CN101804580A - Method for assessing reliability of technology for large numerical control machine - Google Patents

Abstract

The invention provides a method for assessing a technology for a large numerical control machine, comprising the following steps: obtaining frequency response function curve of the large numerical control machine through structure composition dynamic stiffness experiments; employing nonlinear least square method to identify dynamical parameter through curve least square fitting; establishing a non-linear dynamical model of machining process of the numerical control machine by identifying machining technical parameters of cutting force dynamic model in a cutting force experiment; then employing the method of random sampling to simulate tooling motion trail and calculating the number of failpoints to work out probability of technological reliability.With the method of the invention, technological reliability of the numerical control machine can be accurately assessed according to the existing structural characteristics, processing technic characteristics and processing conditions of the large numerical control machine, so that accuracy and high efficiency of technological reliability assessment can be improved and a new method is provided for on-line reliability assessment of the large numerical control machine.

Description

A kind of appraisal procedure of reliability of technology for large numerical control machine

Technical field

The present invention relates to numerical control equipment reliability of technology assessment technology field, specifically is a kind of appraisal procedure towards reliability of technology for large numerical control machine.

Background technology

The Digit Control Machine Tool reliability of technology is meant in the performance that requires to keep crudy in the prescribed time-limit and under the productivity ratio of regulation and realize the technical process that the lathe purposes is determined.That is to say, not only will guarantee the high accuracy that Digit Control Machine Tool is initial, and will keep its precision, efficient and cost in the useful life of regulation, the Digit Control Machine Tool reliability of technology is paid close attention to is the retentivity of Digit Control Machine Tool function and technical performance in process.Digit Control Machine Tool reliability of technology assessment technology is one of a kind of necessary means of the Digit Control Machine Tool reliability of technology being carried out quantification control, its main purpose is to weigh design object and the instructions for use whether Digit Control Machine Tool reaches expection, point out the weak link in the Digit Control Machine Tool process, for design, manufacturing, technology and the maintenance etc. that improve Digit Control Machine Tool point the direction.

The reliability consideration of Digit Control Machine Tool originates from the former Soviet Union of the seventies in last century the earliest, the scholar of the former Soviet Union carries out aspects such as parametric reliability prediction at parametic fault model, reliability of technology and with Monte Carlo Method (Monte-Carlo), according to the particularity of Digit Control Machine Tool, set up the basic theories of Digit Control Machine Tool reliability engineering at aspects such as function, structure, external applied loads.The general thinking of current domestic and international Digit Control Machine Tool reliability consideration is the collection and the analysis of field failure data, start with from the Analysis on Fault Diagnosis of Digit Control Machine Tool, according to Digit Control Machine Tool work and functional characteristics, trouble-shooting pattern and reason propose the reliability corrective measure.The object great majority of research are the bigger general Digit Control Machine Tools of quantity, the approach of field failure data acquisition is to follow the tracks of tens Digit Control Machine Tools for a long time simultaneously, for the colony of like numbers controlled machine provides general appraisal procedure, belong to traditional reliability method basically based on incident.These traditional reliability methods are effective to the lathe manufacturing enterprise of those production in enormous quantities, but the terminal use of Digit Control Machine Tool then is worth not quite.And own wt is big, the quantity of the large-size numerical control machine of the complicated surface processing that can realize high speed and super precision is considerably less, and mostly is to take the conservative mode of using when reality is used, the performance requirement use during not by design.Therefore, the fault of large-size numerical control machine can not find fully in finite time that the large-size numerical control machine reliability data is quite deficient, and general Digit Control Machine Tool reliability assessment technology can not be applicable to large-size numerical control machine fully.

Because the structure and the complicated operations environment of large-size numerical control machine itself, the generation that lathe lost efficacy generally is very difficult predicted, and the failure effect between each functional part, the operating environment that the failure probability characteristic of feature, the inefficacy of feature increase and change and the technological parameter of variation have all increased the complexity of reliability data.Simultaneously, compare with medium and small Digit Control Machine Tool, large-size numerical control machine not only self and workpiece to be machined complexity is huge, and the processing load variations is big, the processing stroke is big.Along with the user is more and more higher to the requirement of machining accuracy, working (machining) efficiency and reliability, machined parameters such as machining accuracy, feed speed, acceleration, reliability are also improving constantly, and then cause under traditional processing conditions the factor aspect the little dynamic characteristic of machining accuracy influence, under the processing conditions of high-speed, high acceleration and big variable load, machining accuracy has been produced remarkable influence.

