Steering Class

Power Steering

Power Steering

 ABE 435

 ABE 435

October 21, 2005

October 21, 2005

 Ackerman

 Ackerman

Geometry

Geometry



 Basic layout forBasic layout for

passenger cars, trucks,

passenger cars, trucks,

and ag tractors

and ag tractors



 δδ_oo = outer steering= outer steering

angle and

angle and δδ_ii = inner= inner

steering angle

steering angle



 R= turn radiusR= turn radius 

 L= wheelbase andL= wheelbase and

t=distance between t=distance between tires tires δ δ_{oo δδ} ii L L tt R R Figure 1.1. Figure 1.1. Pivoting Pivoting Spindle Spindle Turn Turn Center  Center  Center of  Center of  Gravity Gravity δ δ_oo δ δ_ii

 Ackerman

 Ackerman

Geometry

Geometry



 Basic layout forBasic layout for

passenger cars, trucks,

passenger cars, trucks,

and ag tractors

and ag tractors



 δδ_oo = outer steering= outer steering

angle and

angle and δδ_ii = inner= inner

steering angle

steering angle



 R= turn radiusR= turn radius 

 L= wheelbase andL= wheelbase and

t=distance between t=distance between tires tires δ δ_{oo δδ} ii L L tt R R Figure 1.1. Figure 1.1. Pivoting Pivoting Spindle Spindle Turn Turn Center  Center  Center of  Center of  Gravity Gravity δ δ_oo δ δ_ii

Cornering Stiffness and

Cornering Stiffness and

Lateral Force of a

Lateral Force of a

Single

Single

Tire

Tire



 Lateral force (FLateral force (F_yy) is the force produced by) is the force produced by

the tire due to the slip

the tire due to the slip angle.angle.



 The cornering stiffness (CThe cornering stiffness (C_αα) is the rate of ) is the rate of 

change of the lateral force with the s

change of the lateral force with the sliplip

angle. angle. tt α α V V F F_yy Figure Figure 1.2. 1.2. FF_yy acts at a acts at a distance (t) from distance (t) from the wheel center  the wheel center  known as the known as the pneumatic trail pneumatic trail

 

 













F 

F 

C 

C 

Slip Angles

 The slip angle (α) is the angle at which a tire rolls

and is determined by the following equations:

 R g C  V  W   f   f   f  * * * 2       R g C  V  W  r  r  r  * * * 2      W = weight on tires C _α= Cornering Stiffness g = acceleration of gravity V = vehicle velocity (2) (3) t α V F_y Figure 1.2. Repeated

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:

 R  L      r   f   R  L       _{  } (4) (5) α_f =front slip angle

α =rear slip angle _t

δ_i L R δ_o δ_i δ_o Figure 1.1. Center  of  Gravity

Three Wheel



Easier to determine steer angle



Turn center is the intersection of just

two lines

δ R

Figure 1.3. Three wheel vehicle with turn radius and steering angle

Both axles pivot



Only two lines determine steering

angle and turning radius



Can have a shorter turning radius

δ R

Figure 1.5. Both axles pivot with turn radius and steering angle shown

 Articulated

Can have

shorter

turning

radius

 Allows front

and back 

axle to be

solid

 Aligning Torque of a

Single Tire

  Aligning Torque (M_z) is the resultant

moment about the center of the wheel due to the lateral force.

t 

F 

 M 

*

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

Camber Thrust

 Camber thrust (F _Yc) is

due to the wheel rolling at the camber angle

 The thrust occurs at

small distance (t_c) from the wheel center

  A camber torque is then

produced (M_Zc)

F_yc

t_c M_zc

Camber on Ag 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

Neutral Steer



No change in the steer angle is

necessary as speed changes



The steer angle will then be equal to

the

 Ackerman angle.

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.

 y

a

K 

 R

 L

*

 

Understeer Gradient

 If we set equation 6 equal to equation 2 we can see that

K*a_y is equal to the difference in front and rear slip angles.

 Substituting equations 3 and 4 in for the slip angles yields:

r  r    f     f   C  W  C  W  K        (8)  R g V  a _y * 2  Since (9)

Characteristic Speed

 The characteristic speed is a way

to quantify understeer.

 Speed at which the steer angle is

twice the Ackerman angle.

K 

g  L

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

Critical Speed

 The critical speed is the speed

where an oversteer vehicle is no longer directionally stable.

K  g  L V _crit    57.3* * (11)

Lateral Acceleration Gain

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  Lg KV   Lg V  a _y 3 . 57 1 3 . 57 2 2     (12)

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.

rad.

