TW411408B - Speed rate control method and equipment in computer numeric control curve path - Google Patents

Abstract

In the process of parametric curve computer numeric control, stepping rate is the deterministic factor of process quality. This invention proposes parametric curve interpolator with speed rate control and develops operation modes. The modes are constant rate interpolator and accelerate-decelerate interpolator. The operation mode of constant speed rate interpolator could maintain the parametric curve keeping speed rate at the constant value in the implementation process of interpolation. Furthermore, the operation mode will adapt the accelerate-decelerate design of parametric curve interpolator to achieve smoother accelerate-decelerate motions.

Description

V. Description of the invention (1) The invention of the invention The invention of f. This invention relates to a computer numerical control (CNC) processing machine. In particular, it relates to a computer numerical control processing machine designed with a parameter-controlled curve inserter with rate control. )

J Related Skills Description Traditional CAD / CNC system operators first design the required workpieces through computer-aided design (CAD), such as: 3-D curve representation of molds, turbine blades, aircraft models, etc., where the curve representation is in the CAD system Generally, it is a format of parameterized curves, and since general CNC systems only provide straight and circular inserters, CAD 尙 must segment the designed workpiece surface curve and transfer it to the CNC for execution. When the linear inserter of the CNC system receives the segmented information of the surface curve of the workpiece, it then uses some algorithms to generate interpolation points for the tool movement, and these interpolation points are the position input commands for the servo driver. Printed by the Central Bureau of Standards, Ministry of Economic Affairs, Cooperative Society (please read the notes on the back before filling this page) Although the traditional curve processing method is relatively simple, there are still some shortcomings in application: α) The curve is more accurately represented, so the curve must be segmented into a large number of sections and transmitted between CAD and CNC, but it is easy to cause errors when transmitting a large number of signals, such as data loss and noise interference. (2) The discontinuity of the cutting section will cause the surface accuracy of the processed workpiece to deteriorate. (3) Because the curve section is linear, the speed does not change smoothly in each linear section, especially considering the CNC insertion. The automatic acceleration and deceleration characteristics of the gearbox are more obvious. The traditional acceleration and deceleration method is to pass the position command through a low-pass filter to apply the China National Standard (CN'S) Λ4 叱 Grid (2Η) × 2π <, &gt; .ίί) to the paper size of the paper; ~ Central Standard of the Ministry of Economic Affairs Printed by the Consumer Cooperative of the Bureau A-ΙΓ V. Description of the invention (2) The command input is relatively smooth. However, this method will cause radial and chordal height errors for command paths with large changes, such as near the start and end points of the processing curve. Although Kim (DIKim) proposed the use of parameter acceleration and deceleration to achieve the purpose of parameterizing the curve acceleration and deceleration, and because it is the operation of the parameter acceleration and deceleration, the interpolation point has a small radial error, which can make the interpolation The generation of points has the function of acceleration and deceleration, but on some curves dare not really achieve the purpose of rate acceleration and deceleration, the reason is that the parameter space does not correspond to the curve uniformly. In addition, when the curvature radius of the curve is so small that the feed rate command is too large, it will cause obvious position command error. In view of the conventional process of parameterized curve interpolation, the present invention is difficult to control the rate accuracy of the curve, and the feed rate is a decisive factor for the processing quality. Therefore, the design of the parameterized curve inserter with rate control is proposed. Invention: The purpose of the present invention is to provide a mode of operation with a constant rate inserter, which can maintain the constant rate of the parameterized curve during the implementation of the interpolation, so as to ensure the processing rate of the computer numerical control curve path rate control method. And device "Another object of the present invention is to provide a computer numerical control curve path rate control method with an acceleration / deceleration inserter operation mode, which uses a parametric curve inserter's acceleration / deceleration design to obtain a smoother acceleration / deceleration motion. And device. The computer numerical control (CNC) curve path rate control method of the present invention is to operate the curve path processing at the same rate or acceleration / deceleration control, including the following steps: This paper size is applicable to the Chinese National Standard (CMS) Λ4M1 grid (2.0 × 21) 7 credits) 2 156 * 5 ^ ~ — ί ^: Order (please read the precautions on the back of vg before filling in this page) ΙΓ 411408 5. Description of the invention (3) (1) The parameterized curve inserter is in After receiving the information of the curve interpreted by computer-aided design (CAD), iterative method (Iteration) of the parameterized curve is used to generate continuous interpolation points; (2) Only the chord height of the position command error generated by the inserter is considered. The influence of chord height error, without taking into account the radial error; (3) Derive an approximate parameter iteration rule for the parametric curve formulation: (4) Design a parameter iteration rule with rate control , A parameter approximation rule of this representation is proposed to compensate the parameters, and the curve rate control with higher accuracy is obtained through the correlation between the compensation amount and the curve: (5) choose the compensation near zero to In a more reliable parameter iterative result; and (6) the obtained interpolation point Zhi continuous compensation of the control system into the center of the tool moves along a parametric curve. The parameterized curve used in the computer numerical control (CNC) curve path rate control method of the present invention is a non-equidistant B cloud line (NURBS), and the parameter iterative method used by the parameterized curve inserter is Chou (JJChou )with

