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Influence of Tin Bronze Melting and Pouring Parameters on Its Properties and Bells’ Tone

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The most important feature of bells is their sound. Its clarity and beauty depend, first of all, on the bell’s geometry - particularly the shape of its profile, but also on the quality of alloy used to its cast. Hence, if the melting and pouring parameters could influence the alloy’s properties, what influence they would have on the frequencies of bell’s tone. In the article authors present their own approaches to find answers on that and more questions.
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A R C H I V E S
of
F O U N D R Y E N G I N E E R I N G
DOI: 10.1515/afe-2016-0076
Published quarterly as the organ of the Foundry Commission of the Polish Academy of Sciences
ISSN (2299-2944)
Volume 16
Issue 4/2016
17 22
A R C H I V E S o f F O U N D R Y E N G I N E E R I N G V o l u m e 1 6 , I s s u e 4 / 2 0 1 6 , 1 7 - 22 17
Influence of Tin Bronze Melting and Pouring
Parameters on Its Properties and Bells Tone
D. Bartocha *, C. Baron
Department of Foundry Silesian University of Technology, ul. Towarowa 7, 44-100 Gliwice Poland
*Corresponding author. E-mail: dariusz.bartocha@polsl.pl
Received 06.04.2016; accepted in revised form 30.06.2016
Abstract
The most important feature of bells is their sound. Its clarity and beauty depend, first of all, on the bell’s geometry - particularly the shape
of its profile, but also on the quality of alloy used to its cast. Hence, if the melting and pouring parameters could influence the alloy’s
properties, what influence they would have on the frequencies of bell’s tone. In the article authors present their own approaches to find
answers on that and more questions.
Keywords: Tin Bronzes, Parameters of melting and pouring, Bell’s Tone
1. Introduction
The bell is a peculiar kind of art casting, it may be said that it
is double art. On the one hand the bell should be regarded as a
kind of sculpture, mainly in terms of the so-called graphic layout
The shape and proportion of whole bell’s solid is also very
important. The perfect example of modern bell’s graphic layout
may be the new bells of Cathedral Notre Dame in Paris (Fig. 1).
On the other hand the bell is a musical instrument. The whole
craftsmanship of making bells lies in the fact that beside the
beautiful shape and decorations, they emit clean and pleasant to
the ear sound. Only the bell that fulfills both of these conditions,
deserves to the art casting titre. A beautiful bell but with an
unclean sound is not a proper bell. But despite the perfect tone, a
bell designed in Australia might be regarded as a full value bell.
Finite element analysis was used to design this bell with particular
tonal qualities, which was then cast in moulds made using
numerical controlled tools. The bell was designed on a number of
different principles, such as to have harmonic partials or multiple
pitches a planned interval apart. The profiles of this bell are
complex as can been seen from Figure 2 [1, 2].
Fig. 1. Anne-Geneviève one of the new bells of Cathedral
Notre Dame in Paris
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Fig. 2. Special profile of polytone bell by Australian Bell [2]
Church bells are type of idiophone, in which a tuning process
is used to give closely harmonic modes.
Tuning process consists of minor adjustment by turn metal off
the inside of the bell at specific places [4, 5]. Bell tuning is as
much art as science, because removing metal from a particular
annular circle inside the bell, affects the frequencies of multiple
partials in different ways. Also, metal once removed cannot be
replaced. Lehr [6] provides details of experiments showing how
each partial is affected by removal of metal at various points.
Fig. 3. The shape of bell’s profile
In the case of bells, the general pattern of mode frequencies is
fixed by the so called profile [3], which is different in spite of its
origin, the most popular profiles are shown in figure 3. The target
frequencies for the first few modes are in the ratios 0.5 : 1.0 : 1.2 :
1.5 : 2.0 . . . and these can be quite closely matched. The first
mode, called the hum, is not prominent, and the perceived pitch is
usually that of the second mode or ‘prime’, perhaps because it is
reinforced by the harmonically-related modes with relative
frequencies 2, 3 and 4. The tone is complex, particularly because
of the presence of the minor-third interval 1.2. The sound of bells
playing in harmony is therefore, to say the least, ‘characteristic’.
