CN106647637A - Trigonometric function acceleration and deceleration control method for high-quality machining - Google Patents

Abstract

The invention relates to a trigonometric function acceleration and deceleration control method for high-quality machining. The method comprises a pre-interpolation stage and a real-time spline interpolation stage. In the preprocessing stage, a path to be machined is quickly interpolated, key information is recorded, and the trigonometric function speed equation in each acceleration and deceleration section is calculated. In the real-time spline interpolation stage, the real-time feed rate of a cutter is calculated according to the recorded information and the speed equations in the preprocessing stage, and then, next interpolation parameter is calculated in real time using a Newton iteration method, and real-time spline interpolation is carried out. The method is simple in control. Continuous change of speed, acceleration and jerk in the process of machining is realized, and fluctuation in feed rate is reduced. Therefore, the machining precision is guaranteed, overshoot caused by high-speed machining is eased, and flexible acceleration and deceleration control on a servo shaft is achieved. The method is suitable for high-quality processing.

Description

A kind of trigonometric function Acceleration-deceleration Control Method for high-quality processing

Technical field

The present invention relates to Computerized Numerical Control processing technology field, specifically a kind of triangle letter for high-quality processing Number Acceleration-deceleration Control Method.

Background technology

Numeric Control Technology is the basis of modern advanced manufacturing technique and core, and a state is reflected to a great extent The manufacturing technology level of family, is an important symbol for weighing the modernization of industry.

Realize that High-speed machining and high finishing are two important goals of digital control system.The speed of processing is directly closed The efficiency of processing is tied to, and machining accuracy then directly influences crudy.With modern science and technology and life The development of product, machining proposes higher and higher speed and required precision with fields of measurement.At high speed, In high precision, high-quality digital control processing proposes higher wanting to the computing capability and control ability of digital control system Ask, be mainly manifested in two aspects：First digital control system arithmetic speed is fast, and requires that Digit Control Machine Tool is anti- Should be fast, i.e., each coordinate motion part can reach given speed within the extremely short time, and can be in high-speed cruising In rapidly and accurately stop at precalculated position, shorten time；On the other hand require that process motion is flat Surely, impact, step-out, the excess of stroke or vibration are not produced, high accuracy, high-quality processing is realized.The control of acceleration and deceleration System and planning are the important component parts of digital control system trajectory planning, are also the key technology of Development of CNC One of.Therefore, speed planning is the important step in high speed, high accuracy, high-quality digital control processing.

At present, in digital control processing field, conventional velocity planning algorithm includes space rate law of planning, S curve Speed planning method, cubic polynomial speed planning method etc..Traditional linear acceleration and deceleration control method amount of calculation is little, Control is simple, but there is the mutation of acceleration in acceleration or deceleration, it is easy to cause lathe to produce vibration, Have impact on crudy.S curve velocity planning algorithm once accelerate or accelerator in, its rate equation Two sections or three sections calculating of segmentation, control it is more complicated, and its acceleration in an accelerating sections or Braking section is mutated four times, in processed complex parts, may cause trembling for cutter.Cubic polynomial speed Degree planning algorithm control is simple, can realize the consecutive variations of acceleration, but its acceleration is remained and do not connected Continuous, during an acceleration and deceleration, its acceleration mutation still can be mutated twice, and institute is in this way same Sample is unfavorable for that high-quality is processed.

The content of the invention

For above-mentioned weak point present in prior art, the technical problem to be solved in the present invention is to provide one Plant the trigonometric function Acceleration-deceleration Control Method for high-quality processing.

The technical scheme that adopted for achieving the above object of the present invention is：A kind of triangle for high-quality processing Function Acceleration-deceleration Control Method, including pretreatment stage and real-time interpolation stage；

The pretreatment stage is comprised the following steps：Data point to be processed is carried out with centripetalization parametric technique Normalization；High speed interpolation is carried out to path to be processed and key message is recorded；

During the high speed interpolation, feed speed is calculated using the approximate method of circular arc；In each step interpolation The length in the path of interpolation is recorded afterwards；Record the initial of each plus/minus speed process and the speed that terminates and Corresponding interpolation parameters value；Calculate the peak acceleration and maximum acceleration, triangle of each plus/minus speed section Function speed planning equation, and the theoretical plus/minus speed distance of plus/minus speed section is calculated according to displacement equation, obtain The start parameter of plus/minus speed during real-time interpolation；Acceleration and deceleration whole story parameter, trigonometric function rate equation coefficient are protected In being stored to acceleration and deceleration array；

The real-time interpolation stage comprises the following steps：According to the data in acceleration and deceleration array, calculate current Real-time speed at point；Using first order Taylor calculating parameter initial value, with calculating after Newton iterative method The exact value of interpolation parameters, substitutes into parameter curve equation, calculates next interpolated point, so as to carry out in real time Interpolation.

