JPH0792670B2 - Bell design method and bell obtained by this method - Google Patents
Bell design method and bell obtained by this methodInfo
- Publication number
- JPH0792670B2 JPH0792670B2 JP29364489A JP29364489A JPH0792670B2 JP H0792670 B2 JPH0792670 B2 JP H0792670B2 JP 29364489 A JP29364489 A JP 29364489A JP 29364489 A JP29364489 A JP 29364489A JP H0792670 B2 JPH0792670 B2 JP H0792670B2
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- JP
- Japan
- Prior art keywords
- log
- bell
- bells
- diameter
- scale
- Prior art date
- Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
- Expired - Fee Related
Links
- 238000000034 method Methods 0.000 title claims description 15
- 238000004458 analytical method Methods 0.000 claims description 3
- 230000014509 gene expression Effects 0.000 claims description 3
- 238000004364 calculation method Methods 0.000 description 4
- 238000010586 diagram Methods 0.000 description 1
- 238000005516 engineering process Methods 0.000 description 1
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- Electrophonic Musical Instruments (AREA)
- Auxiliary Devices For Music (AREA)
Description
【発明の詳細な説明】 〔産業上の利用分野〕 この発明は，異なる固有振動数（音階）を有する複数個
のベルをそれぞれ規定のタイミングで打ち鳴らして楽曲
を奏でるベルのような場合，これら一連の音階のベルの
形状に連続性を持たせ，かつ，これらを効率的に設計す
るベルの設計方法およびこの方法によって得られたベル
に関するものである。DETAILED DESCRIPTION OF THE INVENTION [Industrial field of application] The present invention is applied to a case where a plurality of bells having different natural frequencies (scales) are struck at prescribed timings to play a musical piece. The present invention relates to a bell design method for efficiently designing a series of bells of a series of scales, and a bell obtained by this method.
従来，ベルの形状は大きくなるほどその固有振動数（音
階）は低くなる等の定性的な傾向は知られていたが，実
際にある特定の音階のベルを設計する場合，その形状は
どのようにすればよいかまでは詳細にはわかっていなか
った。したがって，楽曲を演奏することを目的とするよ
うな正確な音階を要求されるベルの場合には，経験工学
的に個々の音階のベルを製作し，これを基に一連の音階
を有した複数個のベルシリーズとしていた。Conventionally, it has been known that the larger the shape of the bell, the lower its natural frequency (scale) becomes. However, when designing a bell of a certain specific scale, how is the shape of the bell actually designed? I didn't know in detail how to do it. Therefore, in the case of a bell that requires an accurate scale for the purpose of playing music, bells of individual scales are empirically engineered, and multiple bells with a series of scales are created based on this. It was a bell series.
しかし，このような方法では実際には各種音階を有した
複数個のベルの効率的な設計は困難であるし，一連のベ
ルの形状にも連続性を与え難く，さらには，複数個の音
階の異なるベル間での音色にも連続性を与えることが困
難となる。However, with such a method, it is difficult to efficiently design a plurality of bells having various scales, and it is difficult to give continuity to the shape of a series of bells. It is difficult to give continuity to the tones between different bells.
この発明は，このような課題を解決するためのものであ
って，その目的とする処は，このような一連のベルの形
状に連続性を与え，かつ，効率的な設計ができる音階ベ
ルを具現したものである。The present invention is intended to solve such a problem, and the object of the present invention is to provide a scale bell that can provide an efficient design by providing continuity to the shape of such a series of bells. It is a realization.
この発明は，要するに，内挿法と呼ばれる方法を用いて
大きさの異なる二つのベルから中間のベルの断面形状を
決定するものである。なお，ここでの内挿法とは第１図
の模式図に示すような固有振動数解析モデルの各々対応
する節点座標に関して内挿することをいう。すなわち，
固有振動数解析モデルにおいて対応する座標の直径DP,D
Rおよび音階（１次の固有振動数）fP,fRがわかっている
二つのベルP,Rから音階fQ（fP＜fQ＜fR）のベルＱの前
記二つのベルP,Rにそれぞれ対応する座標の直径DQ（DP
＞DQ＞DR）を求めるにおいて,D＝ｃ・fm（c,mは係数）
なる関係式を用いる。In short, the present invention determines a cross-sectional shape of an intermediate bell from two bells having different sizes by using a method called interpolation method. Note that the interpolation method here means to interpolate the corresponding nodal coordinates of the natural frequency analysis model as shown in the schematic view of FIG. That is,
Diameter of the corresponding coordinates in the natural frequency analysis model D P , D
The two bells P, R of the scale f Q (f P <f Q <f R ) and the two bells P, R of which R and the scale (first-order natural frequency) f P , f R are known Diameter of coordinates corresponding to R D Q (D P
＞ D Q ＞ D R ), D ＝ c ・ f m (c and m are coefficients)
Is used.
