The Velocity Ratio of Pulley Systems Explained, velocity ratio of pulley formula, how to calculate velocity ratio

Working out the velocity ratio of pulleys

In simple language velocity ratio of the belt drive is the ratio between the velocities of the follower or driven (N2) and the driver (N1). Where, N1, N2 = Speed of the driver and the follower (driven) respectively in r.p.m (revolution per minute). From the following image, you can understand which one is the driver Pulley and the driven Pulley respectively. The motor-operated Pulley is called the driver pulley and the driving Pulley is being operated by the driver pulley.

Image: Driver (Motor Operated) and Driven Pulley

Now simplest method to understand the velocity ratio can be given as follows:👇

In this above method velocity ratio has been shown. From the above example, we can see that when driver Pulley moves 2 revolutions then the driven Pulley moves only one revolution. This is due to the diameter difference which can be easily understood from the above image.

The velocity ratio of a belt drive is the ratio of the rotational speed of the driving pulley to the rotational speed of the driven pulley. It depends on the diameters of the pulleys and the length of the belt.

The velocity ratio can be calculated using the following formula:

Velocity Ratio = (Diameter of Driving Pulley) / (Diameter of Driven Pulley)

For example, if the diameter of the driving pulley is 6 inches and the diameter of the driven pulley is 3 inches, then the velocity ratio would be:

Velocity Ratio = 6 / 3 = 2

This means that the driving pulley would rotate twice as fast as the driven pulley. If the driving pulley rotates at 100 RPM (revolutions per minute), then the driven pulley would rotate at 50 RPM.

 

Now let's derive the formula for the velocity ratio:

In the above image, you can notice various terminologies related to the velocity ratio

Here in this image, you can find the formula of velocity ratio, which is indirectly proportional to the diameter of the pulley. This formula may be modified if you consider the thickness of the belt.

Example Question 

Thank you so much .

 

To determine the velocity ratio of a belt drive system, you need to know the diameters of the pulleys involved, as well as their rotational speeds. The velocity ratio is then given by the ratio of the angular velocity of the driving pulley to that of the driven pulley. Here are a couple of simple problems to illustrate how to calculate the velocity ratio:

 

Problem 1:

A belt drive system consists of a driving pulley with a diameter of 10 cm and a driven pulley with a diameter of 20 cm. The driving pulley rotates at 1000 rpm. What is the velocity ratio of the belt drive?

 

Solution:

The circumference of the driving pulley is given by:

 

C1 = πd1 = 3.14 x 10 cm = 31.4 cm

 

The circumference of the driven pulley is given by:

 

C2 = πd2 = 3.14 x 20 cm = 62.8 cm

 

The angular velocity of the driving pulley is given by:

 

ω1 = 2πn1/60 = 2π x 1000/60 = 104.72 rad/s

 

The angular velocity of the driven pulley is given by:

 

ω2 = (d1/d2)ω1 = (10/20) x 104.72 = 52.36 rad/s

 

The velocity ratio is then given by:

 

VR = ω1/ω2 = 104.72/52.36 = 2

 

Therefore, the velocity ratio of the belt drive is 2.

 

Problem 2:

A belt drive system consists of a driving pulley with a diameter of 8 inches and a driven pulley with a diameter of 12 inches. The driving pulley rotates at 500 rpm. What is the velocity ratio of the belt drive?

 

Solution:

First, convert the diameters to the same unit, such as centimeters:

 

d1 = 8 inches x 2.54 cm/inch = 20.32 cm

d2 = 12 inches x 2.54 cm/inch = 30.48 cm

 

The circumference of the driving pulley is given by:

 

C1 = πd1 = 3.14 x 20.32 cm = 63.84 cm

 

The circumference of the driven pulley is given by:

 

C2 = πd2 = 3.14 x 30.48 cm = 95.98 cm

 

The angular velocity of the driving pulley is given by:

 

ω1 = 2πn1/60 = 2π x 500/60 = 52.36 rad/s

 

The angular velocity of the driven pulley is given by:

 

ω2 = (d1/d2)ω1 = (20.32/30.48) x 52.36 = 34.91 rad/s

 

The velocity ratio is then given by:

 

VR = ω1/ω2 = 52.36/34.91 = 1.50

 

Therefore, the velocity ratio of the belt drive is 1.50.

 

Here are some important points to remember when working with belt drive systems:

1. Velocity ratio: The velocity ratio of a belt drive system is the ratio of the angular velocity of the driving pulley to that of the driven pulley.
2. Belt types: There are several types of belts used in belt drive systems, including flat belts, V-belts, and timing belts. The type of belt used will depend on the specific application and requirements of the system.
3. Belt tension: The tension in the belt is an important factor in belt drive systems. The belt should be tensioned correctly to ensure proper power transmission and prevent belt slippage.
4. Pulley sizes: The size of the pulleys used in the belt drive system will affect the velocity ratio. Larger pulleys will result in a higher velocity ratio, while smaller pulleys will result in a lower velocity ratio.
5. Belt length: The length of the belt should be carefully selected to ensure proper tension and alignment. A belt that is too long or too short can result in poor power transmission, excessive wear, and premature failure.
6. Maintenance: Regular maintenance is important for belt drive systems to ensure proper performance and prevent problems such as belt wear, slippage, and misalignment. This includes regular inspection of the belt and pulleys, adjustment of belt tension, and replacement of worn or damaged components.

By keeping these important points in mind, you can ensure proper performance and long-term reliability of belt drive systems.