Band brake consists of a band in the form of belt, rope, or steel band (Figure 16.9). When force is applied at the free end of lever, the brand is pressed against the external surface of the drum.
Figure 16.9 Band Brake
Braking torque,
T = (T1 − T2) × r
But
where T1 is tension in tight side and T2 is tension in slack side.
The effectiveness of braking force varies according to the direction of rotation of drum, ratio of length a and b, and the direction of force applied at the end of lever.
Case I: When a > b and F acts in downward direction and drum rotates in counterclockwise direction.
Case II: When a < b and F acts in downward direction and drum rotates in clockwise direction. In this case, the tensions in tight side and slack side are reversed, i.e., T2 > T1 and a > b. Brake will be effective only when T1a > T2b.
When 
F becomes zero or negative, i.e., the brake becomes self-locking.
Case III: When a < b and F acts in upward direction and drum rotates in counterclockwise direction.
As T2 < T1 and b > a, brake will be effective only when T2 × b > T1 × a or 
.
If 
, brake becomes self-locking since force required is zero or negative.
Case IV: When a < b and F acts in upward direction and drum rotates in clockwise direction. T2 > T1 and b > a. When a = b, the band cannot be tightened and thus, brake cannot be applied.
Example 16.9: In a differential band brake as shown in Figure 16.9 (a), following data are given: Drum diameter = 1,000 mm, a = 50 mm, b = 250 mm, θ = 270°, m = 0.3, r = d/2 = 500 mm, F = 500 N. Calculate braking torque.
Solution:
Braking torque, TB = (T2 − T1) × 500 = (2522.73 − 613.65) × 500 = 954.54 Nm
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