CN103116673A - Predictive method of milling machining surface form - Google Patents

Predictive method of milling machining surface form Download PDF

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Publication number
CN103116673A
CN103116673A CN2013100419307A CN201310041930A CN103116673A CN 103116673 A CN103116673 A CN 103116673A CN 2013100419307 A CN2013100419307 A CN 2013100419307A CN 201310041930 A CN201310041930 A CN 201310041930A CN 103116673 A CN103116673 A CN 103116673A
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milling
topography
forecasting methodology
data
predictive
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陈慧群
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陈慧群
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Abstract

The invention provides a predictive method of milling machining surface form which comprises the following steps: step one, arranging cutting parameter data and acquiring a surface roughness measured value; step two, resolving a surface roughness predictive value; step three, combining the surface roughness measured value with the surface roughness predictive value to a module data group and outputting an ultimate predictive module. Compared with the prior art, the predictive method of the milling machining surface form provides a novel surface form predictive method and further resolves the problem of match between the cutting parameter and the machining surface form based on a multiple linear regression thought. The predictive method of the milling machining surface form analyzes mainly from the angle of the features of a predictive system of the milling machining surface form, establishes a multiple linear regression analysis predictive module specific to different machining experiments, and utilizes the module to predict the experiments, and can be popularized to the prediction of residual stress, surface hardness and cutting force and the like in the milling process.

Description

A kind of Milling Process surface topography Forecasting Methodology
Technical field
The present invention relates to a kind of Milling Process surface topography Forecasting Methodology.
Background technology
The Milling Process surface topography directly affects machining precision and the quality of part, and the intension of Milling Process Surface Creation is in depth studied by system, becomes one of important research content of Milling Process technology.In process, the surface topography of workpiece is closely related with the skew of the relative workpiece of cutter that cutter geometric properties and cutting force are induced.
Mainly contain at present following several Milling Process surface topography Forecasting Methodology: (1) sets up CAD and the CAM model of workpiece and cutter according to technological parameter, and utilize the Boolean calculation technology to obtain corresponding milling surface topography, develop a cover pommel and mill the cutting process simulation system; (2) set up based on Z-direction degree of depth workpiece cad model, adopt the arc description workpiece of limited quantity, determine residual high value by these line segments and edge line Boolean calculation, thereby determine surface topography and roughness; (3) use the residual high structure pommel of two directions of feed to mill the characteristic curve of finished surface, the mode by interpolation obtains surface topography; (4) based on the cutting tool geometric model of Machine kinematics model and broad sense, set up general Surface Creation model, the impact that the bias of this model consideration cutter, machining deformation, vibration and the high-order motion effects on surface of lathe generate; (5) use geological information and the cutter location data file prediction cutting force of analytic model, cutter and the workpiece of instantaneous chip-load, and determine pommel milling workpiece surface topography and residual height by Boolean calculation; (6) set up the kinematics model of the relative workpiece of blade point, the numerical solution Nonlinear System of Equations obtains the residual height of every bit and also constructs the finished surface pattern, uses institute's strategy of carrying respectively to ball cutter peace bottom cutter milling process simulation surface topography; (7) adopt the technology that solid modelling is combined with Boolean calculation that the pommel process of milling is carried out geometric modelling and obtained the finished surface pattern.The most technology uses discrete method and interpolation technique and Boolean calculation to predict the finished surface pattern, rarely has the impact of considering workpiece displacement effects on surface pattern, and the coupling of cutting parameter is demanded further solution urgently, and technology acuracy also has much room for improvement etc.
Summary of the invention
In order to overcome above-mentioned the deficiencies in the prior art, the invention provides a kind of Milling Process surface topography Forecasting Methodology.
