Gear Ratio Solver
Use Cogchamp's Gear Ratio Solver to find the optimized carrier-based gearset design for a given ratio(s).
Choose a gearset type, select the relevant equation(s), enter desired ratio(s) and tooth count restrictions, and click Solve.
How it Works
Use this solver to get tooth counts on complex geartrains. The multi-equation feature can be useful for gearsets that use clutches to change operating mode, such as a fixed-ring to fixed-carrier planetary system. It can also be used to coordinate multiple speed ratios of different gears, like rotations & orbits in a solar system model.
All variable names must start with 'Z'. Numbers, letters, and underscores may follow. This solver only looks for integer values of variables.
Select equations from the examples shown or type/modify your own equations. Only basic operators are supported.
Variable ranges can be defined with hyphens (ex. 12-50), commas (ex. 10,12,14,15), or both (ex. 17-30, 43-50).
If the number of possible combinations is small enough, this solver performs an exhaustive search (every combination is tried). Otherwise, it searches randomly over the variable space for a global minimum, then "hillclimbs" in that area for a local optima. For large variable spaces, clicking SOLVE multiple times may give more favorable results.
When this solver looks for a solution, it gives each combination of variables a "score" based on the relative error of each equation evaluated at that combination. When multiple equations are used, the total error is the mean sum of squares. If the desired value is 0, absolute error is used.
If there is a tie between 2 combinations, the lowest total tooth count is favored.