TWI620169B - Method for designing a bronze clock with harmonics sound - Google Patents
Method for designing a bronze clock with harmonics sound Download PDFInfo
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Abstract
一種具簡諧倍頻音之銅鐘的設計方法，用於解決銅鐘無法產生簡諧倍頻音的問題。係包含：輸入一設計參數組，以建立一銅鐘的一數學模型；對該數學模型執行有限元素分析，以產生數個模態振型及相對應的自然頻率；設定該數學模型的數個目標頻率；及計算該數個目標頻率與該數個自然頻率的一誤差平方平均根，利用一數值逼近法修正該數個自然頻率，直到取得該誤差平方平均根之最小值，依據該修正後的數個自然頻率修正該數學模型之設計參數組，依據該修正後的設計參數組修正該數學模型的形狀架構。本發明更包含該設計方法所製成之銅鐘。 A design method of a copper bell with a simple harmonic frequency is used to solve the problem that the copper clock cannot produce a simple harmonic frequency. The system includes: inputting a design parameter group to establish a mathematical model of a bronze clock; performing finite element analysis on the mathematical model to generate a plurality of modal vibration modes and corresponding natural frequencies; setting a plurality of the mathematical models a target frequency; and calculating an error square root mean of the plurality of target frequencies and the plurality of natural frequencies, correcting the plurality of natural frequencies by a numerical approximation method until a minimum value of the square root of the error is obtained, according to the corrected The natural frequency of the mathematical model corrects the design parameter set of the mathematical model, and the shape structure of the mathematical model is corrected according to the modified design parameter set. The invention further comprises a copper bell made by the design method.
Description
本發明係關於一種具簡諧倍頻音之銅鐘及該銅鐘的設計方法，尤其是一種能夠發出簡諧倍頻音之銅鐘及該銅鐘的設計方法。 The invention relates to a copper clock with a simple harmonic frequency and a design method of the copper clock, in particular to a copper clock capable of emitting a simple harmonic frequency and a design method of the copper clock.
在交響樂團中，弦樂器(stringed instruments)及擊樂器(percussion instrument，又稱打擊樂器或敲擊樂器)是演奏各種優美的旋律不可或缺的樂器大類，其中弦樂器係如：鋼琴(piano)、提琴(violin)、吉他(guitar)或胡琴(huqin)等，以吉他弦為例，其振動模態之自然頻率包含基音(fundamental frequency，即第1個自然頻率)及泛音(overtones，即第2、3、4、...個自然頻率)，當該泛音與基音具有整數比例關係時，即稱為「具有簡諧倍頻音(harmonics sound)」，可使音色較為諧和柔美，諸如小提琴、胡琴等弦樂器均有此特性(請詳參「王栢村，蘇集銘，2006，吉他弦之振動與聲音特性探討，中華民國音響學會第十九屆學術研討會論文集，台南，論文編號：A7」論文)。 Among the symphony orchestras, stringed instruments and percussion instruments (also known as percussion instruments or percussion instruments) are indispensable musical instruments for performing various beautiful melodies, such as pianos and violins. (violin), guitar (guitar) or huqin (huqin), etc., taking guitar strings as an example, the natural frequency of the vibration mode includes the fundamental frequency (the first natural frequency) and the overtones (overtones). 3, 4, ... a natural frequency), when the overtone has an integer proportional relationship with the pitch, it is called "having a harmonic sound", which makes the tone more harmonious and feminine, such as violin and huqin. Such stringed instruments have this feature (please refer to "Wang Baicun, Su Jiming, 2006, Vibration and Sound Characteristics of Guitar Strings, Proceedings of the 19th Symposium of the Republic of China Sound Society, Tainan, Paper No.: A7" ).
另一方面，就擊樂器之共鳴方式而言，可略分為膜鳴樂器及體鳴樂器，前者係如：定音鼓(kettledrum)或大鼓(bass drum)等；後者則如：管鐘(chime)或銅鐘等。以銅鐘為例，當敲打銅鐘時，即可產生音律，呈現體鳴樂器的樂音特性，目前多是運用於寺廟或宗教等地，供信徒每日念佛誦經時所用。 On the other hand, in terms of the resonance mode of the percussion instrument, it can be roughly divided into a film-sounding instrument and a body-sounding instrument, the former being such as a kettledrum or a bass drum, and the latter being a chime. Or a bronze bell. Taking the bronze bell as an example, when the bronze clock is beaten, the temperament can be produced, and the musical characteristics of the body-sounding instrument are presented. At present, it is mostly used in temples or religions, and is used by believers to recite Buddhist scriptures every day.
