Hard point tuning to achieve pitch gradient targets using suspension

Hardpoint tuning to achieve pitch gradient targets using suspension “anti” characteristics

Objective

The main objective of this project is to perform hardpoint optimization to achieve the target acceleration and braking pitch gradients using simulations and hand calculations.

Project Deliverables

• Tuned hardpoint set that achieves the pitch gradient targets
• Plots from Adams showing effect of tuning (Overlay curves)
• Completed excel sheet

Below is the link to the excel sheet that contains the final values for all the calculations mentioned in this report. This excel sheet also contains the overlay curves and hardpoint change history table.

https://drive.google.com/open?id=1BfdMigdYeIQyEPDe6ult_YnKHaqjg_as

Introduction

The Anti-effect in suspension describes the longitudinal to vertical force coupling between the sprung and unsprung masses. It results from the slope of the side view swing arm. The slope can be changed by changing the side view instantaneous centre, which in turn is done by hardpoint optimization in Adams. Anti- characteristics tell the fraction of longitudinal load transfer occurring through the springs and that acting through suspension links. The net longitudinal load transfer remains the same as it is governed by height of centre of gravity, Vehicle weight and Wheel base. These anti features are to be added to the suspension to stop pitching movement of the vehicle.

Pitch

Pitch in a vehicle is the shift in vehicle's weight forwards or backwards during braking and acceleration events. The angle made by the vehicle's body in side view is known as pitch angle, which depends on wheel rate and load transfer. Pitch is typically taken as '+' for upward movement of the vehicle nose and '-' for downward movement of the vehicle nose.

Vehicle pitch

There are two types of pitch motions in a vehicle.

1. Dive

During braking, the load transferred from the rear to the front tends to compress the front suspension and extend the rear suspension, as a result of which, the vehicle’s body rotates about Y- axis causing negative vehicle pitch. Anti-dive geometry in front suspensions reduces the bump deflection under forward braking.

Vehicle dive during braking

2. Squat

During acceleration event, the vehicle load compresses the rear suspension and extends the front suspension, which results in positive vehicle pitch. Anti-squat in rear suspensions reduces the bump travel during forward acceleration.

Vehicle Squat

Project – Solution

The following tables contains the inputs to build front and rear suspension models in Adams, the pitch gradient targets and the constraints in the model.

These inputs were fed into the excel sheet. The load transfer was calculated using the following formula.

Load transfer =

On plugging the values from the input table into the above equation, load transfer for the given vehicle design specifications was found to be 3585.72 N.

Assuming acceleration, Front axle weight after load transfer = Front axle static load – Load transferred

Similarly, Rear axle weight after load transfer = Rear axle static load + Load transfer

Front axle weight after load transfer = 8186.28 N

Rear axle weight after load transfer = 11433.72 N

Motion Ratio

Motion ratio is a geometric measure that relates the change in displacement of a force element (spring, damper and roll bar etc.) to change in vertical wheel centre movement. It is the inverse of mechanical advantage and used to relate wheel centre rate to spring rate.

Installation ratio for a simple suspension setup

The installation ratio is commonly used by itself to relate a suspension wheel centre rate to a spring rate. If the change of installation ratio with wheel displacement is zero, then the wheel rate is related to spring rate only by the installation ratio squared with no geometric rate term.

A very low motion ratio indicates a high spring displacement and an ineffective wheel centre rate. The wheel centre movement (Wheel rate) is related to spring rate (spring stiffness) by the formula, given below.

Wheel rate, K_W = K_S x (Motion ratio)²

Since, the spring stiffness is assumed to be linear for the purpose of project, wheel rate is found to be 23.04 N/mm for front wheels and 43.51 N/mm for rear wheels.

Ride rate

Ride rate is the vertical force per unit vertical displacement of the tire ground contact reference point relative to the chassis. This is equal to wheel centre rate modified by the tire vertical rate. For a real tire, the ride rate is always less than the wheel centre rate.

K_W=

Where K_W = Wheel centre rate in N/mm

K_R = Ride rate in N/mm

K_T = Tire rate in N/mm

By substituting the values, Front ride rate = 20.65 N/mm

Rear ride rate = 35.73 N/mm

Once the above calculations were done, suspension models were built in Adams using the inputs given.

