Gear Geometry and Applied Theory Episode 3 Part 1 potx

... φ 1 )N x1 + (−z 1 sin φ 1 + E cot γ cos φ 1 )N y1 −  (x 1 cos φ 1 − y 1 sin φ 1 + E) − p 1 − m 21 cos γ m 21 sin γ  N z1 = 0. (19 .11 .3) Here, m 21 = N 1 /N 2 is the gear ratio; (x 1 , y 1 , z 1 ) ... equations (19 .11 .3) , (19 .11 .4), and (19 .11 .5) yields the relation between the worm surface parameters (u,θ) and the angle of worm rotation, that...

Ngày tải lên: 08/08/2014, 12:21

... of equations ( 21 .3. 13 ) and ( 21 .3. 14 ) or ( 21 .3. 13 ) and ( 21 .3. 16 ) enables us to represent  (a) 2 in two-parameter form as R (a) 2 (θ g ,ψ 2 ) = r (a) 2 (s g (θ g ,ψ 2 ),θ g ,ψ 2 ). ( 21 .3. 17 ) Similar ... coef- ficients b 2 and b 3 of function ( 21. 2 .3) . Here, φ 2 (φ 1 ) =−a 2 φ 2 1 , − π N 1 ≤ φ 1 ≤ π N 1 ( 21. 2.4) |φ 2 (φ 1 )| max = a 2  π...

Ngày tải lên: 08/08/2014, 12:21

... 2: v (1) s = a 33 a 13 + a 23 tan η 1 ( 21. 6 .15 ) v (1) q = a 33 tan η 1 a 13 + a 23 tan η 1 . ( 21. 6 .16 ) Step 3: A = δ a 2 . ( 21. 6 .17 ) Step 4: K  = a 2 13 + a 2 23  v (1) s  2 +  v (1) q  2 − ... applied: tan 2σ (1p) = −2d 13 d 23 d 2 23 − d 2 13 − (k f − k h )d 33 k t − k p = −2d 13 d 23 d 33 sin 2σ (1p) k t + k p = k f +...

Ngày tải lên: 08/08/2014, 12:21

... mechanism m (c) 13 = m (c) 12 · m (c) 23 = ( 1)  N 2 N 1  · ( +1)  N 3 N 2  = ( 1)  N 3 N 1  . ( 23. 2 .11 ) Equations ( 23. 2 .10 ) and ( 23. 2 .11 ) yield ω c ω 1 = N 1 N 1 + N 3 . ( 23. 2 .12 ) The reduction ... S m 1 as follows: n m 1 = L m 1 c L cb L bt 1 n t 1 v (c1) m 1 =  ω (c) m 1 − ω (1) m 1  × r m 1  +  O m 1 A × ω (1)...

Ngày tải lên: 08/08/2014, 12:21

... 1) 2π n  δ (k) 3 < 2π N 3  ( 23. 3.9) δ (k) 3 δ (k) 1 = N 1 N 3 . ( 23. 3 .10 ) (ii) Equations ( 23. 3.8) to ( 23. 3 .10 ) yield the following relation: (k − 1) (N 1 + N 3 ) n = m (k) 1 + m (k) 3 (k = 2, ,n) ( 23. 3 .11 ) (iii) ... addition to Eqs. ( 23. 3 .1) to ( 23. 3 .3) , we use equation N 2 = N 3 − N 1 2 ( 23. 3.4) obtained from Fig. 23. 2.4, and the equ...

Ngày tải lên: 08/08/2014, 12:21

... S 1 (x 1 , y 1 , z 1 ). Then, using the coordinate transformation from S 1 to S  1 (x 1 , y  1 , z  1 ), we will determine the normal N  1 and then obtain a 1 = N  x1 i  1 + N  z1 k  1 . ... (Fig. 25 .1. 1), and y 1 (u c ,θ c ,ψ) + z 1 (u c ,θ c ,ψ) tan λ p = 0. (25 .3. 3) Equations (25 .3. 1) and (25 .3. 3) yield F (u c ,θ c ,ψ) = 0. (25 .3. 4) Th...

Ngày tải lên: 08/08/2014, 12:21

... normal: n x1 =−k 1 (d 1 cos α 1 sin θ 1 + sin α 1 cos θ 1 ) n y1 =−k 1 (−d 1 cos α 1 cos θ 1 + sin α 1 sin θ 1 ) n z1 =−k 1 cos α 1 (27.4.7) P1: GDZ/SPH P2: GDZ References CB672/Litvin CB672/Litvin-v1.cls ... Analysis for Hypoid Gear Drives of Formate and Helixform. Parts 1, 2, and 3. ASME Journal of Mechanical Design, 1 03( 1) , 83 1 13 . Litvin, F....

Ngày tải lên: 08/08/2014, 12:21

... of, 38 , 45, 49, 50, 11 5, 13 7 , 211 , 274, 280, 288, 289, 296, 298, 35 2 noncircular gears, of, 31 8, 32 2 33 4, 33 7, 33 8, 34 1, 34 3 34 6, 34 8, 34 9, 35 5, 35 6, 35 9, 36 0 Circular pitch, 39 0 Clearance, 609 Computer ... 1 03 10 7, 10 9, 11 0, 11 8, 12 6, 12 7 face gears, of, 519 –522, 5 31 , 539 helical gears, of, 39 6, 39 7 internal involute gears, of, 30...

Ngày tải lên: 08/08/2014, 12:21

... N c 2P . (11 .2 .14 ) (ii) It is obvious that E c (φ 2 ) − E (1) c E (2) c − E (1) c = φ 2 2πa . (11 .2 .15 ) (iii) Equations from (11 .2. 13 ) to (11 .2 .15 ) confirm Eq. (11 .2 .12 ). P1: JTH CB672 -11 CB672/Litvin ... − e i ) N i sin 2α c (i = 1, 2). (10 .7 .3) P1: JTH CB672 -11 CB672/Litvin CB672/Litvin-v2.cls February 27, 2004 0:24 11 .3 Conditions of Nonundercutting 31 1 Figur...

Ngày tải lên: 08/08/2014, 12:21

... 0 :36 13 . 8 Root’s Blower 36 9 (v) Equations ( 13 . 7 .1) and ( 13 . 7.2) yield r 2 = r 1  1 + m N 1  . ( 13 . 7 .3) (vi) Taking into account that r 2 r 1 = N 2 N 1 , ( 13 . 7.4) we obtain that N 2 = N 1  1 ... determined in S 1 as X 1 =−r 1 sin φ 1 , Y 1 =−r 1 cos φ 1 . ( 13 . 5 .3) P1: GDZ/SPH P2: GDZ CB672- 13 CB672/Litvin CB672/Litvin-v2.cls Februar...

Ngày tải lên: 08/08/2014, 12:21