然而，製造出好聽的聲音品質銅鐘之核心技術已逐漸流失，使銅鐘無法產生諧和柔美的音色(倍頻音)，亦無法運用於寺廟或宗教以外的演奏場合，導致適用的聲音風格受限。 However, the core technology for making good sound quality copper bells has been gradually lost, making the bells unable to produce harmonic and soft sounds (multipliers), and can not be used in performances other than temples or religions, resulting in a suitable sound style. limit.
有鑑於此，有必要提出一種具簡諧倍頻音之銅鐘及該銅鐘的設計方法，以符合實際需求，提升其實用性。 In view of this, it is necessary to propose a copper clock with a simple harmonic frequency and a design method of the copper clock to meet the actual needs and improve its practicability.
本發明全文所述之「軸向截面」(axial cross-section)，係指由一銅鐘之中心軸線使該銅鐘分為二等分，各具有一「虛擬壁面」，該二等分之銅鐘係沿該中心軸線形成鏡像對稱設置。 The "axial cross-section" as used throughout the present invention means that the copper clock is divided into two equal parts by a central axis of a copper bell, each having a "virtual wall surface", the halving The copper bell system is formed in a mirror symmetrical arrangement along the central axis.
本發明全文所述之「徑向截面」(radial cross-section)，係指由一銅鐘之中心軸線上任一點，沿著徑向延伸而成的平面，且該「徑向截面」與該「軸向截面」互為垂直。 The "radial cross-section" as used throughout the present invention refers to a plane extending from a radial point at a point on a central axis of a copper bell, and the "radial cross section" and the "radial cross section" The axial sections are perpendicular to each other.
本發明係提供一種具簡諧倍頻音之銅鐘的設計方法，以設計可經敲擊產生簡諧倍頻音的銅鐘。 The invention provides a design method of a copper clock with a simple harmonic frequency to design a copper bell which can be beaten to produce a simple harmonic frequency.
本發明另提供一種具簡諧倍頻音之銅鐘，以上述設計方法製造而成，可經敲擊產生簡諧倍頻音。 The invention further provides a copper clock with a simple harmonic frequency, which is manufactured by the above design method, and can generate a simple harmonic octave by tapping.
本發明的一種具簡諧倍頻音之銅鐘的設計方法，係由一電腦系統執行，包含下列步驟：輸入一設計參數組，以建立一銅鐘的一數學模型；該數學模型係具有沿一中心軸線之二軸向截面及數個徑向截面，該數個徑向截面沿該中心軸線由該數學模型的頂端至底端成等間隔的設置，各該徑向截面於該中心軸線、該數學模型的一內表面及一外表面上，分別形成一第一端點、一第二端點及一敲擊點，該第一端點與該第二端點之間具有一第一距離，該第二端點與該敲擊點之間具有一第二距離；對該數學模型執行有限元素分析，以產生數個模態振型及相對應的自然頻率；設定該數學模型的數個目標頻率；及計算該數個目標頻率與該數個自然頻率的一 誤差平方平均根，利用一數值逼近法修正該數個自然頻率，直到取得該誤差平方平均根之最小值，依據該修正後的數個自然頻率修正該數學模型之設計參數組，依據該修正後的設計參數組修正該數學模型的形狀架構。 A design method of a copper clock with a simple harmonic frequency is performed by a computer system, comprising the steps of: inputting a design parameter set to establish a mathematical model of a bronze clock; the mathematical model has a a two axial section of the central axis and a plurality of radial sections along which the plurality of radial sections are equally spaced from the top end to the bottom end of the mathematical model, each of the radial sections being at the central axis, An inner surface and an outer surface of the mathematical model respectively form a first end point, a second end point and a tapping point, and the first end point and the second end point have a first distance Having a second distance between the second endpoint and the tapping point; performing a finite element analysis on the mathematical model to generate a plurality of modal shapes and corresponding natural frequencies; setting a plurality of the mathematical models a target frequency; and calculating the plurality of target frequencies and one of the plurality of natural frequencies The square root of the error is corrected by a numerical approximation method until the minimum value of the square root of the error is obtained, and the design parameter group of the mathematical model is corrected according to the corrected natural frequencies, according to the corrected The set of design parameters corrects the shape structure of the mathematical model.