Yang (DCHYang) proposed a generalized parameter iteration rule based on the iterative method of feed rate control. The computer numerically controlled curve path rate control device of the present invention 'includes: computer for CAD' work The auxiliary design work includes making the parameterized curve format and segmented curve: The computer numerical control (CNC) mechanism 'includes: the parameterized curve inserter' is receiving the parameters interpreted by the computer ---- Γ · I. 1-- ------- Shi κ _ _ _ f _ _ Ding {Please read the notes on the back before filling out this page) Printed on the paper by the Consumers' Cooperatives of the Central Standards Bureau of the Ministry of Economic Affairs This paper applies Chinese National Standards (CNS) 4 Old cases (21〇 &gt; &lt; 2 [) 7 credits) 3 15685 Printed by the Consumer Cooperatives of the Central Bureau of Standards of the Ministry of Economic Affairs A7 Β7 V. Description of the invention (4) The curve information is generated by parameterizing the points of the curve The method generates continuous interpolation points: the controller receives the continuous interpolation points generated by the parameterized curve interpolator and sends control processing signals; the tool receives the control processing signals sent by the controller, and the center Ϊ * along to parameterize Curve movement; and a human-machine interface device, which allows human-computer communication between the operator and the parameterized curve inserter: wherein the parameterized curve inserter can perform a constant-rate interpolation operation mode on the parameterized curve and Acceleration / deceleration insertion operation mode. The parameterized curve inserter device of the computer numerical control curve path rate control of the present invention includes: a constant rate inserter, which keeps the parameterized curve path at a fixed rate during the implementation of the interpolation; an acceleration / deceleration inserter, which makes the The machining curve path can obtain smoother acceleration and deceleration motion. Brief Description of the Drawings Fig. 1 is a block diagram of a processing system for a parameterized curve according to an embodiment of the present invention. Figure 2 is a schematic diagram of the tool moving in a straight line between the two interpolation points, and the inserter generates a position command error. Figure 3 is the compensation amount ~ In the formula, the vector 〇, the curve differential vector and the parameters M, ', 1 /, Geometric relationship between μ. Fig. 4 is the case where the same real number 値 or conjugate imaginary number 値 compensation amount is formed. Β Fig. 5 is the bow curve command path applied in this embodiment. The paper size applies the Chinese National Standard (CNS) A4 specification (210X297 mm) 4 15685 11. 1-I Binding--(Please read the notes on the back before filling out this page) 4. Printed by the Consumer Cooperatives of the Central Bureau of Standards of the Ministry of Economic Affairs 4 ^ 408 A- 1Γ 5. Description of Invention (5) Section 6 The picture shows the first-order approximation (1 st 〇rderappr ο X imati ο η) interpolation rate command result curve rate change situation. Figure 7 shows the variation of the rate of the 2nd order approximation interpolation rate command result curve. Fig. 8 is a graph showing a situation in which the rate command curve of the constant rate operation mode is inserted in the present embodiment. Figure 9 shows the results of parameter compensation and calculation in the constant rate operation mode. Figure 10 is a curve approximation of the 1st order change in the rate difference of the quadratic curve acceleration / deceleration method. Fig. 11 is the 2nd order approximation of the rate difference of the quadratic curve acceleration and deceleration method. Fig. 12 is the curve of the rate difference and constant rate operation mode of the quadratic curve acceleration and deceleration method. Description of drawing number 1 computer (CAD) 2 computer numerical control (CNC) mechanism 3 parameterized curve inserter 4 human-machine interface device 5 controller 6 tool 7 parameter curve information 8 workpiece contour curve 9 tool movement path (please read the back first For the matters needing attention, please fill in (the clever page) i—1 I-----LI JL—. ^ 衣 &quot; .— I —4— j -----. ......... I --I-· '.-I -II1 1ΓΙ ^^ 1 --- V-- This paper size applies to Chinese National Standards (CNS) Λ4 叱 格 U 丨 0X2V? Official exchange) 5 15685 Employees of the Central Standards Bureau of the Ministry of Economic Affairs 4U408 printed by a consumer cooperative Η '—______ Five' Description of the invention (6) 10 Radial error 11 Chord height error 12 Interpolation point Detailed description of the preferred embodiment-Generally, the curve generated by the CAD system is a parametric curve representation, At the same time, the CAD system also provides the related parameter data transmission format of the parametric curve. Therefore, in the design of the CAD / CNC system, the parameter information of the parametric curve can be directly used as the processing information transmission between the CAD / CNC system and the CNC interpolation. The processing system for the parametric curve discussed in the present invention is shown in Fig. 1. In the figure, 1 is a computer, which is used for auxiliary design (CAD), including parametric curve format and segmented curve, and 2 is computer numerical control (CNC). Mechanism, in which the parametric curve inserter 3 receives the parametric curve information 7 interpreted by the computer 1 and generates continuous interpolation points in the parametric curve point generation mode and sends it to the controller 5 so that the center of the tool 6 is along Parametric curve movement, 4 of which are human-machine interface devices, allowing the operator to communicate with the CNC. Common parameterized curves are: Bezier curve, B Spline, and NURBS (non-equidistant B cloud line); the present invention uses NURBS parameterized curves. The process of implementing the parameterized curve inserter 3 is mainly to calculate the parameterized curve points. Generally, the calculation rule of higher curve position and rate accuracy requires more complicated calculation methods and larger calculation amount, which is disadvantageous in the environment where instant commands are generated. Therefore, the choice and design of the calculation method must consider the trade-off between the accuracy of the curve and the calculation time. The most commonly used calculation format is the following iterative method of parameters: ^ «, + Δ (μ,) (Please read the precautions of the back, 6 first. (Fill in this page again) —- The bound paper. The Zhang scale is applicable to the Chinese National Standard ([?] Sixty-four Regulations (210 乂 297 public garbage) 6 156 «5 411438 A 'ΙΓ 5. Explanation of the Invention (7) Ministry of Economic Affairs Printed by the Consumer Standards Cooperative of the Central Bureau of Standards (please read the precautions on the back before filling out this page), where "indicates the parameters of the current sequence, u, + l indicates the parameters of the next sequence, and Δ (ί〇 indicates the The amount of time-related calculations. Under the parameterized curve, Mi represents the parameters of the curve, so this parameter must be substituted into the mathematical expression of the curve to obtain the point in time. In the design of the parameterized curve inserter, for arbitrary The application of the parametric curve mathematical model, because the relationship between the parameters in the parametric curve and the curve or geometric path is not obvious, it is not easy to perform the inverse operation, that is, it is not easy to infer the corresponding parameters from the known curve points, because It is difficult to have good control of the curve rate in the iterative method of the parameter. "In actual processing, the parametric curve inserter will cause the error of the curve rate of the interpolation result due to the inappropriate parameter iteration rule. The curve rate error refers to the phase. The difference between the movement rate between adjacent interpolation points and the feed rate setting of the inserter. When the error of the curve rate is greater, it means that the movement between interpolation points cannot be operated as the feed rate, which often results in excessive positions. Errors, excessively long machining time, and poorly machined workpiece surfaces. Therefore, in the design of the parametric curve inserter, the parameter iterative method must accurately control the curve rate to reduce the error. In addition to the curve rate error, the tool movement caused by the inserter The interpolation point of the time, and the tool moves in a straight line between the two interpolation points, so the position command error generated by the inserter can generally include: radial error and chord height error. The relationship between the direction error, chord height error and the curve can be shown in Figure 2, where 8 is the workpiece contour curve * 9 is the tool movement path, and 10 is the radial direction U is the chord height error, 12 is the interpolation point β, the radial error is the shortest distance between the position point and the curve, and the chord height error is the maximum distance between the secant function and the cutting arc formed by the two position points. This paper scale is applicable to Chinese National Standards (CNS) M specifications (210x) 7 15685 Printed by the Consumer Cooperatives of the Central Standards Bureau of the Ministry of Economic Affairs 4: V. Description of the invention (*) The design of the parametric curve inserter generally causes radial The cause of the error is the rounding error of the floating-point number, and the cause of the chord height error is caused by the incorrect feed rate. Because in the representation of the parameterized curve, the round-cut error can be calculated by a precision computer It is reduced, and the string height error is often much larger than the radial error. Therefore, in the design of the inserter, the present invention only considers the influence of the string height error, and the string height error should be controlled within a basic length unit (BLU). The parametric iterative method of parametric curves is researched. In the methods used by Bedi (S. Bedi), Ali (I. Ali), and QuaiUN. Quan), it is a constant 値. At this time, the iteration method is called uniform. (Uniform) parameter iteration. Although this method is simple, the equidistant selection of parameters does not guarantee the change of the boundary range of the command position and the variation of the curve rate of the command string height because the relationship between the parameters and the curve points is not consistent. Chou and Yang according to the cutting tool path A precise parametric iterative method of the parametric curve is proposed with the dynamic characteristics of the motion system to control the system's position, rate, and acceleration simultaneously. The more precise reason is that Chou and Yang's method adds a dynamic relationship between parameters and time. Kim discusses the parameter iterative method of parameter acceleration and deceleration in the parameterized curve. The method of parameter acceleration and deceleration is used to obtain high-precision position and smooth rate acceleration and deceleration results, but the relationship between the parameters and the curve is not uniform Correspondingly, there may not be the expected acceleration and deceleration behavior in speed. Because the position command and curve rate accuracy produced by the inserter will affect the quality of the processed workpiece; inaccurate position commands will cause insufficient precision processing results, and the curve rate error will cause the extension of the working hours and the speed wave.