In fact, during large-size numerical control machine work, a large amount of machineries, hydraulic pressure, pneumatic, electricly influence each other with mechanism electronics and element, because process system (comprises Digit Control Machine Tool, cutter, anchor clamps and blank) be subjected to internal factor (cutting force and moment thereof, frictional force, vibration, process system element heating etc.) and external factor (environment temperature, the vibration of nearby device, voltage pulsation, air humidity and pollution, operator's intervention etc.) influence, strain can take place in the process system element, wearing and tearing, vibration, thermal deformation, the performance parameter of process system is (as geometric accuracy, kinematic accuracy, rigidity etc.) change, machining accuracy reduces, cause crudy to worsen, in other words, the reliability of technology of Digit Control Machine Tool reduces.And existing Digit Control Machine Tool reliability assessment technology is not considered the performance variation of process system and the reliability of technology situation of change that causes, cause the conservative occupation mode of the many employings of terminal use to come the operating numerical control lathe, thereby reduced the production efficiency and the crudy of Digit Control Machine Tool.

Summary of the invention

The objective of the invention is at the deficiencies in the prior art, a kind of appraisal procedure of reliability of technology for large numerical control machine is provided, take all factors into consideration that various factors has improved the accuracy of reliability of technology to the function and the Effect on Performance of large-size numerical control machine in the machine tooling process.

A kind of appraisal procedure of reliability of technology for large numerical control machine specifically comprises the steps:

(1) Digit Control Machine Tool being reduced to a single-degree-of-freedom has damping system, sets up the frequency response function of system:

$H\left(\mathrm{\ω}\right)=\frac{1/k}{1-{(\mathrm{\ω}/{\mathrm{\ω}}_n)}^2+i2\mathrm{\ξ}(\mathrm{\ω}/{\mathrm{\ω}}_n)}$

Wherein, ω is a driving frequency, ω _nBe intrinsic frequency, ξ is a damping ratio, and k is a stiffness coefficient.By the structure composition dynamic stiffness experiment of Digit Control Machine Tool, measure the frequency response function curve of Digit Control Machine Tool.Adopt nonlinear least square method after the curve The Fitting Calculation, to pick out kinetic parameter: intrinsic frequency ω _n, damping ratio ξ and stiffness coefficient k.

(2), set up cutting force Δ F (t) model of machining according to Taylor empirical equation method:

Wherein, F ₁(t) represent total instantaneous cutting force that instantaneous thickness of cutting causes, F ₂(t) represent the average cutting force that nominal ablation thickness causes, F ₃(t) the expression workpiece material is to the drag of blade incision.D and μ are coefficient, are determined by the cutting force experiment; a _pBe cutting depth, f is the cutting amount of feeding, and s (t) is instantaneous thickness of cutting, s ₀(t) be nominal thickness of cutting, c is the penetration rate coefficient, and N is the speed of mainshaft, and z is a cutter tooth number.

(3) set up the non-linear dynamic model of Computerized Numerical Control Cutting Processes:

Wherein, x (t) is relative movement orbit on the cutting surface normal direction between the blade of cutting and the workpiece, and ξ is a damping ratio, ω _nBe intrinsic frequency, k is a stiffness coefficient, and Δ F (t) is the dynamic change part of cutting force.Adopt fourth-order Runge-Kutta method (Runge-Kutta) to find the solution, obtain the relative motion simulation curve on the cutting surface normal direction, identical basically with measured curve under identical condition when simulation curve, the non-linear dynamic model that shows foundation is believable.

(4) be located under certain Cutting Process condition, utilize the non-linear dynamic model of step 3, relative movement orbit x (t) between the blade of emulation cutting and the workpiece on the cutting surface normal direction utilizes method of random sampling to choose N point, and processing inefficacy territory D in given this section process-cycle _g, calculate failpoint number n _f, then try to achieve Digit Control Machine Tool at above-mentioned process conditions and the technology reliability R=n in the process-cycle _f/ N.

Beneficial effect of the present invention is embodied in: large-size numerical control machine is subjected to various inside/outside portion stochastic factor in process, thereby has influenced the reliability of technology of large-size numerical control machine.Compared with prior art, the present invention has the following significant advantage that is different from conventional method:

1) takes all factors into consideration principal elements such as the current architectural characteristic of large-size numerical control machine, production process property and processing operating mode, directly obtain the current reliability of technology of large-size numerical control machine, and do not need to collect fault data with the long-time running of statistical number controlled machine, improved the efficient of reliability of technology assessment.