本發明的一種具簡諧倍頻音之銅鐘，係使用上述之具簡諧倍頻音之銅鐘的設計方法所製造而成，該銅鐘係包含：一沿中心軸線之二軸向截面；及數個徑向截面，該數個徑向截面沿該中心軸線由該銅鐘的頂端至底端成等間距的設置，各該徑向截面於該中心軸線、該銅鐘的一內表面及一外表面上，分別形成一第一端點、一第二端點及一敲擊點，該第一端點與該第二端點之間具有一第一距離，該第二端點與該敲擊點之間具有一第二距離。 A copper bell with a simple harmonic octave according to the present invention is manufactured by using the above-described design method of a copper bell with a simple harmonic frequency, the copper bell system comprising: a two-axis cross section along a central axis And a plurality of radial sections disposed along the central axis from the top end to the bottom end of the copper bell, each of the radial sections being on the central axis, an inner surface of the copper bell And an outer surface, respectively forming a first end point, a second end point, and a tapping point, the first end point and the second end point have a first distance, the second end point There is a second distance between the tap points.
據此，本發明之具簡諧倍頻音之銅鐘的設計方法及其銅鐘，可藉由使在該外表面上的數個敲擊點，分別由該外表面至該內表面，及再以該內表面至該中心軸線上具有不同的第二距離及第一距離，使該銅鐘經被打擊該敲擊點而產生簡諧倍頻音，可以達成「能使銅鐘發出簡諧倍頻音」、「可運用於需要豐富打擊技巧的演奏場合」及「適合演奏的樂曲風格不受侷限」等功效。 Accordingly, the design method of the copper clock with the simple harmonic frequency of the present invention and the copper clock thereof can be made from the outer surface to the inner surface by a plurality of tapping points on the outer surface, and And the inner surface to the central axis has different second distances and a first distance, so that the copper clock is struck by the tapping point to generate a simple harmonic octave, which can achieve "can make the copper bell emit a simple harmonic "Multiplier", "can be used in performances where you need a lot of hit skills" and "the style of music that is suitable for performance is not limited".
其中該誤差平方平均根的計算方式係如下列方程式所示： ，其中，F(D)為該數個自然頻率 與該數個目標頻率之誤差平方平均根；f N為第N個自然頻率的頻率，f objN為第N個目標頻率的頻率，N為該自然頻率與該目標頻率的編號，且N=1,2,3,...,i，i為該自然頻率與該數個目標頻率的數量，且i≧2。如此，可以使該銅鐘發出符合簡諧倍頻音的功效。 The calculation of the square root of the error is as shown in the following equation: Where F ( D ) is the squared mean root of the error between the natural frequencies and the plurality of target frequencies; f N is the frequency of the Nth natural frequency, f objN is the frequency of the Nth target frequency, N is the The number of the natural frequency and the target frequency, and N = 1, 2, 3, ..., i , i is the natural frequency and the number of the target frequencies, and i ≧ 2. In this way, the copper clock can be made to comply with the effect of the simple harmonic octave.
其中，各該自然頻率與各該目標頻率的一誤差百分比的公式 可如下式所示：，其中，ε r 為第r個自然頻率與第r 個目標頻率之誤差百分比，r=1,2,3,...,N，f N為第N個的自然頻率的頻率，f objN為第N個目標頻率的頻率，N為該自然頻率與該目標頻率的編號，且N=1,2,3,...,i，i為該自然頻率與該數個目標頻率的數量，且i≧2。如此，可以使該銅鐘發出更進一步符合簡諧倍頻音的功效。 Wherein, the formula of each error percentage of the natural frequency and each of the target frequencies may be as follows: Where ε r is the error percentage of the rth natural frequency and the rth target frequency, r=1, 2, 3, ..., N, f N is the frequency of the Nth natural frequency, f objN is The frequency of the Nth target frequency, N is the number of the natural frequency and the target frequency, and N=1, 2, 3, ..., i , i is the natural frequency and the number of the target frequencies, and i ≧ 2. In this way, the bronze clock can be made to further conform to the effect of the simple harmonic octave.
其中，該數值逼近法係為一牛頓法。如此，係具有提升該電腦系統的運算效率的功效。 Among them, the numerical approximation method is a Newton method. In this way, it has the effect of improving the computational efficiency of the computer system.
另包含由該電腦系統將該數學模型的設計參數組轉成一輸出檔案，用以加工一銅鐘，使該銅鐘具有簡諧倍頻音。如此，係具有能夠大量生產的功效。 In addition, the computer system converts the design parameter set of the mathematical model into an output file for processing a copper clock, so that the copper clock has a simple harmonic frequency. In this way, it has the effect of being able to mass produce.
