Establishment of mathematical model of spiral bevel gear

Spiral bevel gear modeling is determined by spiral bevel gear calculation software based on the basic parameters of the tooth and the selection of the corresponding cutting process and machine tool parameters. Taking the spiral bevel gear pair of the main reducer as an example, the digital modeling process of the spiral bevel gear is described in detail. Carry out basic calculation according to the relevant dimensions of the design drawing, and generate the dimension card and the basic dimensions of the drawing according to the given design parameters. The spiral bevel gear in this example is in the high-speed and heavy-duty working environment of the helicopter, and the requirements of the tooth surface are extremely strict. The tooth surface is carburized to make the tooth surface reach high hardness, and the core is not carburized to maintain sufficient strength and toughness. In order to improve the bearing capacity of spiral bevel gear, the tooth surface of spiral bevel gear adopts modified teeth and middle convex teeth. Continuously adjust the modification parameters until qualified static meshing marks are obtained through simulation. The simulation diagram of static meshing marks is shown in Figure 1.

Flatten the big gear tooth surface, establish the relative coordinate system between the small gear tooth surface and the big gear tooth surface, and simulate the meshing relationship between the two tooth surfaces. By inputting part power and load, the working state of spiral bevel gear can be simulated, and the dynamic meshing mark can be simulated. By observing the shape, position, size and other parameters of the dynamic meshing impression, properly adjust the state of the static meshing impression until the dynamic meshing impression meets the design requirements. After the dynamic meshing marks are adjusted to be qualified, the contact stress analysis of the tooth surface under the dynamic meshing state can be observed under the rated power and displayed in different color graphics. The contact stress analysis diagram of the dynamic meshing marks is shown in Figure 2.

The tooth surface is measured by spiral bevel gear measuring machine. Firstly, the theoretical Chua’s coordinate point data and electronic standard spiral bevel gear are read and stored in the measuring machine. Then measure the 45 coordinate points of the part topography and compare them with the theoretical data to control the error. General Aviation Precision spiral bevel gears require 5 in the tooth surface morphology diagram × 9. The difference between the normal coordinates of 45 points in total and the theoretical Chua’s coordinate points is within 0.003mm, which basically has no effect on the meshing marks.

The large wheel and small wheel are processed respectively according to the adjusted shape diagram, and then the assembly test run is carried out. The dynamic meshing marks after the actual test run are shown in Figure 3.

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