# Thickness and deformation of straight bevel gear blank

The simulation results show that the deformation of the split gear is related to the thickness. In order to determine the reasonable thickness of the straight bevel gear split billet, the influence of the thickness change of the straight bevel gear split billet on the z-direction deformation of the split gear will be further explored.

Firstly, the number of teeth in the whole circle of the gear is 90, and the number of teeth contained in the straight bevel gear split blank is 6. Gradually increase the thickness of the straight bevel gear blank, so that the thickness of the straight bevel gear blank increases from 1.2 times of the tooth height to 3.0 times of the tooth height. Take the modulus of gears as 20, 25, 30, 36 and 40. For the gears with these modulus, select different straight bevel gear blank thickness for finite element analysis. Due to the limited space, only the displacement nephogram of the split gear with modulus of 20 in Fig. 1 is shown when the straight bevel gear blank thickness is 1.3 times, 1.6 times, 2.0 times and 3.0 times of the tooth height respectively, Then record the maximum negative displacement in Z direction caused by the bending deformation of the split gear after the simulation processing, and the unit of deformation is mm.

F is the maximum deformation of the split gear in the Z direction, and t is the ratio between the blank thickness of the spur bevel gear and its tooth height. The deformation trend of straight bevel gear can be obtained by fitting the deformation modulus of straight bevel gear in the finite element analysis table 2.

As can be seen from Figure 2, the deformation of the split gear of each module increases first and then decreases in the process of the gradual increase of the thickness of the straight bevel gear blank. The variation trend of the deformation of the gears with different modules is basically the same, but when the ratio of the thickness of the straight bevel gear blank to the tooth height is constant, the larger the module of the straight bevel gear blank, the greater the deformation. From the variation trend of the deformation curve corresponding to the split gear of each module, it can be inferred that when the deformation of the split gear reaches the peak, the deformation of the gear decreases rapidly with the increase of the thickness of the straight bevel gear blank, and then the speed of deformation decline begins to slow down with the increase of the thickness of the straight bevel gear blank, and finally tends to slow down.

In order to more clearly judge the change of deformation reduction speed when the thickness of straight bevel gear split blank increases, the derivative of each modulus split gear deformation function is obtained respectively, and the derivative function is drawn into an image, as shown in Fig. 3. It can be seen from the figure that the deformation of the split gear reaches the peak value when the thickness of the blank is about 1.325 times of the tooth height. When the thickness of the straight bevel gear blank is 1.45 times of the tooth height, the deformation decline speed of the split gear begins to slow down. When the thickness of the straight bevel gear blank increases to 1.8 times of the tooth height, the gear deformation decline speed begins to slow down.

To sum up, in order to control the deformation of the split gear, when selecting the thickness of the straight bevel gear blank, the straight bevel gear blank with the thickness of about 1.325 times the tooth height should be avoided; In order to enable the split gear to participate in the meshing work normally, the use of too thin spur bevel gear blank should be avoided; Considering the economic cost, the straight bevel gear should not be too thick, and the thickness of 1.8 times the tooth height can be selected.

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