# Verification of Involute Harmonic Gear Flexible Wheel Finite Element Model

In order to verify the validity of the solid element finite element model in this paper, the stress results of the finite element model are compared quantitatively with the theoretical solution. Because the toothed ring gear model has the characteristics of variable cross-section and has no theoretical solution, an optical ring finite element model with gear trimmed is established. The maximum radial deformation at the long axis of the flexible wheel u0=m is calculated, and the roller thrust and the circumferential stress of the wave generator are calculated.Comparison of the results of theoretical solutions (2) and (3).

#### 1. Result of aperture finite element model with different radial displacements

The maximum radial deformation u0=m at the long axis of the flexible wheel in this example belongs to large deformation, so that the theoretical stress based on small deformation is smaller than that of the finite element model. Therefore, the maximum radial deformation of the long axis of the flexible wheel is 0.1m, and the deviation of the calculated thrust and circumferential stress of the roller is 0.61% and 0.64% respectively.1.26% shows that when the radial deformation is small enough, the theoretical solution is close enough to the results of the finite element model in this paper, which shows the accuracy and validity of the finite element model in this paper.

#### 2. Thrust and stress of toothed model

The ratio of the roller thrust to the theoretical thrust of Formula (2) is 1.73 for the maximum radial deformation of the flexible long shaft u0=m. The increase of the roller thrust indicates the increase of the flexural rigidity of the teeth to the ring gear. The increase factor of the flexural rigidity caused by the teeth in this example is 1.73. The circumferential stresses at the roller and the short shaft are 109.10 MPa and -115.70, respectively.MPa, the ratio to the theoretical solution is 2.64. The stress increase of the finite element model is the result of the combination of stiffness increase and stress concentration. The stress concentration factor of this example is 1.52 by dividing 2.64 by the bending stiffness increase factor 1.73.

Since the groove is a dangerous section and the ring gear at the roller is heavily loaded, the maximum circumferential stress of the groove at the roller is discussed below.

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