The centripetalization parametric technique is：

Wherein, P_kAnd P_k-1Represent the kth+1 and k-th data point in path to be processed, U_kAnd U_k-1Point Biao Shi not data point P_kAnd P_k-1Corresponding normalized parameter, U₀Represent first data point P₀Corresponding normalizing Change parameter, n represents the number of data point.

The approximate method of the employing circular arc calculates feed speed, specially：

Wherein, u_iFor current interpolated point p_iCorresponding interpolation parameters, T for digital control system interpolation cycle, ρ_iFor Interpolation parameters u_iThe radius of curvature at place, E_cFor the largest chord high level error of processing request, F is the volume of digital control system Journey feed speed.

Length S in the path of the interpolation_iInterpolation parameters u is incorporated into for pretreatment_iThe path passed by during place, Calculated by following formula：

Wherein, S_i-1To be incorporated into interpolation parameters u_i-1When the path passed by, T for digital control system interpolation cycle, V(u_i) it is interpolation parameters u_iThe feed speed at place, V (u_t) it is interpolation parameters u_tThe feed speed at place.

Peak acceleration A and maximum acceleration J of the plus/minus speed section, by comparing | V_e-V_s| and Relation calculate：

IfThen A=A_max, J=J_max；

IfThen A=A_max,

IfThen J=J_max,

Wherein, A_maxFor the peak acceleration of digital control system, J_maxFor the maximum acceleration of digital control system, V_s For the initial velocity of plus/minus speed section, V_eFor the end speed of plus/minus speed section.

The expression formula of the trigonometric function speed planning equation acceleration section is：

The expression formula of braking section is：

Wherein, A is the peak acceleration of plus/minus speed section；J is the maximum acceleration of plus/minus speed section；When t is Between, start time is 0；V_a(t) and V_dT () is respectively the speed of accelerating sections and braking section；V₀It is plus/minus speed section Initial velocity.

The displacement equation be trigonometric function speed planning equation is quadratured after the equation that obtains, specially：

The displacement S of accelerating sections_aT () expression formula is：

The displacement S of braking section_dT () expression formula is：

Wherein, A is the peak acceleration of plus/minus speed section；J is the maximum acceleration of plus/minus speed section；S₀For Initial displacement；V₀It is the initial velocity of plus/minus speed section；T is the time, and start time is 0.

The theoretical plus/minus speed distance is referred under conditions of requirement on machining accuracy is met, from the initial of plus/minus speed Speed V_sPlus/minus speed is to end speed V_eRequired theoretical path；

Theoretical acceleration distance s_aComputing formula be：

s_a=S_a(t_a)-S_a(0)

Theoretical deceleration distance s_dComputing formula be：

s_d=S_d(t_d)-S_d(0)

Wherein, S_a(t_a) for accelerating sections displacement, t_aFor acceleration time, S_d(t_d) for braking section displacement, t_dTo subtract The fast time, and

Wherein, A is the peak acceleration of plus/minus speed section；J is the maximum acceleration of plus/minus speed section.

Data in the array according to acceleration and deceleration, calculate the real-time speed at current point, specially：It is false If current interpolation parameters is u_i, the interpolation moment is t_i, plus/minus speed section x being presently in, then real-time speed V_iCalculating process it is as follows：

If 1) u_i<AD [x] .us, keeps cutter to move with uniform velocity, V_i=V_i-1；

If 2) AD [x] .us≤u_i<AD [x] .ue, then accelerating sections V_i=V_a(t_i), braking section V_i=V_d(t_i)；

If 3) u_i-1<AD [x] .ue, u_i>AD [x] .ue, then x=x+1, V_i=V_i-1；

If 4) when slowing down, u_i<AD [x] .ue and V (u_i)≤AD [x] .ve, then V_i=V_i-1；

Wherein, AD [x] is the xth section of acceleration and deceleration array obtained after pretreatment terminates, AD [x] .us, AD [x] .ue The respectively beginning and end interpolation parameters of the accelerating and decelerating part.

