ADAMS - Project - Hardpoint Tuning to Achieve Pitch Gradient Targets Using Suspension Anti Characteristics

Project Deliverables

• Perform hardpoint tuning to achieve the target acceleration and braking pitch gradients for Double Wishbone Suspension at the front and Multilink Suspension at the rear.

• Adams Plot showing effect of tuning (overlay curves).

• Completed Excel Sheet.

This is the link to the excel sheet which contains input values, calculation of different parameters, values obtained from Adams Post-Processor, Overlay Curves and Hardpoint Change History : https://drive.google.com/file/d/1DAi2JkcsWS4gREILe01PZzNPuZp_vT6Y/view?usp=sharing

INTRODUCTION: Anti Characteristic is a term that describes the longitudinal to vertical force coupling between sprung and unsprung mass. It results from the slope of side view instant center. This slope can be changed by changing the side-view instant center location which is done through hardpoint optimization. It tells us the fraction of longitudinal load transfer occurring through suspension links and that occurring through springs. The net longitudinal load transfer, however, remains the same as it is purely governed by the Center of Gravity Height, Vehicle Weight and Wheel Base.

The sort of analysis that has been attempted here is known as Pitch Analysis. Pitching is the motion of the vehicle body about Y-axis. Car pitches due to the influence of load transfer under braking or acceleration. The angle that the body makes in side-view is known as Pitch Angle which is the function of load transfer and wheel rate. There are two types of pitching motion that a vehicle experiences:

i) Squat: During forward (longitudinal) acceleration the vehicle load transfer tends to compress the rear springs (suspension jounce) and allow the front springs to extend (suspension rebound). Anti-squat characteristics can be designed into the rear suspension geometry. Anti-squat geometry produces a side view swing arm (SVSA)
that predicts suspension component behavior.

ii) Dive: During braking (longitudinal deceleration) the vehicle load transfer tends to compress the front springs (suspension jounce) and allow the rear springs to extend (suspension rebound). Anti-dive is usually designed into both front and rear suspensions (Anti-dive at the front and Anti-lift in the rear). Anti-dive geometry produces a side view swing arm (SVSA) that predicts suspension component behavior.

The deflection of any side of the vehicle under a given load is governed by the longitudinal load transfer and ride rate. The longitudinl load transfer depends on the wheel-base, total mass of the vehicle and CG Height.

⇒Deflection under Load in in/g (∂f or ∂r)=Axle Weight after load transfer/(2*Ride Rate)

⇒Pitch Gradient without compensation in deg/g= (tan-1((∂f+∂r)/wheel base)*(180/π)

PROJECT:

To start with this project, the given excel sheet was filled up with the given inputs of the vehicle. Based on the values of wheel-base, vehicle weight and CG height, the load transfer came out to be 3656.17 N. This value was further used to calculate front and rear axle weights after load transfer depending on the weight distribution.

⇒Front Axle Weight After Load Transfer= 8116.83 N

⇒Rear Axle Weight After Load Transfer= 11503.17 N

After this, the next step was to calculate wheel rate and ride rate from the given values of spring rate, motion ratio and tire rate. Spring rate which is the force/unit deflection is directly proportional to ride frequency. Higher the frequency, stiffer the spring will be. A term known as motion ratio is used to relate the change in displacement of the spring to change in vertical wheel center movement. This wheel center movement is known as wheel rate(Kw) which is expressed using the relation:

⇒Kw=MR²*Ks in lb/in where MR≤1

Motion Ratio is essentially the inverse of mechanical advantage and is used to relate spring rate to wheel center rate. Since wheels are the first point of contact between the road and the vehicle, the displacement of the wheel has a multiplying effect on spring displacement. It is imperative that the motion ratio be kept fairly high so that suspension system is effective enough to damp out the road disturbances. Having a very low motion ratio would translate to a high spring displacement but an ineffective wheel center rate. This is the reason why inclination of springs and pivot points are key factors behind motion ratio. Springs inclined at a very steep angle will reduce the effectiveness of the suspension despite having a fairly high motion ratio. Thus it is pivotal to keep a balance between the two.

⇒ Ride Rate: (Wheel Rate*Tire Rate)/(Wheel Rate+Tire Rate)

⇒ Front Ride Rate: 20.66 N/mm

⇒ Rear Ride Rate: 23.09 N/mm

The next step was to build Double-Wishbone Assembly for the Front Suspension and Multi-Link Assembly for the Rear Suspension. An assembly in Adams is made up of Templates which are then formed to build Sub-Systems and then those sub-systems are used to create an Assembly. This process was followed to create both the assemblies.

•Double-Wishbone Assembly and Parameters: A double-wishbone is an independent suspension design that can be found at the front, rear, or all four wheels. Independent means that a single wheel’s movement is not affected by the other three wheels. In other words, it’s free to move independently of the chassis.

This design offers several advantages, specifically in high performance on- and off-road environments. The key benefit is that, unlike a similar MacPherson strut setup, a double wishbone design doesn’t significantly affect wheel camber with suspension travel. That means a consistent tire contact patch with the road, regardless of body roll or road bumps.

The setup gets its “wishbone” nickname thanks to the the two control arms that hold the wheel knuckle and spindle. The upper and lower control arms typically use ball joints to secure the spindle/hub assembly. The arms are then connected to the vehicle chassis or body, where they’re allowed to pivot.

