Introduction to Vehicle dynamics and suspension systems

A detailed summary of the various areas in vehicle dynamics

Table of contents
  • What is vehicle dynamics and why is it studied?
  • Automotive systems
  • Degrees of freedom and axis systems
  • Loads and moments
  • The Tire and its importance
  • Longitudinal dynamics
  • Lateral dynamics - Understeer and Oversteer, Roll 
  • Wheel alignment angles
  • Vertical dynamics - isolation
  • Suspension systems
  • Vehicle roll over

What is Vehicle dynamics and why is it studied?

To put it simply, Vehicle dynamics is the application of classical mechanics in physics to cars to predict and control motion.

The understanding of various types of Forces, moments and their effects on the vehicle is a critical study to understand and predict the behavior of the vehicle in dynamic conditions.

The study of vehicle dynamics helps to predict

1. Whether a vehicle setup is suitable for roadworthiness?

2. Whether a vehicle when driven with a certain velocity be able to handle turns and corners without overturning?

3. Whether a vehicle will be able to sufficiently isolate road bumps from the occupants

4. Whether a vehicle has directional stability? Does it move the way the driver intends it to?

5.  Are the Tire properties sufficient for grip and road holding?  

And many more such questions are answered by studying the vehicle dynamics

Automotive systems

A typical car has three major system clusters

  • Powertrain
  • Body
  • Chassis

While the powertrain is responsible for propulsion, the chassis is responsible for giving the dynamic character to the vehicle.

The body system is the overall structural system which houses the occupants and all other systems.

Within the chassis – The Tyre, the suspension, the brakes and to a certain extent the structural members decide the dynamics of the vehicle.  The Design of these systems is critical.

The Tire is interface between the vehicle and the road, hence all the forces and moments which are coming onto the vehicle from the road are through the Tires.

The suspension does the primary job of isolation and provides a trajectory for the wheel to travel. The nature of contact of the Tire with the road is heavily dependent on kinematics of the suspension.

Degrees of freedom:

Each Vehicle in space has 6 degrees of freedom

3 in translation and 3 in rotation

Movement in Fore and aft direction

Movement sideways

Movement up and down

Rotation in Rolling

Rotation in turning

Rotation in pitching

The vehicle travelling on road can rotate about its vertical axis which is Yaw (steer) , and it can move Forward while the other degrees of freedom are generally constrained for the most part.

Concept of degrees of freedom is fundamental to understanding motion of the Vehicle as a whole and those of the components/ systems.

Axis systems:

Dynamics analyses are carried out with a fixed co ordinate system which can vary depending on the reference origin

The SAE axis system considers the Centre of gravity as the origin and the 6 degrees of freedom as shown

Loads and Moments:

Motion is caused by Force and moments, hence the first step in analysis is knowing the Forces and moments on the system under study.

Primary Loads which act on a vehicle
  1.  Traction force
  2.  Braking force
  3.  Aerodynamic drag
  4.  Lateral Tire reaction forces
  5.  Vertical Reactions at the wheels
Moments
  1.  Yaw moment which induces steering
  2.  Roll moment
  3.  Pitch moment

Centre of gravity

The role of the Centre of gravity is crucial as the dynamic behaviour is a function of the CG location.

  • Lower centre of gravity on Race cars aids handling
  • Centre location of centre of gravity between front and rear axle also aids in balanced handling.
  • Higher centre of gravity of truck has higher tendency of Roll.

The Tire and its importance:

The most important component of a vehicle which determines the dynamics is the Tire

Its construction and behaviour under loads have been a huge area of study for vehicle dynamicists.  The behaviour under different types of loads (vertical lateral, longitudinal) directly impacts the behaviour of the vehicle.

Fluctuations in Tire construction can affect the dynamics; hence a lot of testing and iteration is required to arrive at an optimal Tire parameter which give a balance of all affects.

  • Tires which are stiffer have better response but inferior in ability to damp vibrations
  • Softer Tires while have better isolation ability are not as responsive to changes in loads, hence handling suffers.
  • Wider tires provide better traction and grip but also higher rolling resistance

Tire size, Width, side wall stiffness, Tread pattern and depth all play a role.

