“…Then, the points on the front face of the hob where the normal line passes through the axis of the grinding wheel are the points on the contact line. The above is the basic principle of calculating the grinding wheel rotation surface and the contact line of the hob front cutter face and then calculating the grinding wheel curved shapes [8][9] [10].…”
Section: Calculation Theory Of Grinding Wheel Curved Shapesmentioning
When calculating the grinding wheel curved shapes, the hob front angle of hob is usually zero by default. In the actual production and processing, there are many hobs whose hob front angle is not zero. In this paper, when calculating the grinding wheel curved shapes, the parameter hob front angle is added to analyze its influence on the grinding wheel curved shapes according to the grinding wheel curved shapes calculated by different hob front angles.
“…Then, the points on the front face of the hob where the normal line passes through the axis of the grinding wheel are the points on the contact line. The above is the basic principle of calculating the grinding wheel rotation surface and the contact line of the hob front cutter face and then calculating the grinding wheel curved shapes [8][9] [10].…”
Section: Calculation Theory Of Grinding Wheel Curved Shapesmentioning
When calculating the grinding wheel curved shapes, the hob front angle of hob is usually zero by default. In the actual production and processing, there are many hobs whose hob front angle is not zero. In this paper, when calculating the grinding wheel curved shapes, the parameter hob front angle is added to analyze its influence on the grinding wheel curved shapes according to the grinding wheel curved shapes calculated by different hob front angles.
“…31 Here, the variable transmission ratio pinion designed using the gear element method is manufactured via CNC end milling on universal multi-axis milling machines, and the prototype is shown in Figure 19. Hobbing 32,33 and grinding 34,35 are high-efficiency gear production process, while the corresponding CNC machines and tools are complex and specialized. Thus, further investigation is required.Figure 19.Prototype of the variable transmission ratio pinion.…”
Section: Manufacture Of Variable Transmission Ratio Pinion Prototypementioning
Variable transmission ratio gears have shown considerable potential as key components of variable speed transmission steering boxes that balance steering portability and sensitivity. The objective of this study is to develop a novel method for designing variable transmission ratio tooth surfaces to circumvent the shortcomings of the meshing theory method. The involute rack of the variable transmission ratio pinion-and-rack pair is considered as a set of countless and infinitely close transverse sections, each of which is referred to as a gear element. Assuming evenly distributed circles in the physical domain of the variable transmission ratio tooth surfaces of the pinion, the problem of generating a tooth surface point is transformed into solving the specific geometric feature intersection point of each circle and corresponding gear element during variable transmission ratio meshing. Thereafter, a mathematical model and algorithm are developed to generate tooth surface points in an approximately even pattern. The normal deviations of the gear-element–generated tooth surface points and the corresponding tooth surface points calculated using meshing theory show that the proposed design method has a sufficiently high accuracy. Finite element models are employed analyzing the contact pattern, contact stress, bending stress, and transmission ratio error. The results indicate that the layout of approximately even tooth surface points using the gear element method is beneficial for improving the fitting precision of tooth surfaces and reducing the contact stress and transmission ratio error. Further, the same derived law of the flank and fillet tooth surfaces is conducive to the continuity of the tooth surfaces, which contributes toward reducing the bending stress. Finally, a prototype is manufactured via CNC end milling. The major contributions lie in a robust and efficient modeling method for variable transmission ratio tooth surfaces, which combined forms a solid foundation for their application.
“…He studied the singularity of the tooth surface contact line and the worm thread surface and proposed a multistep grinding method for the complete grinding of the whole working part. Shi et al [9,10] and Zhou et al [11] analyzed the geometry of a worm surface and described it as the sweep of the lateral contour section. The contour was designated as the contour of the dressing wheel to accurately manufacture the spherical worm and the face gear.…”
This paper presents a method of calculating and correcting of grinding face gears on an internal gear grinding machine. The generating principle of face gears is studied, and the feasibility of grinding motion on an internal gear grinding machine is analyzed. Then, the motions that need to be followed for grinding are analyzed based on the internal gear machine tool structure. Four main error sources causing tooth surface deviation in the grinding movements are proposed. The mathematical modeling of the grinding of face gears containing proposed error sources on an internal gear grinding machine is accurately established. The influence of the error sources on the topological deviations of the tooth surface is explored. A sensitivity matrix is established for the influence of various error factors on the tooth surface deviations. The correction values of each error factor are obtained in the case of existing tooth surface deviations. A theoretical correction result with zero-free tooth surface deviation is obtained via a least-square calculation. Finally, a virtual machining experiment on an internal gear grinding machine is conducted, which proves the accuracy of the proposed method for characterizing grinding and realizing corrections.
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