Compared to prior art, the present invention is based on multiple linear regression thought, a kind of new surface topography Forecasting Methodology is proposed, further solved the matching problem of cutting parameter and finished surface pattern.the main characteristics angle analysis from milling surface topography prognoses system of invention, set up the multiple linear regression analysis forecast model for different machining experiments, and utilize model to launch prediction to experiment, and can be applied to unrelieved stress in milling process, the prediction of the machined parameters such as skin hardness and cutting force, characteristics are: (1) has shown the system performance of the multiple-input and multiple-output of surface topography prediction, point out the non-linear nature of surface topography prognoses system, the generalization ability of multiple linear regression can the control surface pattern, for the planning tool paths optimization provides theoretical foundation, (2) in conjunction with Interpolation Principle and thought, in conjunction with the characteristics of Linear Regression Forecasting Model, the method that the method difference linear regression of the even stochastic distribution of employing predicts the outcome increases the quantity of forecast sample, has improved precision of prediction and robustness.
Description of drawings
Fig. 1 is the process schematic diagram that is applied to surface topography of Milling Process surface topography Forecasting Methodology of the present invention.
Fig. 2 is the flow chart of steps of Milling Process surface topography Forecasting Methodology of the present invention.
Fig. 3 is the surfaceness schematic diagram under workpiece rotational frequency of the present invention and the impact of speed of feed quadrature.
Fig. 4 is predict the outcome comparative analysis schematic diagram with experimental result of unrelieved stress in milling of the present invention.
Embodiment
The present invention is further described below in conjunction with description of drawings and embodiment.
See also Fig. 1 and Fig. 2, the invention provides a kind of Milling Process surface topography Forecasting Methodology.
As shown in the figure, a kind of Milling Process surface topography Forecasting Methodology of the present invention adopts the experimental data meter to utilize the linear regression method prediction to process the rear surface mass parameter, thinking and method in conjunction with the multiple linear regression prediction, adopt Matlab that perfect Multiple Non Linear Regression and the tool box of simulation calculation are provided, set up surface quality prediction multiple linear regression model, pre-generation forecast model after pooled data, and testing model error, and then export final pattern.
1, surface topography forecasting process
Contrast Fig. 2, process is as follows:
Step 1: set the cutting parameter data, the input machined parameters also obtains the surface topography test result.
In high-speed cutting processing, affecting the important evaluation criteria of surface topography---the factor of roughness may be summarized to be four aspects: cutter variable, workpiece variable, cutting parameter variable and working angles variable.Exist the relation of intercoupling between these factors, and be subjected to the impact of many uncontrollable factors in working angles.Traditional surfaceness empirical model (Tipnis model) is (1) formula:
R a = cf l υ k a p m (1) formula
The Milling Parameters that comprises in formula is: amount of feeding f, cutting speed v and axial cutting depth a p(feeding distance).When carrying out Milling Process on numerical control machining center, also need to formulate workpiece rotational frequency n w, speed of feed v fWith radial cutting degree of depth a eWorkpiece rotational frequency n wDetermine by cutting speed and tool diameter that cutter allows.Speed of feed v fBe the major parameter of cutting, it considers that Selected Factors is numerous, comprises part processing precision and surfaceness requirement, cutter and part material, machine tool capability etc.
So speed of feed v fAlso often as selecting parameter.And rose cutter is when milling, feeding distance a eChange directly have influence on the residual height of process redundancy, and the direct effects on surface roughness of residual height exerts an influence.
In the present embodiment, namely the according to the form below experimental sequence obtains 16 groups of experiment cutting parameter data (v f, n w, a e, a p) and surfaceness measured value (R a).
Table 1 orthogonal experiment tables of data
Step 2: providing data formatting.The present invention utilizes workpiece rotational frequency n from machining center practical operation needs w, speed of feed v f, cutting depth a e, and feeding distance a pFour parameters are set up milling surface topography (roughness) forecast model:
R a = cv f l n w k a e m a p q (2) formula
C is the coefficient of rapidoprint and machining condition; L, k, m, q are index undetermined.Be appreciated that c can be according to the difference of rapidoprint and machining condition and different.