Domains of vehicle dynamics:

Generally, the study of mechanics is separated into three domains which are then brought together to study the vehicle dynamics as a whole

  • Longitudinal dynamics
  • Lateral dynamics
  • Vertical dynamics

Longitudinal dynamics:

Longitudinal dynamics is all about

  • Acceleration
  • Braking
It involves:
  1.  How torque is being transferred from engine and how it translates to traction at the wheel
  2.  What should be the Braking forces required to stop the vehicle and how they can be achieved by the braking system.
  3.  Longitudinal forces generated at the Tire contact and their management which is Traction control.

To attain a certain level of speed within a time requires power and torque.   Depending on the performance required the Power and torque requirements are developed along with the traction limits at the Tire contact.

Considering the Inertia of the vehicle the braking energy required is calculated and from that the braking force

Study of Lateral dynamics :

  • Low speed turning and steering geometry
  • Understeer and Oversteer
  • Roll behaviour
Behaviour of Vehicle in turns

While taking a turn, if the driver has to give excessive steering inputs to negotiate the turn, then it means that the vehicle has predominant understeer behaviour.

If the steering inputs lead to an increased response from vehicle tending to take tighter turn than intended, then this is called oversteer behaviour.

There are multiple factors and parameters which govern whether a vehicle will behave more towards under steer or oversteer.

Ideally for true control the vehicles should be neutral steer, but this doesn’t take place in practice and the vehicles need to be tuned accordingly.

The event of roll.

When the vehicle body leans outwards while taking a turn, that motion is called roll.

It is the result of centrifugal force reaction acting at the centre of gravity of the vehicle.

What is a roll centre?

The point about which the body of the vehicle rolls when acting upon by a roll moment during the event of a turn.

It is an imaginary point which is formed based on the geometry of the suspension at that instant. With suspension travel roll centre also changes.

Significance of roll centre?

The distance of the centre of gravity from the roll centre forms the moment arm which decides the extent of the roll moment arm.

Higher the distance more the roll moment will be and more the vehicle will tend to roll.

Finding the roll centre for a double wishbone suspension.

The roll centre is found in the “Front view suspension geometry”

Modifying the roll centre:

Roll can be controlled by controlling the roll centre height.

In a standard double wishbone system, the point location can be changed by

  1. 1. Changing the orientation of the upper control arm
  2. 2. Changing the orientation of lower control arm

Both these changes will shift the instantaneous centre to raise or lower it.

Then the roll centre height will also be changed.

Roll control mechanisms:

Often, the roll centre may not be drastically modifiable in a production car, then other methods of roll control are applied.

The primary way in which Roll is controlled is through the springs but many times this is not enough to control roll motion.

One most widely used method is the usage on Anti roll bar or stabilizer bars

Shown here in red. They are a circular rod bent into a 3D shape and connected at either wheel. When one wheel goes up when the other is stationary. The stabilizer bar pulls the wheel down to equalize their levels.

Thus, counteracting the roll moment.

Wheel alignment angles:

Wheel or more importantly Tire alignment with respect to the Road is critical to the performance.

Small changes in angles can cause huge impact on the dynamic behaviour, Wear and tear and directional stability of the car.  Even possibly a safety hazard if not maintained within specifications.

Here are the angles and their meanings.

Camber and Toe:

Camber is the angle made by the wheel to the vertical when the vehicle is viewed from the front.

Toe is the angle made by the wheel with the horizontal when the vehicle is viewed from the top.

Both these angles hold a lot of significance when it comes to vehicle dynamics and durability of the Tyre.


Tyre wear due to excessive camber and toe

Excessive camber and Toe angles can wear out the Tire much faster and lead to degradation of performance.

More Toe in generally cause vehicle to steer more sharply than Toe out.

Also, Toe in is preferred setting because of the reason that due to forces the wheels tends to Toe out during vehicle running conditions.

Camber thrust:

Excessive camber on the wheel can result in the generation of an additional lateral force on the Tire which tends to modify the behaviour of the Tire. This additional force due to camber is called camber thrust and it is the result of the deformation of tire contact patch due to camber setting.

Caster:

The Angle made by the Steering axis with respect to the vertical when the vehicle is looked at from the side.

When the line is inclined towards rear of vehicle the caster is called positive caster

IF the line is inclined towards front its called negative caster.


Significance of caster:

Caster directly contributed to the Steering effort. Higher the caster more the steering effort will be.

Also, the stability of vehicle can be compromised if the caster on either wheel has a huge difference which can lead to vehicle pulling.