2) obtain the architectural characteristic and the production process property of large-size numerical control machine by experiment, set up the non-linear dynamic model of Computerized Numerical Control Cutting Processes, emulation through working angles, just can obtain the precision of machine tooling, solve the problem that machine dynamic characteristics is obtained preferably, thereby improved the accuracy of reliability of technology assessment.

Description of drawings

Fig. 1 estimation flow schematic diagram of the present invention

Fig. 2 structure composition dynamic stiffness experimental principle

Fig. 3 Milling Force experimental principle

Fig. 4 processing technology reliability assessment

The specific embodiment

The present invention will be further described below in conjunction with the drawings and specific embodiments.

Concrete implementation step of the present invention following (with reference to Fig. 1):

(1) identification of kinetic parameter.Because the reliability of technology of Digit Control Machine Tool is subjected to the frame for movement of lathe and the influence of manufacturing process system, the present invention at first needs to discern the kinetic parameter of lathe frame for movement, i.e. intrinsic frequency ω _n, damping ratio ξ and stiffness coefficient k.Adopt the frequency response function method to come identification equipment kinetic parameter,, adopt parameter identification method, infer the kinetic parameter of lathe promptly according to the relation curve between driving frequency and the response amplitude.Digit Control Machine Tool is reduced to a single-degree-of-freedom damping system, and the frequency response function of this system is:

$H\left(\mathrm{\ω}\right)=\frac{1/k}{1-{(\mathrm{\ω}/{\mathrm{\ω}}_n)}^2+i2\mathrm{\ξ}(\mathrm{\ω}/{\mathrm{\ω}}_n)}$

Wherein, ω is a driving frequency, ω _nBe intrinsic frequency, ξ is a damping ratio, and k is a stiffness coefficient.Thereby obtain the amplitude versus frequency characte and the phase-frequency characteristic of system, that is:

$\left\{\begin{array}{c}\left|H\left(\mathrm{\ω}\right)\right|=\frac{{\mathrm{\ω}}_n^2}{k\·\sqrt{{({\mathrm{\ω}}_n^2-{\mathrm{\ω}}^2)}^2+{\left(2\mathrm{\ξ}{\mathrm{\ω}}_n\mathrm{\ω}\right)}^2}}\\ \mathrm{\φ}\left(\mathrm{\ω}\right)=\arctan \frac{2\mathrm{\ξ}{\mathrm{\ω}}_n\mathrm{\ω}}{{\mathrm{\ω}}_n^2-{\mathrm{\ω}}^2}\end{array}\right.$

By the structure composition dynamic stiffness experiment of Digit Control Machine Tool, measure Digit Control Machine Tool encouraged and tested at point of a knife point gained at point of a knife point along the tool feeding direction frequency response function curve.The a series of amplitude-frequency values of intercepting from the frequency response function curve adopt nonlinear least square method to pick out kinetic parameter: intrinsic frequency ω after the curve The Fitting Calculation _n, damping ratio ξ and stiffness coefficient k.

(2) identification of cutting force dynamic model parameter.The Digit Control Machine Tool process has produced instantaneous cutting force fluctuation owing to be subjected to the influence of various disturbing factors, makes that instantaneous cutting force is to be formed by stacking by the fluctuation cutting force that static cutting force and various disturbing factor cause.According to the Taylor empirical equation method of cutting force modeling, cutting force be with cutting depth and the cutting amount of feeding be the exponential function of variable, that is:

F＝Da _pf ^u

Wherein, F is a cutting force, a _pBe cutting depth, f is the cutting amount of feeding, and D and u are coefficient.a _pWith the technological parameter of f for selecting.D and u then need to obtain by the cutting force experiment.

With formula F=Da _pf ^uBoth sides take the logarithm, lgF=lgD+lga is arranged _p+ μ lgf.Make y=lgF, x ₁=lga _p, x ₂=lgf, β ₀=lgD, β ₁=μ then obtains formula y=β ₀+ x ₁+ β ₁x ₂By the cutting force experiment, obtain a series of data sets (y, x ₁, x ₂), obtain factor beta through linear least squares identification ₀And β ₁Thereby, calculate coefficient D and u.

