Sub module 4.4 Force, torque and power measurement

Quadrant 2 List of animations/Videos:

1. Proving ring calibration is shown http://www.youtube.com/watch?v=Foq-_wqnFzA

2. Load cell calibration is shown http://www.youtube.com/watch?v=sVoRkt2TZrM

3. http://www.youtube.com/watch?v=zfAQ5OlIAkc (load cell manufacturing) 4. http://www.youtube.com/watch?v=oa2UBOUBZak (old plat form scale) 5. http://www.youtube.com/watch?v=SgROKbHXkt0&feature=endscreen (torque sensors) 6. http://www.youtube.com/watch?v=HdJ6tmni0F0 (double beam balance) 7. http://www.youtube.com/watch?v=9Wi51Kf8bzA (prony brake part1) 8. http://www.youtube.com/watch?v=weJhTdnlUAo (prony brake part2) 9. Different types of load cells are discussed

http://www.globalspec.com/learnmore/sensors_transducers_detectors/force_sensing/load_cells

10. The animation shows the stresses developed inside a load cell subjected to torsion loading http://www.strand7.com/html/archive/mechanical/torque.htm

11. Hydraulic load cells are presented http://www.sentinelinstruments.com/bulktank.htm

Illustrations:

1. Design and construction of proving ring is illustrated http://www.nist.gov/pml/div684/grp07/provingringdesign.cfm

2. Load ring (proving ring) photo with information is available http://www.humboldtmfg.com/load_ring_with_dial_gauge.html

3. Line diagram of proving ring is presented http://www.nist.gov/pml/div684/grp07/provingringpatent.cfm

List of questions (FAQ): Questions on force measurement:

1. Write short notes on force sensors. 2. Write a note on load-cell applications 3. Discuss static and dynamic load measurement 4. Discuss the working of a load cell with a neat sketch 5. Discuss the working of a quartz force sensor.

Page 1 of 11

Questions on torque measurement:

6. List the various types of torque measurement 7. Illustrate IR torque sensor 8. Explain the use of slip rings in torque measurement. 9. What is a dynamometer? 10. List the different types of dynamometers available 11. Discuss the principle of dynamometer 12. What are absorption dynamometers? Explain anyone with a neat sketch 13. What are transmission dynamometers? Explain anyone with a neat sketch 14. Explain the measurement of torque using hydraulic dynamometer 15. What are electric dynamometers?

Questions on speed measurement:

16. What are tachometers? Classify them. 17. Discuss the measurement of speed by revolution counter 18. Explain the working principle of stroboscopic tachometer with a neat sketch.

Quadrant 3 Wiki links/reference links/ courses from other university web

1. http://www.nrcs.org.za/siteimgs/LMGenInfo/Article-Load%20Cells.pdf (text) 2. http://www.sensorland.com/HowPage005.html (text) 3. http://www.omega.com/literature/transactions/volume3/load.html (text) 4. http://en.wikipedia.org/wiki/Wheel_speed_sensor (rpm sensor) 5. http://en.wikipedia.org/wiki/Crankshaft_position_sensor (rpm sensor) 6. http://www.hbm.com/en/menu/products/weighing-components/ (load sensors) 7. http://en.wikipedia.org/wiki/Torque_sensor 8. http://www.binsfeld.com/index.php/?gclid=CNrHycLRgLYCFRES6wodDB0A-A

(torque sensor) 9. http://www.efunda.com/designstandards/screws/fasteners_intro.cfm (torque and

tension in bolts) 10. http://en.wikipedia.org/wiki/Horsepower (Engine power measurement) 11. Winther, J. B. (1975). Dynamometer Handbook of Basic Theory and Applications.

Cleveland, Ohio: Eaton Corporation. 12. Martyr, A.; Plint, M. (2007). Engine Testing - Theory and Practice (Third ed.). Oxford,

UK: Butterworth-Heinemann. ISBN 978-0-7506-8439-2. 13. Dynamometer basics are presented

http://en.wikipedia.org/wiki/Dynamometer 14. Engine dynamometer details are presented

Page 2 of 11

http://www.taylordyno.com/catalog/engine-dyno 15. Water brake dynamometer basics are presented

http://www.taylordyno.com/catalog/engine-dyno/hydraulic-dynamometers-water-brake-dynamometers

16. Strain gages for load cells and torque sensors are presented http://www.nmbstraingages.com/strain_gages.html

Quadrant 4 Numerical problems: Problem on rod in tension:

1. A steel bar is to be used to measure a force of 1000 N. Determine a suitable diameter and length of rod for this measurement. Solution: Assuming a deflection of y = 0.0005 m And diameter of rod D = 0.004 m Area of rod A= 12.56 x 10-6 m2 E = 200 x 109 N/m2

K = F/y = 1000/0.0005 = 2 x 106 N/m Therefore, length of rod = L = AE/K = 1.256 m

By adjusting some of the above values, the rod can be made compact, so that it can be used as a force measuring device.