Double wishbone Suspension

The double wishbone suspension design was the most common design for front suspension of American cars. The design uses two lateral control arms to hold the wheel. The upper and lower control arms are usually of unequal lengths. Hence, also called as ‘Short-Long Arm suspension’. The SLA is well adapted to front engine, rear-wheel drive cars because of the package space it provides for the engine oriented in the longitudinal direction. Additionally, it is best suited for vehicles with separate frame for mounting the suspension and absorbing the loads. The camber geometry of an unequal arm can improve camber at the outside wheel by counteracting camber due to body roll, but usually carries less favourable camber at the inside wheel. The upper and lower control arms typically use ball joints to secure the spindle/hub assembly. The arms are connected to the vehicle body/chassis through mounting points, which allow the arms to be pivoted. On drive wheels, the half shafts/ drive shafts are joined to the differential and hub flanges via CV or U joints, permitting each wheel to move up and down. A shock absorber/damper is usually positioned between the upper and lower control arms to supress suspension jounce and facilitate smooth rebound.

Multi-link suspension

Multi-link suspension consists of four links that provide longitudinal and lateral control of the wheels. The purpose of each link is to prevent the six degrees of freedom of the axle. At times, an additional link is used, which constraints the wheel but allows compliance in the bushings. The use of linkages provides flexibility for the designer to achieve the wheel motions. The additional link, also known as toe link restricts steering motion and helps in setting up the toe angle. The camber link controls and defines the camber angle while the integral link takes up acceleration and braking forces/moments. Shock is placed outboard to maximize interior space.

Verification of Baseline model

Once the models were created in Adams, they were verified with the given baseline hard point list to ensure that the models created were in compliance with the desired baseline models.

Parallel Wheel travel simulation

Once the hard points were verified, a parallel wheel travel simulation was performed on both suspension systems with a base value of 100 steps and a bound and rebound value of 100 and -100 mm respectively. The front and rear ride rate values were extracted by plotting Ride rate versus wheel travel in Adams post processor.

Front ride rate – 22.78 N/mm

Rear ride rate – 41.40 N/mm

The front end and rear end deflections were calculated using the below formulae.

Front end deflection =

By substituting the values, Front end deflection = 78.70 mm/g

Rear end deflection =

Rear end deflection = 43.30 mm/g

The side view swing arm length and angle were plotted against wheel travel in Adams post processor and values were entered into the respective field of the excel sheet.

By taking sign convention of Adams into account, the vertical distance of instantaneous centre from contact patch is calculated in 2 steps,

In front suspension, for a positive swing arm length with positive swing arm angle, the arm slopes downwards from the wheel centre.

Therefore, sin (SVSA angle) =

IC vertical distance from contact patch = Tire radius – h₁

IC vertical distance from contact patch = 214.11 mm

For IC horizontal distance, cos (SVSA angle) =

IC horizontal distance = 9646.74 mm

In case of rear suspension, for a positive swing arm length with negative swing arm angle, the arm slopes upwards from the wheel centre.

Sin (SVSA angle) =

IC vertical distance from contact patch = Tire radius + h₂

IC vertical distance from contact patch = 664.75 mm

Cos (SVSA angle) =

IC horizontal distance = 4489.93 mm

Front anti-dive angle =

Front anti-dive angle = 1.271 degree

Rear anti- lift angle =

Rear anti- lift angle = 8.421 degree

100% anti- dive or anti-lift =

= 10.47 degree

Now, front end deflection under load with compensation is given by,

On substituting,

Z_f = 72.96 mm/g

Rear end deflection under load with compensation is given by the formula,

Z_r = 29.27 mm/g

Pitch gradient with compensation =

Pitch gradient with compensation = 2.019

Pitch compensation % =

Pitch compensation % = 16.22

The above calculations were performed for the acceleration event, taking drive ratios into account instead of brake ratios. The calculated values are given in the excel sheet.

Tuning

To achieve the target pitch gradients, a few set of hard points were modified for the front and rear suspensions and the process of hard point modification was iterated for several times till the target pitch gradients were achieved. For the front double wishbone suspension, lca front, lca rear, lca outer and uca outer were modified and corresponding values of anti-dive and anti-lift were noted. The Y- coordinate values of the hard points were not modified since they would have a significant impact on the ride rate and instantaneous centre location, etc.. For the rear multi-link suspension, hardpoints were chosen carefully, as each hardpoint would cause erratic change in the suspension characteristics and cause hindrance in achieving the target. Hpl inner, hpl outer, tl aft, tl aft z, tl forward, tl forward z, tr inner, tr outer, ula front, ula outer and ula rear were modified through several iterations to achieve the targets.

Front hard point table - modified

Rear hard point table - modified

Overlay curves for front suspension

Anti – dive braking

Anti – lift acceleration

Ride rate

Side view swing arm angle

Side view swing arm length

Overlay curves for Multi-link rear suspension

Anti-squat acceleration

Anti-lift braking

Ride rate

Side view swing arm angle

Side view swing arm length