CN108346412B - Piano string code milling method for three-dimensional modeling of string code points of nut - Google Patents

Piano string code milling method for three-dimensional modeling of string code points of nut Download PDF

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CN108346412B
CN108346412B CN201711402549.3A CN201711402549A CN108346412B CN 108346412 B CN108346412 B CN 108346412B CN 201711402549 A CN201711402549 A CN 201711402549A CN 108346412 B CN108346412 B CN 108346412B
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string
string code
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piano
points
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CN108346412A (en
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胡东红
张玲
王胜
陈广
赵志刚
王平江
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Hubei University
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    • G—PHYSICS
    • G10—MUSICAL INSTRUMENTS; ACOUSTICS
    • G10C—PIANOS, HARPSICHORDS, SPINETS OR SIMILAR STRINGED MUSICAL INSTRUMENTS WITH ONE OR MORE KEYBOARDS
    • G10C9/00—Methods, tools or materials specially adapted for the manufacture or maintenance of musical instruments covered by this subclass
    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B23—MACHINE TOOLS; METAL-WORKING NOT OTHERWISE PROVIDED FOR
    • B23C—MILLING
    • B23C3/00—Milling particular work; Special milling operations; Machines therefor
    • G—PHYSICS
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    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F30/00—Computer-aided design [CAD]
    • G06F30/10—Geometric CAD
    • G06F30/17—Mechanical parametric or variational design
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
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    • G06F30/20—Design optimisation, verification or simulation

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Abstract

The invention discloses a piano string code milling method for three-dimensional modeling of a string pillow string code point, which comprises the steps of establishing a standard three-dimensional model of the string code point of a piano string pillow on a resonance disc provided with a piano string iron plate according to the three-dimensional coordinates of the string code point of the string pillow point and the string code point; mounting the resonance disc to be processed on a string code milling machine tool, and establishing a mathematical relation model between the height of the string code point on the resonance disc to be processed and a standard three-dimensional model; according to the mathematical relation model of the height of the chord code point on the resonance disc to be processed and the standard three-dimensional model, the height of each chord code point on the resonance disc to be processed is calculated; and controlling a string code milling machine tool to mill each string code point according to the three-dimensional coordinates of the string code points on the resonance disc to be machined. After a piano capotasto string code point standard three-dimensional model is established, the heights of all string code points can be automatically calculated by only measuring the heights of at least 3 capotastos which are not on the same straight line on a subsequent resonance disc to be processed, so that the measuring times are reduced, and the processing efficiency is improved.

Description

Piano string code milling method for three-dimensional modeling of string code points of nut
Technical Field
The invention relates to the technical field of piano sound source manufacturing, in particular to a milling processing method of piano string codes for three-dimensional modeling of string pillow string code points.
Background
In the traditional piano string code assembling process, a string hanging iron plate is assembled on a resonance disc, and machining allowance is reserved for string codes on the resonance disc. A straight line is drawn from a main nut point to a secondary nut point on the string iron plate, the straight line passes through the string code points, and the piano string code assembling process has a definite regulation on the distance between each string code point and the straight line of the main nut point and the secondary nut point, and generally requires 2-7 mm higher than the straight line of the main nut point and the secondary nut point. In the traditional manual process, the height calibration and milling of the code string points are finished manually.
In a conventional numerical control string code milling process, a resonator disc provided with a string iron plate is first mounted on a numerical control string code milling machine tool, and the heights of two string rest points related to a string code point are measured by a Z-direction height measuring device on the machine tool, so that the height required by the string code point is calculated. And then milling the string code points to the required height.
The common characteristics of the processing technology are as follows: for each code point, the Z-coordinate heights of two capo points need to be measured manually or automatically, and the Z-coordinate height of the capo point is determined accordingly. For numerical control code milling, the measuring processes seriously reduce the processing efficiency.
Disclosure of Invention
In order to overcome the defects of the prior art, the invention provides a piano string code milling method for three-dimensional modeling of a string pillow string code point, which can effectively improve the processing efficiency of piano string codes.