The first order Taylor is：

Wherein, C (u) be SPL equation, u be SPL parameter, u_iFor current interpolation parameters, V_iFor u_iThe speed at place, u_i+1For next interpolation parameters, T is interpolation cycle.

The standard iterative formula of described Newton iteration method is：

Wherein, ξ_kAnd ξ_k+1It is u_i+1Respectively iteration k time with k+1 time after result；F (ξ) is equationof structure, F'(ξ_k) It is its first derivative, the expression formula of F (ξ) is：

F (ξ)=| | C (ξ)-C (u_i)||-V_iT

Wherein, C (u_i) for SPL in u_iThe value at place, C (ξ) is value of the SPL at ξ, under ξ is represented One interpolation parameters u_i+1, V_iFor u_iThe speed at place, T is interpolation cycle.

The present invention has advantages below and beneficial effect：

1. processing flexibility is good, and smoothness is high.The rate curve of the inventive method is trigonometric function curve and line Property polynomial combination, acceleration and jerk curve are trigonometric function curve, in each plus/minus speed stage The consecutive variations of speed, acceleration and acceleration can be realized, so as to realize flexible feed speed control.

2. machining accuracy is high.The inventive method calculates feeding speed in pretreatment stage using the approximate method of circular arc Degree, it is contemplated that the restriction of action error, interpolation parameters is calculated in real time during real-time interpolation with Newton iteration method, is subtracted Little feed speed fluctuation, so as to ensure that machining accuracy.

3. execution efficiency is high.Pretreatment stage is used to collect the related data and calculating speed of the curve to be processed Equation, the real-time interpolation stage need to only use the data of pretreatment stage and carry out real-time spline interpolation, and computing is simple.

4. highly versatile.The inventive method can not only be applied in various SPL interpolation interpolations, and The feed speed control in various interpolating methods (linear interpolation, circular interpolation etc.) can be applied.

Description of the drawings

Fig. 1 is the implementing procedure figure of the inventive method；

Fig. 2 is SPL to be processed；

Fig. 3 is to calculate action error schematic diagram using circular arc approximation method；

Fig. 4 is speed, acceleration and the jerk curve of the inventive method moderating process；

Fig. 5 is the rate curve obtained using present invention processing " butterfly " nurbs curve；

Fig. 6 is the accelerating curve obtained using present invention processing " butterfly " nurbs curve；

Fig. 7 is the jerk curve obtained using present invention processing " butterfly " nurbs curve；

Fig. 8 is the action error curve obtained using present invention processing " butterfly " nurbs curve；

Fig. 9 is the rectangular area in embodiment in " butterfly " curve of comparative selection；

Figure 10 is inventive algorithm and S curve, velocity contrast's curve of cubic polynomial velocity planning algorithm；

Figure 11 is inventive algorithm and S curve, the acceleration correlation curve of cubic polynomial velocity planning algorithm；

Figure 12 is inventive algorithm and S curve, the acceleration contrast song of cubic polynomial velocity planning algorithm Line.

Specific embodiment

Below in conjunction with the accompanying drawings and embodiment the present invention is described in further detail.

Embodiment：The inventive method is carried out into simulating, verifying on PC, programming software used is Microsoft Visual Studio 2010, using C language coding, the SPL selected here is NURBS (Non-Uniform Rational B-Spline) curve.

The major technique interpolation parameters of test environment is as follows：

Operating system：Microsoft Windows XP

CPU：Pentium(R)Dual-Core

Dominant frequency：2.93GHz

Internal memory：4G

Digital control system interpolation parameters is as follows：

Feed rate F=250mm/s；

Peak acceleration A_max=5000mm/s²；

Maximum acceleration J_max=400000mm/s³；

Largest chord high level error Ec=0.001mm；

Interpolation cycle T=3ms；

The present embodiment by taking the processing of representative workpiece program " butterfly " type curve as an example, as shown in Figure 2.

The present invention is used for the speed planning of spline interpolation in digital control processing, its whole interpolation flow chart such as Fig. 1 institute Show.

The inventive method includes pretreatment and real-time spline interpolation two parts.

