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Gearbox Calculator

This Gearbox Calculator can find compatible toothcounts for given transmission ratios.

Gearboxes designed with axially shifted metric (modulus) spur gears must have the same sum of tooth counts for all transmission options on a common shaft. Assume you want to be able to shift between to ratios n1/m1 and n2/m2. Then it is required to find tooth counts such that n1+m1 = n2+m2.

The program provided in this repository can do this for you automatically. A suitable range of tooth count sums is specified, by default ranging from minToothSum=2 to maxToothSum=200. The toothSum is scanned from minToothSum to maxToothSum. For each tooth sum, a set of combinations of tooth counts for all requested transmission ratios is searched for. A given combination is tested to be realizable by scanning the tooth count of the first gear, toothCount1, from minToothSum-1 to the current toothSum. The tooth count of the second gear is computed to yield the current toothSum: toothCount2 = toothSum - toothCount1. If the ratio toothCount1/toothCount2 is compatible with the requested transmission ratio n/m, it is accepted as a valid realization of this transmission ratio. If realizations can be found for the whole set of requested transmission ratios for a given toothSum, this is accepted as a valid solution. This algorithm is the core functionality of this program. It is implemented in Gears.java.

Usage

This program is a commandline utility. The inputs are specified via an input file in JSON format:

{
  "transmissionRatios": [ [2,1],
                          [1,1],
                          [2,5] ],
   "maxToothSum": 100,
   "minToothSum": 20,
   "outputTeethCounts": true
}

The transmissionRatios input parameter defines the list of transmission ratios for which to find tooth count ratios. Each entry is of the form [n, m], e.g., [ [n1, m1], [n2, m2] ] for the example in the description above. This parameter must be specified.

The parameters maxToothSum and minToothSum specify the range of tooth sums to be considered. The default maxToothSum is 200 if it is not specified. The default minToothSum is 2 if it is not specified.

The parameter outputTeethCounts is false by default. It can be set to true in order to have the program output concrete tooth counts if a solution was found.

The program has to be run with the input file as the first parameter:

java -jar gears-1.0.0.jar input.json

A JSON output file will be created, where the input filename /path/to/input.json is used to get the output filename: /path/to/input_out.json.

The output file contents are as follows (for above example):

{
  "solution": [ [2,1],
                [1,1],
                [2,5] ],
  "teethCounts": [ [ [28,14],
                     [21,21],
                     [12,30] ],
                   [ [56,28],
                     [42,42],
                     [24,60] ] ]
}

A unique solution was found. It matches the requested transmissionRatios specified in the input. Concrete realizations are listed, because outputTeethCounts was set to true in the input. Two realizations are found, with teeth sums of 42 and 84.

Download and Maven

The binary can be downloaded directly from this repository: gears-1.0.0.jar

This program is also available on Maven Central for usage in other programs:

<dependency>
  <groupId>de.labathome</groupId>
  <artifactId>gears</artifactId>
  <version>1.0.0</version>
</dependency>