Journal of Materials Engineering and Performance

The Correlation between the Percussive Sound and the
Residual Stress / Strain Distributions in a Cymbal

Journal:Journal of Materials Engineering and Performancer
Fo

Manuscript ID

Manuscript Type:
Date Submitted by the Author:

Technical Paper
28-Sep-2016
Osamura, Kozo; Research Institute for Applied Sciences,
Kuratani, Fumiyasu; Fukui University, Department of MechanicalEngineering
Koide, Toshio; Koide Cymbals
Ogawa, Wataru; Osaka Alloying Works
Taniguchi, Hiroyasa; Osaka Alloying Works
Monjyu, Yoshiyuki; Osaka Alloying Works
Mizuta, Taiji; Osaka Alloying Works
Shoubu, Takahisa; Japan Atomic Energy Agency, Quantum Beam Science
Centerer

Pe

Complete List of Authors:

JMEP-16-08-11209.R2

Re

Keywords:

cymbal, tin-copper alloy, residual strain, synchrotron radiationew

viPage 1 of 19

The Correlation between the Percussive Sound and the Residual Stress /Strain Distributions in a Cymbal
Kozo Osamuraa), Fumiyasu Kuratanib), Toshio Koidec), Wataru Ogawad), Hiroyasu
Taniguchid), Yoshiyuki Monjud), Taiji Mizutad), and Takahisa Shoubue)a) Research Institute for Applied Sciences, Sakyo-ku, Kyoto, 606-8202, Japanb) Department of Mechanical Engineering, University of Fukui, 3-9-1
Bunkyo, Fukui, 910-8507, Japanc) Koide Works, Ltd. (Koide Cymbals), 1-22-32 Kamisyoukakuji, Hirano-ku,
Osaka, 547-0006, Japand) Osaka Alloying Works, Co., Ltd., 45-5-9 Shirakata, Fukui, 910-3138,
Japane) Japan Atomic Energy Agency, Sector of Nuclear Science Research Quantum Beam
Science Center, 1-1-1 Kouto, Sayo-cho, Sayo-gun, Hyogo 679-5148, Japan

rR

ee

rP

Fo

Abstract
The artistic sound of a cymbal is produced by employing a special copper alloy as wellas incorporating complicated and heterogeneous residual stress / strain distributions. In
order to establish a modern engineering process that achieves high quality control forthe cymbals, it is necessary to investigate the distribution of the residual stresses /strains in the cymbal and their quantitative relation with the frequency characteristics ofthe sound generated from the cymbal. In the present study, we have successfully usedsynchrotron radiation to measure the distribution of residual strain in two kinds ofcymbals - after spinforming as well as after hammering. The microstructure and themechanical properties of the cymbals were measured as well their acoustic response.
Based on our experimental data, the inhomogeneous residual stress / strain distributionsin the cymbals were deduced in detail and their influence on the frequency
characteristics of the sound produced by the cymbals were identified.

iew

ev

1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60

Journal of Materials Engineering and Performance

Keywords: cymbal, tin – copper alloy, residual strain, synchrotron radiation, artistic
sound

1

Journal of Materials Engineering and Performance

1. Introduction
The cymbal is a percussion instrument that has existed since ancient times and wasmade from bell metal [1]. It is normally fabricated using one part tin to four parts copper,that is 20% tin. But there have always been some variations. Depending on the
manufacturer, some small but significant amounts of other elements, notably silver, gold,
phosphorus and so on, are added. Bell bronze is a two-phase alloy that includes amajor beta phase and a minor alpha phase. These two phases make the metal harder andmore brittle than a single-phase alloy, affect the hardening process (produced byhammering and lathing), and greatly restricting the use of mechanized techniques for
manufacture.
A typical and traditional process for fabricating a cymbal is shown in Table 1.
Cymbals are made from individually cast ingots which are then hot-forged to form therough shape of the cymbal. The forming process then consists of cupping andspinforming using a spatula to deform the metal into a domed shape in order tointroduce a graded residual stress. In the next turning process, hammering is added tounevenly harden the metal and then the thickness is reduced using a lathe. Particularly
the spinforming and hammering must be entirely performed by a highly skilled handand both labour-intensive processes. These complicated processes that generate theinhomogeneous residual strain produce much of the unique and characteristic musicalsound of the cymbal. This effect is often deliberately enhanced by use of a coarse lathe
tool, and sometimes by a very limited final polishing, leaving the lathe tool marks astone grooves. The broad process for fabricating cymbals mentioned here, is modified byindividual manufacturers. It is important to understand how these modifications result in
more consistent sounding cymbals.

