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.

Friday, July 18, 2014

Toe Compliance Control - Toe Base

We have a seen a lot of teams show up with a rear suspension like the one in this picture –

What I am specifically pointing out is the method of toe control in the rear. There are 2 control arms and the upper one what looks like an implementation of a revolute joint through a bushing. This works in theory but practically there is bound to be compliance in the joint. This is not only form the compliance from the bushing but also from the compliance that arises out of having a tiny toe base.

The definition of the toe base of the vehicle is varied but in general it is the length of the moment arm of that opposes the re-aligning torque that the tyre produces. In this above picture it is the length of the cylindrical section at the outer end of the control arm. This is clearly small as is a definite ‘No No’ for a Formula Student car. The suspension must have a toe link.

In a more conventional suspension system there is a toe bar that prevents the rear suspension from steering. Here the toe base can be more clearly defined as the perpendicular distance of the point where the toe arm meets the upright from the king pin axis. The diagram clearly demonstrates this –

It is important for the toe base to be large. The compliance (or the ‘play’) in the suspension system dramatically reduces as the toe base becomes bigger. This can be simply illustrated by this simple thought experiment. Support you have a spherical bearing with 1 mm of compliance in it. Note: 1 mm compliance is chosen for ease of calculation, if you really have a bearing with 1mm compliance you must throw it away. This compliance will translate to the wheel being compliant when turned in the top view of the car. Here is a plot of the compliance in the wheel in degrees vs the toe base length.

The graph clearly illustrates the importance of having a large toe base. Simply having the toe link will NOT do. The suspension in the next picture will be compliant of this reason.

Rear toe compliance on a Formula Student vehicle will make it handle like a super-market trolley and will lose points in design. Which is why it finds second place in Pat’s “Seven Deadly Sins of FS Design” 

Moral of the story : Toe compliance is evil. Evil can be fought with larger toe-base. Hero wins only with a larger toe base, a little like this one -

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