C-factor Milliken formula

[ARIJ]

I have been working on the steering system of our car for quite some time and we are very close to design completion.... We have calculated the steering ratio and rack speeds etc. which come out to be around 6 and 65mm/rev respectively. But, all the calculations have been done using front view trig.

While trying to verify my calculation results through the C-factor formula given in Milliken i.e. Steer Ratio = (arcsin(C-factor/steer arm length))/(360) i am stuck because I just can't seem to understand why the (c-factor/steer arm length) term is coming out to be greater than 1 (Our c-factor is 2.6667in/rev and our steering arm length is 2.36 in) ... Because of this it has been impossible for me to check if my earlier calculations are alright or not.

So, can you guys please guide me and try and point out what and where the error is.

[ARIJ]

I have been working on the steering system of our car for quite some time and we are very close to design completion.... We have calculated the steering ratio and rack speeds etc. which come out to be around 6 and 65mm/rev respectively. But, all the calculations have been done using front view trig.

While trying to verify my calculation results through the C-factor formula given in Milliken i.e. Steer Ratio = (arcsin(C-factor/steer arm length))/(360) i am stuck because I just can't seem to understand why the (c-factor/steer arm length) term is coming out to be greater than 1 (Our c-factor is 2.6667in/rev and our steering arm length is 2.36 in) ... Because of this it has been impossible for me to check if my earlier calculations are alright or not.

So, can you guys please guide me and try and point out what and where the error is.

[BillCobb]

It's not 360, it's 2*pi. Check your units.

[ARIJ]

<BLOCKQUOTE class="ip-ubbcode-quote"><div class="ip-ubbcode-quote-title">quote:</div><div class="ip-ubbcode-quote-content">Originally posted by BillCobb:
It's not 360, it's 2*pi. Check your units. </div></BLOCKQUOTE>

It says 360 in Milliken and the angles are in degrees so I am pretty sure its 360. Anyway, the problem is not the 360 or the denominator it is that the term (C-factor/steer arm length) is coming to be greater than 1 (Our c-factor is 2.6667in/rev and our steering arm length is 2.36 in) and therefore the arcsin can not be computed.

[Edward M. Kasprzak]

I would have to ask Doug why the arcsin was used in RCVD. I drew a picture to understand where the formula came from and I would use arctan instead, but we may be making different assumptions.

Draw a picture and decide for yourself.

[AxelRipper]

Units:

2.666666667 in/rev

divided by

2.36 in

does not equal

nondimensional (sin/cos/rad)

[BillCobb]

The steer ratio is essentially the ratio of the steer arm and the pinion radius. For a 2.36" steer arm, and a ratio of 6.00:1, the pinion radius would be .3933" = a C-Factor of 2.47"/rev. In the vernacular, that's 62.74 mm/rev. Some suble effects due to the steer arm not perpendicular to the spindle and the tierods not colinear with the rack, but it gets you there.

[DougMilliken]

<BLOCKQUOTE class="ip-ubbcode-quote"><div class="ip-ubbcode-quote-title">quote:</div><div class="ip-ubbcode-quote-content">It's not 360, it's 2*pi. Check your units.

It says 360 in Milliken ... </div></BLOCKQUOTE>
We are not perfect, look for small changes on p.718 in the next (14th?) printing. SAE allows us to make changes as long as they stay on one page.

Early printings include "Comments Requested!" on RCVD p.855. I just checked a 13th (current) printing and find p.855 is blank&lt;grrrr&gt;, another error to fix before the next printing.

[Marvel]

You will get much better idea if you try to derive the formula yourself.
It involves a bit of complex trigonometry(complex because you have to work in 3 dimensions).
Also what I have found is steer ratio is not constant always(please correct me if it is wrong..); but the variation is hardly noticeable.

[BillCobb]

You are not incorrect on both counts. The amount of steering involved in maneuvering at speed is pretty small. A usefull nonlinear ratio with steer angle can be achieved easily via 1 or two Cardan joints that are arranged to deliver a speedup or slow down ratio. The arrangement chosen depends on whether you desire a displacement or torque based "feel" objective.

[Warpspeed]

And then there is Ackermann.
Which wheel should we be measuring ?
Overall steering ratio is certainly of interest, but as the whole steering process is non linear, a single figure is only going to be some kind of average indicator.

[BillCobb]

In the automotive design and development world, you would 'measure' or analyse both. In a handling simulation, if the relationships have nonlinear components (usually sinusoidal and/or exponential), you must integrate the ratio functions to produce the correct road wheel angles. Obviously for large steer angles, this can be a major player in correlation test results.