Pulleys and Belts

Overview

The math for the pulleys is pulled from my Flat Belt Pulley page and my Coal Breaker page 3 which in turn was compiled from “A Treatise on Belts and Pulleys” by John Howard Cromwell published 1888. Like the title suggests also belt information. The Diameter of a Pulley is dictated in part by the desired end-speed of the shaft it is on (the other part being the driving pulley diameter and speed). The width depends on the belt width – and the belt width is calculated by the HP transmitted, RPM and pulley diameter to get Vm and P which you can then use the ‘Width Table’ on page 3 to find..


Crusher Pulley

  • \textbf{HP=45}
  • \textbf{Pulley Diameter = D}
    • D = 64"
    • D = 33.87\text{ mm - O scale}
  • \textbf{Pulley Circumference = C}
    • C=16.755'
  • \textbf{100 RPM}
  • \textbf{Pulley Circumferential Velocity} v_{m} (Pulley Circumference in Feet x RPM)
    • v_{m}=C_f*RPM
    • v_{m}=1689 \text{ FPM}
  • \textbf{Pulley Power = P}
    • P = 33000H/v_m
    • P = 33000*45/1689
    • P = 879
  • \textbf{Shaft Diameter = d}
    • d = 3"
    • d = 1.6\text{ mm - O scale}
  • \textbf{Belt width = b}
    • b=10"
    • b=5.29"\text{ mm - O scale}
  • \textbf{Face Width = B}
    • B = \frac{5}{4}b
    • B = 12\frac{1}{2}"
    • B=6.61\text{ mm - O scale}
  • \textbf{Rounding of Pulley Face = s}
    • s=\frac{1}{20}*b
    • s=\frac{1}{20}*10
    • s=1.05"
    • s=.56\text{ mm - O scale}
  • \textbf{Rim Edge Thickness = k}
    • k = 0.08 + \frac{B}{100}
    • k = 0.08 + \frac{12.5}{100}
    • k=.205"
    • k=.11 \text{ mm - O scale}
  • BREAK
  • \textbf{Pulley Nave Width = w}
    • w = 0.4 + \frac{d}{6} + \frac{R}{50}
    • w = 0.4 + \frac{3}{6} + \frac{32}{50}
    • w = 1.54"
    • w=.815 \text{ mm - O scale}
  • \textbf{Pulley Nave Length = L}
    • L = 2.5w
    • L = 3.85"
    • L=2.04 \text{ mm - O scale}
  • \textbf{Number of Arms = N}
    • N = \frac{1}{2} (5+\frac{R}{b})
    • N = \frac{1}{2} (5+\frac{32}{10})
    • N = 4.1
    • N=\text{5 - Rounding up}
  • \textbf{Arm Width at Nave = h}
    • h=0.24+\frac{b}{4}+\frac{R}{10*N}
    • h=0.24+\frac{10}{4}+\frac{32}{10*5}
    • h=0.24+2.5+.64
    • h=3.38"
    • h=1.8 \text{ mm - O scale}
  • \textbf{Arm Width at Rim = }h_1
    • h_1=\frac{2}{3}*h
    • h_1=\frac{2}{3}*3.38
    • h_1=2.25"
    • h_1=1.2 \text{ mm - O scale}

Crusher Drive Pulley

  • \textbf{HP=45}
  • \textbf{Pulley Diameter = D}
    • D = 80"
    • D = 42.33\text{ mm - O scale}
  • \textbf{Pulley Circumference = C}
    • C=20.94'
  • \textbf{80.65 RPM}
  • \textbf{Pulley Circumferential Velocity} v_{m} (Pulley Circumference in Feet x RPM)
    • v_{m}=C_f*RPM
    • v_{m}=1689 \text{ FPM}
  • \textbf{Pulley Power = P}
    • P = 33000H/v_m
    • P = 33000*45/1689
    • P = 879
  • \textbf{Shaft Diameter = d}
    • d = 3"
    • d = 1.6\text{ mm - O scale}
  • \textbf{Belt width = b}
    • b=10"
    • b=5.29"\text{ mm - O scale}
  • \textbf{Face Width = B}
    • B = \frac{5}{4}b
    • B = 12\frac{1}{2}"
    • B=6.61\text{ mm - O scale}
  • \textbf{Rounding of Pulley Face = s}
    • s=\frac{1}{20}*b
    • s=\frac{1}{20}*10
    • s=1.05"
    • s=.56\text{ mm - O scale}
  • \textbf{Rim Edge Thickness = k}
    • k = 0.08 + \frac{B}{100}
    • k = 0.08 + \frac{12.5}{100}
    • k=.205"
    • k=.11 \text{ mm - O scale}
  • \textbf{Pulley Nave Width = w}
    • w = 0.4 + \frac{d}{6} + \frac{R}{50}
    • w = 0.4 + \frac{3}{6} + \frac{32}{50}
    • w = 1.7"
    • w=.9 \text{ mm - O scale}
  • \textbf{Pulley Nave Length = L}
    • L = 2.5w
    • L = 4.25"
    • L=2.25 \text{ mm - O scale}
  • \textbf{Number of Arms = N}
    • N = \frac{1}{2} (5+\frac{R}{b})
    • N = \frac{1}{2} (5+\frac{32}{10})
    • N = 4.5
    • N=\text{5 - Rounding up}
  • \textbf{Arm Width at Nave = h}
    • h=0.24+\frac{b}{4}+\frac{R}{10*N}
    • h=0.24+\frac{10}{4}+\frac{40}{10*5}
    • h=0.24+2.5+.8
    • h=3.54"
    • h=1.87 \text{ mm - O scale}
  • \textbf{Arm Width at Rim = }h_1
    • h_1=\frac{2}{3}*h
    • h_1=\frac{2}{3}*3.38
    • h_1=2.36"
    • h_1=1.25 \text{ mm - O scale}
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