Design a V-belt drive that transmits power between two pulleys through a belt. Adjust the pulley diameters, centre distance, speed and tension to see the belt speed, wrap angle, the effective friction from the V-groove wedge, the tension ratio and the transmitted power update in real time.
Parameters
Small pulley diameter d
mm
Pitch diameter of the driving pulley
Large pulley diameter D
mm
Pitch diameter of the driven pulley
Centre distance C
mm
Distance between the two pulley centres
Small pulley speed N
rpm
Revolutions per minute of the driving pulley
Max tight-side tension T₁
N
Tension in the tight (pulling) side of the belt
Results
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Belt speed (m/s)
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Small-pulley wrap angle (°)
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Effective friction μ'
—
Tension ratio T₁/T₂
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Slack-side tension T₂ (N)
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Transmitted power (kW)
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V-belt drive diagram — rotation animation
Power flows from the small pulley (driving) to the large pulley (driven) through the belt. The thick red line is the tight side, the thin blue line the slack side. The lower-left inset shows the V-belt wedged in its groove.
The tension ratio follows the belt form of the Euler friction equation. β is the V-groove half-angle, θ the wrap angle on the small pulley, and v the belt speed. The V-groove wedge multiplies the effective friction μ' to 1/sinβ times the bare friction μ. The transmitted power P is the tension difference (T₁−T₂) multiplied by the belt speed v.
What is the V-Belt Drive Simulator?
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When you open a car's engine bay, there's a rubber belt running around pulleys. Why doesn't it just slip off — how does it transmit power?
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Good question. That is a "V-belt drive". A belt runs over two pulleys, and turning one turns the other — it transmits power through friction. But it isn't a flat belt: its cross-section is a "V" (a wedge). The pulley has a matching V-shaped groove cut into it, and the belt drops snugly into that groove.
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What is the benefit of sitting in a V-groove? Wouldn't a flat belt do?
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This is the cleverest part of a V-belt. When tension pulls the belt, the wedge-shaped belt is forced deeper into the V-groove. Its two flanks then press hard against the groove walls. That normal force becomes much larger than the belt tension itself. As a result the apparent coefficient of friction jumps to 1/sin(groove half-angle) times the bare value. With a 17 degree half-angle that is 1/sin17° ≈ 3.4 times. Look at the belt cross-section in the lower-left inset of the canvas. With the same initial tension, a V-belt grips with about three times the force of a flat belt.
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Three times is impressive! So what decides how much power it can transmit?
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The power transmitted is set by the difference between the "tight side" and "slack side" tensions. One side of the belt is pulled taut (tension T₁), the other is slack (tension T₂). The difference (T₁−T₂) multiplied by the belt speed is the transmitted power P. And the maximum ratio T₁/T₂ is governed by the Euler friction equation e^(μ'θ), where θ is the wrap angle on the small pulley. The larger the wrap angle and the higher the friction, the more this ratio grows exponentially, and the more power you can transmit. Watch that steep curve in the "Tension ratio vs wrap angle" chart on the right.
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If I want a larger wrap angle, what should I do?
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In practice you take a generous centre distance C, and you keep the diameter difference D−d modest. A big diameter difference makes the belt leave the small pulley early, cutting the wrap angle. If you still fall short, you can press an idler (tension pulley) against the belt to extend the contact zone. V-belts are cheap, quiet, absorb shock, and slip to protect the machine when overloaded — which is why you find them everywhere, from cars to factory fans and pumps.
Frequently Asked Questions
Because a V-belt has a wedge-shaped cross-section and runs in a matching V-groove in the pulley. When tension pulls the belt down into the groove, the wedge presses against the groove walls and the normal force on the belt's two flanks becomes much larger than the belt tension itself. As a result the apparent coefficient of friction is multiplied by 1/sin(groove half-angle). For a 17 degrees half-angle that is about 3.4 times. So with the same initial tension a V-belt transmits roughly three times the power of a flat belt.