The vibration of bells is essentially linear because of their
great wall stiffness, but there is nevertheless one nonlinear aspect
of the produced sound. This arises because the first mode, which
is responsible for the hum tone, has a shape in which the axial
cross-section of the bell oscillates between two ellipses oriented at
right angles to each other. Since the area enclosed by an ellipse is
smaller than that enclosed by a circle of the same perimeter, this
oscillation at frequency f1 moves air in and out of the bell’s
mouth at frequency 2f1 and generates a tone that reinforces the
prime [3].
One other feature of bell’s vibration is worth mentioning, and
that is that all the modes noted above are actually doubly
degenerated because of the rotational symmetry of the bell. In
practice this symmetry is unlikely to be exact, so the degeneracy
is lifted and each mode actually consists of a closely spaced
doublet, and these generally produce very slow beats that are
clearly audible.
A number of factors affect the amplitude of the various
partials in the sound of a bell. These include:
Mechanical characteristics of the bell, i.e. its shape and wall
thickness and the composition of the metal,
The clapper material and the dynamics of the impact as the
clapper hits the Bell,
The acoustics of the room or building in which the bell is
housed.
Perception of loudness of sounds in the ear also varies with
frequency.
Perrin et al [4] identified 134 modes of vibration, many of
which were doubleted giving almost twice this many partials.
Each mode of vibration was identified by comparing experimental
results with a computer simulation of the bell structure. However
the properties of bell’s material used in simulation are not
introduced.
Gołaś et al [7] in own calculation adopted the following
properties of bell’s material: the Young module of 1.05E+5 MPa,
the Poisson ratio of 0.33 and density of 8600 kg/m3. They
analyzed only three partials: hum, prime and third, differences in
obtained frequencies compared to perfect tuned are quite big.
Expressing the difference between the frequencies in cents, it is
evident that in musical terms the interval between hum and prime
modes differs from perfect octave by about 2 semitones (201
cents), while the interval between minor third and prime differs
from perfect minor third by about 3/4 semitones (76 cents).
According to the equation (1) natural frequencies are the
function of geometry (shape of profile) and properties of material
with which the bell was made. Therefore, in modal analysis
(natural frequencies determination) or designing (new profile, bell
scaling) based on numerical simulation, the fundamental is
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validation of the model, taking into account material properties.
Especially because both the material properties and bell’s
geometry depend of molding, melting and casting processes.
([𝐾]− 𝜔𝑖
2[𝑀]){𝜑𝑖}= {0} (1)
Where:
[K] stiffnes matrix,
[M] mass matrix,
- natural frequencies,
- mode shapes.
How big the differences between frequencies of measured and
calculated partials can be? To answer this question, the authors
have carried out simple experiment. It consists of measuring
profile of well-tuned bell on bridge-type measuring machine
ZAISS Acura 7. The carillon bell without any graphic layout, c3
tone was used. On the basis of measurement the geometric model
of the bell was performed and next it was subjected to modal
analysis with ANSYS Modal. Calculated characteristic own
frequencies of bell were compared with partials obtained in
analysis of bell sound. Analysis by Fourier transform were
performed with Wavanal software created by Bill Hibbert. The
partials chosen are those which determine the strike pitch, the
lowest five partials (hum, prime, tierce, quint and nominal), which
are traditionally tuned by bellfounders, and other prominent
partials as seen in Figure 4.
Fig. 4. Frequencies of prominent partials determined for tested
bell
Mode shapes affecting chosen partials of the bell sound were
determined accordingly to the literature [4] The results are
presented in Fig. 5.