これを対数で表すと,log D＝log c＋ｍ・log fとなり，
これは両対数グラフ上で直線となるから,log cおよびｍ
は縦軸切片および傾きとして求まる。If this is expressed in logarithm, log D = log c + m · log f,
Since this is a straight line on the log-log graph, log c and m
Is obtained as the vertical axis intercept and the slope.
そこで，既知のDP,DR,fP,fRを用いて傾きｍおよび縦軸
切片log cを求めると， ｍ＝（log DP−log DR）／（log fP−log fR） ＝log（DP/DR）/log（fP/fR） log c＝log DP−ｍ・log fP として求まる。Therefore, when the slope m and the vertical axis intercept log c are obtained using known D P , D R , f P , f R , m = (log D P −log D R ) / (log f P −log f R ) = obtained as log (D P / D R) / log (f P / f R) log c = log D P -m · log f P.
このようにして求められた係数c,m,を用いて求めるベル
Ｑの前記直径DQを DQ＝ｃ・（fQ）ｍの関係から求める。The diameter D Q of the bell Q obtained using the coefficients c and m thus obtained is obtained from the relationship of D Q = c · (f Q ) m .
但し，誤差を見越して ｋ＝DQ/（ｃ・（fQ）ｍ）で定義されるｋ値が 0.97≦ｋ≦1.03 の範囲内にあることを条件に採択することを特徴とする
ベルの設計方法を提供するのである。However, in consideration of the error, Bell is characterized in that the k value defined by k = D Q / (c · (f Q ) m ) is within the range of 0.97 ≦ k ≦ 1.03. It provides a design method.
ところで，これらの関係式の有効性を証明するため，最
大外径が直径500mmと200mmの二つのベルを用意するとと
もに，これら二つのベルから断面形状を内挿法によって
最大外径の直径350mmのベルの形状を決定し，これらの
固有振動数を計算した結果を第２図に示す。By the way, in order to prove the effectiveness of these relational expressions, two bells with maximum outer diameters of 500 mm and 200 mm were prepared, and the cross-sectional shape from these two bells was calculated by interpolation to obtain the maximum outer diameter of 350 mm. Figure 2 shows the results of determining the shape of the bell and calculating these natural frequencies.
これによって各ベルの最大直径Ｄと固有振動数ｆとの間
には上記式が近似的に成立することがわかる。なお，上
記式の関係は同一の振動モードに対してのみ成立するこ
とを付け加える。そして，この計算例についての１次か
ら５次までの上記式に関するｃおよびｍの係数値を第１
表に示す。From this, it can be seen that the above equation approximately holds between the maximum diameter D of each bell and the natural frequency f. It should be added that the relationship in the above equation holds only for the same vibration mode. Then, the coefficient values of c and m in the above equations from the 1st to 5th order in this calculation example are set to the first value.
Shown in the table.
ところで，この計算例では最大直径500mmと200mmの高次
成分まで考慮した固有振動数の倍率関係は等しくない。
しかし，その倍率関係が等しい二つのベルから断面形状
を内挿すれば，その内挿されたベルの固有振動数の倍率
関係は前二者の倍率関係と近似的に同一になる。ここ
で，実際のベルはその高次成分まで考慮した固有振動数
の倍率関係が各種音階のベルですべて等しくなければな
らないことを考え合わせれば，この内挿法の優位性が理
解できる。なお，高次成分まで考慮した固有振動数が等
しいとは，上記式のｍの値が１次から高次まですべて同
じであることを意味する。 By the way, in this calculation example, the natural frequency multiplication factors are not the same considering the higher-order components with the maximum diameter of 500 mm and 200 mm.
However, if the cross-sectional shape is interpolated from two bells that have the same magnification relation, the magnification relation of the natural frequency of the interpolated bell becomes approximately the same as that of the former two. Here, the superiority of this interpolation method can be understood by considering that the scaling relation of the natural frequency considering the higher-order components of the actual bell must be the same for all bells of various scales. It should be noted that the fact that the eigenfrequency is considered in consideration of the higher order components means that the value of m in the above equation is the same from the first order to the higher order.
