Quaife's analysis of [MENTION=21305]jvtec95[/MENTION]'s stock rack indicated our rack is a variable gain / ratio. This was surprising as the analysis done by the previous effort to build a quicker rack said it was a linear rack. But Quaife said it was quicker in the center than at the ends, and the new rack would be linear.
The fact that it is variable changes the thinking around how a new gain changes the effort, angles, and the ratio. I did all the original calculations based on the linear pole-2-flag analysis, so I needed to do them again for the variable situation.
The first step was to understand exactly at given angles, how much the rack moves linearly. Quaife didn't / couldn't tell me what the gain was in the center or at the ends. So I decided to measure on my own.
Measurement
I printed out a degree wheel and laid it over the pinion. I made a sharpie mark, then rotated the pinion, making sure to locate the sharpie mark in the same place on each notch. I spent a lot of time trying to make these measurements repeatable, and measured each notch several times, especially between 0 and 360.
Here's my last pass at measurement. 60.25mm is how much the rack sticks out of the housing on each side at center. Then I'd spin X degrees, and measure again with the caliper.
0: 60.2mm
30: 57mm
60: 53.66mm
90: 50.3mm
180: 40.14mm
210: 36.95mm
240: 33.85mm
270: 30.82mm
360: 22.1mm
450: 13.45mm
480: 10.6mm
585: 0mm
I spent most of my time measuring 0 to 360 as it is the area we want to improve the most, and I was trying to figure out exactly where the ratio started changing.
It looks like the ratio is fixed at about 40mm/rev for the first 180 degrees from center. After 180 degrees, it starts dropping, ending with a gain of around 35mm/rev at the end.
It looks like a linearish drop in gain from 180 to 360, then linearish again from 360 to the end.
After some tinkering, measuring, and some working out gain (not so staightfowrard at the end as it changes) I ended up with this table:
1. deg: 0, travel: 0, gain: 40
2. deg: 180, travel: 20, gain: 40
3. deg: 360, travel: 38, gain: 36
4. deg: 585, travel: 60.25, gain: 35
Analysis
I wrote a
new script to handle the variable ratio and the table from above to work out new angles and change in effort. Some notes:
* I asked Quaife to quote the rack for a 48.1mm gain, a 25% increase in quickness. However, measured gain in the center is 40mm/ref, but the last calculations were done at 38.5mm, so 48.1mm is less aggressive than originally thought in the center: 20.2%.
* The pole2flag thread indicated there was like 98mm of rack travel. But there is really 120.5mm of travel. I measured this, Quaife confirmed it, and even the manual states this 120mm figure.
* Because the rack is slower toward the end, a fixed rack with a more aggressive gain, will make quite a big change in effort toward the ends (full lock).
* Our manual states a variable ratio (18.2 - 20.8). Using 18.2 as the center and 20.8 as the end in the calculations as original ratio makes the new ratio _the same_ at the center and end in the new calculations. This feels like a nice check on the measurement work.
My questions for you:
*
Which of these options looks interesting to you? Why?
*
Note the change in effort toward the end of travel (360 & 540 degrees): the change in effort is very large. How do you feel about this?
The original proposed gain: 48.1mm
$ node nsx/steering-ratio/gen-changes-variable.js 48.1
Ratio: center 15.1:1 - end 15.1:1 (note: the same center & end)
LTL: 2.51 (current 3.25)
Angles:
15 -> 12.5 20.2% increase in effort
30 -> 24.9 20.2%
45 -> 37.4 20.2%
60 -> 49.9 20.2%
90 -> 74.8 20.2%
120 -> 99.8 20.2%
180 -> 149.7 20.2%
225 -> 183.4 23.3%
270 -> 217 26.6%
360 -> 284.4 33.6%
540 -> 417.6 36.6%
Going a little more aggressive
$ node nsx/steering-ratio/gen-changes-variable.js 49**
Ratio: center 14.9:1 - end 14.9:1
LTL: 2.46 (current 3.25)
Angles:
15 -> 12.2 22.5% increase in effort
30 -> 24.5 22.5%
45 -> 36.7 22.5%
60 -> 49 22.5%
90 -> 73.5 22.5%
120 -> 98 22.5%
180 -> 146.9 22.5%
225 -> 180 25.6%
270 -> 213.1 28.9%
360 -> 279.2 36.1%
540 -> 410 39.2%
Going a little more aggressive
$ node nsx/steering-ratio/gen-changes-variable.js 50
Ratio: center 14.6:1 - end 14.6:1
LTL: 2.41 (current 3.25)
Angles:
15 -> 12 25% increase in effort
30 -> 24 25%
45 -> 36 25%
60 -> 48 25%
90 -> 72 25%
120 -> 96 25%
180 -> 144 25%
225 -> 176.4 28.2%
270 -> 208.8 31.6%
360 -> 273.6 38.9%
540 -> 401.8 42%
I'm thinking of sticking with the 48.1mm TBH. Between 48.1mm and 50mm, 50mm gain gives only a couple degrees of reduced steering wheel angle between 0 and 120 of original angle, but is more effort at the end.
48.1mm/rev
15 -> 12.5 20.2%
45 -> 37.4 20.2%
120 -> 99.8 20.2%
50mm/rev
15 -> 12 25%
45 -> 36 25%
120 -> 96 25% only ~4.8 fewer degrees
What do you think?