The invention provides a piano string code milling method for three-dimensional modeling of string pillow string code points, which comprises the following steps:
s1, establishing a standard three-dimensional model of the string code points of the piano string pillow on a resonance disc provided with a piano string hanging iron plate according to the X, Y, Z coordinates of the string code points of the string pillow points;
s2, mounting a to-be-processed resonance disc on a string code milling machine tool, and establishing a mathematical relation model of the height of string code points on the to-be-processed resonance disc and a piano string rest string code point standard three-dimensional model;
s3, according to a mathematical relation model of the height of the string code point on the resonance disc to be processed and the piano string resting string code point standard three-dimensional model, the Z coordinate height of each string code point on the resonance disc to be processed is solved;
and S4, controlling the string code milling machine tool to mill each string code point according to the three-dimensional coordinates of the string code points on the resonance disc to be processed.
Preferably, the step S1 includes the following sub-steps:
s11, placing the resonator disc assembled with the piano string hanging iron plate on a string code milling machine tool, wherein the capotasto on the resonator disc and the capotasto on the piano string pillow string code process drawing have a one-to-one correspondence relationship, and measuring by using a measuring device on the string code milling machine tool to obtain a Z-direction coordinate value of the capotasto on the piano string pillow string code process drawing, so that a standard three-dimensional coordinate model of the piano string pillow point is established;
s12, calculating to obtain a three-dimensional coordinate model of piano string code points according to the calculation relationship between the string code point coordinates and the capotasto point coordinates specified by the piano capotasto process drawing;
s13, establishing a standard three-dimensional model of the piano capotasto string code points according to the capotasto point coordinates and the chord code point coordinates on the piano capotasto string code process drawing.
Preferably, the calculation relationship between the coordinates of the string code point and the coordinates of the capo point is as follows:
code point Qj(xQj,yQj,zQj) The coordinates being a certain (main) capotasto Pi1(xPi1,yPi1,zPi1) And a certain (secondary) capotasto point Pi2(xPi2,yPi2,zPi2) A certain point T (x) on the connecting line betweenT,yT,zT) Moving by + delta in the Z directionjI.e. xQj＝xT,yQj＝yT,zQj＝zT+δj。
Preferably, the step S2 includes the following sub-steps:
s21, installing the to-be-processed resonance disc assembled with the piano string hanging iron plate on a string code milling machine tool, wherein the coordinates and the string code points of the to-be-processed resonance disc are in one-to-one correspondence with the string code points and the string code points of the string pillow points on the standard three-dimensional model of the string code points of the piano string pillow;
s22, selecting a plurality of capotasto points which are not on the same straight line on the piano string capotasto standard three-dimensional model, selecting a plurality of capotasto points which are in one-to-one correspondence with the piano string capotasto on the to-be-processed resonator, and measuring the Z-direction height of the capotasto on the to-be-processed resonator by utilizing a measuring device on a string code milling machine tool;
s23, solving to obtain a mathematical relation model coefficient between the Z coordinate height of the last string code point of the resonance disc to be processed and the three-dimensional coordinate of the last string code point of the standard three-dimensional coordinate model of the string code point of the piano string pillow according to the one-to-one correspondence relationship between the last string code point of the resonance disc to be processed and the string code point of the piano string pillow;
s24, establishing a mathematical relation model between the height of the string code point on the resonance disc to be processed and the three-dimensional coordinates of the corresponding string code point on the piano string resting string code point standard three-dimensional model according to the mathematical relation model coefficient.
Preferably, the step S3 includes the following sub-steps:
s31, calculating the Z coordinate heights of a plurality of string code points on the resonance disc to be processed according to the mathematical relation model of the string code point height on the resonance disc to be processed and the piano string occipital string code point standard three-dimensional model, thereby obtaining the three-dimensional model constructed by the plurality of string code points on the resonance disc to be processed;
and S32, obtaining the height coordinates of other chord code points on the resonance disc to be processed by linear interpolation operation of adjacent chord codes in the three-dimensional model obtained in the step S31.
