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Gear Geometry and Applied Theory Episode 3 Part 1

Tham khảo tài liệu 'gear geometry and applied theory episode 3 part 1', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | 19.7 Geometry and Generation of K Worms 583 pi Figure 19.7.2 Coordinate systems applied for generation of K worms. Si is represented as the family of lines of contact of surfaces sc and Si by the following equations n uc 0C Ỷ M1oMocrcu 0c 19.7.1 Nc 0c vCc1 uc 0c f Uc 0c 0. 19.7.2 Equation 19.7.1 represents the family of tool surfaces uc 0c are the Gaussian coordinates of the tool surface and Ỷ is the angle of rotation in the screw motion. Equation 19.7.2 is the equation of meshing. Vectors Nc and vcc1 are represented in Sc and indicate the normal to sc and the relative sliding velocity respectively. It is proven below see Eq. 19.7.8 that Eq. 19.7.2 does not contain parameter Ỷ. Equations 19.7.1 and 19.7.2 considered simultaneously represent the surface of the worm in terms of three related parameters uc 0c Ỷ . For further derivations we will consider that the surface side I of a right-hand worm is generated. The cone surface is represented by the equations Fig. 19.7.3 rc uc cos ac cos 0c ic sin0c jc uc sinac a kc. 19.7.3 584 Worm-Gear Drives with Cylindrical Worms Figure 19.7.3 Generating cone surface. Here uc determines the location of a current point on the cone generatrix a determines the location of the cone apex. The unit normal to the cone surface is determined as _ Nc n Nc Nc X ll c duc dOc 19.7.4 which yields nc - sin ac cos Oc - sin ac sin Oc cos ac T. 19.7.5 The relative velocity is represented as the velocity in screw motion Fig. 19.7.4 vCc 1 -Wc X Ic - Rc X W - p Wc 19.7.6 where Rc Ec ic is the position vector of point O1 of the line of action of W. Equation 19.7.6 yields - sin Yc Zc cos Yc yc vcc1 ứ - cos Yc Xc Ec - p sin Yc 19.7.7 sin Yc Xc Ec - p cos Yc The equation of meshing of the grinding surface with the worm surface after elimination of -ứ sin Yc cos Oc is represented as nc vcc1 f Uc Oc a sin a - Ec sin a. cot Yc p sin a. tan Oc Ec - p cot Yc cos ac _n 1O78. ---------- Y-------------Uc 0 19.7.8 cos Oc where uc 0. Equation 19.7.8 with the given