Calculating bellcrank motion ratios

[BoulderG]

Help, please! I'm trying to redo the motion ratios on my front shocks. They use pushrods and bellcranks. I've been prototyping these in 1/8 flat steel. I've now done five that won't work and it's getting to be a pain to cut, drill, file, install, measure, curse, measure again, curse more, and toss the prototypes.

Can anyone help me with the measurements and formula to compute bellcrank motion ratio? Good sources for this info?

I want a 2.1 motion ratio - one inch of wheel travel is 48/100, or 31/64 inch of shock travel.

Most recently, Prototype3 made a 1.90 motion ratio and Prototype4 made 2.35. I carefully and accurately split the difference in the holes for Prototype5, hoping for the average of 2.12 (close enough). However, it produced a 2.40 motion ratio!

The picture shows the whole left-side bellcrank. Pushrod attaches to the black steel piece, which is what I'm redrilling.

Or, am I doing this the hard way? Is it smarter to make a set that's close and tune with springs? (I'd like to avoid having to buy many sets of springs.)
Thank you for your time and help.

[Brian]

Unless there is magic at 2:1, I would tune with springs. Or make a "prototype" with a slot. Or look for a flaw in my measurement technique...

Brian

[S Lathrop]

You will need to use a 3D drawing package. You have more than one problem you are trying to solve. Not only is the motion ratio critical but how that ratio changes with wheel position is equally important.

I use AutoCad and Mitchel software. I find that it is easier to draw the complete suspension system and use the drawing to input the data points into Mitchel software. There are a lot of other suspension geometry packages, but I have been doing this since Mitchel started.

You will find that using a 3D drawing package will increase the accuracy and ease of locating your data point.

SolidWorks will allow you to study the bell crank motion as well but it is more work.

[Jim Nash]

Is there a reason you are mocking it up in steel? Make your test parts out of wood or something easier to work with. Remove the shocks and set the chassis on blocks at the ride height you want. Then take your measurements between the shock mounting holes.

Jim

[problemchild]

For those of us without fancy computer software or the time to learn how to use it, simple DIY bellcrank templates can be used in simmulation. BoulderG, I think that you are just spending too much time on your test bellcranks. If you get rid of the spring and use some type of rod, you can make a bellcrank out of scrap aluminum (or steel). No need for bearings, bushings, filing or ?. Just drill holes, use the bolt shanks, jack the wheel up and down and measure changes. Drill more holes in the same plate and try again.
I spent several hours doing this exact task on my rear suspension yesterday. I tried 4 different versions and zeroed in on my final selection. My tips ... use 1/4" holes and reducer bushings in pieces being moved for more similiar options in the same test piece .... and using blocks of specific size to move the wheel in specific increments.

Cheers!

[Jonathan Hirst]

Are you assuming that the ratio of hole position wrt to the center of bellcrank rotation is a linear relationship with the wheel motion ratio? (ie splitting the two hole positions will halve the ratio).

As Steve said, it is a 3D problem and you are trying to solve it with a 2D trial and error.

Also, the cumulative error in measurement using the trial and error method, depending on how you are taking your measurements, makes "shooting the gap" decisions hard because your gap may be smaller than the sum error in your measurements.

If you can reassemble your suspension in the previous holes, measure them and get the exact same readings, then you haven't reached the limit of your measurement system.

In that case, based on what your initial measurements returned, and the time investment you have made into the project so far, just keep going using your current plate. Go ahead and slot between the holes and take some equally distanced interim position measurements. If your old data is correct, you should see a max value at or above 2.40. If the data doesn't seem to follow a defined line, you've exceed your measurement set up abilities. If you are happy with the results, the final hole position can be found from your data. Make your final plate design based on that position. Check it once its installed.

So in summary, if your measurement system is giving you good data, keep doing what you are doing and get more interim data. If the points are close enough together, eventually the relationship becomes linear and you can shoot the gap to get the ratio you desire. Right now, you are saying your gap is too large to be considered linear.

This is the the limit of what you can do using trial and error without making a new slot in a different geometry. The suggestions above are good for speeding that process up.

Good Luck. You will learn a great deal doing it this way, however slowly and painfully it may seem right now.


Jonathan

[DaveW]

A few tips that should help.

1. Try to get a constant motion ratio over the planned range of travel. This leads to more predictable handling than either a decreasing or increasing ratio. This is usually easily achieved by making sure the damper shaft is perpendicular to its bellcrank radius AT THE SAME TIME THAT the pushrod is perpendicular to its bellcrank radius.
(NOTE: a side benefit is that radius changes meant to change the motion ratio have more predictable results)
2. Measure the damper and hub motions for each 0.5" motion of the hub with respect to the chassis. Use a range of hub travel of at least 1" in both directions from the in-use position.

