# Finite element analysis of noncircular gear

Due to the removal of part of the mass, especially the thinning of the tooth thickness, the load-bearing capacity of the optimized non-circular gear will inevitably be affected. In order to check the strength and stiffness of the gear, it is necessary to carry out the finite element analysis.

## 1. Pretreatment

Import the 3D model into ANSYS Workbench. Because the transmission is arranged in three branches, in order to improve the calculation efficiency and convergence, the driven gear, bearing and sleeve in contact with the driving gear are set as rigid bodies when analyzing the driving gear. The gear material is set to 38CrMoAl, the contact mode between gears is set to friction contact, the friction coefficient is 0.1, the interface treatment is adjusted to adjust to touch, and other contact modes are set to binding contact.

## 2. Grid generation

Due to the complex structure of the model, which is not conducive to the generation of hexahedral mesh, tetrahedral element is used, and the contact surface and slot are locally refined, so the mesh quality is better.

## 3. Restraint and load application

In order to ensure the reliability of the simulation results, the load is applied based on the worst working condition of each gear.

1) According to the reciprocal curve of transmission ratio in Figure 1, the rotation speed of each gear at its angular displacement is calculated. The coordinate system is established with the rotation axis of each gear as the Z axis, and the rotation speed of corresponding gear is applied with each coordinate system as the reference.

2) When analyzing the driving gear, the spline part is set as a cylindrical support to release the tangential degree of freedom; The rigid driven gear meshed with the driving gear uses the far end displacement constraint to limit its axial and radial motion; The bearing, sleeve and other parts in contact with the driving wheel are constrained by the far end displacement according to their motion state. The analysis of driven gear is the same.

3) Based on each coordinate system, the corresponding load torque is applied to the driving and driven gears.

## 4. Analysis of finite element simulation results

1) Analysis of simulation results of driving gear. The simulation results of the equivalent stress of each driving gear are shown in Fig. 2. Gear 3 and gear 12-1 produce large stress at the meshing position and groove edge of the driven gear, and the equivalent stress at the end point of the tooth surface contact line is the largest, with the values of 336.3 MPa and 442.4 MPa respectively; Gear 12-2 due to 7 × The axial thrust of 104 n acts on the end face of the spline through the sleeve, so the maximum stress is at the contact between the sleeve and the spline, and produces a certain degree of stress concentration, the maximum value is 855.7 MPa, which is close to the yield limit of the material. The fatigue limit of 38CrMoAl after heat treatment can be increased by 25% ～ 35%, and the surface hardness can reach HRC70, and the deformation during heat treatment is very small, which can meet the strength requirements.

The simulation results of the driving gear form variables are shown in Figure 3. The maximum deformation of the gear is located on the gear teeth on the slotted side, and the maximum form variables are not more than 0.019 mm, which is less than the side clearance reserved in the design. The heat treatment can effectively improve the hardness of the gear, so it meets the stiffness requirements.

The simulation results of contact stress of each driving gear are shown in Fig. 4. The contact between the teeth is linear contact, and the larger contact stress is distributed at the position where the driving gear has not reduced the tooth thickness and the driven gear has reduced the tooth thickness. The maximum value is at the end of the contact line, and the values are 351.1 MPa, 1025.1 MPa and 915.5 MPa respectively, meeting the allowable contact stress requirements.

2) The simulation results of driven gear are analyzed. The simulation results of the equivalent stress of each driven gear are shown in Fig. 5. Because there are 2 parts in gear 4, the simulation results of the equivalent stress of each driven gear are as follows × The axial thrust of 104n acts on the end face of the spline through the sleeve, so the maximum stress is at the contact between the sleeve and the spline, and the maximum stress is 290.1 MPa; The simulation results of gear 11-1 and gear 11-2 are similar to those of driving gear 3 and gear 12-1. The maximum stress values are 885.9 MPa and 893.9 MPa respectively. The strength and other requirements can be met after heat treatment by nitriding and tempering.

The simulation results of the shape variables of the driven gears are shown in Fig. 6. The maximum deformation of each gear is located on the tooth after the tooth thickness is reduced. The maximum shape variables are not more than 0.04 mm, which is less than the side clearance reserved in the design. The heat treatment can effectively improve the hardness of the gear, so it meets the stiffness requirements.

The simulation results of contact stress of driven gears are shown in Fig. 7. The contact between teeth is line contact, and the maximum value is at the end of the contact line. The values are 49.01 MPa, 1 046.4 MPa and 1 054.8 MPa respectively, meeting the allowable contact stress requirements.

Finite element simulation results show that the equivalent stress and contact stress of the gear teeth are large, and there is stress concentration in some positions. Therefore, it is necessary to improve the fatigue limit and surface hardness of the gear by heat treatment, So as to prolong the service life.

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