By taking moderating process as an example, pre- interpolation has steps of：

Treat Processing Curve to be pre-processed：First the data to be processed are clicked through with centripetalization parametric method Row normalization, feed speed is determined with the approximate method of circular arc according to the largest chord high level error of requirement on machining accuracy (its schematic diagram is as shown in Figure 3), and the length in interpolation path will be recorded after each interpolation.In addition note is needed Each plus/minus speed process initial and the speed for terminating and corresponding parameter value under record, then calculate each add/ The peak acceleration of braking section and maximum acceleration, so as to calculate the trigonometric function speed of each accelerating and decelerating part Metric draws equation, after asking it first derivative and second dervative, can respectively obtain acceleration and acceleration Equation (speed of moderating process, acceleration and jerk curve are as shown in Figure 4).To rate equation quadrature After point, the displacement equation of each accelerating and decelerating part is calculated；The theory of plus/minus speed section is calculated according to displacement equation Plus/acceleration and deceleration distance, the start parameter of plus/minus speed when finally obtaining real-time interpolation.In Interpolation Process, need by The information such as acceleration and deceleration whole story parameter, trigonometric function rate equation coefficient are saved in acceleration and deceleration array in AD []. After pretreatment terminates, accelerating and decelerating part array AD [n] is obtained, n is the number of plus/minus velocity shooting.

Real-time interpolation：According to the data in acceleration and deceleration array, the real-time speed at current point is calculated, then Using first order Taylor calculating parameter initial value, with the exact value that interpolation parameters is calculated after Newton iterative method, Parameter curve equation is substituted into, next interpolated point is calculated, so as to carry out real-time interpolation.

Real-time spline interpolation：Speed, initial parameter, rate equation information first in plus/minus speed array, Calculate in parameter current u_iReal-time feed speed V at place_i, then calculated in real time using the first order Taylor method of development In real time the iterative initial value of next one interpolation parameters, then calculates the exact value of interpolation parameters with Newton iteration method, Parametric equation is substituted into, next interpolated point is calculated, real-time spline interpolation is carried out.

The formula of described centripetalization parametric method is：

In formula, P_kAnd P_k-1The kth+1 and k-th data point of machining path, U are wanted in expression_kAnd U_k-1Point P is not represented_kAnd P_k-1Corresponding normalized parameter, U₀Represent first data point P₀Corresponding parameter, n tables The number at registration strong point, i.e., the common n point from 0 to n-1.

The approximate method of the employing circular arc calculates feed speed V (u_i) expression formula be：

Wherein, u_iFor current interpolated point p_iCorresponding interpolation parameters, T for digital control system interpolation cycle, ρ_iFor Parameter u_iThe radius of curvature at place, E_cFor the largest chord high level error of processing request, F is being programmed into for digital control system To speed.

Length S in the path of described record interpolation_iParameter u is incorporated into for pretreatment_iThe road passed by during place Footpath, is calculated by below equation：

Wherein, S_i-1To be incorporated into parameter u_i-1When the path passed by, V (u_i) it is parameter u_iThe feed speed at place, V (u_t) For parameter u_tThe feed speed at place.

The initial velocity of described accelerator refers to the speed for accelerating to start, it is assumed that in parameter u_iPlace's acceleration is opened Begin, then the initial velocity value V (u for accelerating_i) should meet：

V(u_i-1)≤V(u_i)<V(u_i+1)

The end speed of described accelerator refer to acceleration terminate after speed, it is assumed that in parameter u_jPlace accelerates Start, then the initial velocity value V (u for accelerating_j) should meet：

V(u_i-1)<V(u_j), V (u_j+1)≤V(u_j)

The initial velocity of described moderating process refers to the speed for starting of slowing down, it is assumed that in parameter u_xPlace's deceleration is opened Begin, then the initial velocity value V (u for slowing down_x) should meet：

V(u_x-1)≤V(u_x),V(u_x)>V(u_x+1)

The end speed of described moderating process refer to deceleration terminate after speed, it is assumed that in parameter u_ySlow down at place Terminate, then the velocity amplitude V (u of end of slowing down_y) should meet：

V(u_y-1)<V(u_y)≤V(u_y+1)

Peak acceleration A and maximum acceleration J during the plus/minus speed, by comparing | V_e-V_s| andRelation calculate：

IfThen A=A_max, J=J_max；

IfThen A=A_max,

IfThen J=J_max,

Wherein A_maxFor the peak acceleration of digital control system, J_maxFor the maximum acceleration V of digital control system_sIt is The initial velocity of plus/minus speed section, V_eThe end speed of plus/minus speed section.