[Stan Clayton]

Geremy, if I recall my high school trig correctly and understand your question correctly, the direct answer is that the motion ratio is determined by the ratio between the input arm (A) and the output arm (B), times the sine of the angle between the two arms.

(A/B)* sin(a) = MR.

If the angle is 90 degrees, sine is 1.0 and the ratio is just A/B.

Hope that helps.

Stan

[Jonathan Hirst]

If the angle is 90 degrees, sine is 1.0 and the ratio is just A/B.
Stan

Stan - That is correct the ratio for the bell crank - but not necessarily the ratio of wheel movement to damper compression/rebound which is the motion ratio he is after. The closest you can get to the motion ratio of the wheel/damper movement linearly equal the rocker ratio is in the situation Dave W talks about. Namely, over small distance when damper / pushrod is acting perpendicular to the radial distance to he centre of the bellcrank.

FWIW - You mentioned you didn't want to buy multiple springs. You don't, you borrow them! Then when finalize what spring rate works best for you, invest in a good quality brand. Just don't shortchange yourself by assuming your "calculated" spring rate to be your ultimate best choice once your car is on the track.

Jonathan

[DaveW]

Stan - That is correct the ratio for the bell crank - but not necessarily the ratio of wheel movement to damper compression/rebound which is the motion ratio he is after. The closest you can get to the motion ratio of the wheel/damper movement linearly equal the rocker ratio is in the situation Dave W talks about. Namely, over small distance when damper / pushrod is acting perpendicular to the radial distance to he centre of the bellcrank.

Jonathan

Even in the case displayed in bold type, which gives a relatively easy way to attain a mostly constant motion ratio, the motion ratio is NOT the ratio of the two radii. It depends on the angle of the pushrod to the A-arm it is attached to, plus other things in the suspension geometry. In my case (Citation 95SF), the bellcrank radius ratio is somewhere near the damper radius being twice the pushrod radius in order to attain approximately a 1:1 motion ratio from the hub to the damper. I.e., the pushrod is moving ~1/2 as much as either the hub or the damper.

[Jonathan Hirst]

[Brian]

Hence why I tend to throw springs at it till it sticks, then just drive it...

I do know what my motion ratio's are, and what the various rates are, I just don't think they actually mean all that much in the end, compared to seeing what it actually does...

Our Jon, on the other hand, does less setup than I do... "Car... Track... Fast... Fun... Again..." And the ever-popular "where do you lift at 8, Jon" - "you mean you actually lift at 8?"

Brian

[BoulderG]

Many thanks to all for sharing your collective wisdom. It's much appreciated. I got a lot of very good suggestions and will forge on ahead.

I hope others will also find this discussion helpful. Thank you.

[R. Pare]

Since no one else has mentioned it, you really don't want that low a motion ratio. At .5, your shocks have little hope of properly controlling the spring energy. More modern thinking will use 1:1 ratios, and often quite a bit higher. If you physical constraints will allow it, shoot for something closer to the 1:1 mark.

[DaveW]

An important thing to beware of, is that when you increase the motion ratio, and the damper movement increases, the effect of damper and other system frictions will increase. So, when increasing the motion ratio, take care to get as low a friction as possible in all components so as to not lose grip. The most critical friction points, IMO, will be the following, in decreasing order of importance:
1. Bellcrank: main pivot and pushrod/damper pivots
2. Damper: seal and piston - reduce side load (hydraulic spring perches?) and run lower damper pressure if possible
3. All other rod ends in the suspension (see posts on reducing rod end stiction)
4. Swaybar and links

As a reference, on my Citation 95SFZ, we run 0.82 (damper moves ~ 0.82 as much as the hub) front, and 0.98 rear, as close as can be measured. The front was not brought all the way to 1.0 so we would have a good compromise between effective damper travel and friction. I would suggest a front motion ratio around 0.7 to 0.85 in your case.

[Stan Clayton]

Stan - That is correct the ratio for the bell crank - but not necessarily the ratio of wheel movement to damper compression/rebound which is the motion ratio he is after.

Ah...thanks Jonathan, I believe you are correct. What you refer to is often called the 'installation ratio', as illustrated below. Imagine yourself squatted down in front of the right front suspension. A represents the right-front a-arm's inboard attachment point; B represents the point along the a-arm where the pushrod attaches, and C the attachment to the upright. There is a thin vertical line and a slightly heavier inclined line representing the pushrod. The angle between these two line is represented by "a".