The invention relates to a piano string code milling method for three-dimensional modeling of string pillow string code points, which comprises the steps of establishing a standard three-dimensional model of the string code points of a piano string pillow on a resonance disc provided with a piano string-hanging iron plate according to X, Y, Z coordinates of the string code points and the string code points of the string pillow; mounting a to-be-processed resonance disc on a string code milling machine tool, and establishing a mathematical relation model of the height of string code points on the to-be-processed resonance disc and a piano string sleeper string code point standard three-dimensional model; according to a mathematical relation model of the height of the string code point on the resonance disc to be processed and the standard three-dimensional model of the string code point of the piano string pillow, the Z coordinate height of each string code point on the resonance disc to be processed is obtained; and controlling a string code milling machine tool to mill each string code point according to the three-dimensional coordinates of the string code points on the resonance disc to be machined. Namely, after a standard three-dimensional model of the string code points of the piano capotasto is established, the heights of at least 3 capotastos which are not on the same straight line on the subsequent resonance disc to be processed are measured, and the heights of all the string code points can be automatically calculated. Thereby reducing the measuring times and improving the processing efficiency.
Drawings
FIG. 1 is a drawing M of a piano nut string code according to the invention0。
FIG. 2 is a three-dimensional coordinate model M of piano capo string code point standard according to the invention21One of the capo points or chordwise code point E is rotated by an angle a about a line passing through point H and parallel to the Y axis to point F.
FIG. 3 shows point F of FIG. 2 continuing to rotate about a line passing through point D and parallel to the X-axis by an angle β to point G and then translating along the Z-axis by a distance ZδTo point S.
Detailed Description
For the purpose of making the objects, technical solutions and advantages of the present invention more apparent, the present invention will be further described in detail with reference to the accompanying drawings and embodiments, it being understood that the specific embodiments described herein are merely illustrative of the present invention and are not intended to limit the present invention.
The invention provides a piano string code milling method for three-dimensional modeling of string pillow string code points, which comprises the following steps:
s1, establishing a standard three-dimensional model of the string code points of the piano string pillow on a resonance disc provided with a piano string hanging iron plate according to the X, Y, Z coordinates of the string code points of the string pillow points;
s2, mounting a to-be-processed resonance disc on a string code milling machine tool, and establishing a mathematical relation model of the height of string code points on the to-be-processed resonance disc and a piano string rest string code point standard three-dimensional model;
s3, according to a mathematical relation model of the height of the string code point on the resonance disc to be processed and the piano string resting string code point standard three-dimensional model, the Z coordinate height of each string code point on the resonance disc to be processed is solved;
and S4, controlling the string code milling machine tool to mill each string code point according to the three-dimensional coordinates of the string code points on the resonance disc to be processed.
As shown in FIG. 1Drawing M of string code of piano capo0Above A1A3A5A7、A2A4A6A8、B1B3B5、B2B4B6、C1C3C5And C2C4C6The identified area is a capo area having a series of capo points, M0XY coordinates of these capo points are provided, and Z coordinate heights of these points are not provided. a is1a2a3a4、b1b2b3And c1c2c3The identified region is a string code region having a series of string code points, M0XY coordinates of these chord points are provided, and Z coordinate heights of these points are not provided. M0And specifying the relative position relationship between the plurality of string code points and the capotasto.
For FIG. 1, M0Code point a of chord pair1～a4、b1～b3And c1～c3And the capotasto point A1～A8、B1～B6、C1～C6The coordinate relationship is described as follows: a is1The XY coordinates of the points being A1A2XY coordinate of a certain point on the line, and a1The Z coordinate height of a point is 2.5 mm above the point, in other words, a1Point is located at A1A2The height of the code is 2.5 mm. Likewise, a2Point is located at A3A4On the connecting line, the height of the code is 3 mm; a is3Point is located at A5A6On the connecting line, the height of the code is 4.5 mm; a is4Point is located at A7A8On the connecting line, the height of the code is 5 mm; b1Point is located at B1B2On the connecting line, the height of the code is 6 mm; b2Point is located at B3B4On the connecting line, the height of the code is 7 mm; b3Point is located at B5B6On the connecting line, the height of the code is 6 mm; c. C1Point is located at C1C2On the connecting line, the height of the code is 6 mm; c. C2Point is located at C3C4On the connecting line, the height of the code is 5 mm; c. C3Point is located at C5C6On the connecting line, the height of the code is 5 mm. M0The heights of other chord code points are required to be obtained by performing linear interpolation calculation on adjacent chord code points in the chord code points.