iew

ev

rR

ee

rP

Fo

1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60

2

Page 2 of 19

Page 3 of 19

Table 1 Process for fabricating a cymbal
Process

Detailed Operation

Original Plating

Ingot Casting
Hot Forging
Cupping

Forming

Spinforming
Thickness Adjusting

Turning

Hammering
Lathing

Fo

FinishingThickness Adjusting
PolishingrP

As emphasized above, the fabrication of a cymbal has been developed by experts
during a long process of using both traditional and empirical techniques. In general, thesound produced by cymbals has three characteristics: a loud sound, a complicated tone
and a long echo. They are all very sensitive to the forming and turning processes. If we
can puzzle out a numerical description of each step of these fabrication processes, it
becomes possible to establish a modern engineering process for achieving high quality
control as well as creating the possibility for completely new-sounding cymbals. As afirst step to establishing such an engineering fabrication methodology, it is important tomake clear the distribution of inhomogeneous residual stress / strain in the cymbal andits relation with the frequency characteristics of generated sound from the cymbal.
Cymbals vibrate in many different mode shapes and radiate sounds with complex
overtones. Their characteristic behaviour has been investigated by means of themeasurement of vibration modes [2, 3] and the numerical analysis of mode coupling
and nonlinear vibrations [4, 5]. The sound of a cymbal depends on its size and shapeand also the manufacturing process (cf Table 1). Even though the sound produced isvery sensitive to processing, very few studies have been done on the effect of the

iew

ev

rR

ee

1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60

Journal of Materials Engineering and Performance

manufacturing process until now.
In the present study, two kinds of cymbals (after spinforming as well as after
hammering) were investigated using a beam of synchrotron radiation to determine the
distribution of residual strain. Also microstructural and mechanical properties were
measured as well as acoustic properties. On the basis of our experimental data, theinhomogeneous residual strain distribution in the cymbals was deduced in detail andtheir influence on the frequency characteristics of the sound discussed.
3

Journal of Materials Engineering and Performance

2. Experimental Procedure
2.1 Samples
Two kinds of cymbals, prepared by KOIDE Cymbal, were used in our present study.
The alloy used for the cymbals was Cu-23%Sn-0.3%Ti alloy [6], which was fabricatedby Osaka Alloying Works. As mentioned in the previous section, one of them was thecymbal after spinforming and the other was produced first by spinforming and thenhammered as shown in Fig. 1. After the spinning process, the cymbal has a domed
shape with diameter of 406 mm and thickness of 2 to 4 mm.

rR

ee

rP

Fo
Fig. 1 The top surface of the two cymbals tested (LHS) after spinforming and (RHS)
after hammering.

iew

ev

1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60

Fig. 2 The areas analyzed for residual strain distribution, where E.P. indicates theexcitation point for the acoustic measurements.
2.2 Residual strain measurements
The diffraction experiments were carried out at room temperature at the BL28B2 stationof SPring-8. It used white X-rays with energies between 30 and 150 keV with twocooled Ge solid-state detectors set to a diffraction angle of 2θ = 11o at the verticaldirection (dv) and horizontal one (dh). The cymbal (s) was placed on the goniometer as
4Page 4 of 19

Page 5 of 19

shown in Fig. 3. Here the data accumulated using the vertical detector (dv) are reported,which give information about the strain along the circumferential direction. The slit
sizes used were 0.05x0.05 mm2 for the entrance and 0.05x5.0 mm2 for the exit. In
addition, a collimator with cross-sectional area 0.05x5 mm2 and 150 mm length wasplaced behind the exit slit in order to restrict the gauge volume.

rP

FoFig. 3 Layout of the cymbal (s) and detectors (dv and dh) for measuring theresidual strain in the cymbal. The bottom surface of the cymbal is clearly shown.

ee

The points selected for analysis were chosen as follows: As shown in Figs. 1 and 2, thecenter of the area chosen for analysis was at L1 where the radius of (L1-L0) was aboutrR

