tailieunhanh - Gear Geometry and Applied Theory Episode 1 Part 9

Tham khảo tài liệu 'gear geometry and applied theory episode 1 part 9', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | Direct Relations Between Principal Curvatures of Mating Surfaces 223 equation is the differentiated equation of meshing in which we take i 1 and represent it as follows n 1 . v 12 - v i P12 x n n. 1 1 x v2 i - 1 2 x víPìl n x vtr x vtr - m 21n k2 x r 1 - R 0. We transform Eq. using the following procedure Step 1 Representing vectors of the scalar product nỉ1 v 12 in coordinate system Sa e f eh we obtain 12 T 1 v 12 n 1 vf nf r . . 12 _vh J 1 _nh Step 2 Using Eqs. we obtain 12 T 1 v 12 n 1 vf K1 vf r . . 12 _vh J . . 1 _vh _ Step 3 Equations and yield 12 T 2 12 T 12 v 12 nr1 vf . . 12 _vh J K1 vf . . 2 Lvh J - vf 12 Lvh J K1 vf . 12 Lvh _ 12 vf . . 12 vh T K1 2 vf . 2 vh Kf v 12 2 Kh 12 2. Step 4 Our next step is directed at the transformation of the triple product vr1 w 12 x n . Representing vectors of the triple product in coordinate system Sa e f eh we obtain - v x n n x w 12 e f T 1 vf n x w 12 eh _ . . 1 Lvh _ Step 5 Equations and yield - v x n n x w 12 e f T 2 vf n x w 12 eh . . 2 Lvh _ - n x v 12 . 224 Mating Surfaces Curvature Relations Contact Ellipse Step 6 Using Eqs. and we represent Eq. as follows 12HT vf . 12 vh K1 n X w 12 e f n X w 12 eh . 2 I vf 2 vh -n 1 1 X v 2 4 - 1 2 X v 1 il n L X vtr X vtr Ị 1 2 m21 n X k2 r 1 R n X u v 12 Kf vf12 2 Kh v 12 2. Finally using Eq. and the first two equations of equation system we obtain the following system of three linear equations in the unknowns vf and v f 11V f ti 2vh2 ti 3 i 1 2 3 . Here t11 b11 t12 t21 b12 t22 b22 t13 t31 b15 t23 t32 b25 t _ n 17 1 X v 2h _ 2 X v 1 l -33 n X Vtr V X vtr J 1 2 m 21 n X k2 r 1 R n X u v 12 Kf vf12 2 Kh v 12 2. For further derivations it is important to recognize that the rank of the system matrix and the augment matrix for equation system is 1. This follows from the fact that the contacting surfaces are in line contact at .

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