# Chassis Stiffness

Chassis Stiffness or Torsional rigidity means the calculated or measured stiffness of the structure alone. While the installed Stiffness is stiffness measured at the hub faces. Torsion stiffness is an important characteristic in chassis design with an impact on the ride and comfort as well as the performance of the vehicle. If your chassis is too soft your car won’t handle. If parts of your chassis can twist or move under hard cornering or braking, your suspension geometry will become far from optimal, which in turn means your tyres will be either facing the wrong direction, at the wrong angle or both, screwing up your handling and braking grip.
In soft and floppy chassis, the twisting force of the engine and transmission when accelerating hard can not only twist the chassis and make your suspension geometry completely wrong, but it can actually twist so much it can rip the differential and even engine mounts cleanly off the chassis in some extreme cases. With this in mind, the goal of design is to increase the torsion stiffness without significantly increasing the weight of the chassis.

To determine chassis stiffness there are several methods :

1) Analytical Method

Determining torsion stiffness based only on the geometry of the chassis can be difficult for a vehicle given the complex geometries that are commonly found. However by expanding on the principles of solid mechanics and making some simplifications a method can be developed to give an approximate value for the chassis. If the applied torque (T) is related to the angle of twist of a chassis (f) through the following equation

T=(JGf)/L=Ktf

Where:

J= Polar moment of inertia

G= Material shear modulus of elasticity

L= Characteristic length of cross section.

2) Simulation Method

The simulation method is based on previously conducted studies where FEA is performed on the chassis. In this method equal and opposite loads are applied at the front suspension mounting locations while the rear mounting locations remain fixed. The equations used to determine the torsion stiffness is based on the total deflection of the mounting locations. The torsion stiffness is calculated using the following equations.

kt=T/f=(FB)/(fd+fp)

Where, fd=tan^-1(vd/(B/2))

fp=tan^-1(vp/(B/2))

In the above equations the torque, T, is represented by the vertical force applied at the mounting locations, F, and the track width of the vehicle, B. The angular deflections fd and fp are based on the vertical deflections for the driver (v) and passenger (p) sides of the vehicle, as well as the track width.

3) EXPERIMENTAL METHOD

The experimental method to determine torsion stiffness is similar to the simulation method described above. In this method linear jack-screw actuators are used to apply vertical deflections at the front suspension mounting locations in gradual increments. The rear mounting locations are held fixed and load cells are placed at each location under each jack stands in order to determine the force applied. Dial indicators are used to measure the deflections at various points along the chassis. The torsion stiffness is found from the following equations:

T=((Rr+Rl)/2)*Ls

θr=(Xl|+|Xr|)/Lr

K=T/θ

In the above equation the torque, T, is based on the reaction forces (Rr and Rl) for the right and left sides respectively, as well as the lateral distance between scales. The angular deflection is again  based on the vertical deflections at the right and left wheels respectively (Xl and Xr) which are found from the measurements on the jack screw actuators. The torsion stiffness, K is based on the torque and angular deflection and is found at several increments of the jack screw actuators. An average value representing the actual torsion stiffness is then found using a least squares regression.

4) LINEARITY OF TORSION STIFFNESS

It is assumed that the torsion stiffness described above follows a linear curve where the stiffness can be accurately determined as the slope of a function involving the torque and the angle of twist. This assumption is based on the fact that the angle of twist is related to the torque through geometric and material properties only as shown in Equation (1). As can be seen in this equation, if the material and geometric properties are constant then the torsion stiffness will be constant as well. This is analogous to that of a linear spring with a linear spring rate.

It is possible that the torsion stiffness could end up nonlinear, in which case a better model would be required to accurately predict the torsion characteristics. In order to determine the nature of the torsion stiffness, the test must be performed for a variety of applied torques and the deflections measured. The resulting data can be analyzed to study the linearity of the torsion stiffness function. The slope of the angular deflection vs. torque plot will represent the torsion stiffness if it is linear. It can be seen that linear torsion stiffness is preferred in order to more accurately predict the chassis behaviour.