This paper size applies to Chinese National Standards (CNS) Λ4ΐ.ί grid (210 X 297 Kg) 8 1368S (please read the precautions on the back before filling this page) Packing ------------ -• Order ------ i ”---» --- 411408

Printed by the Consumer Cooperatives of the Central Standards Bureau of the Ministry of Economic Affairs. 5. Description of the invention (9) Motion will cause vibration and affect the surface accuracy of the processed workpiece. Therefore, in the process of implementing any parametric curve, how to design the iterative process of the parameters to produce position and curve rate accuracy can meet the design requirements, that is, to achieve a low position command string high error and low curve rate error, which is a parametric curve interpolation. Important key to implement implements "In the method of parametric iteration, although the parametric iteration method proposed by Chou and Yang has improved the curve rate variation situation due to the dynamic relationship between parameters and time, the improvement is still due to Taylor The degree of approximation of the expansion is limited, and the curve rate cannot be accurately controlled. For this reason, the present invention proposes a parameter iterative method of feed rate control based on the generalized parameter iteration rule proposed by Chou and Yang to accurately control the curve rate generated by the inserter. The iterative method with rate control is to add the correction amount to the original first-order approximate parameter iteration method of Chou and Yang. Because the correction amount considers the approximate relationship between the parameter and the curve rate, it can greatly reduce the fluctuation of the curve rate. Based on the control of the feed rate, the interpolation point generation of the parametric curve inserter can be operated in constant rate operation mode and acceleration / deceleration operation mode according to the requirements of the processing conditions. The fixed-rate operation mode is to maintain the same curve rate during the curve generation process of the inserter to reduce the processing error caused by the rate change. In the acceleration / deceleration operation mode, because the parameter iteration method of the rate control can obtain high-precision curve rate control, the acceleration / deceleration can be performed on the feed rate parameter in the design of the acceleration / deceleration so that the curve rate is performed in the same acceleration / deceleration mode. Get the real acceleration and deceleration rate results, and you can also fully understand the rate change during acceleration and deceleration "(A) The parametric curve formula (Parametric Curve Formulation) is derived:----I-1-_. _ Ί ai ^ l — ^ Ί —l ^^ i It—— V life · ϋίι (^^^^ 1 I (Please read the notes on the back before filling out this page) The paper size applies to the Chinese National Standard (CNS) (210X297 公 蛋} 9 15685 4114G8 A7 B7 V. Description of the invention (10 In the derivation of the parametric iteration method, it is assumed that e (a) is the expression of parametric curve points, where "is the parameter representation and is a function of time, ie, Μ ^). The definition w (i.) = W,; u (ti + x) = Μί + 1 can be known from Taylor's expansion: 'du 珥 + — dt f \ \ d * u