By following formula as can be known, (2) formula is nonlinear equation, for being used for regretional analysis, makes its linearization, the realization of can taking the logarithm respectively on both sides:.
lnR a=lnc+llnv f+ klnn w++ mlna e+ qlna p(3) formula
Make y=lnR a, a 0=lnc, x 1=lnv f, a 1=l, x 2=lnn w, a 2=k, x 3=lna e, a 3=m, x 4=lna p, a 4=q
In the present embodiment, will show a kind of every column data and get respectively normal logarithm, as R in above-mentioned table 1 aBecome after one column format (1.3185 ,-1.2165 ... ,-0.6928) T.
Step 3: multiple linear regression.
Corresponding equation of linear regression is:
Y=a 0+ a 1x 1+ a 2x 2+ a 3x 3+ a 4x 4(4) formula
This linear equation comprises 4 independent variable x altogether 1, x 2, x 3, x 4, test findings represents with y.In order to determine a 0, a 1, a 2, a 3, a 4Five regression coefficient values, the present invention has done 16 groups and has tested to determine unknown number.Wherein the independent variable of i group is labeled as x with two dimension i1, x i2, x i3, x i4, every group of test findings is y iConsider and wherein may have test stochastic variable error ε i, can set up following multiple linear regression equations by 16 groups of experimental datas:
y 1 = a 0 + a 1 x 11 + a 2 x 12 + a 3 x 13 + a 4 x 14 + ϵ 1 y 2 = a 0 + a 1 x 21 + a 2 x 22 + a 3 x 23 + a 4 x 24 + ϵ 2 . . . y 16 = a 0 + a 1 x 161 + a 2 x 162 + a 3 x 163 + a 4 x 164 + ϵ 16 (5) formula
Can be expressed as with matrix:
Y=Xa+e (6) formula
Wherein, Y is the matrix that the logarithm value of the surfaceness of 16 groups of experiment measurings forms:
Y = y 1 y 2 . . . y 16 X = 1 x 11 x 12 x 13 x 14 1 x 21 x 22 x 23 x 24 . . . 1 x 161 x 162 x 163 x 164 a = a 0 a 1 . . . a 4 e = ϵ 1 ϵ 2 . . . ϵ 16 (7) formula
Utilization experiment cutting parameter data and surfaceness measured value are set up the multiple linear regression equations group between experimental data and test result, are namely that data substitution (5) formula of step 2 is set up the multiple linear regression equations group.
Step 4: prediction rough handling result.
By the least-square principle of parameter as can be known:
A=(X ' X) -1X ' Y (8) formula
Find the solution the coefficient a of multiple linear regression equations, by Cramer's rule or Gaussian transformation, utilize matlab programming to realize that regression coefficient finds the solution, this moment is ε iRegard constant as, can obtain the Prediction of Surface Roughness value, namely obtain predicting prescheme.
Step 5: model error check.Calculate Prediction of Surface Roughness value and the measured value error E (in numerical evaluation, error is inevitable) of utilizing prediction to draw, prescheme is effective if it less than the assigned error threshold values, thinks prediction, directly the generation forecast model; If it is not less than the error threshold values, think that the prediction prescheme is invalid, the data group that should carry out the larger error of error returns interpolation processing, also can carry out denoising and interpolation, until less than the error threshold values.
Regressive interpolation namely returns in the middle of raw data and implants some data, these data only occur as " noise " number, and be these " noises " by certain control strategy, Data Control is processed like this robustness that is conducive to follow-up multiple linear regression model and is unlikely to again to reduce simultaneously accuracy within the specific limits.Its basic thought is to utilize auxiliary variable x jThe linear relationship of=(j=1,2...k) and target variable y is set up regression model, utilizes the information of known auxiliary variable, and the missing values of target variable is estimated.
