# Contact analysis of spiral bevel gear

In order to analyze the lubrication characteristics of spiral bevel gears, it is necessary to analyze the contact of spiral bevel gears, and give the geometric parameters, speed parameters and load of meshing points The contact analysis of spiral bevel gears requires tedious mathematical derivation, and the detailed derivation process is shown in Fig. 1 shows the contact relationship of spiral bevel gear. In order to describe the contact geometry and contact parameters of spiral bevel gear, the coordinate system SR {or, Jr fixed with the large wheel and small wheel is established × PR, Jr, PR} and SL {ol, JL × PL, JL, PL}, PR and PL are the unit vectors of the axis of the big wheel and the small wheel, and the direction is from the big end of the gear to the small end Since the spiral bevel gears rotate around their respective axes PR and PL, their relative sliding speed vs and coiling speed UE vectors can be expressed as:

Where: ω L is the angular velocity of the small wheel, N and N represent the number of small wheel and large gear teeth, RBL and RBR represent the position vector of the conjugate contact point in their respective coordinate system respectively.

The contact ellipse parameters of spiral bevel gear are shown in Figure 2 The parameters of contact ellipse and curvature are closely related to the processing adjustment parameters, tool parameters and hobbing motion parameters of spiral bevel gears.

Where, Δγ Is the included angle.

According to the point contact principle of the surface, the extreme direction of the relative normal curvature is the main direction of the contact ellipse (the direction of the short half axis and the long half axis of the ellipse). By calculating the extreme value of the relative normal curvature, the main normal curvature Kar, KBr of the large wheel surface along the long and short half axes of the contact ellipse and the principal normal curvature Kal, KHL of the small wheel along the long and short half axes of the contact ellipse, as well as the included angle between the long half axis and the long half axis of the ellipse can be obtained τ r. The calculation formula is as follows:

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