+ HOT U) Since the curve rate can be expressed as &lt; C (w) FREE) | du du {Please read the notes on the back before filling this page} So dC (u) du u = ui (2) Contrast ( 2) Differentiate again to get the printed d2u _ -1 dt1 &lt; = (, || &lt; λ ^ (μ) 2 1 ^%). Fd \ du dt Differential calculus shows that fd 4) f \ (d dC (u) V du f V ㈣ 一; u = h, du dt du dt du (3) (4) Substituting equation (4) into equation (3) gives , The Zhang scale is applicable to the Chinese national standard (CNS &gt; A4 specification (210 X 297 mm) 10 156S5 411408 A7 B7 V. Description of the invention (u) fd 1 bucket) f V2 (ut) l 1 du [U = U} d2u dt1 (= t \ dC (u) 3 du du U ^ Ui (5) It is also known through simple differential calculations that fd dC (u) V du / u = ut dC (u) d2C (u) du du2 du

HI (6) Substituting the formula (6) into the formula (5), the quadratic differential of the parameter "is X n du du2 1 d2u wi = i, dC (u) 4 du (7) M JI- Γ. — '' 衣 ™ I-^ &quot; &quot; &quot; Order (Please read the precautions on the back before filling out this page) Printed by the Consumer Cooperatives of the Central Standards Bureau, Ministry of Economic Affairs, if the curve point generation interval is a sampling time * then ^ , &gt; 1 ~ ti = Z Substituting equations (2) and (7) into equation (1) and omitting higher-order terms, the parameter iteration rules for the first and second approximations can be obtained as follows: The parameter iteration rules for the first approximation: V (u) Ts-% dC (u) du U = Mi (8) Parameter iteration rule for quadratic approximation:

Wi + i = «(+ v (uty z Κι1 dC (u) td2C (uf du du2. II broken) II ^ u = u IK («) du This paper size applies to the Chinese National Standard (CNS) A4 specification (210X297) (9) 15685 411408 A7 B7 V. Description of the invention (12 Among them, since the expected curve rate is the feed rate setting 値, the implementation of the parametric curve inserter can be specified as the feed rate when the parameter M = Set 値》 and in the plane coordinate system, because

dC (u) du. noisy) _ d ^ C ^ u) du du2 dCy (u) ’du2 d2Cy (u) .du a L du2 J so dC (u) du fdCx (u), du.

V du du2 J du dCx {u) d2Cx (u); dCy (u) d2Cy (u) 'du du1 du du1, (Please read the notes on the back before filling out this page) The Central Standards Bureau of the Ministry of Economic Affairs, Consumer Cooperatives Printed in application, the iterative rule of the second approximation parameter of the formula (9) has a smaller curve rate error than the iterative rule of the first approximation parameter of the formula (8). (B) Parametric iteration rule design with rate control: As can be seen from the above, the first and second approximation parameter iteration rules represented by equations (8) and (9) are simplified by the higher order in the Taylor expansion of the curve parameters versus time. The secondary term is obtained, but in application, the curve rate accuracy is often limited due to the influence of unknown omitted terms on the curve. In view of this, the present invention proposes a method of parameter compensation, and obtains a more accurate curve rate control through the correlation between the compensation amount and the curve. The design method is to add it to an approximate parameter iterative method represented by equation (8) Umbrella) The compensation amount 'is used to iteratively modify the parameters. Since it is compensated through the first-order approximate parameter substitution method, the calculation of the curve's secondary differential information can be omitted. The compensated parameter iteration formula is: »i + l = Mi + 1 This paper size is applicable to China National Standard (CNS) A4 specification (210X297 mm) 15685 A7 B7 V. Description of the invention (where

Mi + i = Ui v (utyr, \\ dC (u) du is used to obtain the parametric iteration compensation parameter umbrella). The present invention uses a Taylor expansion of the position to the parameter and solves it through the requirements of the feed rate and the curve rate. The amount of compensation. The parameter curve table is defined as, where c («) cx (u) Cy {u \ G⑻ and the curve position of the J axis and the y axis when the parameter a can be expressed respectively, because« i + ι = «ί + ι + 4Μί) via a Taylor expansion approximation,

Cx (ui + l) = Cx (u'i + l) + dCx {\ Μί + 1 du du

Au &gt;) ---- ^ _ 丨 — — — — ^ 1 ---- iT ------ Quan-(Please read the precautions on the back before filling this page) Cooperative Du printing is to make the speed of the path in accordance with the feed rate setting 値, so let also: such as 丨) -C Office)] 2 + [C &gt;, + 1)-c &gt;,) f 〒! — You can get the following quadratic function expression

Us2 + Zs + W = 0 where U = x \ uM) \ Y {^ x) 2 The paper size is applicable to the Chinese National Standard (CNS) A4 specification (210X297 mm) 13 15685 411408] Γ du 5. Description of the invention ( 14) Z = 2 \ DXX '(uMYDYr {^ W = DX1 + DY2-i ^ (ui) T) 1

Dx = a (»; + i) -cx (« j) DY = Cy (u; ^)-Cy ^) ruj and the compensation amount &lt; called) is ^ 1,2 («,) = \ ρχ · χ (um) + dy-y (^ t)] ± y .r (»,„)-Dr- x '卜) -asr.r »/ (« irt) + Ρ' (Η; +1) 2 ( 10) In formula (10), 'the compensation amount is the root of the quadratic equation, so the properties of the root must be discussed and an appropriate root should be selected as the compensation of the rate control parameter iteration method. Definition (please read the back first) Note: Please fill in this page again.) Printed by the Consumer Cooperatives of the Central Standards Bureau of the Ministry of Economic Affairs

