barcode generator vb.net code d1 2 = 180 + 2 = 180 + 2 arcsin (i 1) 2e in Software

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d1 2 = 180 + 2 = 180 + 2 arcsin (i 1) 2e
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BELT DRIVES 14.6
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POWER TRANSMISSION
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FIGURE 14.1 Two-pulley drive.
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Datum length of flexible connector: l = 2e cos + d1 1 2 + d2 360 360
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d1 = 2e cos + [180 2 + i(180 + 2 )] 360 Approximate equation: l 2e + 1.57(d1 + d2) + = 2e + 1.57d1(i + 1) + (d2 d1)2 4e d2 1 (i 1)2 4e
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(14.4)
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(14.5)
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The minimum diameter allowable for the flexible connector selected is often substituted for the unknown parameter d1 (driving-pulley diameter) required for the design. Multiple-Pulley Drives. For the multiple-pulley drive (one driving pulley, two or more driven pulleys), the geometry is dependent on the arrangement of the pulleys (Fig. 14.2). These drives have the following characteristics: Speed ratios: i12 = Included angles: sin 12 = sin 13 = d1 (i12 1) 2e12 d1 (i13 1) 2e13 (14.6) (14.7) n1 d2 = n2 d1 i13 = n1 d3 = n3 d1 i1m = n1 dm = nm d1
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BELT DRIVES 14.7
BELT DRIVES
FIGURE 14.2 Multiple-pulley drives.
sin 1m =
d1 (i1m 1) 2e1m dk (ikm 1) 2ekm
(14.8)
sin km = Angles of wrap:
(14.9)
j = 180 j,j 1 j,j + 1 j where
j = index of pulley j = angle between center distances
(14.10)
1 d1 2 d2 + e23 cos 23 + + e12 cos 12 + 360 360 m dm k dk + + ekm cos km + + e1m cos 1m 360 360
(14.11)
14.1.3 Forces in Moving Belt Friction is employed in transmitting the peripheral forces between the belt and the pulley. The relation of the friction coefficient , the arc of contact , and the belt forces is expressed by Eytelwein s equation. For the extreme case, i.e., slippage along the entire arc of contact, this equation is F 1 = exp F2 180 (14.12)
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BELT DRIVES 14.8
POWER TRANSMISSION
For normal operation of the drive without belt slip, the peripheral force is transmitted only along the active arc of contact w < (according to Grashof), resulting in a force ratio between the belt sides of w F 1 = exp F2 180 (14.13)
The transmission of the peripheral force between the belt and the pulley then occurs only within the active arc of contact w with belt creep at the driven pulley and the corresponding contraction slip at the driving pulley. During operation, the belt moves slip-free along the inactive arc of contact, then with creep along the active arc of contact. If the inactive arc of contact equals zero, the belt slips and may run off the pulley. Along the inactive arc of contact, the angular velocity in the neutral plane equals that of the pulley. Along the active arc of contact, the velocity is higher in the tight side of the belt owing to higher tension in that side than in the slack side. Since this velocity difference has to be offset, slip results. This slip leads to a speed difference between the engagement point and the delivery point on each pulley, which amounts up to 2 percent depending on the belt material (modulus of elasticity), and load: = n v1 v2 (l2 + l) l2 1 2 = = = l2 + l E E v1 (14.14)
For practical design purposes, the calculations for a belt drive are usually based on the entire arc of contact of the smaller pulley (full load), since the active arc of contact is not known, and the belt slips at the smaller pulley first. F1 = m = exp F2 180 (14.15)
Centrifugal forces acting along the arcs of contact reduce the surface pressure there. As these forces are supported by the free belt sides, they act uniformly along the entire belt: Ff = v2A = qv2 (14.16)
With increasing belt velocity v, constant center distance e, and constant torques, the forces F1 and F2 acting along the belt sides as well as the peripheral force (usable force) Fu remain constant, whereas the surface pressure and the usable forces F 1 and F2 in the belt sides are reduced. Usable forces in belt sides: F 1 = F1 Ff = mF 2 F 1 F 2 = F2 Ff = m Peripheral force: Fu = F 1 F 2 = F1 F2 = F 1 1 1 m (14.18) (14.17)
= F2 (m 1)
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