Word for the day: SPEED / REVOLUTION

 

Although each machine is designed to for perform certain specific application and each machine has multiple specifications, certain basic parameters remain unchanged and understanding them properly will make calculating, measuring and make some basic design changes very simple and easier. How fast a machine runs, how fast the shaft (or spindle) rotates, how much torque is produced and how much power is consumed are some examples. Of all these, speed & revolution (term "rotation" can also be used) are most common attributes for any type of machine, independent of their end usage type. In this newsletter, let us understand SPEED & REVOLUTION in its most fundamental form.

 

SPEED & REVOLUTION: There exists no equipment which does not "run" and produce the output. There will be one or more rotating element whose motion will be converted into various forms like reciprocating, oscillating & non-linear outputs. A fan rotates to blow air, a conveyor travels to transport certain goods, and an elevator moves up & down to transfer people and so on. Speed or Velocity (technically called) and Rotation (Rotations per Unit time) are two frequently parameters that can be measured / calculated.

 

In figure-1, it looks like the rabbit is being chased by someone from behind and running as fast as it can to avoid getting caught. Now, if rabbit runs from point A to point B, it will cover certain distance, d. If distance – d – is covered in certain time – t – then the speed or velocity of rabbit is equal to d / t. The speed or velocity is expressed in various units. Few of the commonly used units are shown in the following table.

 

d = 100 centimeter (cm)		t = 12 seconds (s)	Velocity = 100 / 12 = 8.33 cm / s
d = 40 inches (in)		t = 0.2 minutes (m)	Velocity = 40 / 0.2 = 200 inches / minute
d = 3.33 feet		t = 0.5 hours	Velocity = 3.33 / 0.5 = 6.66 feet / hour
d = 10 kilometers		t = 1 hour	Velocity = 10 / 1 = 10 kilometers / hour

 

We can apply this simple formula to calculate linear speed for many day to day applications. Usually, a simple stop-watch is sufficient to calculate the time between two fixed distance points. For example, if the speed of a conveyor belt has to be calculated, locate any one point on the conveyor. Start the conveyor and stop-watch simultaneously. When the located point reaches a fixed distance stop the stop-watch and calculate the speed / velocity. We can calculate it for any object in "linear" motion.

 

Some of the measuring devices available to find speed / velocity are: i) Speedometer (or odometer as it is called in automotive sector) ii) Infrared / Radio Generator (usually used by traffic police to check vehicle speed) iii) Photo electric sensors iv) High speed cameras.

 

 

 

What if the rabbit gets caught in a beautiful giant wheel that is rotating and not moving anywhere? Refer to Figure-2 for understanding this funny condition of rabbit. Since the rabbit is sitting on a wheel it will not have linear motion. Instead, it will have a circular motion and keeps coming back to same position repeatedly. One circular motion of rabbit from point A to same point is called one revolution. How fast it reaches the same point is decided on how fast the wheel is turning in certain time. This is called revolutions per unit time. If the rabbit keeps coming to point A ten times a minute, we can say that the wheel is turning at 10 revolutions per minute or 10 RPM.

 

All rotating machines – motors, pumps, fans, drilling machines – have RPM (or RPS, Revolutions Per Second) as one of their important specifications. The turbo engine on an aero plane, for instance rotates at an incredible 12000 revolutions per minute! Even though the rabbit is rotating on a wheel, it is possible to calculate the "linear speed" which is dependent on wheel diameter and wheel revolutions per unit time. Following formula can be used to calculate the linear speed or velocity.

 

V = P
x d x N / 60, where d = diameter of wheel, N = wheel revolutions per minute. Using this formula, calculations for few of the commonly used units are shown in the following table.

 

d = 100 centimeter (cm)	N = 100 RPM	Velocity = (P x 100 x 100) / 60 = 523.6 cm / second
d = 40 inches (in)	N = 200 RPM	Velocity = (P x 40 x 200) / 60 = 418.8 inches / second
d = 3.33 feet	N = 100 RPM	Velocity = (P x 3.33 x 100) / 60 = 17.28 feet / second
d = 100 centimeter (cm)	N = 200 RPM	Velocity = (P x 100 x 200) / 60 = 10462 cm / second

Note: If the value obtained is very less, not dividing by 60 will give velocity in speed per minute.