The expression formula of the trigonometric function rate equation acceleration section is：

The expression formula of braking section is：

Wherein, t is the time, and start time is 0；V_a(t) and V_dT () is respectively the speed of accelerating sections and braking section Equation；V₀It is the initial velocity of accelerating sections or braking section；A is the peak acceleration during acceleration and deceleration；J is Maximum acceleration during acceleration and deceleration.

The displacement equation refers to the equation obtained after quadraturing to trigonometric function rate equation, is mainly used in meter Calculate and calculate theoretical plus/minus speed distance, the displacement S of accelerating sections_aT () expression formula is：

Braking section S_dT the displacement expression formula of () is：

Wherein, S₀For initial displacement, t is the time, and start time is that 0, A is the maximum during plus/minus speed Acceleration；J is the maximum acceleration during plus/minus speed.

The theoretical plus/minus speed distance is referred under conditions of requirement on machining accuracy is met, from the initial of plus/minus speed Speed V_sPlus/minus speed is to end speed V_eRequired theoretical path.Theoretical acceleration distance s_aComputing formula be：

s_a=S_a(t_a)-S_a(0)

Theoretical deceleration distance s_dComputing formula be：

s_d=S_d(t_d)-S_d(0)

Wherein, t_aIt is the acceleration time, t_dFor deceleration time, computing formula is：

In formula, A is the peak acceleration during plus/minus speed；J is most greatly accelerating during plus/minus speed Degree.

The start parameter of plus/minus speed, refers to when real-time spline interpolation is carried out during the real-time interpolation, and cutter is moved When moving the interpolation parameters, plus/minus speed is proceeded by；By taking moderating process as an example, it is assumed that be currently u from parameter_i, The speed of cutter is in parameter u_jPlace reaches minimum of a value, start parameter u of deceleration_dCalculate by the following method：

1) theoretical deceleration distance s is calculated with displacement equation_d；

2) find interpolation parameters successively forward, find interpolation parameters u_k, its corresponding interpolation path S_kIt is full Foot：

S_j-S_k≥s_d

3) relatively more current interpolation parameters u_iAnd u_kSize, if u_i<u_k, then u_d=u_i, otherwise u_d=u_k；

Wherein, S_jAnd S_kIt is respectively that cutter is incorporated into parameter u from 0_jAnd u_kThe when path passed by.

Described acceleration and deceleration array AD [] have recorded the data of the accelerating and decelerating part for needing to preserve in pretreatment, its shape Formula is：

The calculating process of the real-time speed during the real-time interpolation is：

Assume that current interpolation parameters is u_i, the interpolation moment is t_i, plus/minus speed section x being presently in, then V_iCalculating process it is as follows：

If 1) u_i<AD [x] .us, keeps cutter to move with uniform velocity, V_i=V_i-1；

If 2) AD [x] .us≤u_i<AD [x] .ue, then accelerating sections V_i=V_a(t_i), braking section V_i=V_d(t_i)；

If 3) u_i-1<AD [x] .ue, u_i>AD [x] .ue, then x=x+1, V_i=V_i-1；

If 4) when slowing down, u_i<AD [x] .ue and V (u_i)≤AD [x] .ve, then V_i=V_i-1；

Wherein, AD [x] is the xth section of acceleration and deceleration array obtained after pretreatment terminates, AD [x] .us, AD [x] .ue The respectively beginning and end interpolation parameters of plus/minus speed section.

The expression formula of the first order Taylor method of development is：

In formula, C (u) be SPL equation, u be SPL parameter, u_iFor current interpolation parameters, V_iFor u_iThe speed at place, u_i+1For next interpolation parameters, T is interpolation cycle.

