Second measurement

Measurement of speed of rotation and torque

1. Introduction

The power of motion is the product of torque and angular velocity

][WMP ω⋅=

And since the angular velocity

⋅⋅=

s

radnπω 2

We can write that

][2 WnMMP ⋅⋅⋅⋅= π

So to determine the power of the rotating motion the torque and revolution number must be

measured.

The revolution number of the rotating shaft is the number of revolutions per unit time

⋅=

sn

1

2 π

ω

If the angular velocity is constant the revolution number can be calculated as follows

=

min

1,

1

st

Nn

(N being the number of revolutions during t time).

If the angular velocity is fluctuating the above relation gives an average revolution number for

t time.

From the point of view of the measuring concept the instruments measuring the revolution

number can be divided into three groups: speed indicators measuring the average revolution

number, tachometers measuring the momentary revolution number and the group of the

stroboscopes working on the principle of comparison.

2. Speed indicators

a/ Measurements of small revolution number can be made with stopwatch and by counting

revolutions with naked eye. When the mark on the rotating machine part gets to a certain

place we start the stopwatch and synchronously begin to count with 0!

Having measured the time of some revolutions the number of revolutions per unit time can be

determined.

b/ For higher speed if rotation a special counting device must be used. One of the simplest of

these is the so-called jumping-figure speed counter. The rotating shaft of this device turns

gears. One of them completes one revolution while the other rotates only 1/10, and so on.

Reading the numbers uniformly painted from 0-9 on the cylinder jacket we get the number of

revolutions. Such a device is used in kilowatt-hour meters, tape recorders, speedometers of

cars etc.

c/ Tachoscope is a compounded revolution counter and stopwatch. Both devices can be

started and stopped synchronously witwah pressing the same key (Fig.11). This device can be

mounted up with different joint pieces. Conical rubber joint piece is used when there is a bore

at the end of the shaft. When there is no bore at the end of the shaft or you cannot approach

the shaft-end adhesion disc or a disc of 10 cm circumference can be used. If there is a

rectangular swage in the end of the shaft a pyramid shaped metal peak must be used (Fig.12).

Having put on the appropriate joint piece, and zeroed the device, we have to press it

cautiously to the rotating machine part and when it will rotate synchronously with it then we

can start the revolution counter and the stopwatch with a single pressing of the common

starter. After 20-30 seconds we stop the instrument with a renewed pressing and then

calculate the revolution number from the data indicated on the dial.

From the stopwatch the time is generally read in seconds but in newer watches the result is

give in 1/100 minutes because of the decimal graduation of the dial.

Fig. 11: Tachoscope

Fig. 12: Different joint pieces of tachoscope

d/ Speed indicators working with clockworks count the revolutions only for a fixed time,

generally for 6 seconds. The time measuring device of the instrument connects its pointer for

6 seconds with that shaft of the instrument which joints the rotating machine part. After these

six seconds there is no more connection which means at the same time the end of the

measurement. On the dial the tenfold value of the counted revolutions i.e. r.p.m. (revolution

per minute) can be read. Such is the so called Jacquet indicator. With pressing the starting

button the instrument is zeroed and when it is let out the counting and the clockwork starts.

Therefore the buttons should be let out only when the joint piece rotates together with the

shaft! It is expedient to zero the instrument only with the starting of the new measurement.

The joint pieces are the same as seen in Fig.12.

e/ Electric speed indicators are composed of one or more markers giving voltage pulse and of

a pulse counter operating on electric principle. The marker is generally a photocell in front of

which a disc ensures one or more illuminations at each turning. The electric circuit is closed

by the illuminated photocell. (Fig.13)

This counter can be placed far off the site of the measurement.

Fig. 13: Electric speed indicator with photocell

3. Tachometers

Tachometers work on mechanical principles. In these instruments centrifugal balances rotate

with angular velocities proportional to the revolution number to be measured. The force

acting on the balance tries to dislodge the mass of the balance from the rotating shaft against

the spring-force.

The revolution number corresponding to the state of equilibrium is shown o the dial.

4. Stroboscopes

a/ If we watch a rotating body through a gap which opens only for very short time during a

complete revolution then we always see the same state of phase (the same part) and so the

thing seems to stand. The mechanical stroboscopes work on this principle.

b/ For setting certain revolution numbers a stroboscope disc (Fig.14) illuminated by glow

lamp can be used. Flow lamps supplied by 50 Hz mains flash at voltage-peaks that is 100

times per second (6000 times per minute). We see as stationery that ring of the stroboscope

disc which gets into the same position during the time passed between the two flashes as was

in the time of the former flash. So in Fig.14 the innermost ring (one pair of divisions) seems

to be stationary at the speed of 6000 rpm, or the middle ring (3 pairs of divisions) at 2000 rpm

while the most outside one (5 pairs of divisions) at 1200 rpm looks like immobile.