其中，該第二距離之公式係如下式所示：D21>D22>D23>...>D2N>3,N=1,2,3,...,n，其中，D2N為第N個徑向截面的第二距離，N為該數個徑向截面的編號，N越小表示越接近該銅鐘的頂端，N越大表示越接近該銅鐘的底端，n為該數個徑向截面的數量，且n≧2。如此，係具有方便脫模的功效。 Wherein, the formula of the second distance is as follows: D2 1 > D2 2 > D2 3 > ... > D2 N > 3, N = 1, 2, 3, ..., n, where D2 N Is the second distance of the Nth radial section, where N is the number of the plurality of radial sections, and the smaller N is, the closer to the top end of the copper bell, the larger N is closer to the bottom end of the copper bell, n is The number of the radial sections, and n ≧ 2. In this way, it has the effect of facilitating demolding.
1‧‧‧銅鐘 1‧‧‧Bronze Bell
11‧‧‧內表面 11‧‧‧ inner surface
12‧‧‧外表面 12‧‧‧ outer surface
A‧‧‧軸向截面 A‧‧‧ axial section
B‧‧‧底端 B‧‧‧Bottom
D1N、D11、D12、D13、D14、D15、D16、D17‧‧‧第一距離 D1 N , D1 1 , D1 2 , D1 3 , D1 4 , D1 5 , D1 6 , D1 7 ‧‧‧ First distance
D2N、D21、D22、D23、D24、D25、D26、D27‧‧‧第二距離 D2 N , D2 1 , D2 2 , D2 3 , D2 4 , D2 5 , D2 6 , D2 7 ‧‧‧Second distance
P1N、P11、P12、P13、P14、P15、P16、P17‧‧‧第一端點 P1 N , P1 1 , P1 2 , P1 3 , P1 4 , P1 5 , P1 6 , P1 7 ‧ ‧ first endpoint
P2N、P21、P22、P23、P24、P25、P26、P27‧‧‧第二端點 P2 N , P2 1 , P2 2 , P2 3 , P2 4 , P2 5 , P2 6 , P2 7 ‧‧‧ second endpoint
P3N、P31、P32、P33、P34、P35、P36、P37‧‧‧敲擊點 P3 N , P3 1 , P3 2 , P3 3 , P3 4 , P3 5 , P3 6 , P3 7 ‧ ‧ puncturing points
RN、R1、R2、R3、R4、R5、R6、R7‧‧‧徑向截面 R N , R 1 , R 2 , R 3 , R 4 , R 5 , R 6 , R 7 ‧‧‧ radial section
T‧‧‧頂端 T‧‧‧ top
r‧‧‧中心軸線 R‧‧‧ center axis
S1‧‧‧建模步驟 S1‧‧‧Modeling steps
S2‧‧‧修模步驟 S2‧‧‧Modification steps
S3‧‧‧加工步驟 S3‧‧‧Processing steps
第1圖：本發明之具簡諧倍頻音之銅鐘的設計方法的流程方塊圖。 Fig. 1 is a flow block diagram showing a design method of a copper bell with a simple harmonic frequency sound according to the present invention.
第2圖：本發明之具簡諧倍頻音之銅鐘的結構剖面圖。 Fig. 2 is a cross-sectional view showing the structure of a copper bell with a simple harmonic frequency of the present invention.
為讓本發明之上述及其他目的、特徵及優點能更明顯易懂，下文特舉本發明之較佳實施例，並配合所附圖式，作詳細說明如下：請參照第1圖所示，其係本發明之具簡諧倍頻音之銅鐘的設 計方法的流程方塊圖。在本實施例中，為了使設計出的銅鐘具有簡諧倍頻音的效果，該設計方法可利用一電腦系統連接一資料庫作為執行架構，並由該電腦系統執行一有限元素分析軟體(如：ANSYS)，並可以搭配應用電腦輔助工程分析軟體(CAE)，分析一銅鐘1是否具有接近整數倍之比例關係的簡諧倍頻音，在本實施例中，該設計方法係可以包含一建模步驟S1及一修模步驟S2。 The above and other objects, features, and advantages of the present invention will become more apparent from the aspects of the appended claims. It is the design of the copper bell with the simple harmonic frequency of the present invention. The process block diagram of the method. In this embodiment, in order to make the designed copper clock have the effect of simple harmonic frequency, the design method can use a computer system to connect a database as an execution architecture, and the computer system executes a finite element analysis software ( Such as: ANSYS), and can be combined with the application of computer-aided engineering analysis software (CAE) to analyze whether a copper bell 1 has a harmonic ratio octave that is close to an integer multiple. In this embodiment, the design method can include A modeling step S1 and a modification step S2.