Returning key issue of interpolation is e jProcessing because through after returning, z jEstimated value be:
z ‾ j = β 0 + Σ k = 1 K β k x kj (9) formula
β in formula kBe regression coefficient, for identical x j(j=1,2 ... k), the substitute value that obtains is identical, and this will be the same with mean value interpolation, has the problem of sample distribution distortion.Need to construct the data set of random residual e for this reason.The method of structure has multiple, and a kind of more typical method is, according to auxiliary variable x jWith sample unit's layering, the deviation that will answer unit amount and its average in each layer is considered as residual error e, with returning method
z j = z ‾ j + e j (10) formula
So the estimated value of j missing values can be expressed as:
z j = β 0 + Σ k = 1 K β k x kj + e j (11) formula
When if auxiliary variable is qualitative variable, can adopt the disposal route of dummy variable: if target variable y is qualitative variable, consider by the Logit conversion, carry out the Logistic linear regression.At last, by answer data y jWith recurrence substitute value z j, the estimated value that obtains target variable is:
y ‾ = Σ j = 1 n 1 y j + Σ j = 1 n 0 z j n (12) formula
In actual applications, utilize the regress function that in the Matlab statistics toolbox, utility command provides to be easy to obtain needed regressive interpolation.
Step 6: export final forecast model.Effective interpolation data and measured result after error-tested are merged into a model data group, and so final surface topography forecast model will be more accurate.In the present invention, in above-mentioned table 1, the data group all in assigned error threshold values scope (differ and be no more than 2%), is therefore directly exported final surface topography Empirical rules model:
R a = 17.3258 v f 0.0765 n w - 0.2748 a e 0.4248 a p 0.0965 (13) formula
Step 7: the dominant check of morphology prediction model.After the surface topography forecast model was found the solution, the validity for further decision model was necessary the morphology prediction model is carried out dominant check.
In order to carry out statistical test, need to total sum of square of deviations be decomposed, by regression sum of square S AWith residual sum of squares (RSS) S ETwo parts form, and Bai Youdu is n-1, and total sum of square of deviations S is:
S = Σ i ( y i - y ‾ ) 2 = S A + S E = Σ i ( y ^ i - y ‾ ) 2 + Σ i ( y i - y ^ i ) 2 (14) formula
y ‾ = Σ i y i n (15) formula
y ^ i = ln ( 17.3258 ) + 0.0765 x i 1 - 0.2748 x i 2 + 0.4248 x i 3 + 0.0965 x i 4 (16) formula
In multiple linear regression analysis, regression equation significantly and do not mean that each independent variable is important on the impact of dependent variable, in order better experimental result to be forecast and to be controlled, need to investigate each variable, therefore need to carry out significance test to regression coefficient.
Suppose a 0=0, adopt the statistic algorithm, have
F = a i 2 / C ii S E / ( n - m - 1 ) ~ F ( m , n - m - 1 ) (17) formula
Wherein, C iiBe matrix (X ' X) -1I element on diagonal line, n=16 are the experimental group number, and m=4 is the variable number, and during the milling surface of the work, computing draws C ii=[3.9583,4.1864,4.1892,4.2096] calculate S according to (14) formula~(16) formula E=0.0046, in conjunction with top a i=[0.0765 ,-0.2748,0.4248,0.0965], i=1,2...4, according to (17) formula as can be known:
F 1 = 0.0765 2 / 3.9583 0.0046 / 11 = 3.54 , Can get F with method 2=43.13, F 3=103.01, F 4=5.29.
Look into the F distribution table, when α=0.05, therefore F (4,11)=3.36, regression coefficient a as can be known 1, a 2, a 3, a 4All dominant.The impact that is speed of feed, workpiece rotational frequency, feeding distance and cutting depth effects on surface roughness is all remarkable, and wherein the cutting depth impact is the most remarkable.
