Belt slip and actual output speed

Technical article

Understand Belt slip and actual output speed

This calculator adds a specified total slip to the ideal pulley ratio. It estimates reduced actual output rpm or derives effective overall slip from measured shaft speeds.

What does this quantity describe?

Without slip, n₁d₁ = n₂d₂. A relative speed loss s is applied as 1−s: n₂ = n₁(d₁/d₂)(1−s). s = 0 is ideal motion; s = 0.02 means output speed is two percent below ideal.

Like a tyre on a roller, a friction belt can lag slightly despite continuous contact. If ideal geometry predicts 600 rpm, a two-percent loss delivers only 98 percent, or 588 rpm.

Formula and variables

n₂ = n₁ · d₁/d₂ · (1 − s)

n₂,ideal = n₁·d₁/d₂
n₂ = n₂,ideal·(1−s)
s = 1 − n₂d₂/(n₁d₁)

Symbol / input	Meaning
Actual output speed n₂	Measured or slip-adjusted speed of the driven pulley.
Input speed n₁	Speed of the driving pulley.
Driver pitch diameter d₁	Pitch diameter of the driving pulley.
Driven pitch diameter d₂	Pitch diameter of the driven pulley.
Total slip s	Relative speed loss from the ideal no-slip relation; 0.02 means 2%.

Choose the inputs correctly

n₁ is driver speed and n₂ driven speed. d₁ and d₂ are pitch diameters, not unchecked outside dimensions. Enter s dimensionlessly: 0.02 means 2%. Use simultaneous measurements at stable load.

How to use the calculator

For prediction, solve n₂ and enter geometry, n₁ and a plausible measured or manufacturer slip. For diagnosis, solve s from both measured speeds. An unexpectedly high value calls for checks of tension, load, wear and contamination.

Worked example

n₁ = 1,500 rpm, d₁ = 100 mm and d₂ = 250 mm give 600 rpm ideally. With s = 0.02, n₂ = 600·0.98 = 588 rpm.

Understand the result and units

588 rpm is 12 rpm, or 2%, below ideal geometry. The result does not separate elastic creep from gross sliding.

Speeds convert internally through angular velocity but can be entered in rpm. Diameters may use any correctly selected length units because only their ratio enters.

Elastic creep or gross slip?

Elastic creep occurs as the more highly tensioned belt span stretches and changes strain through pulley contact. Gross slip is macroscopic sliding after traction is insufficient. A speed-derived total cannot separate them; an unusual load-dependent increase needs diagnosis.

Typical applications

Use it for speed reconciliation, troubleshooting, replacement pulley planning and cautious setpoint correction in flat or V-belt drives. Timing belts are positive drives; comparable error there suggests measurement error, tooth jump or incorrect tooth counts.

Assumptions, limits and common mistakes

s is an empirical overall value. The model does not resolve local strain, friction, heat, transient start-up slip or changing loads. Use manufacturer methods for rating.

Common mistake: Enter 2% as 0.02, not 2. Do not swap driver and driven labels, mix outside with pitch diameters, or compare speeds measured at different load states.

Frequently asked questions

How is belt slip calculated?

Use s = 1 − n₂d₂/(n₁d₁) from both shaft speeds and pitch diameters.

What does 2% slip mean?

Actual output speed is 98% of the ideal value predicted by pulley diameters.

Is slip normal for every belt?

Friction belts show elastic creep; substantial gross sliding indicates overload, incorrect tension or poor contact.

Does this apply to timing belts?

Not in normal positive engagement. A deviation suggests tooth jump, wrong geometry or measurement error.

Why use pitch diameters?

The neutral tensile layer travels at the pitch diameter. Outside diameter may differ and would create an apparent error before slip is considered.