Tham khảo tài liệu 'gear geometry and applied theory episode 2 part 8', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | Generation of Double-Crowned Pinion by a Worm 493 Pinion axode Worm axode Figure For illustration of axodes of worm pinion and rack-cutter. the rack-cutter corresponds to rotation of the pinion with angular velocity w p . The relation between V1 and p is defined as V1 p rp where rp is the radius of the pinion pitch cylinder. Step 3 An additional motion of surface X-c with velocity vaux along direction t t of skew rack-cutter teeth Fig. is performed and this motion does not affect the generation of surface Xv . Vector equation v2 v1 vaux allows us to obtain velocity v2 of rack-cutter xc in a direction that is perpendicular to the axis of the worm. Then we may represent the generation of worm surface X . by rack-cutter xc considering that the rack-cutter performs translational motion v2 while the worm is rotated with angular velocity W w . The relation between V2 and w is defined as V2 w rw where rw is the radius of the worm pitch cylinder. 494 New Version of Novikov-Wildhaber Helical Gears Figure Contact lines Lcơ and Lcw corresponding to meshing of rack-cutter Ec with pinion and worm surfaces Eơ and Ew respectively. Worm surface sw is generated as the envelope to the family of rack-cutter surfaces Sc. Step 4 The discussion above enables us to verify simultaneous generation of profile-crowned pinion tooth surface Sơ and worm thread surface Sw by rack-cutter surface X-c. Each of the two generated surfaces Sc and sw are in line contact with rack-cutter surface sc. However the contact lines Lcơ and Lcw do not coincide but rather intersect each other as shown in Fig. . Here Lcơ and Lcw represent the lines of contact between sc and sơ and between sc and sw respectively. Lines Lcơ and Lcw are obtained for a chosen value of related parameters of motion between sc sơ and sw. Point N of intersection of lines Lcw and Lcơ Fig. is the common point of tangency of surfaces sc sơ and sw. Profile Crowning of Pinion .
