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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)

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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)

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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)

Listing 10-2

= F2 (m 1)

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Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright 2004 The McGraw-Hill Companies. All rights reserved. Any use is subject to the Terms of Use as given at the website.

The fatigue life estimates in Table 6.7 are guideline values which should be used only where specific data are unavailable. The values are conservative, and most springs designed using them will exceed the anticipated lives.

6.4.4 Dynamic Loading under Impact When a spring is loaded or unloaded, a surge wave is established which transmits torsional stress from the point of load along the spring s length to the point of restraint. The surge wave will travel at a velocity approximately one-tenth that of a normal, torsional-stress wave. The velocity of the torsional-stress wave VT, in meters per second (m/s) [inches per second (in/s)], is given by VT = 10.1 Gg m/s or VT = Gg in/s (6.7)

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The velocity of the surge wave Vs varies with material and design but is usually in the range of 50 to 500 m/s. The surge wave limits the rate at which a spring can absorb or release energy by limiting the impact velocity V. Impact velocity is defined as the spring velocity parallel to the spring axis and is a function of stress and material as shown: V 10.1S g 2 G m/s or V S g 2 G in/s (6.8)

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