The standard iterative formula of described Newton iteration method is：

Wherein, ξ_kAnd ξ_k+1It is u_i+1Respectively iteration k time with k+1 time after result；F (ξ) is equationof structure, and F ' is (ξ) It is its first derivative, the expression formula of F (ξ) is：

F (ξ)=| | C (ξ)-C (u_i)||-V_iT

In formula, C (u) be SPL equation, C (u_i) for SPL in u_iThe value at place, C (ξ) is SPL Value at ξ, ξ represents next interpolation parameters u_i+1。

Using inventive algorithm, machining simulation is carried out to " butterfly " curve shown in Fig. 2, the SPL Publicly-owned 51 data points.Feed speed curve, accelerating curve and jerk curve difference that experiment is obtained As shown in Fig. 5～7, error curve is as shown in Figure 8.In order to illustrate the trigonometric function acceleration and deceleration of the inventive method The characteristics of control method, five section S curve velocity planning algorithms, cubic polynomial speed of the emulation experiment to commonly use Degree planning algorithm as a comparison, is processed to the curve shown in Fig. 2, and selects the rectangle region in Fig. 9 Domain region as a comparison, the inventive method and S curve, the speed of cubic polynomial velocity planning algorithm, plus Speed and jerk curve are to such as shown in Figure 10～12.

By analysis, can obtain as drawn a conclusion：

1. the inventive method can meet the requirement of machining accuracy, and ensure to add the feed speed in man-hour, accelerate Degree and acceleration are limited less than the maximum of digital control system.From figure 8, it is seen that to buttferfly-type After curve machining simulation, the action error curve for obtaining all is limited in the maximum action of requirement on machining accuracy and misses Differ within 1 μm；From Fig. 5～7 as can be seen that the feed speed curve of inventive algorithm is distributed in digital control system Programming feed rate F in, acceleration and acceleration are also without peak acceleration A more than system_maxWith Acceleration J_maxLimit, this reduces to a certain extent the vibrations of lathe.

2. the inventive method control is fairly simple, and execution efficiency is high, and can guarantee that lathe operates steadily.Pre- place The reason stage is used to record the critical data and calculating speed equation of Processing Curve, and the speed of inventive algorithm Equation is link definition.During the real-time interpolation stage, only using the data of pretreatment stage carries out real-time batten Interpolation, it is simple to operate.From fig. 5, it can be seen that cutter is all moving with uniform velocity within the most of the time, only Have carries out deceleration control to ensure machining accuracy around the corner.Avoiding problems start because of frequently system, Stop caused vibration and affect the situation of work procedure finished surface smoothness decline.

3. the inventive method can improve the flexible feed speed control of digital control system processing, make the operation of lathe more Plus it is steady.From Figure 10～12 as can be seen that during acceleration and deceleration, the rate curve of inventive algorithm, plus Rate curve and jerk curve are all continually varyings, and S curve velocity planning algorithm and three times it is multinomial The jerk curve of the algorithm of formula speed planning is all discontinuous, and during an acceleration or deceleration, S is bent The acceleration of line algorithm can be mutated 4 times, and cubic polynomial algorithm has been mutated twice.Due to the acceleration of cutter Degree reflects the stressing conditions of lathe, and acceleration reflect lathe response speed and traveling comfort it Between relation.The rate equation of inventive algorithm is the combination of trigonometric function formula and linear polynomial, acceleration Equation and acceleration equation are trigonometric function formula, be all it is continuous, so inventive algorithm can reduce because Start for system, stop caused machine vibration, so as to improve crudy.

Claims (11)

1. it is a kind of for high-quality processing trigonometric function Acceleration-deceleration Control Method, it is characterised in that including pre- Processing stage and real-time interpolation stage；

The pretreatment stage is comprised the following steps：Data point to be processed is carried out with centripetalization parametric technique Normalization；High speed interpolation is carried out to path to be processed and key message is recorded；

During the high speed interpolation, feed speed is calculated using the approximate method of circular arc；In each step interpolation The length in the path of interpolation is recorded afterwards；Record the initial of each plus/minus speed process and the speed that terminates and Corresponding interpolation parameters value；Calculate the peak acceleration and maximum acceleration, triangle of each plus/minus speed section Function speed planning equation, and the theoretical plus/minus speed distance of plus/minus speed section is calculated according to displacement equation, obtain The start parameter of plus/minus speed during real-time interpolation；Acceleration and deceleration whole story parameter, trigonometric function rate equation coefficient are protected In being stored to acceleration and deceleration array；

The real-time interpolation stage comprises the following steps：According to the data in acceleration and deceleration array, calculate current Real-time speed at point；Using first order Taylor calculating parameter initial value, with calculating after Newton iterative method The exact value of interpolation parameters, substitutes into parameter curve equation, calculates next interpolated point, so as to carry out in real time Interpolation.

