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Betatronics® Gear Ratio Measurement System.
PURPOSE:
The purpose of the Betatronics® Gear Ratio Measurement System is to verify that the correct
gear ratio is installed in an axle. This equipment is especially important in 4 wheel drive vehicles,
but it is still important in 2 wheel drive for speedometer accuracy and to meet federal standards. The
Betatronics® gear ratio gage is applicable to automotive, SUV, truck, off-road, construction
and other types of gear sets.
Betatronics® ratio measurement equipment has been used to build many millions of axles and has
prevented many incorrect ratios from getting to the final assembly plant. Incorrect parts at
at final assembly are an obstruction to smooth operation of the line. In many installations our
gear ratio measurement is combined with flange runout, case shim measurement, and barcode. Because the
case shim station function must complete to build an axle this is an ideal location for gear ratio
measurement to inhibit an incorrect ratio.
A TABLE of RATIOS:
Following is a table of typical automotive axle tooth counts and the resultant ratios, RATIO MATRIX.
The bold numbers are some typical automotive ratios. Note: tooth counts are usually odd numbers. Very common
ratios for 4 wheel drive are 3.7273 and 4.1000
PIN TEETH 9 10 11 12 13 14 15 16
RING TEETH
35 3.8889 3.5000 3.1818 2.9167 2.6923 2.5000 2.3333 2.1875
36 4.0000 3.6000 3.2727 3.0000 2.7692 2.5714 2.4000 2.2500
37 4.1111 3.7000 3.3636 3.0833 2.8462 2.6429 2.4667 2.3125
38 4.2222 3.8000 3.4545 3.1667 2.9231 2.7143 2.5333 2.3750
39 4.3333 3.9000 3.5455 3.2500 3.0000 2.7857 2.6000 2.4375
40 4.4444 4.0000 3.6364 3.3333 3.0769 2.8571 2.6667 2.5000
41 4.5556 4.1000 3.7273 3.4167 3.1538 2.9286 2.7333 2.5625
42 4.6667 4.2000 3.8182 3.5000 3.2308 3.0000 2.8000 2.6250
43 4.7778 4.3000 3.9091 3.5833 3.3077 3.0714 2.8667 2.6875
44 4.8889 4.4000 4.0000 3.6667 3.3846 3.1429 2.9333 2.7500
45 5.0000 4.5000 4.0909 3.7500 3.4615 3.2143 3.0000 2.8125
46 5.1111 4.6000 4.1818 3.8333 3.5385 3.2857 3.0667 2.8750
47 5.2222 4.7000 4.2727 3.9167 3.6154 3.3571 3.1333 2.9375
48 5.3333 4.8000 4.3636 4.0000 3.6923 3.4286 3.2000 3.0000
49 5.4444 4.9000 4.4545 4.0833 3.7692 3.5000 3.2667 3.0625
Two Types of Systems:
Direct Method:
The direct method measures the rotation of the pinion relative to the case (ring gear). Our digital
resolution is typically 1 count in 9000 at a ratio of 3 to 1, or 1 in 12000 at 4 to 1.
Thus, on a 3.0714 ratio
quantizing is at .0003 in ratio. Since there is no other typical ratio close to 3.0714
the margin for detection is very good.
The worst typical case is for ratios 3.5385 and 3.5455 where the ratio difference is .0070.
One wants a tolerance band around each ratio and a dead band between these allowed bands.
For example a tolerance of +/-.0015 in ratio provides a dead band of
.0040 between the two accept bands for these two ratios.
There are mechanical coupling problems that add noise to this measurement and result in a
distribution about the mean value. At 3.5455 ratio a typical distribution about mean has
a sigma of about .0005, or about 1/10 of the spacing to the 3.5385 ratio.
Indirect Method:
The indirect method counts teeth and calculates the ratio from the tooth counts. Tooth counting is done
when the differential case is in the carrier with the pinion. The margins are very large relative
to counting a 15 tooth pinion relative to a 16 tooth, or a 46 tooth ring gear relative a 47 tooth.
The system detects degraduation of the tooth count signal at a margin far from the point of count error.
Thus, the likelyhood of a false reading is very small because there is a system error before a
count error.
The goal of automotive manufacturing is zero defects or zero wrong parts. Typical axle plants will
produce a million to many million axles per year. However, some batch runs might be as small a few
axles (less than 10 --- not often because this is very inefficent) or as great as thousands. In some
cases batches may run from 50 to several 100. There is a lot of effort to do sequential build, at least
at the shipping point to final assembly. This tends to mean short batches. So gear ratio along with
other items might change in this said range. Since the goal is zero defects and millions of units are
shipped from a plant per year this means error levels in the range of 1/100,000,000 on any given element are needed.
In actualality zero defects are not achieved, but results are really quite good. There are multiple
checks and feedback within a plant that tolerate error levels far worse than 1/100,000,000 per element
and achieve an overall error level from a plant of maybe 1/10,000. We do not suggest that our gear
ratio measurement has anything close to an error rate of 1/100,000,000, but it is a proven effective tool
to help keep the overall plant error rate down.
Generally gear sets (ring and pinion) in the United States are manufactured by lapping, and this in
turn means that the ring and pinion must be treated as a matched pair. These gears are shipped in baskets
with maybe 60 sets per basket. There is a very low probability of mixed ratios within a basket because of
the manufacturing process. The bigger problem in ratio is if a basket is labeled incorrectly or if the
wrong basket is brought to the assembly area.
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Copyright©
2004, 2005 Gordon A. Roberts All
rights reserved. 050128-1029
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