The resonance disc R to be processed, which is provided with the string hanging iron plate, is placed on a piano string code milling machine tool, and the XY plane coordinates and M of the string pillow string code point on the R can be established by adjusting the R position and the zero position tool setting of the machine tool0And the one-to-one correspondence of the upper capotasto chord code point XY plane coordinates.
However, R and M0The Z coordinate height of the upper capotasto string code point needs to be obtained through measurement and calculation.
Firstly, establishing a standard three-dimensional coordinate model M of piano capotasto string code points21{Pk(xPk,yPk,zPk),Qj(xQj,yQj,zQj) K is more than or equal to 1 and less than or equal to s, and j is more than or equal to 1 and less than or equal to m. Optionally placing a resonance disc T provided with a string iron plate on a piano string code milling machine tool, and establishing XY plane coordinates and M of string code points of the top nut of the T by adjusting the position of the resonance disc and zero setting of the machine tool0And the one-to-one correspondence of the upper capotasto chord code point XY plane coordinates.
According to M0Upper capotasto A1～A8、B1～B6、C1～C6XY coordinates of (A) and M0Determining the one-to-one correspondence of the capotasto on the T and the capotasto on the T1～A8、B1～B6、C1～C6XY coordinates of (a). Measuring device on T upper nut point A by using string code milling machine tool1～A8、B1～B6、C1～C6Z coordinate height of (a). Putting T on the occipital pad A1～A8、B1～B6、C0～C6As the Z-coordinate height value of M0Upper capotasto A1～A8、B1～B6、C1～C6The height value of (a). Thus, a standard three-dimensional coordinate model M of the piano capotasto is established21. Obviously, M in this example21Upper capotasto A1～A8、B1～B6、C1～C6XY plane coordinate of (1) is represented by M0Providing a corresponding point of (A), M21Upper capotasto A1～A8、B1～B6、C1～C6The Z coordinate of (A) is defined by the T upper capotasto point A1～A8、B1～B6、C1～C6The Z coordinate height of (a).
According to M0The requirements for the coordinate relations of the capotasto A1-A8, B1-B6, C1-C6 and the chord code points a 1-a 4, B1-B3 and C1-C3 are that the chord code point Qj(xQj,yQj,zQj) The coordinates being a certain (main) capotasto Pi1(xPi1,yPi1,zPi1) And a certain (secondary) capotasto point Pi2(xPi2,yPi2,zPi2) A certain point T (x) on the connecting line betweenT,yT,zT) Moving by + delta in the Z directionjI.e. xQj＝xT,yQj＝yT,zQj＝zT+δjCalculate M21Three-dimensional coordinates of the code points a 1-a 4, b 1-b 3 and c 1-c 3.
Thus, a standard three-dimensional coordinate model M of the piano capotasto is established21. Obviously, M21Three-dimensional coordinates comprising 20 capotasto points and 10 string code points, which are uniformly marked as M21{Pk(xPk,yPk,zPk),Qj(xQj,yQj,zQj),1≤k≤20,1≤j≤10}。
In the actual processing process, any one to-be-processed resonator R assembled with a piano string hanging iron plate is installed on a string code milling machine tool, and the coordinates of 20 string rest points and the coordinates of 10 string code points on the R are recorded as: r { p }k(upk,vpk,wpk),qj(uqj,vqj,wqj) K is more than or equal to 1 and less than or equal to 20, and j is more than or equal to 1 and less than or equal to 10. By adjusting the position of the R and the zero position tool setting of the machine tool, the XY plane coordinates and M of the string code point of the caput string on the R are established21And the one-to-one correspondence of the upper capotasto chord code point XY plane coordinates.