D

C

DX DY χ '(^) ^' (w; +1) The formula (10) can be rewritten as-(D.c'Ji. / Ilc'f-(v ^ yzf Tc- x &quot; d

PI (11) This paper scale applies Chinese National Standard (CNS) A ^ uTTIioTT ^ r 14 15685 4114ϋ8] Γ 5. Description of the invention (15) Among them, the vector D, the curve differential vector and the parameters, "the geometry between i + 1 The relationship can be represented in Figure 3, where Θ is the vector and the angle between the vector and the curve's differential vector. In formula (Π), since \ CxD; \\ C '\\ -Tsl

Ic'lf-r, 2 c z2 and p | f &gt; 〇, annihilation &gt; 0 so {P.f. ^, .o2K} and

I which side. r2W- V2 {u,) ~ L · 3 FI ^ d 'ΤΛ ύη2Θ * sin2 Θ The curve rate produced by the curve inserter when the same number is the parameter' y2M- sin2 θ has the same number, so compensation (please read the first Note: Please write this page again ^ --------, order --- the amount printed by the staff consumer cooperative of the Central Bureau of Standards of the Ministry of Economic Affairs will have the following three situations: ⑴ When 値 ζ sin2 Θ, the compensation amount is as follows: Μ is a different real number 2 — ⑵ When ^ sin2 θ ，, the compensation quantization (",) is the same real number. The paper scale is applicable to the Chinese family standard 隼 (CN_S), \ 4 圯 梠 (2 Η) X public trash) Ifi 15685 41ΗυΒ ΙΓ V. Description of the invention (16 • sin2 Θ

(3) When 値. After comparing the curve rate D and the included angle 0 generated by the curve inserter, it can be known that when the factory 2W-ts, the compensation 2 ("f) is the common imaginary feed rate rh) sin2 θ depends on the vector sign (Z) The angle Θ »with the curve differential vector Θ may therefore form the same real number 値 or conjugate imaginary number 値 compensation amount ~ (Μ) as shown in Figure 4. When C falls near a, b, because the vector is related to The curve differential vector f is almost vertical, so sinWsl is more likely to occur. In other words, the same real number / β Ϋ _ and V \ u,) ^ \ Ts • sin2 θ} 値 or conjugate imaginary number 値 compensation is more likely to occur when the curve curvature is more Near large points. However, in practical applications, the same real number 値 or conjugate imaginary number 値 compensation amount will not occur, because based on the accuracy of the position command, the curve parameter B is not allowed to change the curve with large curvature. At the same time, in the application of a curve with a relatively smooth change, the same real number 値 or conjugate imaginary number 値 compensation amount will not occur. Therefore, the compensation quantization 〇 / 〇 is generally a different real number 实际 in practical applications. By formula (11 ), (Please read the back first Please fill in this page again for further information) Printed by the Central Bureau of Standardization of the Ministry of Finance and Economic Cooperation of Employees c \ 土 C 'c b

