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Mechanics · Transmission and rotation

Pulley ratio, output speed and belt velocity

Use pulley pitch diameters to relate rotational speeds and estimate belt velocity.

Created v1.0

By Thibaut Grzelak, Mechanical Analysis Engineer

Transmission and rotation
01Calculation inputsD₁n₁ = D₂n₂
D₁D₂n₁n₂
Input identificationPitch diameters D₁ and D₂ relate both pulley speeds. An open belt gives the same rotation direction.
%
02

Results

Transmission ratio
—

Ratio D₂/D₁.

Output speed
—

Driven pulley speed.

Output torque
—

Theoretical torque after efficiency.

Belt velocity
—

Tangential speed at the pitch diameter.

Relation and numerical substitutionD₁n₁ = D₂n₂ ; v = πD₁n₁/60

—

Two-pulley transmission. Pitch diameters used. No belt slip. Simplified overall efficiency.

01Formulas and symbols

Formulas used

iD₂ / D₁Transmission ratio
n₂n₁D₁ / D₂Output speed
vπD₁n₁ / 60Belt velocity
T₂T₁iηOutput torque
02Assumptions and limits

Scope of validity

  • Two-pulley transmission.
  • Pitch diameters used.
  • No belt slip.
  • Simplified overall efficiency.
03Validation example

Reference numerical case

  1. D₁ = 100 mm, D₂ = 250 mm, n₁ = 1,500 rpm, T₁ = 10 N·m, η = 95%.
  2. i = 2.5; n₂ = 600 rpm; T₂ = 23.75 N·m; v = 7.854 m/s.
04References

Technical references

  1. Pulley law D₁n₁ = D₂n₂.
  2. Tangential speed v = rω.

Calculation path and sources

Torque, power, speed and ratio belong to the same transmission chain.

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External technical sources

Power transmission

Relations between torque, power, speed and ratio

A ratio trades speed for torque without creating power. Efficiency reduces available torque.

Torque from P and n

With P in kW and n in rpm, the result is in N·m.

T = 9 549,3 · P / n

Ratio

Gears: Z₂/Z₁. Pulleys: D₂/D₁ without slip.

n₂ = n₁ / i

Output torque

Apply ratio and then efficiency.

T₂ = T₁ · i · η