In the present embodiment, call (13) formula funtcional relationship in Matlab, the important evaluation criteria of cutting parameter effects on surface pattern---the impact of roughness in the Multiple Linear Regression Forecasting Models of Chinese of each index of computational analysis surface topography, and output effect figure, both can carry out quadrature analysis this moment, also can carry out the single parameter impact analysis.As space is limited, only show workpiece rotational frequency and speed of feed to the impact of roughness, other parameter Orthogonal Composite or single function influence in like manner can get.See Fig. 3, wherein parameter configuration a e=0.06mm, a p=0.08mm.Therefrom also can draw the conclusion consistent with (13) formula, as in the situation that ceteris paribus, R aWith v fIncrease and increase, with n wIncrease and reduce.Promote the prediction that this law is used for process unrelieved stress, skin hardness and cutting force, method and process and surface topography forecasting process are in like manner, Fig. 4 is used for the predict the outcome comparative analysis with experimental result of milling process unrelieved stress for using this law, also can find out from figure, prediction effect is good.
Above content is in conjunction with concrete preferred implementation further description made for the present invention, can not assert that concrete enforcement of the present invention is confined to these explanations.For the general technical staff of the technical field of the invention, without departing from the inventive concept of the premise, can also make some simple deduction or replace, all should be considered as belonging to protection scope of the present invention.

Claims (10)

1. Milling Process surface topography Forecasting Methodology is characterized in that: comprise the following steps:
Step 1 is set the cutting parameter data, obtains the surfaceness measured value;
Step 2, effects on surface roughness predicted value is found the solution;
Step 3 is merged into the model data group with surfaceness measured value and Prediction of Surface Roughness value, exports final forecast model.
2. Milling Process surface topography Forecasting Methodology according to claim 1 is characterized in that: further comprising the steps in described step 2,
With cutting parameter data and the format of surfaceness measured value;
Utilization experiment cutting parameter data and surfaceness measured value are set up the multiple linear regression equations group between experimental data and test result;
Effects on surface roughness predicted value is found the solution.
3. Milling Process surface topography Forecasting Methodology according to claim 2 is characterized in that: further comprising the steps in described step 2,
Error-tested, the error between gauging surface roughness predicted value and surfaceness measured value less than the assigned error threshold values, thinks that forecast model is effective as it, if it is not less than the error threshold values, thinks that forecast model is invalid; If it is not less than the error threshold values, the data group of carrying out the larger error of error returns interpolation processing, until less than the error threshold values.
4. Milling Process surface topography Forecasting Methodology according to claim 3 is characterized in that: in described step 3,
To merge into a model data group with actual measurement surfaceness measured value as the Prediction of Surface Roughness value of effective interpolation, export final forecast model.
5. Milling Process surface topography Forecasting Methodology according to claim 1, it is characterized in that: in described step 1, described cutting parameter data comprise workpiece rotational frequency n w, speed of feed v f, radial cutting degree of depth a e, and axial cutting depth a p
6. Milling Process surface topography Forecasting Methodology according to claim 2, is characterized in that: in described step 2, the cutting parameter data are got respectively normal logarithm.
7. Milling Process surface topography Forecasting Methodology according to claim 2, it is characterized in that: in described step 2, equation of linear regression satisfies following formula:
y=a 0+a 1x 1+a 2x 2+a 3x 3+a 4x 4
Described a 0=lnc ' x 1=lnv f' a 1=l ' x 2=lnn w' a 2=k ' x 3=lna e' a 3=m ' x 4=lna p' a 4=q °
Described c is the coefficient of rapidoprint and machining condition; L, k, m, q are index undetermined, described n wBe workpiece rotational frequency, a eBe cutting depth, a pBe feeding distance, v fBe speed of feed.
8. Milling Process surface topography Forecasting Methodology according to claim 2 is characterized in that: in described step 2, use Cramer's rule or Gaussian transformation, utilize the matlab programming that the regression coefficient a of multiple linear regression equations is found the solution.
9. Milling Process surface topography Forecasting Methodology according to claim 3, is characterized in that: in described step 2, use the regress function that in the Matlab statistics toolbox, utility command provides to obtain required regressive interpolation.
10. Milling Process surface topography Forecasting Methodology according to claim 1, it is characterized in that: described Milling Process surface topography Forecasting Methodology also comprises step 4: the dominant check of morphology prediction model, described step 4 satisfies following formula,
F = a i 2 / C ii S E / ( n - m - 1 ) ~ F ( m , n - m - 1 )
Wherein, C iiBe matrix (X ' X) -1I element on diagonal line, n are the experimental group number, and m is the variable number, S EBe residual sum of squares (RSS).