160 mm and the radius of cymbal (LE-L0) was 203 mm. In order to investigate the
distribution of local residual strain at L1, the cymbal was shifted along the horizontal
direction (x–direction) step by step as shown in Fig. 4, where the central coordinate x0of the hammering depression was set at the center of hammering depression close to L1.
Each shift along x-direction for each step was xi-xi-1 = 1 mm. At each step, the cymbal
was also shifted in the depth direction (y-direction) so the beam was focused at
positions from the top surface of the cymbal (cf Fig. 1) to the bottom surface. By thesemeans, a total of 49 different diffraction data sets were accumulated from locations
throughout the volume of each cymbal. In the case of the cymbal after spinforming,
where the surface of the cymbal was relatively smooth, the measurements were carriedout in the same area (i.e. at L1) as shown in Fig. 1.
Because a white X-ray source was employed, multiple diffraction peaks wereobserved. In the present experimental conditions, they were the (110), (220), (222),

iew

ev

1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60

Journal of Materials Engineering and Performance(400) and (420) peaks of the β-phase and the (311), (331), (420), (551) and (533)
peaks of the α-phase. An example of part of the experimental procedure is provided
by considering the data shown in Fig. 5: The (222) diffraction peak for the β-phase
was detected while shifting each analyzing position from y= -0.8 mm to 1.2 mm. Figure
5Journal of Materials Engineering and Performance

5 shows that the lattice spacing increases as the analysis position changes from thebottom surface to the top one. In the present study, the spacing of the (420) plane was
employed for residual strain measurements because the (420) diffractions were observed
most frequently and its diffraction intensity was strong enough to ensure sufficient
statistical accuracy. The strain (A) was calculated from the observed lattice constant (a)of the β-phase by using the relation A = (a − a0 ) / a0 ⋅100 [%] , where a0 is the data for
an unstrained powdered sample.

ev

rR

ee

rP

Fo
Fig. 4 Analyzing positions at and around a hammering depression
3 104

iew

after Spinforming
4

2.5 10y= - 0.8 mm

4Intensity (a.u.)

1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60

2 10

1.5 104
y= - 0.4 mm
4

1 10

y= 0 mmy= 0.4 mm
y= 0.8 mm

5000

y= 1.2 mm

x 25
0
0.79

0.8

0.81

0.82

d (A)

6

0.83

0.84

0.85

Page 6 of 19

Page 7 of 19

Fig. 5 The (222) diffraction peak for the β-phase obtained by analyzing positions fromy= -0.8 mm to 1.2 mm in the cymbal after spinforming

2.3 Microstructure analysis and tensile test
After the residual strain measurements, the cymbals were cut for the microstructural
analysis as well as tensile testing. The microstructural analysis was carried out using anelectron probe micro-analyzer (EPMA JEOL JXA-8500F). Tensile testing was carriedout at room temperature using a tensile machine Shimadzu AG-50kNIS. The initial
distance between chucks was kept as 100 mm. A Nyilas type double extensometer (GL= 25 mm) was attached at the center of the sample. The initial cross head speed wasselected as 1.67x10-5[s-1].

rP

Fo

2.4 Acoustic Measurement
In order to investigate the change of sound due to the forming and turning processes,
acoustic measurements were performed. In general, the sound spectrum changes
depending on the position of the excitation point and the position for accumulating thesound data. The main purpose of our study was to investigate the influence of thedifferent fabrication stages on the sound spectra. So, we kept the conditions for the
acoustic measurements on both cymbals the same: The cymbal was struck using theimpulse hammer with 40 N at the excitation point (E.P.) shown in Fig. 2, which was
located at about 20 mm from the edge. The sound radiation was measured using a
microphone placed 100 mm away from the edge of cymbal. The sampling time andfrequency were 2.56 s and 25600 Hz, respectively. Eventually 65,536 data were Fourier– transformed to provide the frequency spectra.

iew

ev

rR

ee

1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60

Journal of Materials Engineering and Performance

3. Experimental Results
3.1 Microstructure
Fig. 6 shows the microstructure of the cymbal after the hammering. It is heavily
deformed with a coarse grained polycrystalline microstructure. The matrix and theprecipitates were analyzed using EPMA and found to be β - and α -phases
respectively. The microstructural observations showed that no micro-cracks occurred in
the cymbal after the hammering. On the other hand, the general experience withcymbals is that most of them are eventually damaged by cracks after extensive use.
The main reason for the cracking is predominantly related to the plastic deformation at7