2. it is according to claim 1 it is a kind of for high-quality processing trigonometric function Acceleration-deceleration Control Method, Characterized in that, the centripetalization parametric technique is：

$\left\{\begin{array}{c}{U}_0=0\\ U_k=U_{k-1}+\frac{\sqrt{|P_k-P_{k-1}|}}{\underset{k=1}{\overset{n-1}{\&Sigma;}}\sqrt{|P_k-P_{k-1}|}},k=1,2...n-1\end{array}\right.$

Wherein, P_kAnd P_k-1Represent the kth+1 and k-th data point in path to be processed, U_kAnd U_k-1Point Biao Shi not data point P_kAnd P_k-1Corresponding normalized parameter, U₀Represent first data point P₀Corresponding normalizing Change parameter, n represents the number of data point.

3. it is according to claim 1 it is a kind of for high-quality processing trigonometric function Acceleration-deceleration Control Method, Characterized in that, the approximate method of the employing circular arc calculates feed speed, specially：

$V\left(u_i\right)=min(\frac{2}{T}\sqrt{{\mathrm{\&rho;}}_i^2-{({\mathrm{\&rho;}}_i-E_c)}^2},F)$

Wherein, u_iFor current interpolated point p_iCorresponding interpolation parameters, T for digital control system interpolation cycle, ρ_iFor Interpolation parameters u_iThe radius of curvature at place, E_cFor the largest chord high level error of processing request, F is the volume of digital control system Journey feed speed.

4. it is according to claim 1 it is a kind of for high-quality processing trigonometric function Acceleration-deceleration Control Method, Characterized in that, length S in the path of the interpolation_iInterpolation parameters u is incorporated into for pretreatment_iWalk during place The path crossed, is calculated by following formula：

$S_i=S_{i-1}+V\left(u_i\right)T=\underset{t=0}{\overset{i-1}{\&Sigma;}}V\left(u_t\right)T+V\left(u_i\right)T$

Wherein, S_i-1To be incorporated into interpolation parameters u_i-1When the path passed by, T for digital control system interpolation cycle, V(u_i) it is interpolation parameters u_iThe feed speed at place, V (u_t) it is interpolation parameters u_tThe feed speed at place.

5. it is according to claim 1 it is a kind of for high-quality processing trigonometric function Acceleration-deceleration Control Method, Characterized in that, peak acceleration A and maximum acceleration J of the plus/minus speed section, by comparing | V_e-V_s| WithRelation calculate：

IfThen A=A_max, J=J_max；

If $|V_e-V_s|>\frac{{\mathrm{\&pi;A}}_{\max }^2}{2J_{\max }},$ Then A=A_max, $J=\frac{{\mathrm{\&pi;A}}^2}{2|V_e-V_S|};$

If $|V_e-V_s|>\frac{{\mathrm{\&pi;A}}_{\max }^2}{2J_{\max }},$ Then J=J_max, $A=\sqrt{\frac{2J}{\mathrm{\&pi;}}|V_e-V_s|}.$

Wherein, A_maxFor the peak acceleration of digital control system, J_maxFor the maximum acceleration of digital control system, V_s For the initial velocity of plus/minus speed section, V_eFor the end speed of plus/minus speed section.

6. it is according to claim 1 it is a kind of for high-quality processing trigonometric function Acceleration-deceleration Control Method, Characterized in that, the expression formula of the trigonometric function speed planning equation acceleration section is：

$V_a\left(t\right)=\frac{A}{2}t-\frac{A^2}{4J}sin\frac{2J}{A}t+V_0$

The expression formula of braking section is：

$V_d\left(t\right)=-\frac{A}{2}t+\frac{A^2}{4J}sin\frac{2J}{A}t+V_0$

Wherein, A is the peak acceleration of plus/minus speed section；J is the maximum acceleration of plus/minus speed section；When t is Between, start time is 0；V_a(t) and V_dT () is respectively the speed of accelerating sections and braking section；V₀It is plus/minus speed section Initial velocity.