請一併參照第2圖，該建模步驟S1，係輸入一設計參數組至該電腦系統中的有限元素分析軟體，以建立一銅鐘1的一數學模型，其中該設計參數組可以包含例如該銅鐘1的形狀、尺寸、材料及邊界條件等參數。舉例而言，該有限元素分析軟體可以採用線性立方體元素(Solid187)，建立該銅鐘1的數學模型之架構，惟不以此為限。 Referring to FIG. 2 together, the modeling step S1 inputs a design parameter set to the finite element analysis software in the computer system to establish a mathematical model of the copper clock 1 , wherein the design parameter set may include, for example. Parameters such as shape, size, material, and boundary conditions of the copper bell 1. For example, the finite element analysis software can use a linear cube element (Solid 187) to establish the mathematical model of the copper clock 1 , but not limited thereto.
其中，該銅鐘1的數學模型之形狀可以係具有沿一中心軸線r之二軸向截面(axial cross-section)A及數個徑向截面(radial cross-section)R1~RN，該數個徑向截面R1~RN沿該中心軸線r由該數學模型的頂端T至底端B成等間隔的設置，各該徑向截面R1~RN於該中心軸線r、該數學模型的一內表面11及一外表面12上，分別形成一第一端點P1N、一第二端點P2N及一敲擊點P3N，該第一端點P1N與該第二端點P2N之間具有一第一距離D1N，該第二端點P2N與該敲擊點P3N之間具有一第二距離D2N，其中，N為該數個徑向截面R1~RN的編號，且N=1,2,3,...,n，n為該數個徑向截面R1~RN的數量，且n≧2，N越小表示越接近該銅鐘1的頂端T，N越大表示越接近該銅鐘1的底端B。 The mathematical model of the copper bell 1 may have a shape of an axial cross-section A along a central axis r and a plurality of radial cross-sections R 1 -R N . A plurality of radial sections R 1 R R N are disposed at equal intervals along the central axis r from the top end T to the bottom end B of the mathematical model, and the radial sections R 1 R R N are at the central axis r, the mathematics An inner end surface 11 and an outer surface 12 of the model respectively form a first end point P1 N , a second end point P2 N and a tap point P3 N , the first end point P1 N and the second end between the points P2 N having a first distance D1 N, the second terminal P2 N between the tapping point P3 N having a second distance D2 N, where, N for the number of radial section of R 1 ~ The number of R N , and N=1, 2, 3, ..., n, n is the number of the radial sections R 1 ~ R N , and n ≧ 2, the smaller the N, the closer to the copper clock The larger the top T, N, the closer to the bottom end B of the copper bell 1 is.
在本實施例中，係將該數個徑向截面R1~RN的數量設定為七個，由於該銅鐘1之頂端T至該徑向截面R1之間這部分的銅鐘數據，對產生倍頻音的影響微乎其微，故，該設計參數組可省略該部分的數據，以減少該電腦系統的運算時間。 In the present embodiment, the number of the plurality of radial sections R 1 to R N is set to seven, and the copper clock data of the portion between the tip T of the copper bell 1 and the radial section R 1 is The effect on the generation of the octave tone is minimal, so the design parameter set can omit the data of the part to reduce the computation time of the computer system.
另一方面，該電腦系統以該有限元素分析軟體建立該銅鐘1的數學模型時，該設計參數組的尺寸參數可設定為高140mm，底部直徑為104.5mm；該設計參數組的材料參數可設定為蒲松比為0.34、密度為8960kg/m3及楊氏係數E=79.2GPa；及該設計參數組的邊界條件可設定為一自由邊界，惟不以此為限。 On the other hand, when the computer system establishes the mathematical model of the copper bell 1 by the finite element analysis software, the size parameter of the design parameter group can be set to be 140 mm high and the bottom diameter is 104.5 mm; the material parameters of the design parameter group can be The Pusson ratio is set to 0.34, the density is 8960 kg/m 3 and the Young's coefficient E=79.2 GPa; and the boundary condition of the design parameter set can be set as a free boundary, but not limited thereto.
