Belt and chain drives transfer rotary motion and power between shafts in machines, vehicles, conveyors, and tools. This cheat sheet helps students organize the main relationships used to compare pulley speeds, sprocket speeds, torque, belt length, and basic design limits. It is useful for quick reference during engineering design projects, robotics builds, and introductory machine design problems.
The most important ideas are speed ratio, power transmission, tension, and correct component selection. Belt drives can slip slightly and are often quieter, while chain drives use sprocket teeth for positive motion with little slip. Good design also checks center distance, wrap angle, allowable tension, service factor, alignment, lubrication, and safety guarding.
Key Facts
- For a belt drive with no slip, N1D1 = N2D2, where N is rotational speed and D is pulley diameter.
- Speed ratio for pulleys is N2 / N1 = D1 / D2 when the belt does not slip.
- Torque and power are related by P = Tω, where P is power, T is torque, and ω is angular speed in radians per second.
- Belt velocity is v = πDN / 60 when D is in meters and N is in revolutions per minute.
- Power transmitted by a belt is P = (T1 - T2)v, where T1 is tight-side tension, T2 is slack-side tension, and v is belt speed.
- Approximate open-belt length is L = 2C + 1.57(D + d) + (D - d)^2 / (4C), where C is center distance and D and d are pulley diameters.
- For roller chains, speed ratio is N2 / N1 = T1 / T2, where T1 and T2 are the numbers of teeth on the driving and driven sprockets.
- Chain pitch line speed is v = pTN / 60, where p is pitch in meters, T is sprocket tooth count, and N is sprocket speed in revolutions per minute.
Vocabulary
- Speed ratio
- The ratio comparing the rotational speeds of two connected pulleys or sprockets.
- Pitch
- The distance from one chain pin center to the next pin center in a roller chain.
- Center distance
- The distance between the centers of two shafts connected by a belt or chain.
- Tight-side tension
- The larger belt tension on the side carrying most of the load during power transmission.
- Service factor
- A multiplier used to increase the design load to account for shock, duty cycle, and operating conditions.
- Wrap angle
- The angle of contact between a belt and a pulley, which affects grip and power capacity.
Common Mistakes to Avoid
- Mixing up driver and driven components is wrong because the speed ratio depends on which pulley or sprocket supplies the input motion.
- Using pulley radius in a formula that requires diameter is wrong because the ratio will be off by a factor if both sides are not treated consistently.
- Ignoring belt slip is wrong when precision matters because real belt drives may not follow N1D1 = N2D2 exactly under load.
- Choosing a chain only by speed ratio is wrong because chain pitch, load rating, lubrication, and sprocket tooth count also control reliability.
- Forgetting service factor is wrong because a drive that works under steady light load may fail under shock loads, frequent starts, or long duty cycles.
Practice Questions
- 1 A motor pulley has a diameter of 80 mm and spins at 1800 rpm. It drives a 240 mm pulley with no slip. What is the driven pulley speed?
- 2 A belt drive has tight-side tension of 500 N, slack-side tension of 180 N, and belt speed of 6 m/s. What power is transmitted?
- 3 A chain drive uses a 15-tooth driving sprocket at 1200 rpm and a 45-tooth driven sprocket. What is the driven sprocket speed?
- 4 Explain why a belt drive may be preferred over a chain drive for a quiet fan system, but a chain drive may be preferred for a timing-critical conveyor.