Journal of Materials Engineering and Performanceand around the region where the cymbal stick strikes the cymbal during use. It is known,that one factor that determines the lifetime of the cymbal relates to its deformability, theso-called ‘softness’ of the cymbal itself, but it is not yet clear how this relates to thedepressed areas produced by hammering.

ee

rP

Fo
Fig. 6 Cross section of the cymbal after the hammeringrR

3.2 Tensile Properties
Fig. 7 shows the stress – strain curves for the two samples quarried along thecircumfrential direction of cymbals after spinforming and hammering. Their tensile
properties were almost the same, - the Young’s modulus (E) and the 0.2% proof stress(R0.2) were determined as 80.8 GPa and 384 MPa, respectively.

iew

ev

1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60

8

Page 8 of 19

500

Circumferential
400

300

200

Fo

Spinforming (----)
Hammering (----)

100

rP

0

0

0.2

0.4

0.6

0.8

1

A (%)

ee

Fig.7 Stress vs strain curve for the two samples quarried from the cymbals after
spinforming and hammering.

rR

In order to evaluate the stress corresponding to the local strain, it is necessary toestablish the functional relationship between stress and strain. For this purpose, thefollowing equation was applied [7],evEb( A)1+1 / n
R=
EA + b( A)1 / n

iew

1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60

Journal of Materials Engineering and Performance

R (MPa)Page 9 of 19(1)

Where E, b and n are the fitting parameters. The result of curve-fitting is shown in Fig.
8, where the open circles are the calculated results using Eq.(1). The calculated results
were found to fit the experimental data well, where E=80.8 GPa, b=900 and 1/n = -1.1.

9

Journal of Materials Engineering and Performance

500

Circumferential

R (MPa)

400

300

200

Spinforming (----)
Hammering (----)

100

Fo
0

0

0.2

rP

0.4

0.6

0.8

1

A (%)

Fig.8 Result of the curve-fitting of Eq. (1) to the experimental data, where the open
circles are the calculated resultsee

3.3 Residual strain measurement
For each cymbal, diffraction data were measured at 49 coordinates of (xi, yi) as shown in
Fig. 4. At each position, different combinations of diffraction peaks were observed
because in these coarse grained polycrystalline samples, the crystal orientation of theevrR

β-phase grains from which most scattering occurred, changed from position to position.
Although the lattice constant derived from all equivalent diffraction peaks is the same,in practice it is not possible to determine an absolute value of the lattice constant towithin an accuracy of higher than 0.02 %. As such, in the present paper, we havedetermined the relative change of lattice parameter from the strong (420) diffraction

iew

1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60

peak of the β-phase in our analysis. This ensures the precision is better than 0.015 %.
Fig. 9(a) shows the change of lattice parameter of the β-phase from the bottom
surface to the center of the thickness of the cymbal after spinforming, around theposition L1. The experimental data are given in the range of between y = -1.2 and 0 mm.
None of the β(420) diffraction peaks were observed in the remaining range between y= 0.4 and 1.2 mm. As shown in Fig. 9(a), the lattice parameter increased linearly fromthe bottom surface to the top. The lattice parameter changes that were observed in the
thickness direction were similar for all the xi positions from x1 to x-2. The residual strain
became zero at the center of cymbal (y = 0 in Fig. 9(a)). The average lattice parameterfor four experimental data at y = 0 was evaluated to be a0(β)=2.8315 A. Thus, given
10

Page 10 of 19

Page 11 of 19

the linearity and the repeatability observed, we can assume that for the spinforming
cymbal, the lattice parameter at the top surface can be found by extrapolating, using thedotted line shown in Fig. 9(a). On the other hand, the magnitude of the lattice parameterand the changes in lattice parameter were different for the different xi positions for thecymbal after hammering as shown in Fig. 9(b). Nevetheless, we found that the lattice
parameter broadly increased linearly with increasing y position again (i.e. from thebottom surface to the top).
2.86
2.85

after Spinforming

Foa(β) (A)

2.84
2.83

rP

2.82
2.81

x1
x0

ee

2.8
2.79
2.78
-1

x-1
x-2

rR

-0.5

0

0.5

1

y (mm)(a)2.86

after Hammering

iew

2.85

ev

2.84
2.83

a(β) (A)

1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60

Journal of Materials Engineering and Performance

2.82
2.81
x1
x0
x-2
x-3

2.8
2.79
2.78
-1

-0.5

0

y (mm)

(b)
11

0.5

1

Journal of Materials Engineering and PerformanceFig. 9 Change of the lattice parameter of β-phase as a function of the depth
coordinate y for the cymbals after the spinforming (a) and the hammering (b).

