# Analysis of coincidence degree of spiral bevel gear

The coincidence degree represents the average value of the number of wheels participating in meshing at the same time. The greater the coincidence degree, the more tooth surfaces participating in meshing at the same time. The bearing capacity and stability of spiral bevel gear transmission are directly related to the degree of coincidence. Keeping a certain degree of coincidence is a necessary condition for continuous transmission of spiral bevel gears. The theoretical calculation formula of coincidence degree of spiral bevel gear is:

Where, εγ Is the total coincidence degree of spiral bevel gear, εα Indicates the end face coincidence, εβ Is the longitudinal coincidence degree. When calculating the coincidence degree, the formula does not consider the processing parameters of spiral bevel gear and the load during transmission, but only the design parameters of spiral bevel gear, and the calculation is complex. In the actual transmission process of spiral bevel gear, the shape and size of the contact area and its position on the tooth surface are constantly changing. The above formula can only approximately calculate the coincidence degree of spiral bevel gear transmission, and can not obtain the actual coincidence degree under different loads.

In the process of load meshing transmission of spiral bevel gear, the teeth enter meshing and produce normal contact force; After exiting the engagement, the normal contact force disappears. The time from generation to disappearance of normal contact force on a single tooth is the time when the tooth actually participates in meshing. Meshing contact time of single tooth Δ Tdifference in time between two adjacent teeth and the beginning of contact Δ T ‘, as shown in the figure. Therefore, the actual coincidence degree of spiral bevel gear transmission can be expressed as:

According to the change law of contact force extracted from the static analysis under different loading conditions, the single tooth meshing time under each working condition is obtained Δ T meshing time interval with adjacent teeth Δ t’。 According to the method of actual coincidence degree, the actual coincidence degree and the coincidence degree calculated according to the formula are calculated respectively.

It can be seen from the above table that during the meshing transmission of spiral bevel gears, the contact area will undergo elastic deformation with the increase of load, which will affect the actual coincidence degree of spiral bevel gears. When the load increases, the actual coincidence value becomes larger. This is because the deformation will make up for the gap between adjacent spiral bevel gears, resulting in the increase of contact range and the increase of actual coincidence degree of spiral bevel gears. This conclusion is consistent with the conclusion in literature [64]. The coincidence degree calculated by the theoretical formula is a fixed value, which fails to reflect the influence of load conditions on the coincidence degree. Therefore, using the finite element calculation method, the actual coincidence degree of spiral bevel gear can be calculated quickly and accurately by considering the deformation of spiral bevel gear under load, so as to provide a better reference for engineering design.

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