Dynamometry Tutorial IMECE

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1 Dynamometry Tutorial IMECE International Mechanical Engineering Congress and Exposition, San Diego, California Dr. Michael L. Jonson The Pennsylvania State University Applied Research Laboratory November 20,

2 Outline Dynamometry Uses Dynamometry Complexity Design Considerations Force transducers Strain gage Piezoelectric force gages Quasi-Steady Dynamometry Unsteady Dynamometry Use of Similitude 2

3 Dynamometry Uses Force and moment measurements Prime mover torque and power determination Engine, motor, propeller, and turbine measurement. Kinesiology Motion and forces of limbs 3

4 Dynamometer Complexity A dynamometer measures force(s) and moment(s). Multicomponent Complicated structure with minimum cross-talk Multiple sensors with an elaborate calibration matrix Rotating For rotating, the power produced by an engine, motor or other rotating prime mover can be calculated by simultaneously measuring torque and rotational speed (RPM). A dynamometer can provide power, absorb power, or both. Time dependent response Inertia complicates calibration and interpretation Allows inference of forces and moments at remote locations 4

5 Dynamometry Design Considerations Choice to measure forces directly For steady or quasi-steady forces by measuring strain is necessary. For unsteady loads dynamics can be exploited Velocity -- using a vibrometer Acceleration --using accelerometers acceleration frequency 5

6 Dynamometry Design Considerations (cont.) Measurement level and frequency requirements Strain gages provide steady levels through weakened structures Piezoelectric sensors provide dynamic response only Cross Talk Mechanical Design Analysis Method Both 6

The Strain Gage A stain gage is usually a metal foil that is adhered to a structure. As the base structure is strained so is the gage and the resistance changes.

7 The Strain Gage A stain gage is usually a metal foil that is adhered to a structure. As the base structure is strained so is the gage and the resistance changes. As the strain gage is stretched along its axis of the gage become longer and narrower thereby reducing its conductivity. The strain gage is typically characterized by its gage factor: R/ R GF G 2 Source: Wikipedia 7

8 Wheatstone Bridge UE R1 R4 U R R R R A R 1 D R 4 Initial balance condition: A C U E R1R3 R2R4 Golden rule: Effects of opposite arms are added. Effects of adjacent arms are subtracted If the unstrained resistances are equal, R 2 R 3 B U A Supply (5V-20V) Signal (mv) U A R R R R U E 4 R1 R2 R3 R

9 Typical Thrust and Torque Cell 9

10 Torque Cell Dan Mihai Ştefănescu, Handbook of Force Transducers: Principles and Components, 10 Springer, 2011

11 Thrust Cell Strain Gage Layout C 4 T 3 C 2 T 1 U E T 2 C 1 Signal (mv) T 4 C 3 U A Supply (20V) Use of eight gages provides additional sensitivity. 11

12 Civil Engineering Application Load Cell 1 Load Cell 2 Erdem Canbay, Ugar Ersoy and Tagrul Tankut, A three component force transducer for reinforced concrete structural testing, Engineering Structures, 26 pp ,

13 Multicomponent Load Cells F axial Strain gage load cell support a column for dynamic load testing F shear M Calibration application 13

14 Calibration Method y f x x is the quantity measured, i.e sensor outputs. y is the quantity to be determined, i.e. loads y1 s11x1s12x2 s16x6 y s x s x s x y s x s x s x or Y SX Notice that the number of sensors can be more than the number of needed loads. The calibration matrix [S] can be determined by supplying sufficient number (p 6) of known load sets (or stages). 14

15 Calibration Method (cont.) Stage Applied Measured 1 y 11 y 21 y 31 x 11 x 21 x 31 x 41 x 51 x 61 2 y 12 y 22 y 32 x 12 x 22 x 32 x 42 x 52 x 62 p y 1p y 2p y 3p x 1p x 2p x 3p x 4p x 5p x 6p Y (p x 3) X (p x 6) or T T Y SX Y X S T Pre-multiplying both sides by T T T X Y X X S X T T S X X X Y T Finally, 1 T 15

16 Calibration Results Load Cell 1 Load Cell 2 Axial load Shear load Bending moment Axial load Shear load Bending moment 16

17 Comparison between predicted and measured loads 17

18 Piezoelectric Sensors Contains piezoelectric materials that provides a charge to an applied stress. Sensors work best in dynamic situations because charge dissipates in most circuits. Very stiff sensors for increased frequency range. 18

19 Measurements in the Rotating Frame Engineers often have choice of installing sensor in rotating or stationary system Advantages Closer to the action Allows understanding of fundamental forcing mechanisms Disadvantages Additional transformations to obtain measurements in the absolute coordinate system. 19

20 High Reynolds Number Pump (HIREP) Jonson, M, Lysak, P, and Willits, S., Smart Materials for Turbomachinery Quieting, 20 Proceeding of the SPIE, Vol. 3991, p. 86, 2000.

