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The contact ellipse on the tangential plane of the flank can be first described according to the given normal, the radius of the ellipse, and the long axis. Then the ellipse is projected onto the actual tooth surface, and the projection point projected from the ellipse to the tooth surface The surrounding tooth surface area is the tooth surface instantaneous contact area, or instantaneous contact ellipse. At present, the tooth surface contact ellipse mentioned in the domestic and foreign literatures is a common term for the instantaneous contact area of ​​the tooth surface. It does not indicate that the tooth surface instantaneous contact area is a plane ellipse in the mathematical sense, so the tooth surface cannot be simply touched. The area is described as an ellipse.
The contact ellipse shown in the multi-layered elliptical representation of the contact zone is a complete instantaneous elliptical contact zone on the tooth surface, with each tooth face in the contact zone participating in the contact, but the load on each tooth face is different. When the contact spot on the actual tooth surface is inspected, the color of the contact spot is from heavy to light outward from the center of the ellipse, and the color of the red powder is also from black to red, which reflects the variation of the contact strength. According to the Hertz contact theory, the load of the elliptical contact zone is an ellipsoidal distribution, and the loads on the different elliptical levels from the inside to the outside are also different. To realize the distribution characteristics of the load in the elliptical contact zone, the model of the elliptical contact zone is designed into a multi-layer elliptical structure. The contact area indicated by the four-layer ellipse as shown.
The contact ellipse on the tooth surface is targeted, and the mathematical model describing the multilayer elliptical contact area can be rewritten as xe2ai2 ye2bi2=1, ze=0ai=ia4, bi=ia4i=1, 2, 3, 4 and according to the contact ellipse solution method. In the projection method or the elliptic function method, the tooth surface data of the multilayer ellipse is obtained. The data is the contact ellipse data of a contact moment, and a contact ellipse data class can be constructed according to the characteristics of the data. When the contact ellipse data of all contact points is found, the data link can be used to visualize the contact ellipse on the tooth surface.
Boundary of the elliptical contact area and the boundary of the cut 5 contact area. When the contact and the cutting are in contact with the hypoid gear, since the tooth surface of the gear is bordered, the theoretical contact point or part of the contact area may be outside the boundary. Contact is called boundary contact. Some contact situations are that the contact point is on the tooth surface, but some contact areas are outside the boundary; similarly, some contacts are theoretical contact points outside the boundary, but due to tooth surface contact deformation or other deformation, two teeth In fact, some of the contact areas are actually in actual contact with the actual state.
Conclusion 1) The construction of the hypoid gear contact visualization model has completely changed the method of describing the contact ellipse only by line segments. The contact ellipse and the contact area are also described by three-dimensional graphics. The contact model is intuitive, image, and easy to roll. Detect contact spots for alignment. 2) The establishment of the digital contact model can quantify the contact ellipse and the contact area, set a series of quantitative indicators for the position, size and shape of the contact area, and establish a contact area evaluation index system that affects the gear transmission performance. The hyperbolic gear performance optimization design provides accurate quantitative metrics.