Meshing stiffness calculation of gear tooth root dynamic strain

The relationship between the tooth root bending strain and the gear meshing stiffness is deduced. Therefore, the meshing stiffness of the gear can be obtained by calculating the bending strain of the tooth root measured by experiment. According to the above theoretical basis, we can get the meshing stiffness of the gear based on the measured dynamic bending strain of the tooth root.

Using the formula, the change trend of root bending stress of healthy gear and gear with moderate pitting corrosion can be calculated respectively in the whole meshing process, as shown in Fig. 1. It can be clearly seen in the figure that pitting on the tooth surface of the gear will reduce the bending stress of the gear. The area of the obvious reduction of the bending stress is from the middle of the double tooth meshing area to the end of the single tooth meshing area, which is the same as the area 1 in the experiment. The above analysis shows that the gear teeth with pitting corrosion fault will provide smaller torque for gear meshing, which also confirms the rationality of the formula.

In the experiment, the FBG sensor is installed at the base circle of the end face of the gear when measuring the bending strain of the tooth root with the light grating sensor. Through the ANSYS Workbench software simulation, along the tooth width direction, the strain of the middle part of the gear tooth is larger than that of the gear tooth end face. Therefore, it is necessary to reflect the actual strain by scaling and translation experiments.

The meshing stiffness of healthy gear and pitting gear can be obtained by using the measured tooth root bending strain and the relationship between the tooth root bending strain and gear meshing stiffness, as shown in Fig. 4-12. The reduction of the meshing stiffness is mainly from the middle part of the double tooth meshing area to the end of the single tooth meshing area, and the second double tooth meshing area, which is basically consistent with the experimental strain reduction area. This shows that the gear pitting failure will reduce the meshing stiffness of the gear.

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