Modal analysis was performed for material properties of bell
bronze accordingly with, in first step ASTM standard (UNS
C91300) and in second [7]. Next the materials properties had been
changed to obtain frequencies of partials as near the measured
ones as possible, the arbitrary partial was nominal. In first
approach only Young’s modulus (E) was changed, in second only
density (ρ) and in third Poisson’s ratio (ν). All obtained results are
presented in Table 1, except ones for Poisson’s ratio because even
the absurd values of ratio were applied, the required frequency
was not obtained.
a) b)
c) d)
e) f)
g)
Fig. 5. Mode shapes affecting partials: a) hum, b) prime, c) tierce,
d) quint, e) nominal, f) super-quint and g) octave nominal.
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Table 1.
The frequencies in [Hz] of the main partials
Tierce
Quint
Nominal
Super-
quint
Octave
Nominal
Ratios based on Prime
1,2
1,5
2
3
4
Calculated on measured prime
1256,4
1570,5
2094
3141
4188
Measured
(Fig. 4)
1246
1565
2087.5
3134.5
4316
ET 12
Equal Temperament
dis3
1244.5
g3
1567.98
c4
2093
g4 3135,96
c5
4186
cis5
4434,92
Calcualted
Ansys Modal
UNS C91300
1278.6
1608.1
2144.6
3212
4424.5
Calcualted
Ansys Modal
[7]
1263.1
1587.8
2119.4
3175.3
4374.6
Calcualted
Ansys Modal
(validated)
E
1244.1
1563.8
2087.5
3127.1
4308.5
Calcualted
Ansys Modal
(validated) ρ
1244.1
1563.8
2087.5
3127.2
4308.7
Calcualted
Ansys Modal
(validated)
ρ, E
1244.1
1563.8
2087.5
3127.1
4308.6
Almost identical frequencies values of particular partials were
obtained for two configurations of density and Young’s module
values: 8600 kg/m3, 1.0186E+5 MPa and 8865 kg/m3, 1.05E+5
MPa. The Poisson ratio value in both cases was 0.33. Despite that,
the mutual relation of density and Young’s module is the basis of
Ashby charts and copper alloys in this chart occupy only a small
area (Fig. 6) such relation, for bronzes and any other materials,
cannot be used for exactly determining the value of one properties
on the basis of second. According to different sources, the value
of Young’s module for tin bronzes, depends on consisting of tin
and the other elements varies between 0.96 1.2E+5 MPa and
density 7400 8900 kg/m3. On the density of tin bronzes, because
they tendency to porosity [13], significantly influence the
parameters of: melt process (time, temperature), liquid metal
treatment (deoxidation, modification) [9-13], hence such a large
range of density values. Thus, the melting process and preparation
of the metal indirectly, and as is evident from the calculations can
significantly affect tone of bells.
The fundamental question therefore is: how big the range of
variation of density, depending on the melting parameters and
liquid metal treatment, can be?
Fig. 6. Ashby chart
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2. Experiment
Trying to find the answer to the above question, the authors
have conducted a number of experimental melts. Within each
group of melts the changes of: type of initial (charge) material,
overheating temperature, pouring temperature as well as refining
and modifying additions, were controlled.
The first group of melts covers two melts that consisted on:
1. melting the charge materials and overheating the liquid
metal to 1200oC, next the furnace was turn off that
liquid alloy was freely cooling down, started from
1200oC after each 50 degrees temperature was
decreased a sample was cast, these samples are denoted
as CD,
2. melting the charge materials and overheating the liquid
metal to 1000oC, next liquid metal was being slowly
heated up and started from 1000oC after each 50
degrees temperature was increased a sample was cast,
these samples are denoted as CU,
Charge materials were technically pure OFHC cooper
(99,99%) and tin (99,9%) in weight ratios 4 : 1.
The second group of melts were conducted identically as the first
with only one difference - namely the charge material was a
CuSn20 alloy prepared in advance by melting pure copper and tin.
Samples cast within each melts are denoted SD and SU
respectively.
The third group of melts were conducted accordingly to data
given in table 2, charge materials were technically pure cooper
and tin as in first group of melts. A treatment method, amount and
type of used material were selected on the basis of literature [9-
12]. Alloy's temperature during metal batch treatment and pouring
samples was in range 1050-1100oC.