Fll sin2 Θ

This paper size applies the Chinese National Standard (CNS) Λ4 grid (: M〇_X 16 156u5 4ii4G8 V. Description of the invention (17) cos (m;) T ^ f-Ipl + jD | j cos2 Θ Order (Factory w ' From μ, when “, + 1 uses a first-order approximate parameter iterative method, # — is generally a relatively small unitary, so it can be known from the Taylor expansion approximation that μ 2_ | p | pw _ 2.1 gives cos θ IP ', ie仏 (% _) has a negative compensation 値 and a compensation near zero, and the negative compensation 値 is far from zero. Since the purpose of compensation 此 here is to compensate for the parameter ~ the deficiency in the curve rate, so the compensation near zero is selected.値 to obtain more reliable parameter iteration results, namely-[ZΜΓ. (')' · + 7 ^,) ^-(^ ,.)-7:) 2-[z) r-x '(a; + 1) -DX-r '(«; + 1] r (' 丨) 2 + r (') 3j' ^ ^^ ^ ~, ΜΊ: —install, _ ^ ^. Order ------ ^ ( (Please read the notes on the back before filling this page.) Printed by the Central Standards Bureau of the Ministry of Economic Affairs, Shellfish Consumer Cooperatives. In the method discussed in this section, the compensation amount is added based on the incorrect interpolation curve rate, so you can get more High curve rate accuracy. In the parameter iteration rule of control, since the curve rate of the generated curve can be accurately controlled, it can be applied to the design of the parameterized curve inserter, and it can have different operation modes depending on the processing conditions. Generally, it depends on the processing conditions. The operation mode of the inserter can be divided into U) constant rate operation mode and (2) acceleration and deceleration operation mode. "Constant rate operation mode" refers to the fact that the inserter can generate a Insert point. Acceleration / deceleration operation mode can be applied to the beginning of the curve movement and the ft scale of this paper. Chinese national standard (CNS) Λ4ί · ί grid (210X; y7A 尨 17 15685 411408 A7 B7) V. Description of the invention Obtain a relatively gentle curve rate change. (C) Apply the iterative method of the feed rate control parameter of this embodiment to design the inserter and compare the processing examples: (C.1) The application example is in the system setting. The system used is a software plug-in program written in C language and executed on a personal computer system with a Pentium 200MHz CPU. In the setting of the parameter curve, the present invention uses a 2 degree NURBS parameterized curve to simulate the bow-tie curve The command path is shown in Figure 5. The related NURBS parameters are set as follows: The control points are: 150 150-150 0 150 »150 0 ·, -150 150 150 2. The weight vector is: F = [l 0_85 0.85 1 0.85 0.85 1] 1113 ,,.. The node vectors are: ί /: 0 0 0 &lt; Please read the notes on the back before filling out this page) Printed by the Central Standards Bureau of the Ministry of Economic Affairs—Industrial and Consumer Cooperatives 4 2 2 4 And with During the iterative process of parameters, the relevant parameters are set as follows: 1. Sampling time: ί = 0.01 sec. 2. Feed rate: / ^ 12 ^ = 2001 ^. (C.2) Constant rate operation mode: due to rate control The design of the parametric curve inserter can precisely control the curve rate of the interpolation result, so during the curve interpolation process, a fixed feed rate can be given to obtain a fixed curve rate interpolation result. Parametric curve interpolation The simulation results of the fixed-rate operation mode of the implement: This paper size applies to the Chinese National Standard (CNS) A4 (210 X 297 mm) 18 ί5685 4114G8 A7 ___B7 V. Description of the invention (19) Here we will compare the iterative design by different parameters The operation mode of the parametric curve interpolator, uniform, 1st order approximation, 2nd order approximation, constant feedra + te interpolation result curve rate changes. The results of the simulation interpolation curve rate of different plug-in operation modes are shown in Figures 6, 7, and 8 | The parameter compensation in the fixed-rate operation mode is shown in Figure 9. The calculation results are shown in Figure 9. The results are summarized in Table 1: Table 1: \ Measure i Speed error mean squared Maximum speed fluctuation ratio Maximum chord error Error with 80MHz CPU calculation time With 200MHz CPU calculation time mode Wee) 2 mm // sec only sec uniform 5.483 xlO5 6.0797 0.1388 11 4 First-order approximation 2.7078 0.01373 0.01739 27 10 Second-order approximation 0.01079 0,00942 0.01738 60 19 Constant rate 3.9642 xlG &quot; * 2.4909 xlO-6 0.01737 77 26 Printed by the Consumer Cooperatives of the Central Standards Bureau of the Ministry of Economic Affairs (please read the back first) Please pay attention to this page before filling in this page) Among them, 1. The measurement of the curve rate error refers to the difference between the curve rate produced by the inserter and the designed feed rate. 2. The formula for calculating the rate of change of the curve rate is 7, which represents the rate of change of the curve rate at each sampling time K represents the rate of the curve produced by the inserter at each sampling time. This paper's dimensions apply Chinese national standards (CNS &gt; A4 specifications ( 210X297 mm) 19 15685 4U408 A7 _B7 V. Description of the invention () 20. Setting the feed rate 3. Uniform Uniform) The parameter interval in the parameter iteration mode is the sampling time. Printed by Zhengong Consumer Cooperative of the Central Standards Bureau of the Ministry of Economic Affairs (please read the notes on the back before filling this page). It is obvious from the simulation results that due to the iterative method of the rate control parameters, the relationship between the curve rate and the compensation rate is taken into account. The interpolation mode of the operation mode has the smallest curve rate error and rate change rate. At the same time, because the parameter iteration method of the 1st-order approximation is compensated, it can be seen that the rate accuracy of the 1st-order approximation after compensation is improved, and it exceeds the rate accuracy provided by the parameter iteration of the 2nd-order approximation. The interpolation method has the largest curve rate error and rate change rate, because the parameters and the curve are not uniformly distributed. In the comparison of the command string height error between interpolation points, the 1st order approximation and the 2nd order approximation are not significantly different from the command string height error of the constant rate operation mode, because the curve rate change in the bow curve used in this simulation is within. The effect of the command string height error between the interpolation points is not significant, but the command string height error of the uniform operation mode is significantly increased compared to other parameter iterative methods *, and the calculation time of each interpolation point is compared with the parameter iterative method. The time required for the interpolation point is only the calculation time of the curve interpolation point, so it will be the least. On the comparison of the 1st-order approximation and the 2nd-order approximation, the 2nd-order approximation requires the calculation of the second-order curve of the curve and the higher-order calculation, so the calculation Time will be more than the 1st-order approximation. Although the rate control parameter iteration method is based on the 1st-order approximation and does not require the second-order differential calculation of the curve, it needs to calculate an additional curve interpolation point and some calculations of the compensation 値, So the amount of calculation will be slightly higher than the 2nd order approximation "Although the parameter iteration method with rate control needs to be higher than the other parameter iteration methods The paper size applies to the Chinese National Standard (CNS) A4 (210X297 mm) 20 15685 411408 A7 B7 V. Description of the invention () 21 The amount of calculation, but the curve rate accuracy of the inserter is higher than the other parameter iterative methods Many, based on this high-precision curve rate control, the controller or workpiece design engineer can grasp a clearer process: At the same time, compared with the sampling time, the proportion of the calculation time of the interpolation point in the fixed-rate operation mode is very small, so The calculation time is acceptable in the real-time implementation process. To sum up the degree of change in the curve rate, the parametric curve inserter has the smallest curve rate error in the fixed rate operation mode, followed by the 2nd blind approximation operation mode and the 1st order. Approximate operation mode, uniform parameter operation mode has the largest curve rate error. (C.3) Acceleration and deceleration operation mode: The Central Consumers Bureau of the Ministry of Economic Affairs, the Consumer Cooperative Cooperative, printed the traditional acceleration and deceleration method by passing the position command through a low-pass filter To produce a smoother command input. However, this method will make the command path with large changes The radial and chord height errors of the diameter, such as near the start and end points of the processing curve. In view of this, Kim proposed the use of parameter acceleration and deceleration to achieve the purpose of parameterizing the curve acceleration and deceleration, and at the same time it is the operation of the parameter acceleration and deceleration Therefore, the interpolation point has a smaller diameter error. Although the parameter acceleration and deceleration method proposed by Kim can make the generation of the interpolation point have the function of acceleration and deceleration, the speed acceleration and deceleration cannot be really achieved on some curves. The reason is that the parameter space does not correspond to the curve uniformly. In order to obtain the true acceleration and deceleration of the curve in the curve movement at an appropriate control rate, the present invention proposes a parameterized curve interpolation for the application of the feed rate parameter acceleration and deceleration Acceleration / deceleration operation mode of the controller. During the iterative process of parameters with rate control, the workpiece designer can accurately grasp the change of the rate, so it can be used as the feed rate 156S5 (Please read the precautions on the back before filling this page } This paper size applies to China National Standard (CNS) A4 (210X297 mm) 411408 A7 __B7_ DESCRIPTION invention () parameter 22 achieved deceleration, acceleration and precise control of the rate at which geographical Save deceleration changes. The parameter iteration method with rate control is to control the parameter iteration so that the curve rate of the inserter can meet the setting of the feed rate 値 ^ (*), so the feed rate parameter ^ («0 Perform the acceleration and deceleration operations. Then the feed rate parameter calculated by the acceleration and deceleration is substituted into the parameter iteration formula of the feed rate control to make the curve rate change as expected. In this way, more accurate acceleration and deceleration control can be obtained. More Accurate Machining Results》 The same application can also be used in the parameter iteration laws of 1st and 2nd order approximations, or other parameter iteration laws related to the feed rate. However, to accurately grasp the changes in acceleration and deceleration rates during acceleration and deceleration, The parametric iteration method must make the curve rate of the inserter accurately reflect the setting of the feed rate. Therefore, it is recommended to use the parameter iterative method with rate control proposed by the present invention to implement the acceleration and deceleration operation mode of the parametric curve inserter. Simulation results of the acceleration and deceleration operation mode of the curved curve inserter: Printed by the Consumers Cooperatives of the Central Bureau of Standards, Ministry of Economic Affairs (please read the first Please fill in this page again for attention} In the simulation of the acceleration and deceleration operation mode of the parametric curve inserter, because the acceleration and deceleration rates are the same process, only the initial acceleration process of the parametric curve inserter is compared. The simulation in this section will compare three kinds of iterative methods related to the feed rate: the first (1st) step-like, the second (2nd) step-like, and the iterative method of the rate control parameter applied to the curve rate during acceleration and deceleration. Changes in the situation, and at the same time to observe the results of the parameter iteration rule applied to different acceleration and deceleration methods, this section will compare three commonly used acceleration and deceleration methods-linear acceleration and deceleration, quadratic curve acceleration and deceleration (parabolic), and exponential acceleration and deceleration. Because of the quadratic curve The acceleration / deceleration method is an acceleration / deceleration method that smooths the rate change. * This paper size applies to the Chinese National Standard (CNS) A4 specification (210X297 mm) 22 1S6S5 411408

