Page 153 - Analysis and Design of Machine Elements

Belt Drives
where h is thebeltheightand D is the sheave diameter. Since the diameter of driving 131
sheave is normally smaller than that of driven sheave, the bending stress in the driv-
ing sheave is greater than that in the driven sheave . Too small a dimension of
b1 b2
a sheave will drastically increase bending stress and reduce belt life. To avoid excessive
bending stress, the minimum sheave diameters for driving sheaves for standard V-belts
of types Y, Z, A, B, C, D and E are recommended as 20, 50, 75, 125, 200, 355 and 500 mm,
respectively [4].
To sum up, the contributors to the maximum stress in a belt can be expressed as:
max
= + + (6.19)
max 1 b1 c
The maximum stress occurs where the belt enters the small sheave and the bending
stress is the major part. A belt experiences a rather complex cycle of stress variation as
thebeltrepeatedlypassesaroundsheaves.

6.2.5 Potential Failure Modes
During operation, a belt is subjected to fluctuating stresses at any cross section, varying
from + to + + , as the belt goes through a full revolution. Fatigue, therefore,
c
c
1
2
b1
becomesapotentialfailuremodeinbeltdrives.
Belt drives are applied where rotational speeds are relatively high, usually at the first
stage of speed reduction from an electric motor. If a belt works at a low speed or the belt
tension becomes too large, slippage may occur easily, which may cause severe wear on
the belt. Both adhesive or abrasive wear may be potential failure modes in belt drives.
Besides, if belt drives operate at an elevated temperature, in a corrosive environment
or in adverse loading conditions, degradation in belt material properties, that is, cord
breakage and fabric cover cracking, are also potential failure modes [2].

6.3 Power Transmission Capacities

6.3.1 The Maximum Effective Tension

To prevent slippage, there should be a limitation on the maximum effective tension F .
ec
From Eqs. (6.6) and (6.10), the maximum effective tension at critical slippage state can
be expressed as
( 1 )
F = 1 − F 1 (6.20)
ec
e f
To prevent fatigue failure and to ensure a belt has sufficient fatigue strength and ser-
vice life, the maximum stress max shouldnot exceed theallowablestressofbelt[ ],
that is,
max = + + ≤ [ ]
1
c
b1
Therefore
≤ [ ]− − c
1
b1