Table 2.
Amount and type of substances used in the third series of melts.
No of sample
1M
2M
3M
4M
5M
6M
Substance or the
way of
modification
-
Raw stic
45s
CuP
Mg
Mn+CaC2
Tophut
Weight of
metal/addition
[g]
-
-
3300/10
2950/0.9
2600/40+20
2250/5
3. Results
On charts in figures 7 9 the changes of density and hardness
are shown. Both hardness and density were measured on samples
cast during the experimental melts.
Fig. 7. Density [Mg/m3] and hardness HB changes of bronzes in
first series of melts
Fig. 8. Density [Mg/m3] and hardness HB changes of bronzes in
second series of melts
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Fig. 9. Density [Mg/m3] and hardness HB changes of bronzes in
third series of melts
4. Discussion
Influence of overheating and pouring temperatures on
investigated bronze’s density are significant, particularly in the
case of the alloy melts directly from pure cooper and tin. The
higher the pouring temperature, the lower the density of solid
alloy in room temperature. This trend occurs for both in the case
of lowering the temperature of the superheated bath as well as in
the case of increasing the temperature of the alloy. Especially
large impact on reducing final density had initial bath overheated.
Remelted alloy, used in second part of experiment, has not
behaved in analogical way. Although decreasing of density and
hardness was observed for increasing temperature, its relation is
not unequivocal. A lack of significant differences in density and
hardness of samples cast of overheated alloy and these cast of
gradually heating alloy. Moreover both density and hardness of
samples from second group of melts are clearly higher in compare
with first group. Melting in advance of pure material probably
caused alloy slightly impurifying. Impurities in crystallization
process are acting as nucleus and decreasing its sensitivity to
overheating and pouring temperature.
All of materials and operations used in third part of
experiments have caused an increase in density and hardness, in
comparison to a reference sample no 1M. However, for all
samples, obtained results are very near to these from second part
of investigations obtained in the similar temperature. Slightly,
among others, stand out particularly taking into account hardness
the sample no 4M, in its case the addition of magnesium to liquid
metal was used. Because to high affinity of magnesium to oxygen
applied, addition caused good bath deoxidation, what effected the
lack of interdendritic micropores and formation of concentrated
shrinkage cavity. What in the case of bells cast in traditional
manner is unacceptable
5. Conclusions
The results of carried out investigations can be summarized as:
1. Preparation CuSn20 alloy directly from pure cooper and tin is
not recommended. In case of such alloys the bath overheating
causes significantly decreased density and hardness, which
results in a significant discrepancy between the expected and
obtained frequencies partials of bell’s tone. In extreme cases we
will not be able to properly tune the bell.
2. The alloy component pre-melting and preparation CuSn20 alloy
as a charge material for target melt eliminates this tendency
almost completely. However, it is not recommended for
excessive overheating of the liquid alloy and the use of too high
pouring temperature.
3. Liquid metal treatment should be reduced to necessary
minimum, if the good quality charge materials are used
generally it should be limited to protect bath surfaces against
from the atmosphere influence.
References
[1] McLachlan, N., Cabrera, D., (2002). Calculated Pitch
Sensations for New Musical Bell Designs, Proceedings of
the 7th International Conference on Music Perception and
Cognition, Sydney. 600-603.
[2] McLachlan, N., (2002). Sculpting Sound: New Bell Designs
and Attitudes, Music Forum 8.
[3] Fletcher, N.H., (1999). The nonlinear physics of musical
instruments. Rep. Prog. Phys. 62, 723-764.
[4] Perrin, R., Charnley, T. & de Pont, J. (1983). Normal modes
of the modern English church bell J. Sound Vibr. 90, 29-49.
[5] Rossing, T. D., & Perrin, R. (1987). Vibration of bells Appl.
Acoust. 20. 41-70.