Then set up cutting force dynamic model Δ F (t), that is:

Wherein, F ₁(t) represent total instantaneous cutting force that instantaneous thickness of cutting causes, F ₂(t) represent the average cutting force that nominal ablation thickness causes, F ₃(t) the expression workpiece material is to the drag of blade incision.a _pBe cutting depth, s (t) is instantaneous thickness of cutting, s ₀(t) be nominal thickness of cutting, c is the penetration rate coefficient, and N is the speed of mainshaft, and z is a cutter tooth number.Instantaneous thickness of cutting s (t) computing formula is:

$s\left(t\right)=\left\{\begin{array}{cc}x\left(t\right)-y\left(t\right),& x\left(t\right)>y\left(t\right)\\ 0,& x\left(t\right)\≤y\left(t\right)\end{array}\right.$

Wherein, y (t) is the ripple degree of depth of surface of the work, and x (t) is relative movement orbit on the cutting surface normal direction between the blade of cutting and the workpiece.When blade in the working angles exceeded outside the surface of the work, instantaneous thickness of cutting was zero, and this moment, the incision drag of workpiece material was zero, i.e. c=0.

(3) foundation of process kinetic model.Set up the non-linear dynamic model of Digit Control Machine Tool process:

Wherein, x (t) is relative movement orbit on the cutting surface normal direction between the blade of cutting and the workpiece, and ξ is a damping ratio, ω _nBe intrinsic frequency, k is a stiffness coefficient, and Δ F (t) is the dynamic change part (seeing formula 1) of cutting force.Adopt fourth-order Runge-Kutta method (Runge-Kutta) to find the solution, obtain the relative motion simulation curve on the cutting surface normal direction between cutting blade and the workpiece, simulation curve coincide basically with measured curve under identical condition, and the non-linear dynamic model that shows foundation is believable.

(4) reliability of technology probability calculation.Be located under the Cutting Process condition, utilize the model of formula (2), relative movement orbit x (t) between the blade of emulation cutting and the workpiece on the cutting surface normal direction, utilize method of random sampling to choose N point (N is a natural number) on last arbitrary section of the x (t) and processing inefficacy territory D in given this section process-cycle _g, i.e. machined surface roughness R _αProcessing inefficacy territory when surpassing L, L is given inefficacy threshold values.Calculate R _αValue is less than the number n of L _fThereby, try to achieve Digit Control Machine Tool and be: R=n in above-mentioned process conditions and the technology reliability in the process-cycle _f/ N, failure probability is: F _R=1-n _f/ N, promptly obtain Digit Control Machine Tool above-mentioned process conditions and in the process-cycle gained processing work surface roughness less than probability or the reliability of technology of L.

Describe below in conjunction with a concrete example:

At first test and discern kinetic parameter by comprehensive dynamic stiffness.With reference to Fig. 2, comprehensive dynamic stiffness experiment is to adopt hammering method the milling cutter point of a knife partly to be carried out the power hammering blow experiment of multiple spot excitation spot measurement, by being fixed on the response of the accelerometer measures system architecture on the cutter, through obtaining the frequency response experimental data after the signal analysis, calculate the intrinsic frequency ω of system by parameter identification method _n, kinetic model parameters such as damping ratio ξ, stiffness coefficient k.

With certain turnning and milling combined numerically controlled machine is example, and its movable member is ram, standard milling head etc.Ram can move (move left and right) along X-axis, can move (moving up and down) along the Z axle simultaneously, and the standard milling head can be along the rotation of C axle, and cutter can rotate along the B axle.Under lathe coordinate system, the moving range of each is: X-axis is (3.53 ,-0.53), and the Z axle is (0.16 ,-1.85), and the C axle can 360 ° of revolutions, and the B axle is (90 °, 90 °).At the trial in order to obtain the rigidity field, space of Digit Control Machine Tool, with above each be divided into three sections, respectively get four measuring points, have 256 kinds of situations, in each case lathe is tested, thereby is obtained the rigidity field, space (with reference to table 1) of lathe.