117

.

0

75

12

 / 

105

 R

 L

 

Basic System Components

 – 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

Cylinders



Between the steered wheels

 Always double acting



Can be one or two cylinders



Recommended that the stroke to bore

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)  A B D E F G C 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:

 The flow from the supply to the valve can

be calculated as:

Q_L=flow to the load from the valve A₁=larger valve orifice Q_S=flow to the valve from the supply A₂=smaller valve orifice C_d=discharge coefficient ρ=fluid density

(1)

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:

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:

U=Underlap of valve

(10)

(11)

 If P_L and x_v are taken to be 0 then, the leakage

Open Center Flow Gain

 In the null position, the flow gain

can be determined by (Merritt, pg. 97):

The variables are the same as defined in the previous slide.

Pressure Sensitivity

 Pressure sensitivity is an indication

of the effect of spool movement on pressure

 It is given by the following equation

from Merritt:

Open Center Pressure

Sensitivity

 In the null position, the open center

pressure sensitivity is:

U = underlap

(Merritt, 1967) (13)

Open Center System



Fixed Displacement Pump

 – Continuously supplies flow to the steering valve

 – Gear or Vane



Simple and economical



Works the best on smaller

Open Center Circuit,

Non-Reversing



Non-Reversing-Cylinder ports are blocked in neutral valve position, the operator must steer the wheel back to straight

Metering Section

Open Center Circuit,

Reversing

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

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

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

Closed Center Circuit with

priority 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

 Arrangements

Steering valve

and metering

unit as one

linked to

steering wheel

Metering unit at

steering wheel,

steering valve

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

Kingpin Torque (T

_k 

)

 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)

Kingpin Torque

Kingpin Torque



 Information Information about about the the tire tire is is needed. needed. If If wewe

assume a uniform tire pressure then

assume a uniform tire pressure then thethe

following equation can be used.

following equation can be used.

W=Weight on steered axle (lbs) W=Weight on steered axle (lbs)

II_oo=Polar moment of inertia of tire =Polar moment of inertia of tire printprint  A=area of tire print

 A=area of tire print μ

μ.= Friction Coefficient.= Friction Coefficient

2 2 * * * * E E   A  A  I   I  W  W  T  T      oo  (1)(1)

Kingpin Torque

Kingpin Torque



 If the pressure distribution is known If the pressure distribution is known then thethen the

radius of

radius of gyration gyration (k) c(k) can be an be computed. computed. TheThe

following relationship can be applied.

following relationship can be applied.

 A  A  I   I  k  k 22 _ oo 2 2 2 2 8 8  E  E   B  B W W** μ μ T  T _k k    

 If there is no If there is no information available about the tireinformation available about the tire

print, then a circular tire print can be assumed using

print, then a circular tire print can be assumed using

the nominal tire width as the diameter

the nominal tire width as the diameter

(2) (2)

(3) (3)

Calculate Approximate

Calculate Approximate

Cylinder Force (F

Cylinder Force (F

_c

_c

)

)

 R

 R

T 

T 

F 

F 

_C 

_C 

_

_

K 

K 

F

F

R = Minimum Radius Radius ArmArm T

T = Kingpin Torque= Kingpin Torque

(4) (4) Figure 3.11 Geometry Figure 3.11 Geometry Diagram (Parker) Diagram (Parker)

Calculate Cylinder Area (A

_c

)

P

F 

 A

 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

Determine Cylinder Stroke (S)

Figure 3.11 Geometry Diagram (Parker)

Swept Volume (V 

) of Cylinder



Swept Volume (in

) One Balanced Cylinder

S 

 D

 D

V 

*

(

)

*

4

 

Swept Volume of Cylinder



Two Unbalanced Cylinders

) * 2 ( 4 * _{2 2}  R  B s  D D S  V     



One Unbalanced Cylinder

 – Head Side

 – Rod Side

-Same as one balanced

S   D V _s B * 4 * 2    (7) (8)

Displacement

n

V 

 D

s

D= Displacement

n= Number of steering wheel turns lock to lock V_s = Volume swept

Minimum Pump Flow

231

*

 _N 

_s

 D

Q



N_s = steering speed in revolutions per minute Q = Pump Flow is in gpm per revolution

D = Displacement

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

Hydraulic Power Assist



Hydraulic power assist means that a

hydraulic system is incorporated with

mechanical steering



This is the type of power steering used

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

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