隨後，該電腦系統以該有限元素分析軟體對該數學模型執行有限元素分析，以取得該數學模型的數個模態振型及相對應的自然頻率。在本實施例中，不論係以該有限元素分析軟體建立該數學模型，或是執行有限元素分析取得該數學模型的數個模態振型及相對應的自然頻率，皆為本發明所屬技術領域中具有通常知識者可以理解，在此容不贅述。 Subsequently, the computer system performs a finite element analysis on the mathematical model with the finite element analysis software to obtain a plurality of modal shapes of the mathematical model and corresponding natural frequencies. In this embodiment, whether the mathematical model is established by using the finite element analysis software, or performing finite element analysis to obtain a plurality of modal vibration modes of the mathematical model and corresponding natural frequencies, the technical field belongs to the present invention. Those who have the usual knowledge can understand it, and I won't go into details here.
該修模步驟S2係由該電腦系統設定該數學模型的數個目標頻率，在本實施例中，該目標頻率的數量可以設定為三個，且該三目標頻率係為接近整數倍的比例關係，可如表一所示。其中，表一所記載之模態數，係表示為該銅鐘之模態順序排序，例如：F-07為第七個分析模態振型。 The repairing step S2 is to set a plurality of target frequencies of the mathematical model by the computer system. In this embodiment, the number of the target frequencies may be set to three, and the three target frequencies are proportional to an integer multiple. , as shown in Table 1. The modal number described in Table 1 is expressed as the modal sequence of the copper clock. For example, F-07 is the seventh analytical mode vibration mode.
該電腦系統計算三自然頻率與該三目標頻率的誤差平方平均根，利用一數值逼近法(Approximation Method)修正該三自然頻率，直到取得該誤差平方平均根的最小值，依據修正後的三自然頻率修正該數學模型的設計參數組，並依據修正後的設計參數組修正該數學模型的形狀架構，使該數學模型可作為後續鑄造及加工該銅鐘1的憑據。其中，例如但 不限制地，該數值逼近法可以為一牛頓法(Newton’s method)或該有限元素分析軟體之最佳化函式(如：ANSYS之SUBP、SWEEP)等。 The computer system calculates the square root of the error of the three natural frequencies and the three target frequencies, and corrects the three natural frequencies by using an Approximation Method until the minimum value of the square root of the error is obtained, according to the corrected three natural The frequency is corrected by the design parameter set of the mathematical model, and the shape structure of the mathematical model is corrected according to the modified design parameter set, so that the mathematical model can be used as a credential for subsequent casting and processing of the bronze clock 1 . Among them, for example Without limitation, the numerical approximation method may be a Newton's method or an optimization function of the finite element analysis software (eg, SUBP, SWEEP of ANSYS).
在本實施例中，該電腦系統可以先計算該銅鐘1的數學模型的三自然頻率與三目標頻率的最小誤差平方平均根，作為使該設計參數組最佳化的一目標函數(Objective Function)，可如下式(2)所示：
其中，為了使該數學模型能夠產生更貼近整數倍之比例關係的簡諧倍頻音，較佳係使各該自然頻率與各該目標頻率的一誤差百分比小於1%，該誤差百分比的公式可如下式(3)所示：
隨後，以該三自然頻率修正該數學模型的設計參數組，並以修正後的設計參數組修正該銅鐘1的數學模型之形狀，使依據該銅鐘1的數學模型加工而成的銅鐘1可經敲擊而發出簡諧倍頻音。 Subsequently, the design parameter set of the mathematical model is corrected by the three natural frequencies, and the shape of the mathematical model of the copper clock 1 is corrected by the modified design parameter set, so that the copper clock processed according to the mathematical model of the bronze clock 1 is processed. 1 can be sent to make a simple harmonic octave.
