ADAMS- Kingpin Geometry Optimization To Achieve Steering Related Parameters

Objective: Perform Kingpin Geometry Optimization on a Double Wishbone Suspension below to achieve the following targets:

oCaster angle : ~4.00 deg

oCaster moment arm : ~21.00 mm

oKPI angle : ~13.00 deg

oSteer axis offset (resultant) : ~85.00 mm

oSteer axis longitudinal offset : ~0.00 mm

oScrub radius : ~20.00 mm

The link contains the excel sheet to the list of hardpoint changes that were performed to achieve the targets : https://drive.google.com/file/d/10wjZ6vKVNCQdiii-YuRRV84HcLqTDFfy/view?usp=sharing

KingPin Inclination Angle: It is the main pivot member or pin in a steering mechanism. In modern independent front suspension like double wishbone, kingpin is no longer a physical component but a virual axis about which knuckle pivots. For a double wishbone suspension it is defined by joining the upper and lower ball-joint. It is positive when the top leans into the body and negative when top leans outside body.

Due to kingpin inclination, the body of car tends to raise when it is steered. The axis about which the body turns is tilted thus adding a self-centering effect when the wheels return to their position.

Scrub Radius: It is the distance between the point where the center of wheel touches on the ground and the projection of kingpin on the ground. Scrub radius affects transmission of road disturbances in general. A negative scrub is when steering axis projection is outboard of tire center and positive scrub is when projection is inboard of tire center. Zero scrub radius is when the projection intersects the tire print.

A negative scrub radius is more desireable. If we consider a situation where left wheel of the car is on a slippery surface whereas the right wheel is on a high friction surface then due to this imbalance a moment is created. If the car has a positive scrub radius then the left wheel will have a lower moment and the right wheel will have a greater moment leading to instability effects due to both the moment imbalance adding up. Whereas if the car has a negative scrub radius, the larger moment on the right wheel tries to cancel out the moment imbalance thus inducing a stablizing effect.

Caster Angle: It is the inclination of kingpin in side view. Positive caster is when kingpin leans towards the back of car at the top and negative when kingpin leans towards front. The distance between the wheel center on ground and caster projection on ground is known as mechanical trail. In a positive caster, when the wheels are steered this trail, also known as \'Caster Moment Arm\' adds a self-centering torque `F_y*X`. The caster angle should not be kept too high as it can make the steering feel heavy and also mask the breakaway point of tires.

Kingpin Offsets: These offsets exist when the kingpin doesn\'t pass through the wheel center in front and side view and are measured at wheel center length. Longitudinal offset should be kept to minimum for stability purpose.

Hardpoints Modification: In order to perform the optimization routine, the first task is to run the simulation using Baseline Hardpoints that are used when Double Wishbone Suspension Assembly was created in Adams. Based on the values of the different steering related parameters, it was then decided which course of action should be taken to achieve all the targets.

Lower Control Arm Outer, Upper Control Arm Outer and Wheel Center hardpoints were optimized to achieve the targets. The outer hardpoints control most of the steering related parameters. The Y-axis of the above-mentioned hardpoints were optimized to achieve kingpin inclination angle, scrub radius and steer axis resultant offset targets. This is pretty intuitive since these parameters especially kingpin and scrub radius are calculated using front view geometry which is Y-axis in this case. It is difficult to independently control all the parameters but these could be controlled in sets. The below image lists the hardpoint modification exercise done to achieve the required targets.

With KPI, Scrub radius and Steer axis offset (resultant) targets achieved, the next step was to acheive the targets for caster angle, moment arm and steer axis offset longitudinal. These are parameters that are primarily controlled in the lontiduinal direction or X-axis because they are calculated using side-view geometry. A similar hardpoint modification exercise was done to acheieve the targets. During this exercise, KPI, scrub radius and SA offset resultant were also being monitored, should any change happen to those parameters. While KPI and scrub radius remained constat the resultant steer axis offset was difficult to contain within the target range as chaning the X-axis hardpoints of UCA and LCA also affected it.

Modifed Hardpoints List and Animation of Steering At 540°

Overlay Curves: These plots show the effect of hardpoint tuning on different parameters.

°Caster Angle: The baseline value of caster angle was 5.4° whereas the target value was 4°. Reducing the caster angle would reduce the inclination of the kingpin at the top. A positive caster indicates that the kingpin at the top is leaning towards back of the car.

°Caster Moment Arm: The base value was 8.6mm whereas the target was 13mm. This increase in caster moment arm would lead to an increased in aligning moment of the car but would result in a greater masking of the breakaway point of the tire during limit handling conditions. The steering will also feel heavy due to increased moment arm.

°Kingpin Inclination Angle: It was increased from 10.6° to 13° which would result in an increase in self-centering torque of the car and a greater tilt of the top of the top of kingpin towards the inside of car.

°Scrub Radius: With the scrub radius decreased from 33 to 20, a condition known as squirm will occur. The downsides of positive scrub radius that were discussed above would be considerably reduced thus giving more stable braking conditions and even wearing out the tyre lesser than it would have.

°Steer Axis Offset Resultant And Longitudinal: With the longitudinal offset increase from -18 to 0mm, the car would be more stable.