以上は，最大直径についてであるが，その他の部位の直
径についても同様である。即ち、上記関係式を用いて求
めようとする座標値（高さ）の直径を逐次求めて行けば
よい。The above is the maximum diameter, but the same applies to the diameters of other parts. That is, the diameter of the coordinate value (height) to be obtained by using the above relational expression may be sequentially obtained.
一方，計算には誤差が伴うから，求めようとするベルの
直径の採用値Ｄと計算によって得た計算値（ｃ・fm）と
の比であるｋ値が 0.97≦ｋ≦1.03 の範囲内であれば許容できるとするものである。On the other hand, since there is an error in the calculation, the k value, which is the ratio of the adopted value D of the diameter of the bell to be calculated and the calculated value (c · f m ), is within the range of 0.97 ≦ k ≦ 1.03. If so, it is acceptable.
次に，一連のベルの外面の形状は相似形であることが意
匠上からも望ましいため，高さＨは Ｈ＝ｎ・Ｄ（ｎは係数） とし，直径Ｄの関数として求める。そして，この係数ｎ
はベルの形状を全体的にバランスがとれ，デザイン的に
も優れたものとするため， 0.60≦H/D≦1.00 の範囲に設定する。Next, since the shape of the outer surface of the series of bells is desirable to be similar from the viewpoint of design, the height H is calculated as H = n · D (n is a coefficient) and is obtained as a function of the diameter D. And this coefficient n
In order to balance the shape of the bell as a whole and to improve the design, set the range of 0.60 ≤ H / D ≤ 1.00.
このように，内挿法によれば直径，高さおよび肉厚等の
形状要素の一貫した連続性を与えることができるのであ
る。ここで，ベルは第３図に示すような一般的なベル形
状とし，最大直径Ｄとはリップ部の最大外径を，また，
高さＨとは下端と首部までの長さをいうものとする。Thus, the interpolation method can provide a consistent continuity of shape elements such as diameter, height and wall thickness. Here, the bell has a general bell shape as shown in FIG. 3, and the maximum diameter D is the maximum outer diameter of the lip portion,
The height H means the length from the lower end to the neck.
また，このベルのシリーズが主として楽曲を奏でる目的
のために設計されるものであることから，参考までに音
響学上の音階（例示のものはラ）と１次の振動数の関係
を第２表に示しておく。In addition, since this Bell series is designed mainly for the purpose of playing music, for reference, the relation between the acoustic scale (the example is LA) and the first-order frequency is Shown in the table.
〔実施例〕 以上のようにして設計されるベルの基本寸法，すなわ
ち，直径および高さの設定例の一つを以下の第３表に示
す。 [Examples] Table 3 below shows one example of setting the basic dimensions of the bell designed as described above, that is, the diameter and height.
また，この設定値を基準にして設計されたベルの基本寸
法を第４図に示す。 Fig. 4 shows the basic dimensions of the bell designed based on this set value.
以上，この発明によれば，ベルの基本寸法がベルの音階
を基本的に支配する基本振動数の関数として決定される
ため，音階と基本寸法に関して個々のベル間で有機的に
連続性が保たれ，その上，種々の音階を有したベル断面
形状についても内挿法を用いることにより，連続性をも
たせることが可能となり，さらには，非常に効率的に種
々の音階ベルを設計することが可能となる。したがっ
て，デザイン性にも優れ，かつ，複数個のベルシリーズ
に関して音色および音量にも連続性をもたせることがで
きるのである。As described above, according to the present invention, since the basic dimension of the bell is determined as a function of the fundamental frequency that basically controls the scale of the bell, organic continuity is maintained between the individual bells with respect to the scale and the basic dimension. In addition, it is possible to provide continuity by using the interpolation method even for bell cross-section shapes with various scales, and it is possible to design various scale bells very efficiently. It will be possible. Therefore, the design is excellent, and the tone and volume of multiple Bell series can be made continuous.
第１図は断面形状の内挿を示す模式図，第２図は固有振
動数の計算結果を示すグラフ，第３図はベルの断面図，
第４図は基本振動数（１次の固有振動数）と基本寸法の
関係を示すグラフである。1 is a schematic diagram showing the interpolation of the cross-sectional shape, FIG. 2 is a graph showing the calculation result of the natural frequency, FIG. 3 is a cross-sectional view of the bell,
FIG. 4 is a graph showing the relationship between basic frequency (first-order natural frequency) and basic dimensions.
