Gear Geometry and Applied Theory Episode 1 Part 9 pot

... a 22 : v (1) s a 11 + v (1) q a 12 = a 13 v (1) s a 12 + v (1) q a 22 = a 23 a 11 + a 22 = κ  . (9. 3 .11 ) Step 4: The solution of equation system (9. 3 .11 ) for the unknowns a 11 , a 12 , and a 22 allows ... equations: κ (1)  = κ (2)  − κ  (9. 3 .14 ) tan 2σ (12 ) = 2a 22 g 2 − (a 11 − a 22 ) = 2n 2 − κ  sin 2η 1 g 2 − 2n 1 + κ  cos 2η 1 (9. 3 .15...

Ngày tải lên: 08/08/2014, 12:21

...  1 that is represented in S 1 by the following equations (Fig. 9. 4.3): x 1 = r b1 (sin θ 1 − θ 1 cos θ 1 ), y 1 = r b1 (cos θ 1 + θ 1 sin θ 1 ), z 1 = 0. (9. 4.23) Figure 9. 4.3: Profile  1 of gear ... θ 1 cos(θ 1 − φ 1 ) ] i f +r b1 [ cos(θ 1 − φ 1 ) + θ 1 sin(θ 1 − φ 1 ) ] j f (9. 4.42) where (θ 1 − φ 1 ) is constant [see Eq. (9. 4. 39) ]....

Ngày tải lên: 08/08/2014, 12:21

... µ 0 − s 1 (θ 1 ) y (O 1 ) f =−ρ 1 (θ 1 ) sin µ. (12 .A.25) Here, µ = arctan  ρ 1 (θ 1 ) ρ θ  ,ρ θ = dρ 1 dθ 1 , s 1 (θ 1 ) =  θ 1 0 ρ 1 (θ 1 ) sin µ dθ 1 . P1: GDZ/SPH P2: GDZ CB672 -13 CB672/Litvin ... (12 .A . 19 ) (iii) The displacement of the point of tangency along the gear centrode is determined as s 1 =  θ 1 0 ds 1 (θ 1 ) =  θ 1 0  dx 2...

Ngày tải lên: 08/08/2014, 12:21

... express the gear ratio that is represented by Eqs. ( 19 .2.8), ( 19 .2 .9) , and ( 19 .2 .10 ) in terms of the number of worm threads N 1 and the number of gear teeth N 2 [see Eq. ( 19 .3 .11 )]. 19 .3 DESIGN ... respectively, as r 1 (u 1 (φ 1 ),θ 1 (φ 1 )) (18 .13 .10 ) r 2 (u 2 (φ 1 ),θ 2 (φ 1 )). (18 .13 .11 ) Results of Investigation The results of investigation...

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 ... of nonstandard gears. where m pg is the angular velocity ratio by transformation of motion from the pinion to the gear. Equations (10 .9 .17 ), (10 .9 .18 ), and (10...

Ngày tải lên: 08/08/2014, 12:21

... 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, tha...

Ngày tải lên: 08/08/2014, 12:21

... µ i = r i (φ i ) dr i dφ i . (12 .2.4) Equations (12 .2 .1) , (12 .2.3), and (12 .2.4) yield tan µ 1 =− m 12 (φ 1 ) ± 1 m  12 (φ 1 ) (12 .2.5) tan µ 2 =± m 12 (φ 1 ) ± 1 m  12 (φ 1 ) . (12 .2.6) Here, m  12 = (∂/∂φ 1 )[m 12 (φ 1 )]. Function ... m 12 (φ 1 ) + m  12 (φ 1 ) ≥ 0. (12 .5.3) (ii) For the driven gear we obtain 1 + m 12 (φ 1 ) +...

Ngày tải lên: 08/08/2014, 12:21

... λ b1 sin(θ 1 + µ 1 ) y 1 = r b1 sin(θ 1 + µ 1 ) − u 1 cos λ b1 cos(θ 1 + µ 1 ) z 1 = u 1 sin λ b1 − p 1 θ 1 (14 .3 .11 ) n 1 = [ −sin λ b1 sin(θ 1 + µ 1 ) sin λ b1 cos(θ 1 + µ 1 ) cos λ b1 ] T . (14 .3 .12 ) Angles ... (Fig. 14 .3.2): x 1 = r b1 cos(θ 1 + µ 1 ) + u 1 cos λ b1 sin(θ 1 + µ 1 ) y 1 =−r b1 sin(θ 1 + µ 1 ) + u 1 cos λ b1 cos(θ...

Ngày tải lên: 08/08/2014, 12:21

... impressive. The geometry, design, and manufacture of helical gears was the subject of research presented in the works of Litvin et al. [ 19 95 , 19 99 , 2001a, 2003], Stosic [ 19 98 ], and Feng et al. [ 19 99 ]. The ... (Figs. 14 .3.2 and 14 .3.3) φ, φ 1 , and φ 2 angle of gear rotation (Figs. 14 .4 .1 and 14 .5 .1) η 2 half of the angular tooth thickness on pitch ci...

Ngày tải lên: 08/08/2014, 12:21

... Litvin [ 19 68], Colbourne [ 19 87], Townsend [ 19 91 ] , and Litvin et al. [ 19 99 , 2001a, 2001c, 2001d] and the theory of shaving and honing technological processes are discussed in the works of Townsend [ 19 91 ] ... Korn, 19 68] and is represented by functions {u 1 (φ 1 ),ψ 1 (φ 1 ), u 2 (φ 1 ),ψ 2 (φ 1 ),φ 2 (φ 1 )}∈C 1 (16 .3.3) that allow us to obtain the...

Ngày tải lên: 08/08/2014, 12:21