Tolerance analysis of gear trains by static analogy

Assembly-level geometric errors such as backlash, center distance errors and shaft misalignments may adversely affect the operation of a gear train. The tolerance analysis method proposed in the paper estimates these errors from tolerance specifications on gears and mounting parts (shafts, bearings, housings). The problem is solved by analogy with an equivalent problem of force analysis: on a properly defined structure, external forces correspond to the assembly-level error, and calculated internal forces and support reactions provide the sensitivities of part tolerances on the total error. Previously developed for generic assemblies, the approach proves especially simple for gear systems compared to existing methods of tolerance analysis, as it relies upon structural analysis procedures that are customary in mechanical design. The method based on static analogy includes a two-level classification of geometric errors, which helps overcome the complexity of tolerance analysis problems for gearings. Two examples of gear trains of different types and configurations are presented to demonstrate the calculation procedure and verify its correctness by comparison with geometric considerations.