When table 1C axle and B axle fixed position, lathe is in the Stiffness Distribution of each measuring point

??X	??Z	??k	??ω n	??ξ
					??-3530	??-160	??2.74224715905e+009	??7.3100984211e+003	??0.0745490949
??-3530	??-720	??2.63542832644e+009	??7.3726498374e+003	??0.0790478693
					??-2530	??-160	??2.76715273308e+009	??7.4621540895e+003	??0.0715786762
??-2530	??-720	??2.64317639259e+009	??7.5446929319e+003	??0.0999999999
					??-2530	??-1280	??2.53129824957e+009	??7.4190840864e+003	??0.0994068557
??-2530	??-1850	??2.48813972124e+009	??7.3032905850e+003	??0.0999999999
					??-1530	??-160	??2.73378844094e+009	??7.3888143199e+003	??0.0917955241
??-1530	??-720	??2.63552612466e+009	??6.7508379928e+003	??0.0999999999
					??-1530	??-1280	??2.53804369140e+009	??7.4744859646e+003	??0.0984738430
??-1530	??-1850	??2.46057959411e+009	??7.5363225483e+003	??0.0999999999
					??-530	??-160	??2.69748336521e+009	??7.4016042403e+003	??0.0966093344

??X	??Z	??k	??ω n	??ξ
					??-530	??-720	??2.64353387725e+009	??7.4438788060e+003	??0.0999999630
??-530	??-1280	??2.46944811681e+009	??7.4672432865e+003	??0.0999987585
					??-530	??-1850	??2.46944801350e+009	??7.4242805147e+003	??0.0999999999

Test by Milling Force and to choose working process parameter.As shown in Figure 3, the Milling Force experimental principle is that test specimen is installed on the piezoelectric type dynamometer, and the milling test specimen behind the force signal of measuring in real time process charge amplifier and the data collecting card, is sent to computer then.The data of gathering obtain the average Milling Force of X, Y and three directions of Z after programmed process.

Carry out the Milling Force experiment according to the Milling Force experiment condition shown in the table 2, obtain Milling Force experiment measured data.According to the Milling Force experimental data, when milling depth is 3mm, adopts linear least square to simulate coefficient D=1462.3 and μ=0.6598, thereby set up Milling Force Model: F=Da _pf ^u=2727.7a _pf ^0.6892

Table 2 Milling Force experiment condition

The speed of mainshaft (r/min)	?400
		Feed speed (mm/min)	?50，100，150，200，250，300，350，400，450，500
Cutter tooth number	?10
		Milling depth (mm)	?1，1.5，3，4
Test specimen	?CU #4?200mm×180mm×120mm

Experiment shows: the predicted value of Milling Force Model and the average deviation between the measured value are 5.4623 (N), coincide better.Reach a conclusion thus: this Milling Force Model is reasonably basically, satisfies requirement of actual application.

By top structure composition dynamic stiffness experiment of on this turnning and milling combined numerically controlled machine, carrying out and Milling Force experiment, calculate Milling Force Model parameter D=1462.3 and μ=0.6598, kinetic parameter is as shown in table 1.In addition, the cutter number of teeth is that z=10, the speed of mainshaft are that N=400rpm, penetration rate coefficient are c=0.012.These parameters are updated in the formula 2, thereby set up the non-linear dynamic model of this turnning and milling combined numerically controlled machine Milling Processes, and adopt fourth-order Runge-Kutta method (Runge-Kutta) to find the solution formula.

The correctness of the non-linear dynamic model of setting up in order to verify is carried out the Milling Process experiment.Numerical control equipment is that 1.2mm and feed engagement are milling workpiece under the processing operating mode of 0.0625mm with the milling depth, and actual measurement obtains the relative movement orbit on milling surface normal direction between milling blade and the workpiece.Simultaneously, under identical condition, carry out emulation with the non-linear dynamic model of setting up, obtain the relative motion simulation curve on milling surface normal direction between milling blade and the workpiece, simulation curve and measured curve coincide basically, and the non-linear dynamic model that shows foundation is believable.

Carry out the processing technology reliability assessment at last, promptly change, in real time evaluation and predicting machine bed process reliability by the precision of analyzing the lathe outlet terminal.Processing technology reliability assessment process as shown in Figure 4.The present invention is an example with the processing propeller blade, studies the processing technology reliability assessment.

Suppose that structure composition dynamic stiffness parameter and the cutter parameters thereof of this turnning and milling combined numerically controlled machine in a process-cycle is constant, based on the emulated data of numerical control equipment Milling Processes non-linear dynamic model analyzed numerical control equipment in some process-cycles different fabrication process conditions (with reference to table 3) to the influence of reliability of numerical control equipment.