21 Rotor Unsteady Force Instrumentation Front View Side View z flow Hub z Flange D D C C d A A y x B B Drive Shaft Unsteady Force Sensors F X = F A + F B + F C + F D M Y = d(f D F B ) M Z = d(f A F C ) 21

22 Coordinate System Effects z z y t y ycos zsin z ysin zcos y The primed system is rotating with speed Ωt. 22

23 Coordinate Transformation The moments are a vector quantity and the shaft rotation is causing the coordinate system to change. We need to resolve the time dependent transformation according to the following formula. M M cos M y y' z M M sin M z y z' sin cos 23

24 Sensors in the Rotation Frame Processing sensors in the rotating frame. M M cos t M sin t y y' z M M sin tm cost z y z' M M t y y' cos y M M cos t z' z' z Now all the data becomes modulated by shaft rate. 24

25 Sensors in the Rotation Frame (cont.) Substituting for the moment in the relative frame: M M cos t cos t M cos t sin t y y' y z' z M M cos t sin t M cos t cos t z y' y z' z Using the following identities: 1 1 cos cos cos cos cos sin sin sin

26 Moments in absolute coordinates Substituting for the identities: M y ' M M y cos cos sin sin 2 t y t t y t z z 2 t t t t M y ' M M z sin t y t sin t y t cos t z t cos t z t 2 2 z ' z ' The moments in the rotating frame are modulated by +/- Ω. For turbomachinery, tonal forces, moments, and noise in the stationary frame happen at multiples of blade rate. For this to happen according to the previous equation, all the frequencies for forces in the rotating frame must be shifted by plus or minus shaft rate. We need M y and M z need to be related in a certain way which is normally a phase shift such as φ z =φ y -π/2. Another way of determining this is by assuming a predicted spectrum in the stationary frame and then determining it in the rotating frame. 26

27 Use of similitude For a rigid rotor, the broadband unsteady thrust spectrum is a function of several parameters GT GT D, n,, V, Pv,, c, f In non-dimensional parameters G T Assumptions F J,, Re, M, f / n nd Advance ratio is constant Cavitation index is high enough so cavitation does not occur Reynolds number: small influence Mach number: small Jonson M., Young, S., Decomposition of Structural and Hydrodynamic Contributions for Unsteady Rotor Thrust, Proceedings of the ASME Noise Control and Acoustics Division, NCA-Vol. 21, p. 77,

28 Propeller and thrust dynamometer 28

29 Calibration without propeller 29

30 Unsteady Thrust due to Grid Turbulence 30

31 Non-dimensional Thrust Spectrum Poor collapse at high frequencies. 31

32 Decomposition Method Consider an elastic rotor G T H f / n S f / f nd where H is the hydrodynamic excitation and S is the structural response These terms are solved iteratively or through least squares. A degree of arbitrariness is introduced requiring the engineer to assume a level for S 0 such as at η 0. G, ij i j nd H is j 0 32

33 Transformed Variable Space 33

34 Results 34

35 General Procedure 35

36 Conclusions Dynamometry uses, complexity, and design approach was discussed. Example dynamometry using strain and piezoelectric force gages was provided. Using similitude, additional physics can be gained from the dynamometry. 36

37 References Dan MihaiŞtefănescu, Handbook of Force Transducers: Principles and Components, Springer, 2011 Erdem Canbay, Ugar Ersoy and Tagrul Tankut, A three component force transducer for reinforced concrete structural testing, Engineering Structures, 26 pp , 2004 Jonson, M, Lysak, P, and Willits, S., Smart Materials for Turbomachinery Quieting, Proceeding of the SPIE, Vol. 3991, p. 86, Jonson M., Young, S., Decomposition of Structural and Hydrodynamic Contributions for Unsteady Rotor Thrust, Proceedings of the ASME Noise Control and Acoustics Division, NCA-Vol. 21, p. 77,

38 Acknowledgements Jon Bechtel, Tyler Dare, and Steve Hambric 38

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