What is the Motion Ratio?

Motion ratio/installation ratio is a geometric measure that relates the wheel centre displacement and spring rate, it decides the amount by which the spring compresses for the applied load at the wheel centre when the vehicle undergoes a bump. Our aim is to keep the motion ratio as close as ‘1’, if it is then the wheel rate will be equal to the spring rate. This motion ratio is a parameter which decides how efficiently the suspension system performs under loading conditions.

Installation Ratio And Its Estimation:

The installation ratio in simple terms is the inverse of the motion ratio.

Motion ratio can be estimated by the means of your spring rate and wheel rate. Additionally, you can estimate your motion ratio with the help of the mounting points of your suspension system. Let’s dive a little further into these methods individually. These methods are usually used for estimating motion ratio in static conditions. During dynamic conditions, the motion ratio of the suspension is subject to change based on various parameters such as suspension geometry, spring parameters, wheel parameters, mounting points etc.

Method-1:

This approach involves the use of spring stiffness/rate and wheel rate parameters. This is pretty much straightforward and can be used if you are sure of your frequency targets to be achieved. Or if you know the spring parameters which are to be used in your vehicle. The mathematical expression is as follows:

Here, the wheel rate is the force required to move the wheel centre by unit displacement, and the spring rate is the spring stiffness value of the spring element you have chosen.

This method fails, if you are not able to choose a spring rate value and you have not given a proper frequency target. This can be seen when you are in a team which develops an entirely new vehicle lineup, instead of existing products. In that case, the second method helps you by taking the suspension geometry into consideration to calculate the motion ratio.

Method-2:

This method as mentioned before uses the mounting points of the spring. Let’s look into this in a detailed manner.

Independent Suspension

The majority of the independent suspension has a geometry comprising a lower link on which the spring is mounted and the other end of the spring is attached to the chassis. Let us consider a simple A-arm suspension as an example.

Here, D1 is the horizontal length between the lower spring mounting and the lower arm mounting point on the chassis.

D2 is the horizontal distance between your wheel center point and the lower arm mounting point on the chassis

A is the angle made by the spring in the horizontal axis.

Using these values, the motion ratio can be estimated as

`MR=((D1)/(D2))^2*cos(90-A)`

Where, cos(90-A) is called the angle correction factor. 

Beam Axle Suspension

For estimating the motion ratio of a beam axle suspension it is a bit different because those are dependent types and so the spring mounting angles do not play a major role in estimating the motion ratio.

Here d3 spring mounting center distance and d4 is the track width with respect to the wheel centers. The motion ratio is calculated as.

`MR=(d3)/(d4)`

And that’s how the motion ratio parameters calculation approach is chosen. Both the above methods go hand in hand, to help us in standardizing the motion ratio of the suspension.