2002) Slip Angles The slip angle (α) is the angle at which a tire rolls and is determined by the following equations: f W f *V 2 Cf * g * R Wr *V 2 r Cr * g * R α (2) (3) V Fy t W = weight on tires C α= Cornering Stiffness g = acceleration of gravity Figure 1.2. Repeated V = vehicle velocity (Gillespie, 1992) Steering angle The steering angle (δ) is also known as the Ackerman angle and is the average of the front wheel angles δi δo For low speeds it is: L R (4) For high speeds it is: L f r R Center L of Gravity R δi (5) δo αf=front slip angle αr=rear slip angle t Figure 1.1. Repeated (Gillespie, 1992) Three Wheel Figure 1.3. Three wheel vehicle with turn radius and steering angle shown R δ Easier to determine steer angle Turn center is the intersection of just two lines Both axles pivot R δ 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 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 Aligning Torque of a Single Tire Aligning Torque (Mz) is the resultant moment about the center of the wheel due to the lateral force. M z Fy * t Figure 1.7. Top view of a tire showing the aligning torque. α (6) V Fy t Mz (Milliken, et. al., 2002) 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) 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) Camber on Ag Tractor Pivot Axis Φ Figure 1.10. Camber angle on an actual tractor Wheel Caster The axle is placed some distance behind the pivot axis Promotes stability Steering becomes more difficult Pivot Axis Figure 1.11. Wheel caster creating stability (Milliken, et. al., 2002) 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) 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) α times the lateral acceleration. V L K * ay R (7) ay t Figure 1.2. Repeated (Gillespie, 1992) 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: K Wf Cf Wr Cr (8) Since 2 V ay g*R (9) (Gillespie, 1992) Characteristic Speed The characteristic speed is a way to quantify understeer. Speed at which the steer angle is twice the Ackerman angle. Vchar 57.3 * L * g K (10) (Gillespie, 1992) 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) Critical Speed The critical speed is the speed where an oversteer vehicle is no longer directionally stable. Vcrit 57.3 * L * g K (11) Note: K is negative in oversteer case (Gillespie, 1992) 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 V2 ay 57.3Lg 2 KV 1 57.3Lg (12) (Gillespie, 1992) Example Problem 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: Load lb/tire Cornering Stiffness lbs/deg Cornering Coefficient lb/lb/deg 225 74 0.284 425 115 0.272 625 156 0.260 925 218 0.242 1125 260 0.230 Determine the steer angle if the minimum turn radius is 75 ft: We just use equation 1. L 105 / 12 0.117 rad. R 75 Or 6.68 deg Basic System Components Steering Valve Cylinder/Actuator Filter Reservoir Steering Pump Relief Valve – Can be built into pump 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 Actuators There are three types of actuators – Rack and pinion – Cylinder – Vane The possible travel of the actuator is limited by the steering geometry 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) 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 B H 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 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 QS=flow to the valve from the supply Cd=discharge coefficient PS=pressure at the supply A1=larger valve orifice A2=smaller valve orifice ρ=fluid density PL=pressure at the load (Merritt, 1967) 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 Flow Gain Lands ground to change area gradient 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) 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) 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) Open Center Pressure Sensitivity In the null position, the open center pressure sensitivity is: (13) U = underlap (Merritt, 1967) 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 Open Center Circuit, NonMetering Reversing Section Non-ReversingCylinder ports are blocked in neutral valve position, the operator must steer the wheel back to straight Open Center Circuit, Reversing Reversing – Wheels automatically return to straight Open Center Circuit, Power Beyond Any flow not used by steering goes to secondary function Good for lawn and garden Auxiliary equipment and Port utility vehicles 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 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 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 Closed Center Circuit with priority valve With steering priority valve – Variable volume, pressure compensating pump – Priority valve ensures adequate flow to steering valve 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 Arrangements Steering valve and metering unit as one linked to steering wheel Metering unit at steering wheel, steering valve remote linked Design CalculationsHydraguide 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) 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) Kingpin Torque Information about the tire is needed. If we assume a uniform tire pressure then the following equation can be used. Io T W * * E2 A (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) Kingpin Torque If the pressure distribution is known then the radius of gyration (k) can be computed. The following relationship can be applied. k 2 Io A (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 2 B Tk W*μ E2 8 (3) (Parker, 2000) Calculate Approximate Cylinder Force (Fc) TK FC R (4) Fc= Cylinder Force (lbs) R = Minimum Radius Arm TK= Kingpin Torque Figure 3.11 Geometry Diagram (Parker) (Parker, 2000) Calculate Cylinder Area (Ac) Ac Fc P (5) Fc=Cylinder Force (lbs) P=Pressure rating of steering valve Select the next larger cylinder size -For a single cylinder use only the rod area -For a double cylinder use the rod end area plus the bore area (Parker, 2000) Determine Cylinder Stroke (S) Figure 3.11 Geometry Diagram (Parker) Repeated (Parker, 2000) Swept Volume (Vs) of Cylinder Swept Volume (in3) One Balanced Cylinder VS 4 * (D D ) * S 2 B 2 R (6) DB=Diameter of bore DR=Diameter of rod S = Stroke Vs = Swept volume (Parker, 2000) Swept Volume of Cylinder One Unbalanced Cylinder – Head Side Vs * DB2 4 *S (7) – Rod Side -Same as one balanced Two Unbalanced Cylinders *S 2 2 Vs (2 * DB DR ) (8) 4 (Parker, 2000) Displacement Vs D n (9) D= Displacement n= Number of steering wheel turns lock to lock Vs = Volume swept (Parker, 2000) Minimum Pump Flow D * Ns Q 231 (10) Ns = steering speed in revolutions per minute Q = Pump Flow is in gpm per revolution D = Displacement (Parker, 2000) Steering Speed The ideal steering speed is 120 rpm, which is considered the maximum input achievable by an average person The minimum normally considered is usually 60 rpm 90 rpm is common (Parker, 2000) Hydraulic Power Assist Hydraulic power assist means that a hydraulic system is incorporated with mechanical steering This is the type of power steering used on most on-highway vehicles Full Time Part Time Power Steering Part Time – The force of the center springs of the valve gives the driver the “feel” of the road at the steering wheel. Full Time – The valve is installed without centering springs. Any movement of the steering wheel results in hydraulic boost being applied. (Vickers, 1967) Electrohydraulic Steering Electrohydraulic steering can refer to – A hydraulic power steering system driven with and electric motor – A power steering system that uses wires to sense the steering wheel input and actuate the steering valve Electric Motor An electric motor can be used to power the steering pump instead of the engine – Lowers fuel consumption – Allows for more flexibility of design SKF Electro-hydraulic Steering Considerations for E-H System Design Simulation of end stops Operational environment Safety Steering functions Force feedback