c/ The electronic stroboscopes illuminate the rotating or vibrating body with flashing lamps of

variable frequencies. If the frequency of the flashes corresponds to the speed if the rotating

object, the object seems to be stationary. The frequency i.e. the revolution number can be read

on the instrument.

d/ On the principle of comparison there operate also the Frahm’s reeds. This instrument

consists of a series of lamellas (reeds) of known natural frequencies fixed only at one end of

each. The bearing of the rotating shaft or the frame of the machine vibrates with the same

frequency as the revolution number. When contacting smoothly the Frahm’s reeds to the

vibrating frame of the machine that lamella (reed) begins to vibrate of the greatest amplitude

which has a natural frequency nearest the frequency of the excited vibration (resonance)

Fig. 14: Stroboscope disc

5. Measurement of torque

The task may arise in two different ways; whether you want to determine the torque of the

shaft of a power machine or of a machine. For measuring the torque produced by power

machine Prony brake, water brake, balance generator etc. can be used. For measuring the

torque required by the actually working machine balance motor is of use.

Fig. 15: Prony brake

a/ The friction torque of the Prony brake balances the torque got out of the shaft of the power

machine. So the work gout out of the power machine will become heat due to friction. The

Prony brake consists of two brake shoes each of which embraces rather less than one-half of

the brake drum fixed to the shaft of the power machine (Fig.15). If the shaft rotates with a

constant angular velocity the torques are in equilibrium

DFM F ⋅=

where M is the torque to be measured.

The arm of the brake is turned by its own weight and by the torque originated from the

frictional force; its equilibrium is assured by the torque of supporting force at the end of the

brake arm – measured by the balance:

kFsGDFF ⋅=⋅+⋅

From these two equations

0MkFsGkFM −⋅=⋅−⋅=

The value of the basic torque (M0) as well as the length of the arm (k) are the characteristic

data of the Prony brake. With a symmetrical form (two arms) the value of M0 can be equal to

zero.

With measuring the force F the torque of the power machine can be calculated. With

synchronously measuring the revolution number we can get the power, too. This power

increases the intrinsic energy of the surrounding so the cooling of the brake must be thought

of. On form of the cooling is to lead the cooling water into the empty brake drum (Fig.15). On

the effect of the fluid friction the cooling water rotates together with the brake drum and

forms a ring inside of that. The warmed up cooling water departs through a pipe opposite to

the sense of rotation. In the state of equilibrium as much water departs through the impact

tube as was introduced. The quantity of the cooling water needed can be calculated from the

mechanical power with the supposition that only the intrinsic energy of cooling water was

increased:

tcQM ∆⋅⋅⋅=⋅ ρω

where M [Nm] is the torque produced by the power machine,

ω [rad/s] the angular velocity of the brake drum,

Q [l/s] flow rate of the cooling water,

ρ = 1 kg/l density of water

c = 4187 J/kg°C specific heat capacity of water,

∆t = 40°C the supposed temperature-rise of the cooling water in the brake

drum.

b/ The stationary part of the balance generator or balance dynamo (balance machine) is not

fixed to the frame but it can turn in the bearings (Fig16). Electromagnetic interaction between

the coils of stationary and turning parts wants to turn the stationary part. In the case of

generator the driven rotating part wants to “move with itself” the stationary part. In the case of

motor the rotating part “pushes off” the stationary part i.e. a torque starts on the housing

opposite to the sense of rotation. These torques are balanced (and measured) by the weights

put on the plates of the arms of the stationary part.

The equilibrium of the torques are to be examined separately on the stationary and turning

parts and we take into account other – relatively small torques, too.

Fig. 16: Balance machine

The equilibrium of the turning part is shown by the constant speed of rotation.

The balance generator is driven by the torque M (Fig.17). The equilibrium of the turning part:

VFE MMMM ++=

The equilibrium of the stationary part in case of horizontal arms:

kGsQMM FE ⋅=⋅±+

(In the Fig. sQ ⋅ is + !)

The state of equilibrium of the stationary part is indicated by the congruency of pointers fixed

on it and on the bracket.

In the equations:

M is the torque to be measured. This torque is produced by the power machine and is

transmitted by the coupling to the rotating part of the generator,

ME is the electromagnetically generated torque acting on the turning and stationary parts

MF is the torque generated by bearing friction and brush friction,

MV ventilation torque is composed of the torque caused by the friction of the air and the

torque needed for the driving of ventilator delivering the cooling air.

G is the weight needed for balancing the stationary part,

k is the length of arm

Q is the weight of the stationary part

s is the distance of the centre of gravity of the stationary part from the vertical plane

through the shaft.

From these equations:

sQMkGM V ⋅±+⋅=

For determining the last two terms we have to make a measurement in idle running. In this

case we operate the balance machine as a motor independently from the power machine and

keeping the direction of the rotation (Fig.17).