V. Explanation of the invention (") The simulation results of the interpolation curve rate of SJthtt applied to the quadratic curve acceleration / deceleration method with different parameter iterative methods are shown in Figures 10, 11, and 12. Parameter iterations The maximum curve rate difference between three different acceleration and deceleration modes is listed in Table 2. Table 2: Rate error method linear quadratic exponential iterative square mm / / sec mm / / sec mm / / sec first order approximation 6.0 3 χ 1〇'1 5.6 7 8 0 χ 10 5 1.6247 first order approximation 5.4 0 1 8 χ ΙΟ'3 4.9210 xlO &quot; 3 2.7 7 2 6 χ 10'2 Constant rate 5.5 8 93 xlO-6 4.6621 xlO ^ 1.1 3 87 xlO-4 Printed by the staff consumer cooperative of the Central Standards Bureau of the Ministry of Economic Affairs

L --- '-!-Fl · — ί ^ 衣 l · (Please read the notes on the back before filling out this page. J In the process of accelerating the bow curve, the curve ’s curvature gradually changes from small to large, so During parameter iteration, the error of the curve rate will gradually increase as shown in Figures 10, 11, and 12. However, when comparing different parameter iteration methods, using the parameter iteration method with rate control is significantly better than the other and feed. Iterative method of rate-related parameters. On the comparison of different acceleration and deceleration methods, the exponential acceleration and deceleration method has the largest curve rate error, and the curve rate change of the quadratic curve acceleration and deceleration method is smooth and the rate error is the smallest. The above simulation results show that during the acceleration and deceleration, when the feed rate is smoothly changed in the form of a quadratic curve, the parameter iterative method with rate control can make the curve rate produced by the inserter have high accuracy. Quadratic curve change. In other words, the feed rate change curve during acceleration and deceleration is designed so that the insertion result of the parameterized curve inserter has the designed acceleration. When the change with the deceleration rate, the parametric curve inserter designed by the parameter iterative method with rate control can make the inserter's acceleration and deceleration rate results as designed, especially when the high-speed feed rate curve moves. Paper size applies Chinese National Standard (CNS) A4.UL (210x2 ^ 7 公 | ί:) 15685 ~ Printed by the Consumer Cooperatives of the Central Standardization Bureau of the Ministry of Economic Affairs 4114G8 V. Description of the invention (24) From the above examples and comparisons It can be known from the examples that the present invention proposes a design method of a parametric curve inserter with rate control, and according to the control purpose of the curve rate, there are a constant rate operation mode and an acceleration / deceleration operation mode to respond to different processing conditions. The rate control parameter iterative method, because the compensation amount I that takes into account the relationship between the parameter and the curve rate, is added to the design of the inserter to obtain accurate curve rate interpolation results. Because the rate change will affect the surface roughness of the processed workpiece Therefore, the fixed-rate operation mode is designed to maintain the movement rate between adjacent interpolation points during the parameterization curve implementation process. In the discussion of the parameterized curve inserter acceleration / deceleration operation mode, the present invention proposes an iterative method of the rate control parameters required by high precision, so it can be applied to the control of the curve rate acceleration / deceleration, by smoothly changing the progression. The feed rate and precise feed rate control parameters are iterative to make the interpolation results of the parameterized curve inserter curve curve acceleration and deceleration rates change as expected. In terms of calculation time, although the parameters proposed by the present invention The curved curve interpolation method requires more calculation processes, but the results can more accurately control the position and speed of the curve path ', so that the workpiece processing results can be more accurate. The speed of the computer and processor chip is faster and faster, and the processing quality The increasingly demanding present 'parametric curve inserter design proposed by the present invention provides good position and curve rate accuracy at the same time》 ---.-- ^ Γ ».-- I.. 士卜 _hi ^ __ S ___- T I_____ households (please read the notes on the back before filling out this page) This paper has been used in China National Standard (CNS) A4 «L grid (210X297 credit) 24 15685

