Chapter-4 •
Design Requirements of Suspension
•
Roll Centers, Roll Axis
•
Squat and Dive
Vehicle Suspension • Suspension refers to the use of front and rear springs to suspend a vehicle’s frame, body, engine & power train above the wheels.
Vehicle Suspension • Suspension refers to the use of front and rear springs to suspend a vehicle’s frame, body, engine & power train above the wheels.
Suspension Elements
Roll Centre and Roll Axis
Roll Center •
•
Center at which the sprung mass pivots about during a roll situation (lateral acceleration) This is a dynamic point: moves around throughout suspension travel
Roll Axis It is the line connecting the roll centres of front and rear suspensions •
Roll Centre Virtual Reaction Point
Required Roll stiffness of the suspension is determine by the roll moment. Which is dependant on Roll center height
Resistance to Rolling
Suspension Roll Stiffness
s
K : Roll stiffness of the suspension K s : Vertical Spring rate of the left and right springs s:
Lateral separation between the springs
:
Roll angle of the body
s
s s s s 1 M cG K s K s K s s 2 K 2 2 2 2 2
If a roll bar is included then
1
M cG K s s 2 K r ( K K r ) 2
K φ Roll stiffness of the suspension 0.5K ss 2
Roll Angle and Roll Rate
Roll Angle and Roll Rate 2
Roll angle
Wh1V /( Rg ) K f K r Wh1
Wh1a y K f K r Wh1
Roll Rate
d da y
Wh1 K f K r Wh1
The roll rate is usually in the range of 3to7degree s/g on typical passenger cars
Roll Moment
Roll Moments 2
M K f ' f
Wh1V /( Rg ) K f K r Wh1
W f h f
2
M K r ' r
Wh1V /( Rg ) K f K r Wh1
W r hr
V
2
Rg
V
F zf t f
2
Rg
F zr t r
The Roll moments magnitude depend on K f and K t which in turn depend on suspension stiffness
1. 2.
3.
In general, the roll moment distribution on vehicles tends to be biased toward the front wheels due to a number of factors: Relative to load, the front spring rate is usually slightly lower than that at the rear (for flat ride), which produces a bias toward higher roll stiffness at the rear. However, independent front suspensions used on virtually all cars enhance front roll stiffness because of the effectively greater spread on the front suspension springs. Designers usually strive for higher front roll stiffness to ensure under-steer in the limit of cornering.
4.
Stabilizer bars are often used on the front axle to obtain higher front roll stiffness.
5.
If stabilizer bars are needed to reduce body lean, they may be installed on the front or the front and rear. Caution should be used when adding a stabilizer bar only to the rear because of the potential to induce unwanted oversteer.
Solid Axle Roll Centers • The suspension roll axis and roll center can be determined from the layouts of the suspension geometry in the plan and elevation views. • For the analysis we consider the concept of a “virtual reaction point.” • The virtual reaction point is analogous to the “instant center” used in kinematic analysis of linkages • Physically, the virtual reaction point is the intersection of the axes of any pair of suspension control arms. • Mechanistically, it is the point where the compression/tension forces in the control arms can be resolved into a single lateral force.
A general procedure for finding roll centers:
•
In a plan view of the suspension find the linkages that take the side forces acting on the suspension. Determine the reaction points A and B on the centerline of the vehicle for forces in the links. In the case of paired control arms, this is a virtual reaction point.
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Locate the points A and B in the side elevation view, thereby identifying the suspension roll axis.
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The roll center is the point in the side view where the roll axis crosses the vertical centerline of the wheels.
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In the four-link geometry, the change in slope of the roll axis during cornering is often relatively large compared to other live axles. This means considerable change in roll steer and lateral load transfer, which are undesirable effects.
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Also, the roll center is located relatively high compared to other suspensions, putting excessive roll moment on the rear wheels.
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On the other hand, the high roll center helps to reduce the tramp and shake of the axle.
Four-Link Rear Suspension •
In a four-link suspension with a solid axle, the lateral force acting on the wheel in the top view must react as tension and compression forces in the control arms.
•
The two long arms establish a virtual reaction point ahead of the axle at B, while the two short arms have a virtual reaction point behind the axle at A.
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In effect, each pair of arms acts like a • triangular member pivoting at their respective virtual reaction points with these points establishing the suspension roll axis.
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Consequently, the lateral force will be distributed between the two points in inverse proportion to the length of the arms in order to achieve moment equilibrium on the axle (i.e., a large force at A and a small force at B).
The two forces at A and B must add up to Fy acting in the transverse vertical plane through the wheel centers. Given that points A and B are at different heights above the ground, their resultant at the axle centerline must be on the line connecting the two. This is the roll center for the axle.
Independent Suspension Roll Centers
Positive swing arm independent suspension
Parallel horizontal link independent suspension
Negative swing arm independent suspension
Inclined parallel link independent suspension
Independent Suspension Roll Centers
Macpherson strut independent suspension
Swing axle independent suspension
Roll Centers of Dependent Suspension
Hotchkiss Suspension
Four Link Rear Suspension
Roll Centers of Dependent Suspension
Three Link Rear Suspension Four Link with Parallel Arms
What is the Effect if Roll Centre Located on Ground or Located Below the Ground? • Jacking forces are the sum of the vertical force components experienced by the suspension links. The resultant force acts to lift the sprung mass if the roll centre is above ground, or compress it if underground. Generally, the higher the Roll Centre, the more Jacking force is experienced
Squat and Dive •
Squat - Squat is the dipping of a car's rear end that occurs during hard acceleration.
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Squat is caused by a load transfer from the front to the rear suspension during acceleration.