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CN105269402A (en) * 2015-10-13 2016-01-27 南京航空航天大学 Method for predicating surface roughness of titanium alloy material based on milling
CN106825068A (en) * 2017-01-13 2017-06-13 北京科技大学 A kind of Forecasting Methodology of operation of rolling belt steel surface roughness
CN107609231A (en) * 2017-08-24 2018-01-19 中南大学 A kind of worm screw grinding worm surface microscopic topographic emulation mode and system
CN107644125A (en) * 2017-09-04 2018-01-30 上海交通大学 A kind of method for improving Milling Process surface and being glued sealing effectiveness
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CN108127481A (en) * 2017-12-15 2018-06-08 北京理工大学 A kind of Forecasting Methodology of the workpiece surface appearance based on Flank machining
CN108229046A (en) * 2018-01-16 2018-06-29 厦门理工学院 A kind of three-dimensional modeling method for being machined machined surface in face work technique
CN108647413A (en) * 2018-04-27 2018-10-12 北京理工大学 A kind of fine Surface Location Error and stability Comprehensive Prediction Method
CN109332820A (en) * 2018-09-29 2019-02-15 中南大学 A kind of processing of ultrasonic vibrating machining gear teeth face pattern and control method
CN110091216A (en) * 2019-05-13 2019-08-06 江苏师范大学 The monitoring of milling noise and milling vibration and its correlation analysis system and method
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CN112355713A (en) * 2020-09-24 2021-02-12 北京航空航天大学 Method, device and equipment for predicting cutting force based on image
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CN113168491A (en) * 2020-03-06 2021-07-23 大连理工大学 Method for simulating surface appearance of flutter-free milling

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CN103394972A (en) * 2013-08-05 2013-11-20 上海理工大学 Milling surface roughness online prediction method based on acoustic emission signals
CN105269402A (en) * 2015-10-13 2016-01-27 南京航空航天大学 Method for predicating surface roughness of titanium alloy material based on milling
CN106825068B (en) * 2017-01-13 2019-05-03 北京科技大学 A kind of prediction technique of operation of rolling belt steel surface roughness
CN106825068A (en) * 2017-01-13 2017-06-13 北京科技大学 A kind of Forecasting Methodology of operation of rolling belt steel surface roughness
CN107609231A (en) * 2017-08-24 2018-01-19 中南大学 A kind of worm screw grinding worm surface microscopic topographic emulation mode and system
CN107644125A (en) * 2017-09-04 2018-01-30 上海交通大学 A kind of method for improving Milling Process surface and being glued sealing effectiveness
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CN108127481A (en) * 2017-12-15 2018-06-08 北京理工大学 A kind of Forecasting Methodology of the workpiece surface appearance based on Flank machining
CN108229046A (en) * 2018-01-16 2018-06-29 厦门理工学院 A kind of three-dimensional modeling method for being machined machined surface in face work technique
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CN109332820A (en) * 2018-09-29 2019-02-15 中南大学 A kind of processing of ultrasonic vibrating machining gear teeth face pattern and control method
CN109332820B (en) * 2018-09-29 2020-06-02 中南大学 Method for processing and controlling tooth surface appearance of gear processed by ultrasonic vibration
CN110091221A (en) * 2019-05-13 2019-08-06 成都工业学院 A kind of die surface processing method
CN110091216B (en) * 2019-05-13 2021-06-01 江苏师范大学 Milling noise and milling vibration monitoring and correlation analysis system and method
CN110091216A (en) * 2019-05-13 2019-08-06 江苏师范大学 The monitoring of milling noise and milling vibration and its correlation analysis system and method
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CN110328558A (en) * 2019-07-10 2019-10-15 哈尔滨理工大学 Milling of Titanium Alloy surface appearance feature consistency distribution process control method
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