[6] Lehr, A., (1965). Contemporary Dutch Bell-Founding Art;
Hedendaagse Nederlandse Klokkengietkunst, Neth. Acoust.
Soc. Publ. 7. 20-49.
[7] Gołaś, A. & Filipek, R. (2009). Numerical Simulation for the
Bell Directivity Patterns Determination. Arch. of Acoustics.
34(4), 415-427.
[8] Fletcher, N. H., Rossing, T.D. (1998). The Physics of
Musical Instruments. Springer.
[9] Czochlarski, J., Bukowski, Z. (1935). Deoxidation of brasses
and bronzes. Messages Institute of Metallurgy. Warszawa.
[10] Bydałek, A.W. (2009). The analysis of carbon attendance in
copper alloys as reason of gas porosity. Archives of Foundry
Engineering. 9(3), 25-28.
[11] Bydałek, A.W. (1999). The copper alloys melting in the
reduction Conductions. Solidification of Metals and Alloys.
1(40), 87-92.
[12] Bydałek, A.W. (2005). The analysis of the influence melting
conduction copper alloys on the porousity. Archives of
Foundry. 5(17), 27-36.
[13] Bartocha, D. & Baron, C. (2015). „The Secret” of Traditional
Technology of Casting Bells. Archives of Foundry
Engineering. 15(si 3), 5-10. (in Polish).
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Experimental measurements of the frequencies and nodal patterns of all the partials of a good quality 214 kg English church bell up to about 9 kHz have been made. By matching these with the results of finite element calculations can understanding of the physical mechanisms generating the various partials has been achieved. This has made possible the production, for the first time, of a classification scheme for the partials with a firm physical basis, and has given considerable new insight into church bell design. In particular it is now clear just how crucial to the production of the bell's characteristic timbre is the thick ring near its rim. Temporarily at Darwin College, University of Cambridge, Silver Street, Cambridge CB3 9EU, England.
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The analysis of various sound sources is performed on the basis of their directivity patterns. The literature does not contain any information about directivity patterns of bells that are instruments broadly applied to sacral purposes or to create a certain sound space from the aesthetic point of view. The paper presents the methodology of determining the bell directivity patterns by an example of the Russian bell. This example was applied because exact values of geometrical parameters and measuring data of the bell were available. The model was created by means of FEA (finite element analysis). It included a coupling between the bell and its surrounding acoustic medium. During the modal analysis, the first three natural frequencies of the bell were calculated, and then, using the harmonic analysis, the directivity patterns were determined for the frequencies. Afterwards, the transient response of the system in selected measuring points was determined. The obtained results are important for bell-founders and architects because thanks to the knowledge of directivity patterns, the constructions supporting the bells can be designed in a better way and the sound propagation can be determined more precisely. The presented method of auralisation of the bell sound makes the cooperation between the designer and the receiver fairly convenient.
Article
Musical instruments are often thought of as linear harmonic systems, and a first-order description of their operation can indeed be given on this basis, once we recognise a few inharmonic exceptions such as drums and bells. A closer examination, however, shows that the reality is very different from this. Sustained-tone instruments, such as violins, flutes and trumpets, have resonators that are only approximately harmonic, and their operation and harmonic sound spectrum both rely upon the extreme nonlinearity of their driving mechanisms. Such instruments might be described as `essentially nonlinear'. In impulsively excited instruments, such as pianos, guitars, gongs and cymbals, however, the nonlinearity is `incidental', although it may produce striking aural results, including transitions to chaotic behaviour. This paper reviews the basic physics of a wide variety of musical instruments and investigates the role of nonlinearity in their operation.
Deoxidation of brasses and bronzes Messages Institute of Metallurgy
  • Czochlarski
Czochlarski, J., Bukowski, Z. (1935). Deoxidation of brasses and bronzes. Messages Institute of Metallurgy. Warszawa.
Vibration of bells Appl
  • Rossing
Rossing, T. D., & Perrin, R. (1987). Vibration of bells Appl. Acoust. 20. 41-70.