3.4 Residual strain distrribution
Using the lattice parameter data shown in Fig. 9, the residual strain was evaluated.
The change of residual strain along the thickness direction is shown in Fig. 10 for thecymbal after spinforming. The maximum compressive strain at the bottom surface (y=-1.2mm) was on average of -0.24 %. The compressive strain reduced linearly towards
the center. The strain distributions were nearly the same, independent of the xi positions.
Hence using extrapolation, we found that the maximum tensile strain at the top surface
was estimated to be 0.24 % at y = 1.2mm.
The change of residual strain as a function of thickness is shown in Fig. 11 for thecymbal after hammering. The magnitude of residual strain was quite strongly dependent
on the xi position. Here (to aid with comparison) the dotted line indicates therP

Fo

distribution of residual strain in the cymbal after spinforming. The residual strains tend
to shift towards the compressive strain side at the centre of the hammered depression(i.e. at x0) as expected, while the residual strain increased with increasing y position
from the bottom surface to the top surface. Within the experimental data indicated here,
the maximum compressive strain was recorded as 0.71 % at y= -0.4 mm of x0.

rR

ee

1

ev

after Spinforming

A (%)

0.5

iew

1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60

0

x1
x0
x-1
x-2
cal

-0.5

-1
-1

-0.5

0

0.5

1

y (mm)

Fig. 10 Residual strain distribution as a function of thickness for several xi positions forthe cymbal after spinforming
12

Page 12 of 19

after Hammering
0.5

0

-0.5
x1
x0
x-2
x-3
cal

Fo
-1

rP
-1

-0.5

0

0.5

1

y (mm)

Fig. 11 Residual strain distribution as a function of thickness for several xi positions foree

the cymbal after hammering.
3.3 Residual stress distribution
The residual stress was evaluated from the residual strain by using the functional
relation given by Eq. (1). The residual stress distribution as a function of thickness isshown in Fig. 12 for the cymbal after spinforming. The maximum compressive stressgenerated at the bottom surface (at y= -1.2 mm) had an average of -172 MPa. When
extrapolating to the top surface (at y = 1.2 mm), the maximum tensile stress was foundto be 172 MPa.

iew

ev

rR

400

after Spinforming200

R (MPa)

1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60

Journal of Materials Engineering and Performance

A (%)

Page 13 of 19

0

-200
x1
x0
x-1
x-2
cal

-400

-600
-1

-0.5

0

y (mm)

13

0.5

1

Journal of Materials Engineering and PerformanceFig. 12 Residual stress distribution as a function of thickness for several xi positions forthe cymbal after spinforming
400

after Hammering

R (MPa)

200

0

Fo
-200

rP

x1
x0
x-2
x-3
cal

-400

-600
-1

ee
-0.5

0

0.5

1

y (mm)

rR

Fig. 13 Residual stress distribution as a function of thickness for several xi positions forthe cymbal after hammering.

ev

The change of residual stress for the cymbal after hammering is shown as a function of
thickness in Fig. 13, where the dotted line indicates the distributuion of residual stress inthe cymbal after spinforming. The stress was mostly compressive. The maximum
compressive stress measured was -376MPa and the maximum tensile stress was
257MPa as far as the experimental data are shown in Fig. 13.

iew

1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60

3.4 Strain / stress distribution around a hammaring depression
The depressions (as shown in Fig. 4.) were produced by hammering. The strain andstress distribution around a depression are shown in Figs. 11 and 13. Instead of Fig. 11,
where the residual strain around a hammering depression is plotted as a function of y,four experimental data points at y = 0 and 0.4 mm are plotted as a function of (xi – x0)
and shown in Fig. 14. If it is assumed that the distributuion of residual strain issymmetric around the depression, it is possible to link each four experimental data andto depict the distribution as shown by the dotted lines. Thus we can see the broadfeatures of the residual strain distribution around the hammering depression. At the
14