Claims (3)
標の直径DP,DRおよび音階（１次の固有振動数）fP,fRが
わかっている二つのベルP,Rから音階fQ（fP＜fQ＜fR）
のベルＱの前記二つのベルP,Rにそれぞれ対応する座標
の直径DQ（DP＞DQ＞DR）を求めるにおいて， Ｄ＝ｃ・fm（c,mは係数）なる関係式を用いる。 これを対数で表すと， log D＝log c＋ｍ・log fとなり，これは両対数グラフ
上で直線となるから,log cおよびｍは縦軸切片および傾
きとして求まる。 そこで，既知のDP,DR,fP,fRを用いて傾きｍおよび縦軸
切片log cを求めると， ｍ＝（log DP−log DR）／（log fP−log fR） ＝log（DP/DR）/log（fP/fR） log c＝log DP−ｍ・log fP として求まる。 このようにして求められた係数c,m,を用いて求めるベル
Ｑの前記直径DQを DQ＝ｃ・（fQ）ｍの関係から求める。 但し，誤差を見越して ｋ＝DQ/（ｃ・（fQ）ｍ）で定義されるｋ値が 0.97≦ｋ≦1.03 の範囲内にあることを条件に採択することを特徴とする
ベルの設計方法。1. A scale f Q from two bells P, R whose diameters D P , D R and scales (first-order natural frequencies) f P , f R of corresponding coordinates in a natural frequency analysis model are known. (F P <f Q <f R )
In calculating the diameter D Q (D P > D Q > D R ) of the coordinates corresponding to the two bells P and R of the bell Q, the relational expression D = c · f m (c and m are coefficients) To use. If this is expressed in logarithm, log D = log c + m · log f, which is a straight line on the log-log graph, so log c and m can be obtained as the vertical axis intercept and slope. Therefore, when the slope m and the vertical axis intercept log c are obtained using known D P , D R , f P , f R , m = (log D P −log D R ) / (log f P −log f R ) = obtained as log (D P / D R) / log (f P / f R) log c = log D P -m · log f P. The diameter D Q of the bell Q obtained using the coefficients c and m thus obtained is obtained from the relationship of D Q = c · (f Q ) m . However, in consideration of the error, Bell is characterized in that the k value defined by k = D Q / (c · (f Q ) m ) is within the range of 0.97 ≦ k ≦ 1.03. Design method.
直径Ｄに対する高さＨの比率H/Dが 0.60≦H/D≦1.00 の範囲内となるように設定することを特徴とする特許請
求の範囲第項記載のベルの設計方法。2. The shape of the outer surface of each bell is similar,
The bell designing method according to claim 1, wherein the ratio H / D of the height H to the diameter D is set within the range of 0.60≤H / D≤1.00.
ベルの設計方法によって得られた三個以上のシリーズの
ベル。3. A bell of three or more series obtained by the method for designing a bell according to claim 1 or 2.
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| JP29364489A JPH0792670B2 (en) | 1989-11-11 | 1989-11-11 | Bell design method and bell obtained by this method |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| JP29364489A JPH0792670B2 (en) | 1989-11-11 | 1989-11-11 | Bell design method and bell obtained by this method |
Publications (2)
| Publication Number | Publication Date |
|---|---|
| JPH03154098A JPH03154098A (en) | 1991-07-02 |
| JPH0792670B2 true JPH0792670B2 (en) | 1995-10-09 |
Family
ID=17797385
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| JP29364489A Expired - Fee Related JPH0792670B2 (en) | 1989-11-11 | 1989-11-11 | Bell design method and bell obtained by this method |
Country Status (1)
| Country | Link |
|---|---|
| JP (1) | JPH0792670B2 (en) |
Families Citing this family (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| AUPQ361399A0 (en) * | 1999-10-22 | 1999-11-18 | Australian Bell Pty Ltd | Improvements in or relating to bells |
| GB2578319B (en) | 2018-10-23 | 2023-05-24 | John Taylor Bell Foundry Loughborough Ltd | A bell and a method of designing a bell |
-
1989
- 1989-11-11 JP JP29364489A patent/JPH0792670B2/en not_active Expired - Fee Related
Also Published As
| Publication number | Publication date |
|---|---|
| JPH03154098A (en) | 1991-07-02 |
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