Experimental Model Analysis Of Free-Free Tennis Racket Using A

“Star Structure”Star Structure

Dr. Abdulkarim M. AlotaiwiAssistant professor-Mechanical Engineeringss sta t p o esso ec a ca g ee g

objectivesobjectives

1. The main objective of this experiment is to analysis the impact of the vibration in tennis racket frame.

2 Th d bj ti f thi i t i t2. The second objectives of this experiment is to establish confidence and familiarity when dealing with the structural softwarethe structural software .

3. The third objective is to use the software to acquire data and analyzed such as (mode shape, natural da a a d a a y ed suc as ( ode s ape, a u afrequency and damping ratio).

2

Experiment ToolsExperiment Tools

1. Tennis racket.2. FFT analyzer.3. Accelerometer (piezo type).4. Amplifier.5. Computer with data acquisition cards.6. Impact hammer with sensitive sensors.7. Connecting wires.

3

Experiment procedureExperiment procedure1 Measure the dimensions of the tennis racket1. Measure the dimensions of the tennis racket.2. divide the tennis racket in to 49 point around the

racket frame. 3. Set up the equipment as shown in figure 1, and

attach the accelerometers using wax.4 set up the vibration directions (X Y Z)4. set up the vibration directions (X,Y,Z) .5. Configure the FFT analyzer in frequency response

mode with rang 0-KHz.

4

Experiment procedureExperiment procedure

6. In “Star Structure” ,define geometry and prepare to accept the frequency response data from FFT analyzeranalyzer.

7. Carefully excite the racket with the Impact hammer for all points When the response is good accept the dataall points. When the response is good, accept the data in “Star Structure”.

8. Analyze the mode shape, natural frequency etc.. in 8 a y e e ode s ape, a u a eque cy e c“Star Structure”. If the result is not acceptable, repeat step no.7.

5

Equipment SetupEquipment Setup

6 Figure 1. Equipment Setup.

Experiment resultsExperiment results

# 1:141.27 H z

12

3 45 6 7 8 9 1011

12 131415

16

1718

1920

21

272829

303132

333435

3637

38394041424344454647

4849

Z

2223

2425

26

30424344454647

X

Y

• Figure 2. Mode 1: 1st Bending Mode Along X Axis.

7

Experiment resultsExperiment results# 2:401.54 H z

123456789

101112131415

161718192021

22232425

26

27282930 31 3233 34

35 3638 39 40 41

42 43 44

45 46474849

Z

101126 3738 39

X Y

• Figure 3. Mode 2: 2nd Bending Mode Along X Axis.

8

Experiment resultsExperiment results# 9:835.24 H z

56789

1011

20

21

2223

26 3031

34 3839

4041

4243 44

45 4647

48

• Figure 4. Mode 4: 3rd BendingZ

123

451213

141516

1718192223

24

25

2728

29

3233

3435

36

374849

Figure 4. Mode 4: 3 Bending Mode Along X Axis.

XY

# 9:835.24 H z

123

4141516

24

27

28

29

3233

3435

3637

3839

40 42 45 464748

49

Z

56

7891011

1213171819

20

21

222325

26 30

31

4041

4243 44

45 46

9 XY

Experiment resultsExperiment results

# 7:896.86 H z

1231415

16

1718

19

2427

282933 34

35 363738

3940 42 4849

Z

12345

67891011

1213

14

2021

2223

25

2630 31

32 41 4243 44 45 4647

4849

XY

• Figure 5. Mode 6: 4th Bending Mode Along X Axis.

10

Experiment resultsExperiment results

1 2 34

567

89

10113738

3940

41

4243

444546 47

48 49

# 3:557.47 H z

9

121314

151617

1819

2021

272829

3132

33

3435

36

Z

21

222324

25

26

30

X

Y

• Figure 6. Mode 3: 1st Bending Mode Along Y Axis.

11

Experiment resultsExperiment results

1 2 3 4

567

83839

4041

42 43 4445 46 4748 49

# 5:882.66 H z

89

1011

1213

141516171819

20

272829

31

33

3435

36

37

38

Z

2122

2324

25

26

3031

32

X

Y

• Figure 7. Mode 5: 1st Torsion Mode.

12

Experimental resultsExperimental results

1 24243

44 4546 47

4849

# 8:932.40 H z

3456

7891011

121314151617

2728

29

30

31

3233

34353637

38394041

Z

18

1920

212223

2425

26

30

X Y

• . Figure 8. Mode 7: 2nd Torsion Mode

13

Experiment resultsExperiment resultsD i R ti [%]F [H ]C iM d Damping Ratio [%]Frequency [Hz]ComparisonMode

0.660141.271st bending mode along X axis1

0.411401.542nd bending mode along X axis2 0.411401.542 bending mode along X axis2

0.0406557.471st bending mode along Y axis3

0 647835 243rd bending mode along X axis4 0.647835.243 bending mode along X axis4

0.314882.661st torsional mode in XY plane5

0.139896.864th bending mode along X axis6

0.354932.402nd torsional mode in XY plane7

* 0.763834.085th bending mode along X axis*8

0.351836.45Coupled mode 4 and mode 8**9

14

Experiment resultsExperiment results

15Figure 9. Frequency Response at measuring point 3.

Experiment resultsExperiment results

16 Figure 10. Frequency Response at measuring point 20.

ConclusionsConclusionsI thi i t th ib ti f t i k t i• In this experiment, the vibration of a tennis racket is investigated.

• 8 different modes are found between 0 to 1 KHz8 different modes are found between 0 to 1 KHz. • 4 bending modes along X axis,1 bending mode along Y

axis and 2 torsional modes were determined.• Remaining one mode shows large interaction with 3rd

bending mode and the mode shape of this mode is not clearly identifiedclearly identified.

17

ConclusionsConclusionsd th• The result of 3rd and 4th bending modes are not very

clear; especially the racket handle shows inharmonic trend with the elliptic part of the rackettrend with the elliptic part of the racket.

• In the tennis racket test the sensor was located at point 21 For future work the sensor location has to bepoint 21. For future work the sensor location has to be carefully reconsider .

• The head of the impact hammer was selected based e ead o e pac a e as se ec ed basedon the type of the structure; it is important to hit the same point in the same direction for each average time.

18

ConclusionsConclusions

• Two obstacles were faced. First, was having random noise in the FRF record Second was having twonoise in the FRF record. Second, was having two peaks close to each other.

• It is important that to distinguish between the randomIt is important that to distinguish between the random noise which excite in the excitement work and the modes number .

• The largest amplitude (i.e., strain) was usually found in the second bending mode, but other modes, 1st & 3rd

bending mode and 2nd torsional mode show significant amplitude in certain case.

19

ConclusionsConclusionsLargest deflection in the first bending mode in each of• Largest deflection in the first bending mode in each of X and Y axis were observed on each tip. The 2nd

bending mode had the largest deflection at the tip of th h dl ith i ifi t d fl ti i th iddl fthe handle with significant deflection in the middle of the elliptic part

• In torsional modes, the largest deflection is found in , geach corner of the racket.

• The boundary condition of the system has huge influence on the result Therefore the boundaryinfluence on the result. Therefore, the boundary condition should remain the same over the experiment.

20

Thank you for your time; and ifThank you for your time; and if you have any questions I will y y q

be happy to answer them.

21