 

As you can see from the table, the velocity increases with increase in wheel diameter as well as RPM. Using the same formula and if velocity is known, we can calculate the diameter or RPM of the wheel as well. Let us now ask the poor rabbit to sit on a flat conveyor fitted on to a big roller. The conveyor is travelling from point A to B in 10 seconds and the distance is 100 centimeters. Refer to figure-3 for this condition.

 

By now we know how to play around with the basic formula, let us substitute the relevant values to obtain the RPM of motor required. The roll diameter is assumed to be 50 centimeters.

 

Now substituting the relevant values, we will have this equation: V = P x D x N / 60 centimeters per second. Velocity, v = 100 / 10 = 10 centimeters per second. D = 50 centimeters.

10 = P x 50 x N / 60 which when changed becomes, N = 10 x 60 / P x 50 = 36.7 revolutions per second, which is nothing but 36.7 x 60 = 2202 Revolutions Per Minute (RPM). Now, instead of 100 centimeters, if the rabbit should travel at 50 centimeters in 10 seconds, then the RPM will reduce by 50% to 1101. This simple and interchangeable formula can be used to determine either RPM or Diameter or Linear Speed of a conveying system, if other values are known.

 

As we all know, for the wheel to rotate, it must be coupled to a prime mover which can be an engine, electric motor or any other rotating machine and RPM of these elements may differ. So, how do we obtain the desired RPM? From the above formula, we know that the RPM and hence velocity can be varied by altering the diameter. Let us now apply the same formula to obtain different diameter and arrive at the value. Refer to fiture-4 for understanding. The conveyor wheel system remains same; but, in addition it is connected to a prime mover with wheel diameter D centimeters.

 

Since the "driven" and "driving" wheels are connected by "power transmission elements" – like chain, belt, gear about which we will discuss in subsequent newsletters – the velocity remains same. Refer to figure-4 for understanding.

For same velocity, we can therefore conclude that as the diameter of "driven element" increases, its RPM REDUCES and vice-versa. This conclusion is applicable to any inter-connected rotating elements independent of the end application. Instead of 50 centimeters, if the "driving" wheel diameter was 200 centimeters, the RPM of "driven" element will increase to 2880. Instead,, if the diameter of "driven" wheel is 50 centimeters (same as "driving" element") the "driven" element's RPM will be same at 1440.

 

Transmission gears, belt driven multiple-pulley system like the ones found on old lathes, chain conveyors like the ones found in bag conveyors have various combinations of wheels on driven and driving side to alter the speed. The latest bicycles with gears fitted to rear wheel is one of the most common examples of changing speed by varying sprocket diameter. There are many other sophisticated methods of controlling the RPM / Speed using advanced techniques. But when the fundamentals are understood clearly, the application and selection of a suitable speed controller also becomes an easy task. We will discuss on the interesting methods of controlling speed in subsequent newsletters.

 

Once speed / velocity is determined, we can also determine its next "related" parameter called "acceleration" which is scientifically defined as "Rate of change of speed." (Acceleration = Velocity / Unit Time = Distance / Unit Time x Unit Time). In plain terms, it is nothing but how "soon" (fast) an element can reach its speed / velocity. It is expressed in distance unit (meter, centimeter, kilometer etc.) per square of the time. For example, centimeter / second² is one of the units for acceleration. If a conveyor can reach 100 centimeter per second velocity in 2 seconds, its acceleration is 100 / 2 = 50 centimeter / second² (50 cm/sec²).

To conclude, if higher speed / velocity, acceleration and (or) RPM is required for an application, it directly increases the Horse Power (energy) of the "driving" element. Also, for a fixed value of horse power (energy), any alteration in the speed will affect the torque generated. The horse power (energy) is DIRECTLY PROPORTIONAL to RPM & Torque. An increase in acceleration also increases the horse power. Few basic relational formulae are given in figure-5.

 

An exhaustive quick table showing various basic and day-to-day useful conversion formulae will be published soon.

 

A small end note on calculating average speed: This note might take you back to school days. And many of you will be familiar with it. But since we had an elaborate explanation on velocity, this deems to be an appropriate location to re-iterate how to calculate the average speed (velocity) which is essential for determining day to day efficiency / productivity calculations for any continuously running machines or machine systems. Now let us make the poor rabbit to run for longer distance, but at different speeds and learn to calculate the average speed. Refer to figure-6

 

Figure-6