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Belt Drive Speed Calculator

Run the Belt Drive Speed Calculator MicroSim Fullscreen

This sketch is built on the FanPedia MicroSim kit. To run it in the p5.js editor, add the ../shared-libs/ files it loads (fanpedia-sim.css, fanpedia-core.js, fanpedia-p5.js, fan-models.js, fan-drawings.js), or their published URLs, to the editor's index.html before pasting ch03-belt-drive-speed-calculator.js.

About This MicroSim

A belt drive sets the fan speed with two grooved wheels: the motor sheave and the fan sheave. The fan speed follows from the motor speed and the ratio of the two pitch diameters:

  • Fan speed = motor speed × motor sheave pitch diameter ÷ fan sheave pitch diameter

The drawing shows both sheaves to scale, joined by a V-belt. The readout gives the ratio (motor sheave ÷ fan sheave) to three decimals, the fan speed in RPM and a label: "fan slower than motor", "fan same as motor" or "fan faster than motor". Belt slip is not modeled, so the sim gives the ideal speed.

The sim starts with three challenges, in this order:

# Motor speed Motor sheave Fan sheave Fan speed
1 1,760 RPM 5.0 in 8.0 in 1,100 RPM
2 1,760 RPM 6.0 in 12.0 in 880 RPM
3 1,160 RPM 9.0 in 6.0 in 1,740 RPM

Type the fan speed before the drive turns. An answer is correct when it is within ±10 RPM. You get two attempts: a wrong answer shows the calculation, and a second wrong answer shows the fan speed and the challenge counts as missed. When a challenge is resolved, the drive turns and the fan speed appears next to your answer. Mastery is 3 of 3 on the first attempt.

After challenge 3, Explore mode unlocks. Choose a motor speed (1,160, 1,760 or 3,500 RPM, illustrative nominal speeds) and move either sheave: the motor sheave from 3.0 to 12.0 inches and the fan sheave from 4.0 to 24.0 inches, in 0.2-inch steps. The drawing, ratio, label and fan speed update at once, from 145 RPM up to 10,500 RPM. The first time you enlarge the fan sheave, the sim notes "Bigger fan sheave: fan speed went down." Explore mode is never scored.

How to Use

  1. Read challenge 1 and type the fan speed in RPM in Your answer. Press Check (or Enter).
  2. A correct answer reads "✓ Correct: 1,100 RPM." in a solid green box. A wrong one reads "✗ Not quite." with the calculation in a dashed red box; use the second attempt.
  3. Press Next challenge (or Enter) and repeat. "Challenges correct: n of 3" keeps the running score.
  4. After challenge 3, press Start exploring. The panel shows the first-attempt score and the mastery line. Enlarge the fan sheave and watch the fan speed fall; then make the motor sheave larger than the fan sheave and read the label. Start over clears the score.

Keyboard: Enter checks the answer, and Enter again goes to the next challenge. Tab reaches the answer box, every button, the motor speed menu and both sliders; the arrow keys move a focused slider.

Data label: "Illustrative nominal motor speeds · Belt slip not modeled", at the bottom left of the drawing.

Iframe Embed Code

You can add this MicroSim to any web page by adding this to your HTML:

<iframe src="https://moroshek.github.io/FanTASTIC-textbook/sims/ch03-belt-drive-speed-calculator/main.html"
        height="717px"
        width="100%"
        scrolling="no"></iframe>

Lesson Plan

Learning Objective

The learner will calculate the fan shaft speed of a belt drive from the motor speed and the two sheave pitch diameters, to within ±10 RPM (Bloom: Apply, verb: calculate).

Audience

Adult professional development: new application engineers, sales staff, representatives and facilities staff who have read "The Drive Train" in Chapter 3.

Duration

10 minutes

Prerequisites

  • Drive train, direct drive and belt drive (Chapter 3)
  • Sheave, V-belt and pitch diameter (Chapter 3)
  • Motor speed in RPM

Activities

  1. Challenges (5 min): Solve the three drives with a calculator before pressing Check. Write down the ratio for each one.
  2. Exploration (3 min): At 1,760 RPM, set the motor sheave to 5.0 inches and move the fan sheave from 8.0 to 16.0 inches. Record the fan speed at 8.0 and 16.0 and explain why it halves.
  3. Misconception check (2 min): Find two sheave pairs with the same difference (for example 5.0 and 8.0, and 9.0 and 12.0) and show that they give different fan speeds, because the ratio, not the difference, sets the speed.

Common Misconceptions Addressed

  • A larger fan sheave makes the fan turn faster: Explore mode shows the fan speed fall as the fan sheave grows, and says so the first time.
  • A belt drive always slows the fan down: challenge 3 has a larger motor sheave, and the fan turns faster than the motor.
  • Fan speed depends on the difference between the sheave sizes: the readout shows the ratio, and the activity compares pairs with the same difference.

Assessment

  • The running line "Challenges correct: n of 3" counts challenges solved on either attempt. At the end the sim shows "First-attempt score: n of 3" and the mastery line; mastery is 3 of 3 within ±10 RPM on the first attempt.
  • Changing sheaves in Explore mode is not evidence of mastery. Ask the learner which sheave to change, and in which direction, to speed up a fan by about 8 percent (the chapter's 5.0 to 5.4 inch motor sheave example: 1,100 to 1,188 RPM).

References

  1. Belt (mechanical) - Wikipedia overview of belt drives, sheaves and speed ratios.
  2. Pulley - Wikipedia article on pulleys (sheaves) and belt and pulley systems.
  3. FanPedia: The Fan & Blower Encyclopedia - Twin City Fan's reference; page 173 notes that belt-driven fans reach the exact point of rating through a sheave change.