On drive wheels, the axle half-shafts are joined to the differential and hub flanges via CV or U-joints, permitting each wheel to move up and down. It also allows side-to-side steering movement in front-wheel-drive applications. A shock absorber (damper) is usually positioned between the upper and lower control arms to suppress suspension bounce.

•Multilink Suspension and Parameters: Where a McPherson setup only technically needs two controlling arms to keep it rigid, a multi-link needs a minimum of three lateral bars and one vertical or longitudinal. Each arm’s purpose is to limit and/or prevent the six degrees of an axle’s freedom; up and down, left and right and fore and aft. Sometimes some of the arms have ‘elbow’ joints along their length to achieve the necessary clearance around an axle while still achieving the proper angle of attack to fix to the hub.

After creating the assemblies, parallel wheel travel using baseline hardpoints was first run to extract different parameters. These baseline parameters would serve as a reference to the direction in which the hardpoint tuning would proceed. Parallel Wheel Travel was run with 100 mm jounce and rebound. The front and rear ride rate was first extracted using the Adams Post-Processor. It came out to be 22.77 N/mm and 32.07 N/mm. Based on these values the front and rear end deflections came out to be 80.26 mm/g and 56.99 mm/g. This further was used to calculate the Pitch Gradient Without Compensation (2.71 °/g).

Next, the values of SVSA length, SVSA Angle and anti % are extracted from the post-processor. These values were used to calculate deflection under load and pitch gradient with compensation. Hand Calculations were also carried out seperately to obtain the anti percentages and deflection. The formulas given were used in succession to arrive at the value of front and rear end deflection using hand calculation.

• Front IC Vertical Distance from contact patch (mm): Tire Radius - `Sin`(Radians(Front SVSA Length)*Front SVSA Angle)

• Front IC Horizontal Distance from contact patch (mm): Cos(Radians(SVSA Length)*SVSA Angle)

• Front/Rear Anti Dive/Lift Angle: `tan^-1``((IC Vertical Distance)`/`(IC Horizontal Distance)) ``*`180`/``pi`

• Front or Rear Swing Arm Angle for 100`%` Anti Dive/Lift: `tan^-1``(h/L)`*180`/``pi`

where, d is swing arm distance
h is CG Height
L is wheelbase

• Front/Rear Anti Dive/Lift `%`: ( F/R Anti Dive/Lift Angle*`phi`)/(F/R Swing Arm Angle for 100`%` Anti Dive/Lift)`*100`

φ is drive/brake proportion factor

• Front/Rear End Deflection With Compensation: F/R End Def Without Compesnation*(100-F/R Anti Dive/Lift)/100

• Pitch Gradient With Compensation `°`/`g`: `tan^-1`((Front def+Rear def)`/`Wheelbase)*180`/``pi`

• Pitch Compensation `%` : (Pitch Grad without comp-pitch grad with comp)/(pitch grad without comp)*100

Baseline Braking Pitch Compensation value & % - 2.18 °/g and 19.48 %

Baseline Acceleration Pitch Compensation value & % - 2.64 °/g and 2.48 %

The below image is of the Baseline Hardpoints for Double-Wishbone Suspension

The below image is of the Baseline Hardpoints for Multi-Link Suspension

HARDPOINT MODIFICATION: Since pitch compensation values were higher than the target braking (1.60) and acceleration (2.25) pitch gradient, the hardpoint tuning was done to gradually reduce the pitch gradient values. Y coordinate of any hardpoint was kept constant since changing those would have a drastic impact on the pivot point of wheel and suspension links which in turn affect ride rate and pitch gradient without compensation significantly. The aim was to keep this value as close as possible to the baseline parameters. So, only X and Z coordinates of any hardpoint were being modified. For the front suspension, front, rear and outer hardpoints of Lower Control Arm and Upper Control Arm were modified. For the rear suspension, trailing link forward, trailing link aft and control link was modified. After modifying any parameter, the change in anti-dive or anti-lift under acceleration and braking was being noted based on which the values of pitch gradient with compensation were updated. By noticing what influence changing a hardpoint or a combination of hardpoints had, the next set of hardpoints were then tuned accordingly. This process was iterated several times until the target pitch gradient value of braking and acceleration were obtained. The table below depicts how the pitch gradients changed throughout this exercise as well as it shows which suspension\'s hardpoint was changed to arrive at those values. During this exercise, it was observed that to achieve the target braking pitch gradient, the anti percentages needed to be kept significantly high enough. Whereas for acceleration, front suspension\'s anti-lift `%` had a greater influence than rear suspension\'s anti-dive `%`.

The below image is of the Tuned Hardpoints for Double-Wishbone Suspension: \'Modified\' has been commented against all those hardpoints that were changed.

The image below is of the Tuned Hardpoint for Multi-Link Suspension: \'Modified\' has been commented against all those hardpoints that were changed.

Overlay Curves For Front Double-Wishbone Suspension:

•RIDE RATE-

•SIDE VIEW SWING ARM LENGTH-

•SIDE VIEW SWING ARM ANGLE -

•ANTI-DIVE BRAKING % -

•ANTI-LIFT ACCELERATION % -

Overlay Curves For Rear Multi-Link Suspension:

• RIDE RATE-

•SIDE-VIEW SWING ARM LENGTH -

•SIDE VIEW SWING ARM ANGLE -

•ANTI-LIFT BRAKING % -

•ANTI-SQUAT ACCELERATION % -

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