Radial and tangential error analysis of double-flank gear measurement

To clarify or interpret the measurement results of double-flank gear measurement (DFGM), the mathematical model of radial and tangential error analysis of double-flank gear measurement is established. Using differential method, the mathematical model of surface-to-surface contact stage is concerned, and also the tip-to-surface interference stage is involved. The error sources including the base radius error (or profile slope deviation) and the tooth space angle error (or single pitch deviation) of the gear to be measured are concerned. A case study of the gear parameter with the gear contact ratio 1.77 is discussed to explain the tooth contact process, in which the critical contact points are listed for determining the rotation angle. The radial and tangential composite deviations are simulated under different sign combination or different value of the error sources to cover as many results as possible. The simulation results are compared with the measurement results on a gear measuring device (GMD) using double flank rack probe (DFRP), whereby the simulation parameters are determined through the gear profile slope deviation and the single pitch deviation of the gear measured on a Gear Measuring Center Klingelnberg P26. The curves of the simulation results and the measurement results on GMD are consistent to each other. For gear grade 6 according to ISO 1328-1:2013, the allowable value of the total profile deviation is 11.5 μm. The simulation results are compared with the measurement results on a gear measuring device (GMD) based on double flank rack probe (DFRP). The difference between the peak to peak value of the simulation results and the mean line of the measurement results within the evaluation range is 1 μm in radial direction and 1.3 μm in tangential direction, which means the simulation results has better consistency with the measurement results. The radial and tangential error analysis of DFGM can not only be used in simulation of the results, but also in interpreting the DFGM measurement results, which is helpful for gear measurement and quality control.