Page 14 of 19

Page 15 of 19

centre of the depression, the residual strain is strongly compressive but at the outercircumference of the depression, the residual strain can become tensile. The residualstrains are more strongly compressive as one approaches the back of the cymbal(comparing y = 0.4 mm with that at y = 0 mm). Using the same procedure, thedistribution of residual stress around a hammering depression was estimated as shownin Fig. 15. The maximum compressive stress was 330 and 273 MPa at y = 0 and 0.4 mm,
respectively.
0.4

after Hammering
0.2

Fo

A (%)

0

-0.2
-0.4
-0.6
-0.8
-1

-2

-1

0

y=0
y=0 caly=0.4 mmy=0.4 mm cal
1

rR

-3

-4

ee

rP

2

3

4

xi - x0 (mm)Fig. 14 Estimated distribution of residual strain around a hammering depression for thecymbal after hammering

400

iew

ev

y=0
y=0 caly=0.4mmy=0.4mm cal

after Hammering200

R (MPa)

1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60

Journal of Materials Engineering and Performance

0

-200

-400
-4

-3

-2

-1

0

1

2

3

4

xi - x0 (mm)Fig. 15 Estimated distribution of residual stress around a hammering depression for thecymbal after hammering
15

Journal of Materials Engineering and Performance

3.5 Frequency distribution of sounds
Typical results from our acoustic measurements, in the frequency range of human
audible sound, are shown in Fig. 16. The frequency dependence of the sound pressure isindicated in the range between 0 and 8 kHz for both cymbals (i.e. after spinforming andafter hammering). Several pressure peaks are observed. A common feature for both
cymbals was the eight large peaks indicated by ▽. Their intensities are stronger by
29 % on average for the hammered cymbal. The second feature was that the peakindicated by ▲ that appears for the cymbal after spinforming, but disappers after
hammering. The third feature was that several new peaks indicated by ▼ appear forthe cymbal after hammering. In general, the peak intensities (sound pressure) arestronger for the hammered cymbal. So it is clear that the hammering offers apronounced effect, generating intense and complicated artistic sounds.

iew

ev

rR

ee

rP

Fo

1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60

Fig. 16 Frequency dependence of sound pressure for two cymbals after spinforming andafter hammering
4. Discussion
Empirically it has been long recognized that the spinforming provides the basic
frequency pattern of the cymbal which consists of the wide distribution from low tohigh frequencies. The hammering increases the intensity of the sound from the cymbal(cf Fig. 16) and strongly modifies the frequency distribution particularly enhancing thehigh frequency components. The successive lathing and finishing processes modifies
16

Page 16 of 19

Page 17 of 19

the sound pressures produced.
Thus the special sounds produced by the cymbals should be strongly related withthe storaged large residual stress / strain in the cymbal. The deformation into the cup
shape during the spinforming process produced stored compressive and tensile stress /strain which were found to have maximum amplitudes of 344 MPa / 0.34%, respectively.
The additional inhomogeneous deformation produced during the hammering process
produced very large additional stored compressive stresses / strains reaching to 376
MPa / 0.71 % at the center of hammering depression.
This work shows that the latter inhomogeneous stress / strain distribution at thehammering depression strongly affects the frequency distribution. It has also been
recently analyzed by one of coauthors using finite element analysis (FEA) [4, 8] andalso by applying a thermal stress to reproduce a local stress distribution. The
FEA/thermal results showed each mode of the cymbal has a different sensitivity to thethermal load. The eigenfrequencies of some modes decreased as the bending modulus
decreased. This led to a change in the frequency response and in the deformation shapeby hammering that significantly improved the sound radiation efficiency. The
experimental observations of the change in frequency distribution mentioned in Section
3.5 are qualitatively consistent with the results from the FEA.
A similar technique of storing residual stress/strain has been used to improve
circular saws for cutting wood [9]. This approach suppresses "snaking" in the circularsaw when it rotates at or close to its critical speed. This is a vibrational resonancephenomenon called critical speed instability [10]. In order to reduce this instability, thesaws can be “tensioned” to increase the dynamic stiffness of saws. Typically, thetensioning is carried out by hammering or rolling the sawblade surfaces. Further new
techniques such as heat tensioning and thermal tensioning are also becoming popular. In
all of these methods, the tensioning induces stored in-plane stresses in the sawblade.
When favorably distributed, these stresses substantially stiffen the sawblade andimprove its cutting stability. However according to Barz [11], hammer tensioning isvery much an art, and great skill and experience is required to achieve good results.
When done well, hammering can be as effective as more modern methods. However,hammer tensioning is usually not recommended for general use because the results canbe very variable. Also, the hammer blows make the sawblade surface uneven and caninitiate fatigue cracks. It is emphasized that the various techniques using for “tensioning”
circular saws might yet offer routes for further improvement of cymbals