Because the piano string hanging iron plate has good performanceThe shape and the contour of each string hanging iron plate are considered to be consistent. The method comprises the following steps of designing a standard three-dimensional model M, designing a resonant disc, designing a string hanging iron plate, designing a string code milling machine tool, and designing a resonant disc R to be processed and the standard three-dimensional model M on the string code milling machine tool according to the standard deviation of the base reference of the resonant disc, the assembling error of the string hanging iron plate, the installation position posture error of the resonant disc on the string code milling21There is a difference in the position and posture of (a). The difference is just like M21The whole body is slightly rotated and translated in a three-dimensional space to obtain R.
Due to R and M21The upper capotasto point chord code points are distributed in a wider range on an XY plane and distributed in a narrower range in a Z direction, and as can be seen from figure 1, the R resonance disc base is rectangular, so that the R posture can be conveniently adjusted, and the upper edge and the left edge of the R are ensured to be coincided with the X axis and the Y axis. Thus, M can be replaced21The difference in pose from R is described as: m21The XY coordinates of each capotasto point string code point are equal to the XY coordinates of the capotasto point string code point corresponding to the R, or a one-to-one correspondence relationship exists; by mixing M21Rotating around a line parallel to the X-axis and the Y-axis and translating along the Z-axis can make M21And the string code point of each capo point on the R is equal to the three-dimensional coordinate value of the string code point of the corresponding capo point on the R.
As shown in FIG. 2, M21One capotasto point or code point E (x) one,ye,ze) Around and through H (x)h,yh,zh) A straight line, which is point and parallel to the Y axis, is rotated by a small angle alpha to reach F (x)f,yf,zf) Points E, H and F are approximately at the same level, and the relationship is approximately:
xf≈xe (1-1)
yf≈ye (1-2)
zf≈ze+(xe-xh)tanα (1-3)
for the same reason, as shown in FIG. 3, F (x)f,yf,zf) Point onPassing around D (x)d,yd,zd) A straight line, which is point and parallel to the X axis, is rotated through a small angle beta to reach G (X)g,yg,zg) Points F, D and G are approximately at the same level, and the relationship is approximately as follows:
xg≈xf (2-1)
yg≈yf (2-2)
zg≈zf+(yf-yd)tanβ (2-3)
then, the G point is translated by a distance Z along the Z directionδTo S (x)s,ys,zs) The following relationships are given:
xs＝xg (3-1)
ys＝yg (3-2)
zs＝zg+zδ (3-3)
substituting the formula (1-1,2,3) into the formula (2-1,2,3), substituting the formula (2-1,2,3) into the formula (3-1,2,3), and simplifying to obtain:
xs＝xe (4-1)
ys＝ye (4-2)
zs＝ze+xetanα+yetanβ-xhtanα-ydtanβ+zδ (4-3)
let a ═ tan α, b ═ tan β, and c ═ xhtanα-ydtanβ+zδThe above formula can be written as:
xs＝xe (5-1)
ys＝ye (5-2)
zs＝ze+axe+bye+c (5-3)
if E is M21Code points of the upper nut, S (x)s,ys,zs) And the chord code point of the capo point corresponding to the E on the R is the relation between the S point and the E point, which satisfies the above formula. Therefore, only the coefficients a, b, c need to be obtained, and the M can be used21And calculating the coordinates of the string code points of the corresponding capotasto points on the R according to the three-dimensional coordinates of the string code points of the capotasto points.