Claims (1)

4i: 4G8 as C8 D8__ VI. Patent application scope 1. A computer numerical control (CNC) curve path rate control method, which uses constant speed control to operate curve path processing, including the following steps: (1) Parameterized curve inserter is receiving After the information of the curve is interpreted by computer-aided design (CAD), continuous interpolation points are generated by the parameter iteration of the parameterized curve; 1 (2) Only the chord height of the position command error generated by the inserter is considered The influence of the error (chord height error), regardless of the radial error (radial error); (3) Derive a parametric curve formula (parametriccurveformu 1 ati ο η) an approximate parameter iterative rule; (4) design parameters with rate control Iterative rule, which proposes parameter compensation for an approximate parameter iterative rule of the representation, and obtains more accurate curve rate control through the correlation between the compensation amount and the curve; (5 &gt; choose a compensation near zero to obtain a more reliable Parameter iterative results of the; and (6) send the continuous interpolation points of the compensation to the control system to make the tool center along the Parametric curve movement. Printed by the Shellfish Consumer Cooperative of the Central Bureau of Standards of the Ministry of Economic Affairs ------------ ^ ------ Order (please read the precautions on the back before writing this page) 2. For example, a computer numerically controlled curve path rate control method in the scope of patent application, where the parameterized curve used is a non-equidistant B cloud line (NURBS). Rate control method, in which the parameter iterative method used by the parametric curve inserter is based on the generalized parameter iterative rule proposed by Cbou and Yang. Iterative method of feed rate control is proposed. (CNS) A4 is now (210X297 mm) jj IJ685 ~ ABCD Printing Policy of Male Workers Consumer Cooperatives, Central Ladder Standard Bureau, Ministry of Economic Affairs, Patent Application Scope 4. A computer numerical control (CNC) curve path rate control method Deceleration control operation curve path processing includes the following steps: (1) After receiving the information of the curve interpreted by computer aided design (CAD), the parameterized curve inserter uses the parameter iterative method of the parameterized curve (Iterat ion) produces continuous interpolation points; &gt; (2) considers only the effect of chord height error of the position command error produced by the inserter, and does not consider the radial error: (3) Derive an approximate parameter iterative rule for the parametric curve formulation: (4) Design a parameter iterative rule with rate control, and propose a parameter iteration for the approximate parameter iterative rule for the expression, and then use the correlation between the compensation amount and the curve. Get more accurate curve rate control; (5) choose compensation near zero to get more reliable parameter iteration results; and (6 &gt; send the continuous interpolation point of the obtained compensation to the control system to make the tool The center moves along the parameterized curve. "5. For example, the computerized numerical control curve path rate control method of the 4 items in the scope of the patent application, wherein the parameterized curve used is a non-equidistant B cloud line (NURBS). 6. For example, the computer-controlled numerical control curve path rate control method of the 4 items in the patent scope, wherein the parameter iterative method used by the parameterized curve inserter is based on the generalized parameter iterative rule proposed by Chou and Yang. Controlled parameter iteration method &lt; Please read the notes on the back before filling in this page) Installation · Ηπ This paper size is free to use China National Kneading Rate (CNS) 8 4 rules ^ grid (210X297 mm) 26 15685 4ί4υ8 Β8 C8 D8 Printed by the staff of the Central Bureau of the Ministry of Economic Affairs, F. Cooperative, Co., Ltd. 6. Application for patent scope 7.-A kind of computer-controlled numerical control curve path rate control device, including: computer for auxiliary design (CAD), the auxiliary design includes parameterization Curve format and segmented curve: A computer numerical control (CNC) mechanism includes: a parametric curve inserter that generates continuous interpolation points by generating points of the parametric curve after receiving the parametric curve information interpreted by the computer ; The controller receives the continuous interpolation points generated by the parametric curve inserter and sends the processing signal: the tool receives the sent by the controller The processing signal is controlled, and the center moves along the parameterized curve. The human-machine interface device allows human-computer communication between the operator and the parameterized curve inserter: The parameterized curve inserter can be used for the parameterized curve. It is used for fixed-rate insertion operation mode and acceleration / deceleration insertion operation mode. 8. —A parameterized curve inserter device for computer numerically controlled curve path rate control, including: a constant rate inserter that keeps the parameterized curve path at a fixed rate during the implementation of the interpolation: and an acceleration / deceleration inserter , So that the processing curve path obtains a smoother acceleration and deceleration movement. ^^ 1 n I. (Please read the precautions on the back before filling out this page) This paper size is in accordance with Chinese National Standard (CNS) A4 wash case (210X297 mm) 27 15685