Problem on cantilever beam:

2. A small cantilever beam is made of spring steel having E = 200 GPa. The beam is 5

mm in wide and 1 mm thick, with a length of 25 mm. (i) Calculate the indicated force when the cantilever deflection is measured to be 2 mm. (ii) If all the dimensions are subject to measurement uncertainties of 0.5 %, determine the % uncertainty in the estimated spring constant. (iii) What is the uncertainty in the estimated force if the deflection itself is 0.5 % uncertain. Solution: E = Young’s modulus of steel = 200 x 109 N/m2

L = cantilever length = 0.025 m t = beam thickness = 0.001 m b = beam width = 0.005 m y = cantilever tip deflection = 0.002 m I = moment of inertia = bt3 /12 = 0.005 x 0.0013 /12 m4 (i) F = indicated force = 3EIy/L3 = 32 N (ii) uI = ± √ (𝑢𝑏2 +(3ut)2) = ± √ (0.52 + (3x0.5)2) = 1.58 %

Page 3 of 11

uk = ± √ (𝑢𝐼2 +(3uL)2) =± √ (1.582 + (3x0.5)2) = 2.18 % K= spring constant = 3EI/L3 = 16000 N/m Uncertainty in the estimated spring constant = 16000 ± 2.18 x 16000/100 = 16000 ± 349 N/m

(iii) uF = ± √ (𝑢𝑘2 + 𝑢𝑦2 ) = ± √ (2.182 + 0.52) =2.24 % Uncertainty in the estimated force = F = 32 ± 2.24 x 32/100 = 32 ± 0.717 N

Problem on Prony brake dynamometer:

3. A shaft transmitting power from an IC engine is made of steel with E = 200 GPa, and has a diameter of D=0.02 m. the nominal value of torque on the shaft is 30 Nm. Determine (i) torque arm length of the prony brake, when the weight in the pan is 100 N, (ii) ) the shear stress on the surface of the shaft (iii) the strain induced in the load cell bonded on shaft surface at 45o to shaft axis. Solution:

D = shaft diameter = 0.02 m T = torque = 30 Nm F = weight in the pan = 100 N

(i) Torque arm length = L = T/F = 30/100 = 0.3 m (ii) Shear stress on the surface of the shaft = τ = TD/(J2)

Polar moment of inertia = J = πD4 /32 = 1.57x10-8 m4 τ = 0.191 x 108 N/m2

(iii) Strain induced = s = τ / E = 95.5 µ strain Problem on seismic instrument:

4. A large seismic instrument is fabricated so that m = 65 kg and c/cc = 0.7. A spring with k = 3 kN/m is used so that the instrument will be relatively insensitive to low-frequency signals for displacement measurements and relatively insensitive to high-frequency signals for acceleration measurements. (i) Calculate the value of linear acceleration that will produce a relative displacement of 4 mm on the instrument. (ii) Calculate the value of w1 /wn such that (x2 – x1 )o /xo = 0.99. Solution: Displacement = x = 4 mm = 0.004 m Spring constant = k = 3 kN/m Spring force = F = kx = 3000 x 0.004 = 12 N Seismic mass = M = 65 kg Linear acceleration = a = F/M = 12/65 = 0.185 m/s2 Using the following expression: W = (w1 / wn )

Page 4 of 11

(x2 – x1 )o /xo = W2 /( (1-W2)2 + ( 2(c/cc)(W))2 )1/2

After substitution and simplification, we get W = 2.47

5. An accelerometer has a maximum displacement of 0.2 m, seismic mass of 0.025 kg and spring constant of 2 x 103 N/m. Calculate the natural frequency and the maximum acceleration that can be measured. Solution: k = spring constant = 2x103 N/m m = seismic mass = 0.025 kg x = maximum displacement = 0.2 m

Fn = Natural frequency = (1/2π)(k/m)1/2 = (1/2π)(2x103/0.025)1/2 = 45 Hz a = Maximum acceleration = k x /m = 2x103 x 0.2 / 0.025 = 16000 m/s2

Multiple choice questions

1. Elastic elements used for measurement of force give a. High sensitivity and slow response if they are stiff b. Low sensitivity and fast response if they are stiff c. Low sensitivity and slow response if they are stiff d. None of the above

2. Piezoelectric load cell can be used for measurement of

a. Dynamic force only b. Dynamic and static force provided the load cell has a small time constant c. Dynamic and static force provided the load cell has a large time constant d. None of the above

3. Torque of rotating shafts is measured by a strain gauge mounted on the shaft. The

supply to the bridge circuit is given to it and output is taken out from it by using a. Only slip rings b. Only rotary transformers c. Rotary transformers, slip rings and telemetry system d. None of the above

4. Commercial hydraulic load cells which can measure a maximum force of -------- are

available a. 10 kN b. 50 kN c. 10 MN

Page 5 of 11

d. 50 MN

5. Pendulum scale used for force measurement works on the principle of a. Comparing the unknown force with a known force b. Converting the unknown force to power and comparing it with known power c. Converting the unknown force to torque and comparing it with a known torque d. None of the above

6. Tachometers are used for measurement of

a. Displacement b. Angular velocity c. Vibration d. time

Answer table

1. b 2. c 3. c 4. d 5. c 6. b

Fill in the blanks 7. Force or weight depends on the mass and ------ 8. Torque measuring device is known as ---- 9. The main types of dynamometers are -------------------- and ------------------ 10. In absorption dynamometers, the power produced by the engine is absorbed by -------- of

the brake and is transformed into heat . 11. A belt dynamometer is introduced to measure directly the difference between the -------- of

the belt while it is running. 12. A hydraulic dynamometer operates on -------- principle . 13. The centrifugal force tachometer measures the speed by means of ----- 14. The eddy-current tachometer produces an----signal in the form of continuous drag due to

eddy currents induced in the cup.