7. it is according to claim 1 it is a kind of for high-quality processing trigonometric function feed speed control side Method, it is characterised in that the displacement equation be trigonometric function speed planning equation is quadratured after the side that obtains Journey, specially：

The displacement S of accelerating sections_aT () expression formula is：

$S_a\left(t\right)=S_0+\frac{A}{4}{t}^2+\frac{A^3}{8J^2}cos\frac{2J}{A}t+V_{0}t$

The displacement S of braking section_dT () expression formula is：

$S_d\left(t\right)=S_0-\frac{A}{4}{t}^2-\frac{A^3}{8J^2}cos\frac{2J}{A}t+V_{0}t$

Wherein, A is the peak acceleration of plus/minus speed section；J is the maximum acceleration of plus/minus speed section；S₀For Initial displacement；V₀It is the initial velocity of plus/minus speed section；T is the time, and start time is 0.

8. it is according to claim 1 it is a kind of for high-quality processing trigonometric function Acceleration-deceleration Control Method, Characterized in that, the theoretical plus/minus speed distance is referred under conditions of requirement on machining accuracy is met, from plus/minus The initial velocity V of speed_sPlus/minus speed is to end speed V_eRequired theoretical path；

Theoretical acceleration distance s_aComputing formula be：

s_a=S_a(t_a)-S_a(0)

Theoretical deceleration distance s_dComputing formula be：

s_d=S_d(t_d)-S_d(0)

Wherein, S_a(t_a) for accelerating sections displacement, t_aFor acceleration time, S_d(t_d) for braking section displacement, t_dTo subtract The fast time, and

$t_a=\frac{\mathrm{\&pi;}A}{J},t_d=\frac{\mathrm{\&pi;}A}{J}$

Wherein, A is the peak acceleration of plus/minus speed section；J is the maximum acceleration of plus/minus speed section.

9. it is according to claim 1 it is a kind of for high-quality processing trigonometric function Acceleration-deceleration Control Method, Characterized in that, the data in the array according to acceleration and deceleration, calculate the real-time speed at current point, tool Body is：Assume that current interpolation parameters is u_i, the interpolation moment is t_i, plus/minus speed section x being presently in, then in fact Shi Sudu V_iCalculating process it is as follows：

If 1) u_i<AD [x] .us, keeps cutter to move with uniform velocity, V_i=V_i-1；

If 2) AD [x] .us≤u_i<AD [x] .ue, then accelerating sections V_i=V_a(t_i), braking section V_i=V_d(t_i)；

If 3) u_i-1<AD [x] .ue, u_i>AD [x] .ue, then x=x+1, V_i=V_i-1；

If 4) when slowing down, u_i<AD [x] .ue and V (u_i)≤AD [x] .ve, then V_i=V_i-1；

Wherein, AD [x] is the xth section of acceleration and deceleration array obtained after pretreatment terminates, AD [x] .us, AD [x] .ue The respectively beginning and end interpolation parameters of the accelerating and decelerating part.

10. it is according to claim 1 it is a kind of for high-quality processing trigonometric function feed speed control side Method, it is characterised in that the first order Taylor is：

$u_{i+1}=u_i+\frac{V_i}{|\frac{dC\left(u\right)}{du}{|}_{u=u_i}}T$

Wherein, C (u) be SPL equation, u be SPL parameter, u_iFor current interpolation parameters, V_iFor u_iThe speed at place, u_i+1For next interpolation parameters, T is interpolation cycle.

A kind of 11. trigonometric function feed speed control sides for high-quality processing according to claim 1 Method, it is characterised in that the standard iterative formula of described Newton iteration method is：

${\mathrm{\&xi;}}_{k+1}={\mathrm{\&xi;}}_k-\frac{F\left({\mathrm{\&xi;}}_k\right)}{F^{\&prime;}\left({\mathrm{\&xi;}}_k\right)}$

Wherein, ξ_kAnd ξ_k+1It is u_i+1Respectively iteration k time with k+1 time after result；F (ξ) is equationof structure, F'(ξ_k) It is its first derivative, the expression formula of F (ξ) is：

F (ξ)=| | C (ξ)-C (u_i)||-V_iT

Wherein, C (u_i) for SPL in u_iThe value at place, C (ξ) is value of the SPL at ξ, under ξ is represented One interpolation parameters u_i+1, V_iFor u_iThe speed at place, T is interpolation cycle.