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Gear Geometry and Applied Theory Episode 2 Part 2

Tham khảo tài liệu 'gear geometry and applied theory episode 2 part 2', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | 11.3 Conditions of Nonundercutting 313 and Nc N2 is given d Nc sin c A cos 2 N2 cos A sin 2 -ra2 sd Nc r a . 11.3.11 - r Nc sin c A sin 2 N2Cos c A cos 2 ra2cos I I. Nc 2-a2 The first guess for the solution of system 11.3.11 is based on considerations similar to those previously discussed Step 1 Transforming equation system 11.3.11 we obtain r ỵ r cos2 c A 2 rac . 11.3.12 r2 n2 1 rac Nc 1J We take for the first guess Nc 0.8N2 and obtain c A from Eq. 11.3.12 . Parameter 2 is determined from Eq. 11.3.10 . Step 2 Knowing Nc c and 2 for the first guess and using the subroutine for the solutions of equation system 11.3.11 we can determine the exact solution for No. of Gear Teeth Figure 11.3.5 Design chart for pressure angle ac 30 . 314 Internal Involute Gears Table 11.3.1 Maximal number of shaper teeth Pressure angle Generation method Gear teeth Shaper teeth Axial 25 N2 31 Nc 0.82N2 3.20 ac 20 Axial 32 N2 200 Nc 1.004N2 9.162 Two-parameter 36 N2 200 Nc N2 17.6 Axial 17 N 2 31 Nc 0.97N 2 5.40 ac 25 Axial 32 N2 200 Nc N2 6.00 Two-parameter 23 N2 200 Nc N2 11.86 ac 30 Axial 15 N2 200 Nc N2 4.42 Two-parameter 17 N2 200 Nc N 2 8.78 Nc. Computations based on the above algorithms allow us to develop charts for determination of the maximal number of shaper teeth Nc as a function of N2 and the pressure angle ac. An example of such a chart developed for axial generation and two-parameter generation is shown in Fig. 11.3.5. Table 11.3.1 developed by Litvin et al. 1994 allows us to determine the maximal number of shaper teeth for various pressure angles. 11.4 INTERFERENCE BY ASSEMBLY We consider that the internal gear with the tooth number N2 was generated by the shaper with tooth number Nc and the condition of nonundercutting was observed. Then we consider that the internal gear is assembled with the pinion with the tooth number N1 Nc. The question is what is the limiting tooth number N1 that allows us to avoid interference by assembly. Henceforth we consider two possible cases of