Equilibrium of the turning part:

FVE MMM +=0

That of the stationary part:

sQMkGM FE ⋅±+⋅= 00

From these two equations:

kGsQMV ⋅=⋅± 0

And so the torque is to be measured in generator running:

( ) kGGM ⋅+= 0

The measurements in idle running are generally made with various speeds of rotation. The

sense of the value of G0 depends on the fact whether the balance machine is used as a motor

or a generator and on which side the weight must be put in case of idle running.

Fig. 17: Equilibrium on balance machine

c/ Water brake balances the torque of the power machine with the torques of the forces arising

between the stationary and rotating blade-rows. The rotating blades are turned by the power

machine to be measured while the stationary blades are not let to move by the torque of the

weights put on arms attached to them (Fig.18). The torque can be calculated when knowing

the length of the arms and the weights. The torque is delivered by the liquid (water) between

the two pars. Due to rotation the water forms a ring between the blades. The breadth of this

ring (the filling of the water break) can be changed and by this the torque can be regulated.

Fig. 18: Water brake

6. Measuring exercise

On the first measuring rig power is measured by Prony brake. The team fixes a certain

operational point with arbitrary braking condition and each student calculates power and

flow-rate. For measuring the force at the end of the arm of the balance a commercial balance

is used.

The arm of the Prony brake k = 0.974 m, the basic torque M0 = 12.4 Nm.

Fig. 19: Test rig

The second rig is a group of machines consisting of direct current balance motor and a

balance dynamo connected by clutch (Fig.19). (So this is practically composed of two rigs.)

The task is to determine the efficiencies of both the balance motor and the balance generator

in the function of load at n = 2000 r.p.m. constant speed of rotation.

The efficiency of the electric machines (η) against the load (x) is shown in Fig.20. In this

diagram the curves of the useful power: Pu and the input Pin can also be seen.

The electrical power which is in the case of motor the input and in the case of dynamo the

output should be determined by the current measured with ammeter and the voltage by

voltmeter. The value on the scale must be multiplied by a constant stated on the instrument

(cV and cA). So we get the voltage in volts and the current in amperes.

The mechanical power can be calculated by the torque of the weights put on the plate of

balance motor and the revolution number measured.

The mass m0 – stated with the measurement in idle running – at n = 2000 rpm for both

balance machines

kgm 02.00 =

From this

gmG ⋅= 00

So the torque produced by the motor

( ) kgmmM ⋅⋅−= 0

And the torque used by the dynamo

( ) kgmmM ⋅⋅+= 0

can be calculated.

For the calculation of the load we need the nominal effective useful power (output). This

datum of the dynamo can be read from the nominal electric data on the data plate of the

machine since the useful power of the dynamo is the electric power.

WP D 15401 =

The nominal useful power of the motor is the mechanical power produced by the nominal

voltage and current. This was determined by measurement formerly:

WP M 13001 =

In the report the type of the machine measured, the types of the instruments used, and also

their numbers must be written in the form as follows:

The type of the balance machine: Its works number:

;;; 10 WPkgmmk ===

Voltmeter: division

VcV =

Ammeter: division

AcA =

Speed indicator:

To record the measuring data the left side of the table in Fig.20/a must be used.

Relations to be used when evaluating:

( )

=

=′⋅=

⋅=⋅⋅⋅⋅⋅±=′⋅=

ν

ωπ

xIcI

MsnkgmmPUcU

A

mechV min/60/20

Fig. 20: Efficiency of the machine

In the formula of Pmech from the ± signs only that should be used which is appropriate to the

machine measured. The formulas of x and η depend also upon the machine measured

(whether it is a dynamo or a motor).

The values of efficiencies gained should be drawn in the function of the load on a millimeter

paper of A4 form.

As practical scales are recommended the following ones:

cmcm x /%5;/%5 == λλη

In the diagram the revolution number at which the measurement was made, the date as well as

the name of the student who prepares it should be indicated!

To the measurement 2 blank papers should be brought.

On one of these, please prepare at home the table needed for the measurement of the electric

machine, the list of instruments and the relations to be used, all in the sense of the above; on

the other paper will be prepared the record of the measurement with Prony brake.

Also at home should be prepared the η – x co-ordinate system on a sheet of paper of A4 size.

The result of the measurement made on balance machine will be drawn on it.

IUP

IcI

UcU

s

n

el

A

v

⋅=

′=

′=

⋅⋅=

min/60

2 πω

Measurement Evaluation

n U’ I’ M ω U I Pel M Pmech x Η

Ser

ial

nu

mb

ers

1/min div. div. kg rad/s V A W Nm W - -

1.

2.

3.

4.

5.

6.

Motor: Dynamo:

( ) kgmmM ⋅⋅−= 0 ( ) kgmmM ⋅⋅+= 0

ω⋅= MPmech

MP

Px mech

1=

DP

Px el

1=

el

mech

P

P=η

mech

el

P

P=η