1. Simulation of gear shaping
In order to verify the correctness of non-circular gear profile, matlab programming is used to simulate gear shaper cutter machining. The simulation results are shown in Fig. 1 ~ 2. The simulation results show that:
(1) The calculated profile of non-circular gear can perfectly envelope the machining profile of gear shaper cutter and meet the requirements of accurate design of tooth profile;
(2) There was no undercutting phenomenon;
(3) The interference between the gear shaper cutter and the tooth tip of non-circular gear needs to trim part of the tooth tip.
2. Building 3D model
The tooth profile coordinates (XCK, yck) of non-circular gear generated by MATLAB are imported into UGNX software for modeling, and the tooth top is trimmed with the equidistant line of pitch curve of non-circular gear (offset is 0.8mn), so that the interference of tooth top in Fig.1-2 can be avoided, and all tooth heights can be kept consistent. Fig. 3 shows the 3D model of non-circular gear, in which (a) ～ (c) respectively show that the driving non-circular gear rotates 0 °、 one hundred and twenty °、 two hundred and forty ° The meshing state of the gear when it is engaged; It can be seen from the partial enlarged drawing that the working tooth surfaces of the two gears are in good condition, and there is backlash on the non working tooth surfaces. The 3D model is projected into 2D engineering drawing, and the minimum backlash is 0.08 mm, which meets the requirements of accurate design.
3. Strength check by finite element method
The driving non-circular gear rotates 6.074 rad counterclockwise around O1, and the driven non-circular gear rotates 6.183 rad clockwise around O2. At this time, the transmission ratio is the maximum value u, and the tooth force is the maximum. Therefore, it is necessary to check the tooth strength under this working condition. In order to save computing resources, the 3D model of non-circular gear is simplified, and only the 3D model near the meshing gear is retained; The gear width is reduced to 1% of B.
The simplified 3D model was imported into ANSYS Workbench for static analysis, and the young’s modulus of 40Cr was defined as 2 × 1011pa, Poisson’s ratio is 0.3; Because the two gears remain stationary, the tooth contact type is defined as bonded; Because the tooth width of the simplified 3D model is reduced to 1% of B, the torque applied to the 3D model of the driving noncircular gear needs to be reduced to 1% of T; The cylindrical support is defined for the rotation centers of the driving and driven noncircular gears. Since the driving noncircular gear needs to apply torque, the tangent direction of the driving noncircular gear is changed to free, and the other directions are fixed.
As shown in Figure 4, the finite element model adopts hexahedral mesh. In order to improve the accuracy of contact stress calculation, the mesh size of meshing area is about 0.1 mm, and the other mesh size is about 0.5 mm. As shown in Figure 5, the maximum stress is 76.827 MPa, which appears in the contact part of the tooth surface. It is less than the yield limit of 40Cr of 500 MPa and the allowable contact stress of 669.3 MPa, which meets the strength design requirements.
4. Trial production of non-circular gear
Novick ar2300 precision CNC WEDM is selected as WEDM machine tool, and the machining accuracy is less than or equal to 0.005 mm, 1.0 ≤ RA ≤ 1.6. 65 Mn hot rolled steel plate with thickness of 5 mm was selected. As shown in Figure 5, the rotation center hole of the non-circular gear is installed on the fixed cylindrical shaft, the gap between the shaft and the hole is fit, and the center distance between the two shafts is 160 mm. The driving noncircular gear can drive the driven noncircular gear normally, and the rotation is flexible without jamming, which indicates that the design of tooth profile, backlash, tooth height and tooth root transition curve of noncircular gear is reasonable.