Machinery's Handbook, 31st Edition
2534
Friction Brakes Friction Brakes
Formulas for Band Brakes.— In any band brake, such as shown in Fig. 1, in the tabulation of formulas, where the brake wheel rotates in a clockwise direction, the tension in that part of the band marked x equals P e 1 1 − µθ The tension in that part marked y equals P e e 1 − µθ µθ . P = tangential force in pounds at rim of brake wheel e = base of natural logarithm = 2.71828 μ = coefficient of friction between the brake band and the brake wheel θ = angle of contact of the brake band with the brake wheel expressed in radians . deg deg 180 57296 1 radian radians radian = π = See also Conversion Tables of Angular Measure starting on page 103. For simplicity in the formulas presented, the tensions at x and y (Fig. 1) are denoted by T 1 and T 2 respectively, for clockwise rotation. When the direction of the rotation is re- versed, the tension in x equals T 2 , and the tension in y equals T 1 , which is the reverse of the tension in the clockwise direction. The value of the expression e μθ in these formulas may be most easily found by using a hand-held calculator of the scientific type; that is, one capable of raising 2.71828 to the power μθ . The following example outlines the steps in the calculations. Table of Values of e μθ
Proportion of Contact to Whole Circumference, 2 π θ
Leather Belt on
Wood
Cast Iron
Steel Band on Cast Iron, μ = 0.18
Slightly Greasy; μ = 0.47
Very Greasy; μ = 0.12
Slightly Greasy; μ = 0.28
Damp; μ = 0.38
0.1 0.2 0.3 0.4
1.12 1.25 1.40 1.57 1.62 1.66 1.71 1.76 1.81 1.86 1.97 2.21 2.47 2.77 3.10
1.34 1.81 2.43 3.26 3.51 3.78 4.07 4.38 4.71 5.07 5.88 7.90
1.08 1.16 1.25 1.35 1.38 1.40 1.43 1.46 1.49 1.51 1.57 1.66 1.83 1.97 2.12
1.19 1.42 1.69 2.02 2.11 2.21 2.31 2.41 2.52 2.63 2.81 3.43 4.09 4.87 5.81
1.27 1.61 2.05 2.60 2.76 2.93 3.11 3.30 3.50 3.72 4.19 5.32 6.75 8.57
0.425 0.45 0.475 0.525 0.55 0.5
0.6 0.7 0.8 0.9 1.0
10.60 14.30 19.20
10.90
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