Wednesday, July 30, 2014

Suspension Design Kinematics - Degrees of Freedom

Suspension design starts off as a kinematic problem that the designer must solve. There are very easy methods to evaluate the basic sanity of the solution that one might have thought of. An independent suspension with its steering locked has one degree of freedom. This degree of freedom (DOF) is the travel of the suspension. When a design solution for the suspension is thought of, it is important to do the degree of freedom analysis.

For example, this double ‘a-arm’ suspension in the figure below has an upper and lower control arm with a toe rod which has ball joints on either end. 

The DOF of this suspension system can be simply analysed like this –

*The A-arms being joined to the chassis by 2 ball joins is actually an over constrain. The ideal solution would be to have a ball joint at one of the pick-ups and a ball joint in a slider on the other pick up. This is however not practical and usually the kinematic over-constrained is persisted with, to better distribute loads. Think is this in the same way as a door having multiple hinges when kinematically a single hinge would do. This is also the ‘a-arm’ must be manufactured with precision on a jig. Any misalignment will cause compliance in the structure.

** The 2 ball joints are usually rod-ends in a toe rod. The rod-ends are not ideal ball joints. The limited articulation does not allow the tie rod to spin about its axis and this constrains another degree of freedom associated with the spinning of the toe-rod within its place.

It has one degree of freedom which means that baring interference the suspension travel is easily achieved without any of the members flexing.

This degree of freedom analysis is important to determine if a suspension configuration would work or not. For, example these pictures below illustrate another solution to toe control in the rear where the tie rod is welded on to the control arm.

People who have read this blog post would be quick to point out that the toe base here is too small. The load path is not great because forces apply bending moments on the control arm. However, this suspension solution also does not fare well with the DOF analysis.

Such suspension solution might function like a 1 DOF system if the over-constrains are redundant. However, slight misalignment or manufacturing tolerance error would cause components to go through high stress cycles and eventually break. For the sake of completion the correct way to get the DOF correct in the above solution is to have a control rod, with ball joints at either end as the lower control arm instead of an ‘a-arm’.

DOF is only one of the criterions that must be kept in mind. The DOF solution in the suspension system in the picture below is good. However, there can still be an issue with the toe compliance here. Even though the toe base is reasonably large the toe rod pick-up is a cantilever on the upright. It will see a lot of bending moments and cause compliance due that bit flexing.

This blog post is originally written for the Formula Student India website and has been cross posted from here.

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