Page 176 - Analysis and Design of Machine Elements

Analysis and Design of Machine Elements
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the number of sprocket teeth is increased. If the number of sprocket teeth is sufficiently
large, that is, more than 21, the chordal action may be hardly noticeable [5]. Therefore, a
large number of sprocket teeth or a chain with a small pitch give a uniform chain speed
and smooth operation.
7.2.3 Force Analysis
7.2.3.1 Tension in Tight Side
In a chain drive, the upper side is in tension, called the tight side, and the lower side is
called the slack side. Power is transmitted by the tight tension side. Figure 7.4 illustrates
a chain drive transmitting power. Initially, the load is applied to a chain roller by the
driving sprocket teeth in contact. From the roller, the load is transmitted, in turn, to a
bushing, pin and a pair of link plates (see Figure 7.2). Along the tight side of chain, the
load is further transmitted to the driven sprocket by successive link plates, pins, bushings
and rollers. The driven sprocket is then forced to rotate under constant tension imparted
to the chain from the driving sprocket [3, 5]. At high speeds, centrifugal force may add
significantly to the chain.
The tight side tension force F , therefore, consists of effective peripheral force F from
1 e
the transmitted power, the tension induced by centrifugal force F and sagging force F
c f
due to the weight of chain, expressed as
F = F + F + F f (7.14)
e
c
1
where the effective peripheral force F is determined by the transmitted power P and
e
the speed of chain v,expressed as
1000P
F = (7.15)
e
v
The tension induced by centrifugal force F is analogous to that of belts as
c
F = qv 2 (7.16)
c
where q is mass of chain per unit length and can be found in design handbooks or man-
ufacturers’ catalogues. Chain drives are thus usually used in a low speed stage in a power
train where the speed is lower and the torque and force larger.
The sagging force F relates to the weight of chain, the centre distance and layout of
f
chain drive. Detailed calculations can be found in reference [9].
7.2.3.2 Tension in Slack Side
The slack side tension force includes only centrifugal force F and sagging force F ,
f
c
expressed as
F = F + F (7.17)
2 c f
7.2.3.3 Dynamic Forces
The periodical variation of both chain speed and angular velocity of driven sprocket,
as well as the impact during meshing between the chain and sprocket, inevitably induce
dynamic forces. The dynamic force caused by periodical variation of chain speed is com-
puted by
F = ma c (7.18)
d