Digital real tooth surface modeling of hypoid gear based on non characteristic block interpolation technology

Hypoid gear is widely used in aviation, automobile and other fields. As an important index to predict its dynamic performance, the meshing performance of tooth surface directly affects the overall performance of transmission system. In the actual use of hypoid gear, due to the influence of gear machining error, installation error and poor working lubrication, the tooth contact surface will produce friction loss. In order to accurately predict the dynamic performance and service life of hypoid gear with wear, the primary problem to be solved is to realize the construction of digital real tooth surface of hypoid gear.

Complex surface reconstruction is one of the most studied key technologies in the construction of digital real tooth surface. Scholars at home and abroad have done a lot of research. Konno et al. Proposed the method of covering G1 continuous Gregory surface on NURBS curve network. Based on the idea of profit and loss correction, Lin Hongwei et al. Proposed an algorithm for iterating non-uniform B-spline curves and surfaces; Sun Dianzhu et al. Proposed an algorithm for constructing G1 continuous quintic triangular B é zier surface from triangular mesh surface; Jia Ming and others proposed two methods of surface local coordinated design based on rectangular topological region to redesign the local rectangular topological clipping region across multiple surfaces.

The research on digital tooth surface construction methods of hypoid gears at home and abroad is mainly divided into two categories:

One is to use the surface interpolation algorithm to construct the interpolation surface. This method has high precision and can reflect the measurement point information of the tooth surface. However, in order to improve the surface smoothness, the screening fairing algorithm needs to be used many times, which makes the calculation process more cumbersome. The typical interpolation method is linear interpolation; The digital interpolation tooth surface construction method of hypoid gear is improved. The linear interpolation method is combined with the area weight interpolation method to predict the tooth surface data points outside the measurement area. The interpolation method has good accuracy for the construction of real tooth surface with limited data points.

The second is to use the fitting curve to approximate the discrete data points with weight. This method does not require all the data points to fall on the construction surface, which is less accurate than the interpolation surface, but the smoothness of the fitting surface is better. Sun Dianzhu, a domestic scholar, put forward the theory and research of parameterized B é zier free-form curve and surface for the tooth surface of involute gear; Fang Zongde and others studied the simulation of the real tooth surface of spiral bevel gear based on NURBS surface × 9-point discrete square matrix and bicubic NURBS surface fitting. However, due to the limited measurement data points of the tooth surface, the application scope of the above method is mainly the smooth tooth surface after grinding. When applied to the tooth surface with irregular conditions such as tooth surface wear, because most of the measurement data points are separated from the structural tooth surface, the structural tooth surface can not reflect the real tooth surface. In the above discrete data preprocessing technology, data region segmentation is the bottleneck problem in the construction of digital real tooth surface.

(1) A non feature based discrete tooth surface data block technology is proposed to judge the wear area of tooth surface, reduce the calculation of tooth surface interpolation algorithm and improve the construction efficiency of digital tooth surface.

(2) The tooth surface interpolation algorithm is improved. While calculating the change of control vertices and weight factor adjustment of the constructed tooth surface, the construction error △ EI compensation is considered to retain the measured tooth surface data as much as possible. At the same time, when the measured data points are limited, the algorithm can predict the tooth surface data in the unmeasured area and improve the accuracy of digital tooth surface construction.

(3) In the aspect of constructing tooth surface fairing, based on the traditional “noise point” algorithm, a “noise point” moving fairing algorithm is proposed. The biggest advantage of this method is that it is combined with the improved tooth surface interpolation algorithm to improve the smoothness of the constructed tooth surface on the premise of retaining the actual tooth surface data of the wear area to the greatest extent.

Based on the original research, aiming at the problem of constructing the digital real tooth surface of hypoid gear with wear, a non feature-based tooth surface discrete data block technology is proposed. Combined with the tooth surface interpolation algorithm, the digital real tooth surface of hypoid gear is constructed based on NURBS surface. At the same time, in order to improve the smoothness of digital tooth surface on the premise of ensuring accuracy, the traditional smoothing algorithm is improved. The feasibility of the proposed method is verified by example analysis and comparison.

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