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Dive- Dive is the dipping of a car’s front end that occurs during braking
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Dive is caused by a load transfer from the rear to the front suspension during braking
Squat and Dive Video
Squat and Anti-squat Hard/Quick Acceleration Force or Weight Movement
Direction of Travel
•
During acceleration the load on the rear wheels increases due to longitudinal weight transfer. The load on the rear axle is:
W r • •
W (
b
L
ax h
g L
)
The second term on the right side of this equation is the weight transfer effect. The weight is transferred to the axle and wheels principally through the suspension. Therefore, there is an implied compression in the rear suspension which, in the case of rear-drive vehicles, has been called “Power Squat.” • Concurrently, there is an associated rebound in the front suspension. The combination of rear jounce and front rebound deflections produces vehicle pitch. • Suspension systems may be designed to counteract the weight transfer and minimize squat and pitch.
Squat and Anti-Squat • Anti-Squat forces can be generated on a rear drive axle by choice of suspension geometry • All suspension are functionally equivalent to a trailing arm with regard to the reaction of forces and moments onto the vehicle
Forces Acting on a Rear Solid Drive AxleAcceleration
Rear Solid Drive Axle •
The system is analyzed by applying NSL for the torques around the pivot point “A.” The sum of these torques must be zero when the system is in equilibrium.
M A W rs d
W h g L
a x d W rs d W r d F x e 0
Where, Wrs = Static load on the axle = Static load in the suspension Wr = Change in the suspension load under acceleration This equation can be solved for the change in rear suspension load.
W h e W r a x F x K r r g L d Where: Kr = Rear suspension spring rate r = Rear suspension deflection (positive in jounce) The front suspension is undergoing a rebound deflection because of the longitudinal load transfer, and has a magnitude of : W f
W h a x g L
K f f
The pitch angle of the vehicle, p, during acceleration is simply the sum of the suspension deflections divided by the wheelbase. Thus we can write:
p
r f
L
1
W h a x
L g L K r
1
F x e
1
W h a x
L K r d L g L K f
Since Fx is simplify the mass times the acceleration, (W/g)a x, the equation can be written : p
p
1 W h a x
L g L K r
1 W L g
a x (
1 W a x e
L g K r d
1
h
K r L
1
1 W h a x
L g L K f
e
K r d
1
h
K f L
)
From this equation it is easy to show that zero pitch angle is achieved when the following condition is satisfied : e d
h L
h K r L K f
Condition for anti-squat
Rear suspension lift to compensate rebound of front suspension
Anti-Squat Geometry Rear suspension will not deflect down (jounce)when load transfer happens to the rear due to acceleration
h
e e/d=h/L for anti squat
L
d
% anti-squat = (e/d)/(h/L) •
•
The anti-squat equation (e/d = h/L) defines a locus of points extending from the tire contact point on the ground to the height of the CG over the front axle. Locating the trailing arm pivot at any point on this line will provide 100% anti-squat
• Satisfying the equation with inclusion of the second term implies that the rear suspension will lift to compensate for rebound of the front suspension, thereby keeping the vehicle level. • The complete equation may be interpreted as the full anti-pitch relationship. Because the ratio of suspension stiffnesses is nominally 1, the anti-pitch condition is approximately:
e d
h L
h L
(Full anti-pitch)
h 2 L
Anti-Pitch Geometry The equation implies that the rear suspension will lift to compensate for rebound of the front suspension, thereby keeping the vehicle level.
h
e
L
d
L/2
• The locus of points for anti-pitch extends from the tire contact point on the ground to the height of the CG at the midwheelbase position. • Anti-pitch is achieved when the trailing arm pivot is located on the line from the center of tire contact on the ground to the CG of the vehicle. • Normally some degree of squat and pitch is expected during vehicle acceleration, so full compensation is unusual. • Anti-squat performance cannot be designed without considering other performance modes of the vehicle as well. When the trailing arm is short, the rear axle may experience “power hop” during acceleration near the traction limit. • The goals for anti-squat may conflict with those for braking or handling. In this latter case, placing the pivot center above the wheel center can produce roll oversteer.
Suspension Linkages: Rear Solid Suspension Trailing Arm Anti-Squat bar
Anti roll bar
Bar to constrain Y- motion and Z motion (anti pitch)
Anti-Squat and Anti-Pitch Bars
Dive and Anti Dive Hard/Quick Braking Force or Weight Movement
Vehicle Movements
Direction of Travel
• The longitudinal load transfer incidental to braking acts to pitch the vehicle forward producing “ brake dive.” • Just as a suspension can be designed to resist acceleration squat, the same principles apply to generation of anti-dive forces during braking
Anti-dive Suspension Geometry • Virtually all brakes are mounted on the suspended wheel (the only exception is in-board brakes on independent suspensions), the brake torque acts on the suspension and by proper design can create forces which resist dive. • Using an analysis similar to that developed for the fourwheel-drive anti-squat example given previously, it can be shown that the anti-dive is accomplished when the following relationships hold: Front suspension:
e f d f
Rear suspension:
tan f
h
L
er h tan r d r (1 ) L
Where: = Fraction of the brake force developed on the front axle eg: 60: 40.
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To obtain 100% anti-dive on the front and 100% anti-lift on the rear, the pivot for the effective trailing arm must fall on the locus of points defined by the defined ratios.
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If the pivots are located below the locus, less than 100% anti-dive will be obtained; if above the locus the front will lift and the rear will squat during braking.
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In practice, 100% anti-dive is rarely used. The maximum anti-dive seldom exceeds 50%.
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Full anti-dive requires that the pivot be located above the point required for full anti-squat. Thus acceleration lift would be produced on solid drive axles.