請參照第2圖所示，其係本發明之具簡諧倍頻音之銅鐘的立 體結構示意圖。該銅鐘1係以上述設計方法所製造而成，其中，該銅鐘1的尺寸及材質，均不加以限制。該銅鐘1係具有一沿中心軸線r之二軸向截面A及數個徑向截面R1~RN，該數個徑向截面R1~RN沿該中心軸線r由該銅鐘1的頂端T至底端B成等間距的設置，各該徑向截面R1~RN於該中心軸線r、該銅鐘1的一內表面11及一外表面12上，分別形成一第一端點P1N、一第二端點P2N及一敲擊點P3N，該第一端點P1N與該第二端點P2N之間具有一第一距離D1N，該第二端點P2N與該敲擊點P3N之間具有一第二距離D2N，其中，N為該數個徑向截面R1~RN的編號，且N=1,2,3,...,n，n為該數個徑向截面R1~RN的數量，且n≧2，N越小表示越接近該銅鐘1的頂端T，N越大表示越接近該銅鐘1的底端B。 Please refer to FIG. 2, which is a schematic diagram of the three-dimensional structure of the copper clock with the simple harmonic frequency of the present invention. The copper bell 1 is manufactured by the above-described design method, and the size and material of the copper bell 1 are not limited. The bell 1 A system having two axial cross-section along the central axis r is a radial section and a plurality of R 1 ~ R N, a plurality of radial section of the R 1 ~ R N r along the central axis of the bell 1 The top end T to the bottom end B are disposed at equal intervals, and each of the radial sections R 1 R R N forms a first on the central axis r, an inner surface 11 of the copper bell 1 and an outer surface 12 End point P1 N , a second end point P2 N and a tap point P3 N , the first end point P1 N and the second end point P2 N have a first distance D1 N , the second end point P2 N and the tapping point P3 N have a second distance D2 N , where N is the number of the plurality of radial sections R 1 ~R N , and N=1, 2, 3, ..., n, n is the number of the plurality of radial sections R 1 ~ R N , and n ≧ 2, the smaller N is the closer to the top end T of the copper bell 1 , the larger N is the closer to the bottom end of the copper bell 1 B.
其中，為了使該銅鐘1鑄造加工後方便脫模，因此，各該徑向截面R1~RN的第二距離D2N可由該銅鐘1的頂端T至底端B逐漸縮小，以方便脫模。另，在鑄造銅鐘時，若銅鐘之厚度(即該差值)太薄，則會大幅增加銅鐘之澆灌難度，因此，該銅鐘1之厚度較佳係大於3毫米，故該銅鐘1之第二距離D2N的公式可如下式(1)所示：D21>D22>D23>...>D2N>3,N=1,2,3,...,n (1)其中，D2N為第N個徑向截面的第二距離，N為該數個徑向截面R1~RN的編號，N越小表示越接近該銅鐘1的頂端T，N越大表示越接近該銅鐘1的底端B，n為該數個徑向截面R1~RN的數量，且n≧2。 Wherein, after an order for the bell to facilitate demolding the casting process, and therefore, each of the radial section of R 1 ~ R N is a second distance D2 N by the bell to the top T to the bottom B 1 is tapered to facilitate Demoulding. In addition, when casting a copper bell, if the thickness of the copper bell (ie, the difference) is too thin, the difficulty of watering the copper bell is greatly increased. Therefore, the thickness of the copper bell 1 is preferably greater than 3 mm, so the copper The formula of the second distance D2 N of the clock 1 can be expressed by the following formula (1): D2 1 > D2 2 > D2 3 > ... > D2 N > 3, N = 1, 2, 3, ..., n (1) wherein D2 N is the second distance of the Nth radial section, N is the number of the plurality of radial sections R 1 to R N , and the smaller N is, the closer to the top T of the copper bell 1 is, N The larger the value, the closer to the bottom end B of the copper bell 1, n being the number of the plurality of radial sections R 1 -R N , and n ≧2.
具體而言，本發明之具簡諧倍頻音之銅鐘使用時，藉由敲擊該銅鐘1之數個敲擊點P3N的位置，可以使該銅鐘1激發出數個自然頻率，該數個自然頻率之中頻率最低者係為一基音，即標準音符之頻率(如：C5之頻率為523.25Hz)，該基音以外的自然頻率則分別形成一泛音(如：C6之頻率為1046.5Hz)，使各該泛音與該基音的頻率比係可以形成接近整數倍之比例關係的簡諧倍頻音的效果。例如但不限制的，亦可使該基音與泛 音形成特定比例的和弦。 Specifically, when the copper clock with the simple harmonic frequency is used in the present invention, the copper clock 1 can be excited by several natural frequencies by tapping the positions of the plurality of tapping points P3 N of the copper clock 1. The lowest frequency among the plurality of natural frequencies is a pitch, that is, the frequency of the standard note (for example, the frequency of C5 is 523.25 Hz), and the natural frequencies other than the pitch form an overtone (for example, the frequency of C6 is 1046.5 Hz), so that the frequency ratio of each of the overtones and the pitch can form a harmonic octave effect close to an integer multiple. For example, but not limited to, the pitch and the overtone can be formed into a specific proportion of chords.