Interior process conditions of process-cycle of table 3

Process conditions	Value
		The speed of mainshaft (r/min)	??200，300，400，500
Feed speed (mm/min)	??150，200，250，300，350，400，450，500
		Milling depth (mm)	??2，2.5，3，3.5，4，4.5，5
Cutter tooth number	??10
		Cutter	Agree receive KC725M
Test specimen	Screw

As shown in Table 3, numerical control equipment has 4 * 8 * 7=224 process combination in this process-cycle.Therefrom extract the most representative 20 process conditions, and they are input in the numerical control equipment process non-linear dynamic model of having set up carry out simulation analysis, calculate the input performance indications-surface roughness R of numerical control equipment _α, as shown in table 4.

Table 4 fabrication process condition and surface roughness

The fabrication process condition that provides according to table 3 carries out value, adopts method of random sampling to generate N random sampling point, and the process conditions of random sampling gained are input in the non-linear dynamic model, obtains N R _αValue.Get N=1000, and processing inefficacy territory D in given this section process-cycle _g(L=11um), i.e. machined surface roughness R _αProcessing was lost efficacy when surpassing 11um.Automatically calculate R by the MATLAB program _αValue is less than the number n of L _f=543, thereby try to achieve numerical control equipment in above-mentioned process conditions and the technology reliability in the process-cycle be: R=n _f/ N=0.543, failure probability is: F _R=1-n _f/ N=0.457.This result shows: numerical control equipment above-mentioned process conditions and in the process-cycle gained processing work surface roughness be 54.3% less than the probability of 11um.

Claims (4)

1. the appraisal procedure of a Digit Control Machine Tool reliability of technology specifically comprises the steps:

(1) kinetic parameter of identification number controlled machine comprises intrinsic frequency ω _n, damping ratio ξ and stiffness coefficient k;

(2), set up cutting force Δ F (t) model of machining according to Taylor empirical equation method:

Wherein, F ₁(t) represent total instantaneous cutting force that instantaneous thickness of cutting causes, F ₂(t) represent the average cutting force that nominal ablation thickness causes, F ₃(t) the expression workpiece material is to the drag of blade incision, and D and μ are coefficient, determines a by the cutting force experiment _pBe cutting depth, s (t) is instantaneous thickness of cutting, s ₀Be nominal thickness of cutting, c is the penetration rate coefficient, and N is the speed of mainshaft, and z is a cutter tooth number;

(3) set up the non-linear dynamic model of Computerized Numerical Control Cutting Processes:

Wherein, x (t) is relative movement orbit on the cutting surface normal direction between the blade of cutting and the workpiece;

(4) reliability of technology probability calculation utilizes the non-linear dynamic model of step (3), and the described relative movement orbit x of emulation (t) chooses any N point on arbitrary section of the x (t), and the processing inefficacy territory D in given this section process-cycle _g, calculate failpoint number n _f, promptly try to achieve described Digit Control Machine Tool at above-mentioned process conditions and the technology reliability R=n in the process-cycle _f/ N, thus failure probability is F _R=1-n _f/ N.

2. method according to claim 1 is characterized in that, described kinetic parameter is tried to achieve by following process:

At first, Digit Control Machine Tool is reduced to a single-degree-of-freedom damping system, and sets up the frequency response function of system:

$H\left(\mathrm{\ω}\right)=\frac{1/k}{1-{(\mathrm{\ω}/{\mathrm{\ω}}_n)}^2+i2\mathrm{\ξ}(\mathrm{\ω}/{\mathrm{\ω}}_n)}$

Wherein, ω is a driving frequency, ω _nBe intrinsic frequency, ξ is a damping ratio, and k is a stiffness coefficient;

By the structure composition dynamic stiffness experiment of Digit Control Machine Tool, measure the frequency response function curve of Digit Control Machine Tool again;

Utilize nonlinear least square method after the curve The Fitting Calculation, can pick out described kinetic parameter at last.

3. method according to claim 2 is characterized in that, said instantaneous thickness of cutting s (t) draws by following computing formula in the step (2):

$s\left(t\right)=\left\{\begin{array}{cc}x\left(t\right)-y\left(t\right),& x\left(t\right)>y\left(t\right)\\ 0,& x\left(t\right)\≤y\left(t\right)\end{array}\right.$

Wherein, y (t) is the ripple degree of depth of surface of the work.

4. according to the described method of one of claim 1-3, it is characterized in that described processing inefficacy territory D _gRefer to machined surface roughness R _αThe processing inefficacy territory that forms when surpassing predetermined inefficacy threshold values L.

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