Vehicle Pulling:

Caster is One of the root causes for vehicle pulling not the only root cause but is often found to have a considerable effect.

What is pulling? When the Vehicle self-steers itself towards the left or the right without any input from the driver for a certain distance tending to lose control of direction and calling for continuous correction by the driver, it’s called pulling.

There are many contributing factors for this event originating from Tires, to vehicle architecture.

In terms of Caster, when there is a differential between the left and Right caster. A moment gets generated which tends to steer the wheels in a certain heading. All this happens at the wheel end.

Study of Vertical dynamics:

Vibration isolation

    At the most basic level – It is a mechanism which isolates the vehicle passengers from the harshness of road conditions by providing a spring and damper system which absorbs the energy.

    Vibration Isolation is carried out by a spring damper system. A spring which absorbs energy and a Damper which dissipates gradually.

    A block diagram of basic system is shown below:

    A more advanced version used to design spring and damper is the Quarter car model which indicates a corner of a car (front left, front right )

    Separating the mass into two portions and adding another spring element for the Tire .

    The sprung mass is the mass above the spring which is suspended by the spring while the unsprung mass is the part of the vehicle not suspended by the spring like the Tire, wheel ends.

    This mathematical model which is solved by differential equations is a reference for each wheel of the vehicle and helps in arriving a reference value of spring stiffness and damping constant.

    Suspension systems

    Employs a kinematic mechanism which constrains the wheel to travel on a specific path

    Suspension design directly impacts how a vehicle also behaves in turning, braking, and accelerating affecting the vehicle dynamics.

    Each suspension configuration has their own pros and cons and are selected based on best suitability with vehicle requirement.

    Kinematics of suspensions:

    Apart from the obvious function of isolating vibration the suspension also acts like a connection between the body /chassis and the wheel constraining it to only travel along a specific path. Thus, controlling the kinematics (Properties of motion) of the wheel.

    The wheel has 6 degrees of freedom, the suspension linkage system ideally constrains 5 degrees of freedom and allows the wheel to travel in only one degree of freedom. That is vertical up and down direction.

    In practice, this may not be achieved but suspension geometries are designed to tend towards this condition.

    Depending on kinematics there are two basic types of suspensions .

    Independent suspensions – When the vehicle goes over a pot hole. The droop of one wheel does not affect the position of the other. Both the wheels are connected mechanically.

    Dependent suspensions – In the same event the droop of one wheel will influence the other wheel as well and the other wheel will tend to move down. Both the wheels are connected with a rigid beam.

    There are a third hybrid type called Semi dependent suspensions where the two wheels are connected by a flexible element rather than a rigid element.

    Double wishbone system

    The most common system used in passenger cars, ATVs, pickups generally in the front.

    Mcpherson strut

    A derivation of the double wishbone where instead of the Upper control arm , it is replaced by a strut directly connected to the knuckle and which rotates with the knuckle in steering.

    Simpler and with lesser parts but has its limitations.

    Very common in hatchbacks and sedans

    Multi link system

    The most versatile, which can come in many varieties .

    The 5 links responsible for constraining 5 degrees of freedom are arranged in space to control the trajectory of the wheel .

    Complexity adds costs and hence is more costlier than generic double wishbones.

    Rigid Axle Leaf spring suspensions

    The oldest type of suspension system which is still used widely in large trucks and pickup trucks today.

    The leaf springs are connected to the frame through brackets at one end the bracket has single pivot joint while on other end, there is an extra linkage with two pivot joints . One connecting to the spring and other to the frame. This is a shackle bracket and it is crucial for the leaf spring working

    When the leaf spring compresses, these shackle brackets allow the deformation of spring. They release the constraint of leaf in the direction of its span.

    Twist Beam suspensions

    It employs a welded structure called as the twist beam which is designed to twist as and when the load on one wheel exceeds the other.

    The suspension travel is governed by range of flexing of the structural member.

    Roll Over  of a vehicle

    Another event in vehicle driving which is a cause of accidents is the Vehicle rollover. Study of vehicle dynamics also covers the event of rollover of a vehicle. The roll over is basically the moment when the vehicle loses static or dynamic equilibrium and flips due to the moment (torque) generated at the tire.  For trucks and vans which are taller and hence prone to roll over, this analysis becomes crucial for design




        Categories: : Automotive engineering

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