Page 6 of 11

Answer table 7. Acceleration 8. Dynamometer 9. Absorption type, Transmission type 10. Frictional resistances 11. Tensions 12. Water brake 13. Centrifugal force 14. Analog

True/False/yes/no 15. Rope brake dynamometer is costly and complex in construction 16. DC electric dynamometer is the most versatile and accurate dynamometer 17. Strain gauge load cells convert force into electrical output 18. Pneumatic load cell operates on the force-balance principle

Answer table

15. N 16. Y 17. Y 18. Y

Assignments questions and solutions

1. List the basic devices used to measure weight Ans: Roman steelyard, spring scale, analytical balance, platform scale, pendulum scale

2. How force is measured? Ans: Force measurement uses a mechanical elastic member or a set of members. Application of load to the member results in an equivalent linear deflection. The deflection is either directly viewed and used as a measure of force, or a secondary transducer is employed to convert the displacement into another form of output, usually electrical signal.

3. List the devices used to measure force. Ans: Proving ring, strain gage load cell, piezoelectric load cell, hydraulic load cell, pneumatic load cell

Page 7 of 11

4. What is a dynamometer? Explain its principle. How they are classified? Ans: It is a torque measuring device Principle: A rotor driven by the engine under test, is mechanically, hydraulically or electromagnetically coupled to a stator. For every revolution of the shaft, the rotor periphery moves through a distance 2πR against the coupling force, F. Hence, the work done per revolution is W=2πRF. The external moment or torque is equal to SxL, where S is the scale reading and L is the arm length. This moment balances the turning moment RxF, ie, SxL=RxF. Therefore, work done/revolution = 2πSL and work done/minute = 2πSLN. Hence brake power is given by bp=2πNT Watts, where T is the torque, N is rpm. ( For more details and for a schematic diagram, refer Internal Combustion Engines by Prof. V. Ganesan , III edition, TMH education Pvt. Ltd., page 525) Classification: Dynamometers are broadly classified into two main types: 1. Absorption dynamometers: They measure and absorb the power output of the

engine to which they are coupled. The power absorbed is usually dissipated as heat by some means. A few examples are prony brake, rope brake, hydraulic dynamometer, eddy current dynamometer.

2. Transmission dynamometer (torque meters): In these dynamometers, the power is transmitted to the load coupled to the engine after it is indicated on some type of scale.

5. List the various devices used in the measurement of torque

Ans: Torque is measured by the following: 1. Absorption dynamometer: Prony brake

Rope brake 2. Hydraulic dynamometer 3. Electric dynamometer: Eddy current dynamometer,

DC motors and generators, AC motors and generators Swinging field DC dynamometer

4. Fan Dynamometer 5. Transmission dynamometer: Epicyclic train dynamometer

Belt transmission dynamometer Torsion dynamometer

6. Non-contact torque transducer 7. Strain gage torque sensor

Page 8 of 11

6. List the various devices used to measure rotational speed of IC engines Ans: IC Engine speed measuring devices are listed below: 1. Mechanical Tachometer 2. Optical rpm meter 3. Mechanical counter and timers 4. Stroboscope 5. Electric counters 6. Electronic pulse counters 7. Magnetic pick-up

7. How do you classify speed measuring devices

Ans: Classification of speed measuring device is as follows: 1. Mechanical tachometers: Revolution counter, Centrifugal force tachometer 2. Electrical tachometers: Eddy-current tachometer

DC tachogenerator AC tachogenerator Stroboscope tachometer

Self answered questions and answers: 1.Mention some of the applications where the quantities such as force, acceleration, torque and power need to be measured

Ans: Please refer web resource: nptel.iitm.ac.in/IIT-MADRAS/Mechanical_Measurements, Sub-module 4.4

2.Mention the many methods used for the measurement of force. Ans: Please refer web resource: nptel.iitm.ac.in/IIT-MADRAS/Mechanical_Measurements, Sub-module 4.4

3.Discuss the following with schematic diagrams: Platform balance, acceleration measuring system, brake drum dynamometer

Ans: Please refer web resource: nptel.iitm.ac.in/IIT-MADRAS/Mechanical_Measurements, Sub-module 4.4 (Fig. 47,51,60)

Test your skills:

1. Visit the engine laboratory in your institute, and identify the various dynamometers coupled with the engines, to measure torque. Also learn how to use them to measure torque.

2. Identify the dynamometers shown below:

Page 9 of 11

(a)

(b)

Page 10 of 11

(c )

3. Identify the following apparatus:

Page 11 of 11