At M21Above 3 capotasto points not in a straight line, e.g. A1、C5、C2、B6A total of 4 capotasto points, each of which is expressed as (x)1,y1,z1)、(x2,y2,z2)、(x3,y3,z3)、(x4,y4,z4). Selecting 4 capotasto points corresponding to the R one by one, and respectively recording as (u)1,v1,w1)、(u2,v2,w2)、(u3,v3,w3)、(u4,v4,w4) Wherein w is1～4Is unknown. Measuring the Z-direction height w of the 4 nut points by using a measuring device on the nut code milling machine tool1～4。
The standard three-dimensional coordinate model of the string code point of the piano capo is M21{Pk(xPk,yPk,zPk),Qj(xQj,yQj,zQj) K is more than or equal to 1 and less than or equal to s, j is more than or equal to 1 and less than or equal to m, wherein P isk(xPk,yPk,zPk) Three-dimensional coordinate model, Q, representing s capotasto pointsj(xQj,yQj,zQj) A three-dimensional coordinate model representing m chord code points. Be equipped with the waiting of piano string iron plate and process the sympathetic response disk R and install on the string sign indicating number mills the lathe, and s capotasto point coordinates and m string sign indicating number point coordinates on R are: r { p }k(upk,vpk,wpk),qj(uqj,vqj,wqj) K is more than or equal to 1 and less than or equal to s, j is more than or equal to 1 and less than or equal to M, and M21The s capotasto points and the m string code points have one-to-one correspondence. At M21N capotasto points (P) which are not on the same straight line are selectedki(xi,yi,zi),3≤n≤s,1≤i≤n,1≤kiS or less, and selecting n capotasto points (p) corresponding to the R one by oneki(ui,vi,wi),3≤n≤s,1≤i≤n,1≤kiS, wherein w isiUnknown, using the string code to mill the measuring device on the machine tool to measure the upper nut point p of Rki(ui,vi,wi) Z-direction height w ofi。
According to the formula (5-3), the following relationships are provided:
wi＝zi+xia+yib+c
the coefficients a, b, c can be found by using the least squares method. Firstly, the mean square error is calculated to obtain:
Figure BDA0001519688900000081
and (3) solving the partial derivative of M to obtain:
Figure BDA0001519688900000082
Figure BDA0001519688900000083
Figure BDA0001519688900000084
simplifying to obtain:
Figure BDA0001519688900000085
Figure BDA0001519688900000086
Figure BDA0001519688900000087
solving the equation set to obtain coefficients a, b and c, and establishing an R upper chord code point qj(uqj,vqj,wqj) Z coordinate height w ofqjAnd M21Three-dimensional coordinate Q of upper corresponding string code pointj(xQj,yQj,zQj) The mathematical relationship between: w is aqj＝zQj+axQj+byQj+c。
Will M21Code point a of upper chord1～a4、b1～b3、c1～c3The three-dimensional coordinate value (x, y, z) of (a) is substituted into (w) is z + ax + by + c, and the corresponding chord code point a on R is calculated1～a4、b1～b3、c1～c3Z coordinate height w. According to R upper chord code point a1～a4、b1～b3、c1～c3And calculating the Z coordinate heights of all the capo points on the R through linear interpolation.
And finally, controlling the string code milling machine tool to mill each string code point on the R according to the three-dimensional coordinates of all the string code points on the R.
The invention relates to a piano string code milling method for three-dimensional modeling of string pillow string code points, which comprises the steps of establishing a standard three-dimensional model of the string code points of a piano string pillow on a resonance disc provided with a piano string-hanging iron plate according to X, Y, Z coordinates of the string code points and the string code points of the string pillow; mounting a to-be-processed resonance disc on a string code milling machine tool, and establishing a mathematical relation model of the height of string code points on the to-be-processed resonance disc and a piano string sleeper string code point standard three-dimensional model; according to a mathematical relation model of the height of the string code point on the resonance disc to be processed and the standard three-dimensional model of the string code point of the piano string pillow, the Z coordinate height of each string code point on the resonance disc to be processed is obtained; and controlling a string code milling machine tool to mill each string code point according to the three-dimensional coordinates of the string code points on the resonance disc to be machined. Namely, after a standard three-dimensional model of the string code points of the piano capotasto is established, the heights of at least 3 capotastos which are not on the same straight line on the subsequent resonance disc to be processed are measured, and the heights of all the string code points can be automatically calculated. Thereby reducing the measuring times and improving the processing efficiency.
The above-described embodiments of the present invention should not be construed as limiting the scope of the present invention. Any other corresponding changes and modifications made according to the technical idea of the present invention should be included in the protection scope of the claims of the present invention.