iew

ev

rR

ee

rP

Fo

1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60

Journal of Materials Engineering and Performance

5. Summary
17

Journal of Materials Engineering and Performance

The artistic sounds of a cymbal are realized by employing a special copper alloy as wellas the creation of complicated and inhomogeneous residual stress / strain distributions
by an expert in the art. In order to establish modern engineering processes to achieve
high quality control of cymbals, it is necessary to investigate the distribution of residual
stress / strain in the cymbal and their quantitative relation with the frequency
characteristics of the sound generated by the cymbal.
In the present study, we have succeeded in measuring the distribution of residualstrain in two kinds of cymbals after spinforming as well as after hammering, by meansof synchrotron radiation. We have also measured their microstructure, mechanicalproperties and acoustic response. On the basis of these experimental data, theinhomogeneous residual stress / strain distribution in the cymbals was measured andanalyzed in detail and their influence on the frequency characteristics of the sound was
identified and discussed.

rP

Fo

Acknowledgements:
The authors express their hearty thanks for Dr Kentaro Kajiwara of JASRI for his
valuable scientific suggestion and experimental support. The diffraction experiments
were performed at BL28B2 of Spring-8 as the research subject of industrial application(Proposal No. 2013A1346).

rR

ee

References[1] N. H. Fletcher and T. D. Rossing; The Physics of Musical Instruments, Springer Verlag (1998)[2] G. D. Giulio, E. Esposito, C. Santolini and L. Scalise; Experimental Vibrational
Analysis of Drum Cymbals, Proceedings of the 19th International Modal Analysis
Conference, 2001, 724-730[3] R. Perrin, G. M. Swallowe, S. A. Zietlow, and T. R. Moore; The normal modes ofcymbals, Proceedings of Spring Conference of the Institute of Acoustics 2008:
Widening Horizons in Acoustics, Proceedings of the Institute of Acoustics Vol. 30. Pt.2,
pp.460-467, 2008
[4] T. Kawai, F. Kuratani, T. Yoshida and T. Masumoto; Sound Radiation Characteristics
of Cymbals based on Mode Shapes, Proceedings of 52th JSME Hokuriku Shin-etsu
branch conference, Paper No.0311, (2015) (in Japanese).
[5] A. Chaigne, C. Touze´ and O. Thomas; Nonlinear vibrations and chaos in gongs andcymbals, Acoust. Sci. & Tech. 26, 5 (2005) pp.403-409[6] http://koidecymbal.com/lineup/index.html

iew

ev

1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60

18

Page 18 of 19

Page 19 of 19[7] K. Osamura, S. Machiya , Y. Tsuchiya , H. Suzuki, T Shobu, M Sato, S. Harjo, K.
Miyashita, Y. Wadayama, S. Ochiai and A. Nishimura; Thermal Strain Exerted on
Superconductive Filaments in Practical Nb3Sn and Nb3Al Strands, Supercond. Sci.
Technol. 26 (2013) 094001 (8pp).
[8] F Kuratani, T Yoshida, T Koide, T Mizuta and K Osamura, Understanding the effectof hammering process on vibration characteristics of cymbals, MoViC RASD (2016)[9] G.S. Schajer; Understanding saw tensioning, Holz als Rob- und Werkstoff 42 (1984)425~430[10] C. D. Mote Jr and L. T. Nieh; On the foundation of circular-saw stability
theory. Wood and Fiber 5 (1973) 160-169[11] E. Barz,: Vergleichende Untersuchungen ueber das Spannen vonKreissaegeblaettern mit Maschinen und mit Richthaemmern. (Comparative studies oftensioning of circular sawblades with machines and by hammering). Holz Rob und
Werkstoff 21 (1963) 135-144. CSIRO Australia Translation No. 6583

iew

ev

rR

ee

rP

Fo

1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60

Journal of Materials Engineering and Performance19