Handbook of Mechanical Engineering Calculations ar Episode 2 Part 4 pot

24.1

SECTION 24

MECHANICAL AND ELECTRICAL

BRAKES

Brake Selection for a Known Load 24.1

Mechanical Brake Surface Area and

Cooling Time 24.3

Band Brake Heat Generation,

Temperature Rise, and Required

Area 24.6

Designing a Brake and Its Associated

Mechanisms 24.8

Internal Shoe Brake Forces and Torque

Capacity 24.15

Analyzing Failsafe Brakes for

Machinery 24.17

BRAKE SELECTION FOR A KNOWN LOAD

Choose a suitable brake to stop a 50-hp (37.3-kW) motor automatically when power

is cut off. The motor must be brought to rest within 40 s after power is shut off.

The load inertia, including the brake rotating member, will be about 200 lb
ft2

(82.7 N
m2 ); the shaft being braked turns at 1800 r/min. How many revolutions

will the shaft turn before stopping? How much heat must the brake dissipate? The

brake operates once per minute.

Calculation Procedure:

1. Choose the type of brake to use

Table 1 shows that a shoe-type electric brake is probably the best choice for stop￾ping a load when the braking force must be applied automatically. The only other

possible choice—the eddy-current brake—is generally used for larger loads than

this brake will handle.

2. Compute the average brake torque required to stop the load

Use the relation Ta
Wk 2

n/ (308t), where Ta
average torque required to stop the

load, lb
ft; Wk 2
load inertia, including brake rotating member, lb
ft2

, n
shaft

speed prior to braking, r/min; t
required or desired stopping time, s. For this

brake, Ta
(200)(1800)/ [308(40)]
29.2 lb
ft, or 351 lb
in (39.7 N
m).

3. Apply a service factor to the average torque

A service factor varying from 1.0 to 4.0 is usually applied to the average torque

to ensure that the brake is of sufficient size for the load. Applying a service factor

of 1.5 for this brake yields the required capacity
1.5(351)
526 in
lb (59.4

N
m).

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Source: HANDBOOK OF MECHANICAL ENGINEERING CALCULATIONS

24.2 DESIGN ENGINEERING

TABLE 1 Mechanical and Electrical Brake Characteristics

4. Choose the brake size

Use an engineering data sheet from the selected manufacturer to choose the brake

size. Thus, one manufacturer’s data show that a 16-in (40.6-cm) diameter brake

will adequately handle the load.

5. Compute the revolutions prior to stopping

Use the relation Rs
tn/ 120, where R
number of revolutions prior to stopping;

other symbols as before. Thus, Rs
(40)(1800)/ 120
600 r.

6. Compute the heat the brake must dissipate

Use the relation H
1.7FWk 2

(n/ 100)2

, where H
heat generated at friction sur￾faces, ft
lb/min; F
number of duty cycles per minute; other symbols as before.

Thus, H
1.7(1)(200)(1800/ 100)2
110,200 ft
lb/min (2490.2 N
m/ s).

7. Determine whether the brake temperature will rise

From the manufacturer’s data sheet, find the heat dissipation capacity of the brake

while operating and while at rest. For a 16-in (40.6-cm) shoe-type brake, one man￾ufacturer gives an operating heat dissipation Ho
150,000 ft
lb/min (3389 5 N

m/ s) and an at-rest heat dissipation of Hv
35,000 ft
lb/min (790.9 N
m/ s).

Apply the cycle time for the event; i.e., the brake operates for 400 s, or 40/ 60

of the time, and is at rest for 20 s, or 20/ 60 of the time. Hence, the heat dissipation

of the brake is (150,000)(40/ 60) (35,000)(20/ 60)
111,680 ft
lb/min (2523.6

N
m/ s). Since the heat dissipation, 111,680 ft
lb/min (2523.6 N
m/ s), exceeds

the heat generated. 110,200 ft
lb/min (2490.2 N
m/ s), the temperature of the

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MECHANICAL AND ELECTRICAL BRAKES