The maximum ratio between the tight-side tension T₁ and slack-side tension T₂ is set by the belt form of the Euler friction equation (capstan equation): T₁/T₂ = e^(μ'θ), where μ' is the effective friction coefficient and θ is the wrap angle on the small pulley in radians. The larger the wrap angle and the higher the friction, the larger the tension ratio grows exponentially, and the more power can be transmitted. Exceed this ratio and the belt slips.
The wrap angle θ is the angle over which the belt contacts the small pulley: θ = π − 2·asin((D−d)/(2C)), where D is the large pulley diameter, d the small pulley diameter and C the centre distance. The larger θ, the larger the tension ratio grows exponentially and the higher the capacity. To increase it, use a longer centre distance C, keep the diameter difference D−d small, or add an idler/tension pulley to extend the contact zone.
Advantages: cheap and quiet, tolerant of shock loads and slight shaft misalignment, no lubrication required, and a slipping belt acts as built-in overload protection. V-belts are everywhere, from automotive accessory drives to industrial fans, pumps and machine tools. Disadvantages: a few percent of power is lost to belt flexing and slip, and the belt needs periodic re-tensioning as it wears and stretches.
Real-World Applications
Automotive accessory drives: A V-belt (or a multi-rib serpentine belt) distributes power from the engine crankshaft to the alternator, water pump, air-conditioning compressor and power-steering pump. Because several accessories must be driven by one belt in a cramped engine bay, an automatic tensioner keeps the tension constant and preserves the wrap angle on each pulley.
Industrial fans and pumps: Blowers, cooling-tower fans and centrifugal pumps use a V-belt and pulley pair to step the motor speed up or down to match the impeller. Because changing the pulley diameter ratio alone adjusts the speed ratio, V-belts are convenient for tuning airflow or flow rate on site. Unlike a direct coupling, they also absorb shaft misalignment and start-up shock.
Machine tools and agricultural machinery: Lathe and drill-press spindle drives, compressors, and the cutter drives of combines and mowers all use V-belts where reliable power transmission and overload protection are needed. When a blade jams on foreign material, the belt slips and saves the gears and shafts — a "mechanical fuse" role.
Pre-study for power-transmission design: Before working through a belt maker's detailed selection tables (with all their correction factors), a basic-equation tool like this one gives you the order of magnitude of belt speed, tension ratio and transmitted power. If the wrap angle or tension ratio comes out at an extreme value, you can decide early to revise the pulley diameters or centre distance. Conversely, if the catalogue selection differs by an order of magnitude, it is a sanity check that points to an input mistake in speed or tension.
Common Misconceptions and Pitfalls
The most common pitfall is "just tension the belt hard and it won't slip". It is true that higher tension increases the power that can be transmitted, but excessive tension puts a large radial load on the bearings, shortens bearing life, bends the shaft and shortens the belt's own life. In practice you tension to the minimum needed for the transmitted power plus a sensible margin. Treat the tight-side tension T₁ in this tool as a value to be set while watching the bearing load.
Next, "a V-belt doesn't slip, so the speed ratio is exact". A V-belt always has a few percent of "creep" (elastic slip), and small gross slip occurs under load. The actual output-pulley speed is therefore slightly lower than the theoretical value calculated from the diameter ratio. For applications needing precise synchronisation, use a toothed (timing) belt or gears; V-belts suit jobs where "a roughly correct speed ratio, no lubrication, quiet and cheap" is good enough.
Finally, "the effective-friction equation ignores centrifugal force". The tension ratio e^(μ'θ) used here is a basic equation that neglects the centrifugal force acting on the belt itself due to rotation. As belt speed rises, the centrifugal tension can no longer be ignored: it effectively reduces the pressing force on the pulley, so the transmission capacity levels off or even falls. V-belts are generally recommended up to around 30 m/s; above that, a design corrected for centrifugal effects is needed. Treat this tool as a guide for basic trends.