為了驗證本發明之具簡諧倍頻音之銅鐘的設計方法的可靠性，該電腦系統係一實驗模態分析軟體(如：SIGLAB)，對該銅鐘1的數學模型執行實驗模態分析，以取得該數學模型的數個模態振型及相對應的自然頻率。將表二所記載之有限元素分析及實驗模態分析的自然頻率，分別作為上式(2)的目標頻率及自然頻率，可以求出該銅鐘1的數學模型的自然頻率與目標頻率的最小誤差平方平均根為4.36%，因此可以得知，該銅鐘1的數學模型之有限元素分析與實驗模態分析的自然頻率，各自與模態振型對應良好，且表二之實驗模態分析的頻率比，係呈現接近1：2整數倍之倍頻音，表三之頻率比具有接近1：2：4整數倍之倍頻音，據此，可以證明本發明設計方法的可靠性。 In order to verify the reliability of the design method of the copper bell with the simple harmonic frequency of the present invention, the computer system is an experimental modal analysis software (such as SIGLAB), and the experimental modal analysis is performed on the mathematical model of the bronze clock 1 To obtain several modal shapes of the mathematical model and corresponding natural frequencies. The natural frequency of the finite element analysis and the experimental modal analysis described in Table 2 can be obtained as the target frequency and natural frequency of the above formula (2), and the natural frequency and the minimum target frequency of the mathematical model of the bronze clock 1 can be obtained. The square root of the error is 4.36%. Therefore, it can be known that the finite element analysis of the mathematical model of the copper clock 1 and the natural frequency of the experimental modal analysis correspond to the mode shape, and the experimental modal analysis of Table 2 The frequency ratio is a multiplier that is close to an integer multiple of 1:2. The frequency ratio of Table 3 has a multiplier that is close to an integer multiple of 1:2:4, according to which the reliability of the design method of the present invention can be proved.
其中，該設計方法還可以另包含一加工步驟S3，係由該電腦系統將該數學模型的設計參數組轉成一輸出檔案，供加工廠商據以加工(如：採用雷射加工技術等)一銅鐘1，使該銅鐘1具有接近整數倍之比 例關係的簡諧倍頻音。 Wherein, the design method may further comprise a processing step S3, wherein the computer system converts the design parameter set of the mathematical model into an output file for processing by the processing manufacturer (eg, using laser processing technology, etc.) Bronze bell 1, making the copper bell 1 have a ratio close to an integral multiple The simple harmonic octave of the relationship.
綜上所述，本發明之具簡諧倍頻音之銅鐘的設計方法及其銅鐘，可藉由使在該外表面上的數個敲擊點，分別由該外表面至該內表面，及再以該內表面至該中心軸線上具有不同的第二距離及第一距離，使該銅鐘經被打擊該敲擊點而產生簡諧倍頻音，可以達成「能使銅鐘發出簡諧倍頻音」、「可運用於需要豐富打擊技巧的演奏場合」及「適合演奏的樂曲風格不受侷限」等功效。 In summary, the design method of the copper bell with the simple harmonic frequency of the present invention and the copper clock thereof can be made from the outer surface to the inner surface by a plurality of tapping points on the outer surface. And then having the second surface and the first distance from the inner surface to the central axis, so that the copper clock is struck by the tapping point to generate a simple harmonic octave, which can achieve "can make the copper bell "Simplified harmonic octave", "can be used in performances where you need a lot of hit skills" and "the style of music that is suitable for performance is not limited".
雖然本發明已利用上述較佳實施例揭示，然其並非用以限定本發明，任何熟習此技藝者在不脫離本發明之精神和範圍之內，相對上述實施例進行各種更動與修改仍屬本發明所保護之技術範疇，因此本發明之保護範圍當視後附之申請專利範圍所界定者為準。 While the invention has been described in connection with the preferred embodiments described above, it is not intended to limit the scope of the invention. The technical scope of the invention is protected, and therefore the scope of the invention is defined by the scope of the appended claims.
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| JPH03174594A (en) * | 1989-12-02 | 1991-07-29 | Hotta:Kk | Chime device |
| TWI530939B (en) * | 2014-08-21 | 2016-04-21 | 國立屏東科技大學 | Method for design a board with harmonics sound and percussion instruments with boards |
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| JPH03174594A (en) * | 1989-12-02 | 1991-07-29 | Hotta:Kk | Chime device |
| TWI530939B (en) * | 2014-08-21 | 2016-04-21 | 國立屏東科技大學 | Method for design a board with harmonics sound and percussion instruments with boards |
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