The upper end of the pushrod moves upward and inboard in response to a bump at A according to the ratio of lengths AB and AC times the square of cosine of angle "a". If A and B are co-located, then their ratio is 1:1. Just measure the two lengths on your car and divide the longer length into the shorter, like this example: 12"/15"=0.8.

To find the cosine of angle "a", measure the angle of the pushrod from vertical with a protractor, Smartlevel, etc., then use a trig table or your computer's calculator to find the cosine of that angle. Let's say you measure the angle of the pushrod at 30 degrees from vertical. Open your computer's calulator, click on the View button, and then click on Scientific. The display should now show you more math functions if you normally have the View set to Standard. Enter 30 and click the "cos" button on the left side, then click the "x^2" button to its lower right. The number in the window (if you are doing the 30 degree example) should read: 0.75. To follow our example, now click the "times" button at right, then 0.8, and the window should display: 0.6. This is the installation ratio. If the tire moves up one inch, the upper end of the pushrod will move 0.6" in this example.

You can combine the installation ratio with the bellcrank ratio to get an accurate overall motion ratio of your car' suspention where the bellcrank line A is close to 90 degrees to the path of the pushrod. (Where it is not, you can add a third factor to compensate for the angle offset, but I'll leave that as an exercise for the curious.)

Presuming in Geremy's photo above that A and B are 90 degrees apart, and that length B is 1.5 times length A, for every distance the A moves along its circle, B will move 1.5 times as far. To calculate how much point B on the bellcrank should move in response to the tire lifting, simply multiply the installation ratio by the bellcrank ratio. Using the values from our example above: 0.6 x 1.5 = 0.9, or a 0.9:1 ratio.

Since the outer suspension geometry is usually fairly difficult to change, the easiest way to change the total ratio may be to change the ratio of the bellcrank lengths. Again using our example above, if Geremy really wants a ratio of 2:1, we can work backwards to find the right bellcrank ratio to produce that motion ratio.

2 / 0.6 = 3.33. If you drill a new hole A such that the length of B is 3.33 times as long as the length A, you should see a 2:1 motion ratio.

Have fun!

Edit: corrected units.

[Stan Clayton]

Dave and Richard bring up good points about motion ratios. Too low or too high bring their own issues, so don't go too extreme. I have measured our Ralt Atlantic's stock motion ratios in the .75 to .80 range, though I know that there were numerous aftermarket kits to raise the ratios to as high as 1.2:1. I've also measured Swift 008 and 014 Atlantics at .98 to 1.03 stock. Hope that helps.

[DaveW]

So, when increasing the motion ratio, take care to get as low a friction as possible in all components so as to not lose grip. The most critical friction points, IMO, will be the following, in decreasing order of importance:
1. Bellcrank: main pivot and pushrod/damper pivots
2. Damper: seal and piston - reduce side load (hydraulic spring perches?) and run lower damper pressure if possible
3. All other rod ends in the suspension (see posts on reducing rod end stiction)
4. Swaybar and links

In case you want to measure how much friction your suspension has, here's a pretty easy method:

1. Install all the suspension on the car as normal. Use the lowest rate springs you have available so the deflections you'll take later are as large as possible. Make sure all the fasteners are tightened to their normal torque so having the fasteners loose doesn't screw up the values. Set the car, with wheels and tires at normal pressure, on the floor.

2. Pull up on the front of the chassis as far as you can, and SLOWLY let it back down until it stops moving. Measure the front spring lengths and record. Push down on the front of the chassis as far as you can, and slowly let it back up until it stops. Measure the front spring lengths and record. Subtract the 2nd measurement from the 1st. Average the left and right readings and then divide that average by 2. Multiply the result by the spring rate.

3. Repeat for the rear.

This is how much friction (at the damper) the suspension has. Multiply this value by the motion ratio (less than 1.0 if the damper moves less than the hub) to get the friction value at the wheel. The front is more critical than the rear, because the front tires have to respond much more rapidly than the rear to steering inputs. The rear has a longer time to respond, and is usually more heavily loaded, so a little friction in the rear is not as bad as the same amount in the front.

I've seen more than 50 lb of friction at the wheels in this test - that is absolutely horrible, and grip will suffer. A reasonable target is less than 10 lb. The friction value I've been able to obtain for the front suspension on my FC is ~1-3 lb at the wheel, which is quite good. When you do the scale check for cross weight, etc., you will see the results repeat within your friction value, even without the "settling" procedure mentioned below.

You always see crews jumping on the car to "settle" the suspension for weight measurements. What they are doing is trying to overcome excessive friction. If the friction is low enough to be acceptable, very little of this "settling" will be necessary.