Page 181 - Analysis and Design of Machine Elements

Chain Drives
Figure 7.8 shows a chain engaging a sprocket before and after wear. From the geomet- 159
rical relationship in the figure,
p +Δp
D +ΔD = ∘
180
sin
z
Incorporating Eq. (7.2), we have
Δp
ΔD = ∘ (7.26)
180
sin
z
When wear happens, pitch increases. If the pitch increment, Δp, that is the amount
of wear, keeps constant, increasing the number of teeth z will consequently increase the
variation of diameter, ΔD. This implies that the chain will ride high to the top of sprocket
teeth or, more likely, even jump off the sprocket. Normally, when wear-induced chain
elongation reaches 3%, the chain should be replaced [3].
When the height of sprocket teeth stays constant, the allowable variation of diame-
ter ΔD is limited. Increasing the number of teeth z will reduce pitch elongation, thus
limiting the allowable amount of wear and eventually reducing the life of the chain.
In order for a chain to operate smoothly at moderate and high speeds, driving sprock-
ets should have more than 17 teeth and driven sprockets should normally have no more
than 120 teeth. It is preferable to have an odd number or, better yet, prime number of
teeth on sprockets and an even number of links in the chain [4]. Such an arrangement
will allow each sprocket tooth to mesh with all links instead of meshing with the same
link continually. Thus, wear is expected to be evenly distributed and chain life is even-
tually prolonged. The recommended numbers of teeth for sprockets are 17, 19, 21, 23,
25, 38, 57, 76, 95 and 114 [2].
The speed ratio of a chain drive is limited to eight, usually within the range of 2–3.5 to
ensure a sufficient contact angle. A large speed ratio reduces the contact angle and the
number of teeth in engagement and, consequently, increases the load carried by each
tooth and wear on the sprocket teeth. The contact angle on a small sprocket should be
∘
no less than 120 .

7.4.4.2 Determine the Required Power Rating of a Single-Strand Chain, P
0
Considering the operating condition, the number of sprocket teeth and the number of
strands, the required power rating of the selected chain P canbemodified by
0
K K z
A
P = P (7.27)
0
K
p
7.4.4.3 Select Types of Chain and Pitch, p
Select the type of chain and pitch p according to the required power rating of a
single-strand chain P and the speed of a small sprocket. Pitch p is the characteristic
0
parameter of a chain drive. It indicates the relative size of a chain and sprockets. The
larger the pitch, the larger the chain size and the higher the load carrying capacity.
However, chordal action and resultant vibration, impact and noise are more severe with
alarge pitch.