Claims (3)

1. A piano string code milling method for three-dimensional modeling of string pillow string code points is characterized by comprising the following steps:
s1, establishing a standard three-dimensional model of the string code points of the piano string pillow on a resonance disc provided with a piano string hanging iron plate according to the X, Y, Z coordinates of the string code points of the string pillow points;
s2, mounting a to-be-processed resonance disc on a string code milling machine tool, and establishing a mathematical relation model of the height of string code points on the to-be-processed resonance disc and a piano string rest string code point standard three-dimensional model;
s3, according to a mathematical relation model of the height of the string code point on the resonance disc to be processed and the piano string resting string code point standard three-dimensional model, the Z coordinate height of each string code point on the resonance disc to be processed is solved;
s4, controlling a string code milling machine tool to mill each string code point according to the three-dimensional coordinates of the string code points on the resonance disc to be machined;
the step S1 includes the following sub-steps:
s11, placing the resonator disc assembled with the piano string hanging iron plate on a string code milling machine tool, wherein the capotasto on the resonator disc and the capotasto on the piano string pillow string code process drawing have a one-to-one correspondence relationship, and measuring by using a measuring device on the string code milling machine tool to obtain a Z-direction coordinate value of the capotasto on the piano string pillow string code process drawing, so that a standard three-dimensional coordinate model of the piano string pillow point is established;
s12, calculating to obtain a three-dimensional coordinate model of piano string code points according to the calculation relationship between the string code point coordinates and the capotasto point coordinates specified by the piano capotasto process drawing;
s13, establishing a standard three-dimensional model of the piano capotasto string code points according to capotasto point coordinates and chord code point coordinates on the piano capotasto string code process drawing;
the step S2 includes the following sub-steps:
s21, installing the to-be-processed resonance disc assembled with the piano string hanging iron plate on a string code milling machine tool, wherein the coordinates and the string code points of the to-be-processed resonance disc are in one-to-one correspondence with the string code points and the string code points of the string pillow points on the standard three-dimensional model of the string code points of the piano string pillow;
s22, selecting a plurality of capotasto points which are not on the same straight line on the piano string capotasto standard three-dimensional model, selecting a plurality of capotasto points which are in one-to-one correspondence with the piano string capotasto on the to-be-processed resonator, and measuring the Z-direction height of the capotasto on the to-be-processed resonator by utilizing a measuring device on a string code milling machine tool;
s23, solving to obtain a mathematical relation model coefficient between the Z coordinate height of the last string code point of the resonance disc to be processed and the three-dimensional coordinate of the last string code point of the standard three-dimensional coordinate model of the string code point of the piano string pillow according to the one-to-one correspondence relationship between the last string code point of the resonance disc to be processed and the string code point of the piano string pillow;
s24, establishing a mathematical relation model between the height of the string code point on the resonance disc to be processed and the three-dimensional coordinates of the corresponding string code point on the piano string resting string code point standard three-dimensional model according to the mathematical relation model coefficient.
2. The piano string milling method for three-dimensional modeling of a string code point of a nut of claim 1, wherein the calculation relationship between the string code point coordinates and the string code point coordinates is as follows:
code point Qj(xQj,yQj,zQj) The coordinate is a main chord sleeper point Pi1(xPi1,yPi1,zPi1) And minor chordPillow point Pi2(xPi2,yPi2,zPi2) A certain point T (x) on the connecting line betweenT,yT,zT) Moving by + delta in the Z directionjI.e. xQj＝xT,yQj＝yT,zQj＝zT+δj。
3. The piano string milling method for three-dimensional modeling of nut string code points according to claim 1, wherein the step S3 includes the following substeps:
s31, calculating the Z coordinate heights of a plurality of string code points on the resonance disc to be processed according to the mathematical relation model of the string code point height on the resonance disc to be processed and the piano string occipital string code point standard three-dimensional model, thereby obtaining the three-dimensional model constructed by the plurality of string code points on the resonance disc to be processed;
and S32, obtaining the height coordinates of other chord code points on the resonance disc to be processed by linear interpolation operation of adjacent chord codes in the three-dimensional model obtained in the step S31.
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