tailieunhanh - Gear Geometry and Applied Theory Episode 1 Part 10

Tham khảo tài liệu 'gear geometry and applied theory episode 1 part 10', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | Tooth Contact Analysis 253 Figure Applied coordinate systems. The numerical solution of the system of nonlinear equations is based on application of a respective subroutine see for instance More et al. 1980 and Visual Numerics Inc. 1998 . The first guess for the solution can be obtained from the data provided by the local synthesis. We illustrate the discussed method of TCA with the following simple problem of a planar gearing. Problem Consider three coordinate systems S1 S2 and S f that are rigidly connected to driving gear 1 driven gear 2 and the frame f respectively Fig. . Gear 1 is provided with involute profile S1 that is represented in S1 by the following equations Fig. x1 rb1 sin 01 01 cos 01 y1 rb- cos 01 01 sin 01 Z1 0- Figure Profile S1 of gear 1. 254 Computerized Simulation of Meshing and Contact Figure Profile E2 of gear 2. Gear 2 is provided with involute profile s2 that is represented in S2 by the equations Fig. X2 rb2 -sinỚ2 Ớ2 cos Ớ2 y2 rb2 -cos Ớ2 - Ớ2 sinỚ2 Z2 0- Solution The application of the basic principle of tooth contact analysis enables us to determine the conditions of meshing of Si and s2 in coordinate system S f using the following procedure 1 We determine the unit normals ni and n2 to Si and s2 in coordinate systems Si and S2 respectively. The unit normals to Si and s2 must be of the same orientation at the point of tangency of the profiles. 2 Then we represent profiles Si and s2 in coordinate system S f and derive the equations of their tangency. 3 Using the equations of tangency we can obtain three equations of the following structure fi ới - ội Ớ2 Ộ2 0 f2 ới - ệi rbi rb2 E 0 f3 ới Ớ2 rbi rb2 E ới - ội 0. Tooth Contact Analysis 255 4 The analysis of the obtained equations shows that the ratio d01 d02 is constant and is represented as d01 d91 rb2 d02 d 2 rb1 5 We can determine the line of action by the vector function r f1 91 01 and prove that the line

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