CN102172990B - Method for predicting surface roughness in single-point diamond turning - Google Patents

Abstract

The invention relates to a method for predicting surface roughness, in particular to a method for predicting surface roughness in single-point diamond turning. The method solves the problem that the conventional method for predicting the surface roughness has high predication error. The method comprises the following steps of: extracting amplitude information of relative vibration between a cutter and a workpiece in the processing process from the detection result of a processed surface, establishing corresponding relationships between the main shaft revolving speed and the material property and between the relative vibration and the expansion effect, calculating a profile curve of the processed surface after the expansion effect happens, finding the corresponding equivalent amplitude according to the specific processing material and the main shaft revolving speed so as to obtain equivalent relative vibration between the cutter and the workpiece, superposing the equivalent relative vibration and the profile curve of the processed surface after the expansion effect happens to obtain a new surface profile curve, performing data processing on the new curve and calculating the surface roughness. The method is used for predicting the surface roughness in the single-point diamond turning.

Description

A kind of Forecasting Methodology of surface roughness in single-point diamond turning

Technical field

The present invention relates to a kind of Forecasting Methodology of surface roughness, be specifically related to a kind of Forecasting Methodology of surface roughness in single-point diamond turning.

Background technology

General little cutting-in, low feeding and the high rotating speed of adopting of single-point diamond turning processing, to guarantee nano level surface roughness, but material is removed with surface formation mechanism very complicated in the process, at present, in the research of surface roughness in single-point diamond turning prediction, the basic thought of setting up shaggy Forecasting Methodology based on cutting theory is based under certain assumed condition the Relative Vibration between theoretical roughness of surface and cutter and workpiece is superposeed, and there is following problem in existing Forecasting Methodology:

1, the Relative Vibration between cutter and workpiece is in lathe idle running and do not carry out predicting under the machining condition, so it can not be reflected in the Relative Vibration information between cutter and workpiece in the actual processing really.

2, the material behavior and the cutting parameter impact on vibrating on cutter and workpiece that do not have consideration to be cut.

3, the calculating of theoretical roughness of surface is to consider from how much angle purely, but in the actual working angles, since the complicated variations such as the elasticity that material occurs recovery and plastic deformation, the height of the residual region of the reflection reality that the theoretical roughness of surface that purely calculates from geometric angle can not be correct.

4, do not consider that material behavior and cutting parameter recover the working angles Elastic and the impact of plastic deformation.

Because the existence of the problems referred to above, the predicated error of existing Forecasting Methodology is larger, and the predicated error of Ra value is about 10%.

Summary of the invention

The present invention has the larger problem of Prediction of Surface Roughness method error now for solving, and then proposes a kind of Forecasting Methodology of surface roughness in single-point diamond turning.

The present invention addresses the above problem the technical scheme of taking to be: the establishment step of the Forecasting Methodology of a kind of surface roughness in single-point diamond turning of the present invention is as follows:

Step 1, choose typical workpiece for measurement material, change feeding rotating speed, the speed of mainshaft and back engagement of the cutting edge contrived experiment scheme, carry out in advance single-point diamond machining experiment at ultra-precision machine tool;

Step 2, the surface outline curves that adopts the detection of contact pin type contourgraph to process typical workpiece for measurement;

Step 3, extract the process amplitude information of Relative Vibration between cutter and workpiece from the testing result of machined surface, the amplitude information of Relative Vibration obtains by the following method between described cutter and workpiece:

Step 3 (one), according to the surface outline curves and the data that detect, being radial diameter maximum place take the outermost of processing work end face sets up X, Z coordinate system as initial point, extract point of a knife and radially representing in the actual process Relative Vibration between cutter and workpiece with respect to the profile of workpiece in radially reflection, X-direction is the tool feeding direction, Z-direction is cutter cutting-in direction, and then radially the number of cutter profile is:

Wherein L is for radially detecting length, and s is the amount of feeding of cutter revolution, and the number that extracts data from the detection curve of machined surface also is N;

Coordinate is x on the X-axis of step 3 (two), extraction data _i=x ₁+ (i-1) △ x=x ₁+ (i-1) s(2), i=1 wherein, 2 ..., N, thus the point of a knife coordinate data that can obtain extracting is (x _i, Z _i(x _i)), the contour curve of Relative Vibration is between the cutter that extracts from machined surface and workpiece: Z _m(x _i)=Z _i(x _i)-min (Z _i(x _i)) (3), i=1 wherein, 2 ..., N-1, the surface roughness that the contour curve of above-mentioned Relative Vibration causes: ${\mathrm{Ra}}_m=\frac{1}{N}\underset{i=1}{\overset{N}{\mathrm{\Σ}}}|z_m\left(x_i\right)-\frac{\underset{i=1}{\overset{N}{\mathrm{\Σ}}}{Z}_m\left(x_i\right)}{N}|---\left(4\right),$ I=1 wherein, 2 ..., N;

Step 3 (three), the Relative Vibration between cutter and workpiece equivalence is simple harmonic oscillation, the equation of establishing its simple harmonic oscillation is: $Z_h\left(x\right)=\stackrel{\‾}{A}\sin \left(2\mathrm{\πfx}\right)---\left(5\right),$ Its discretization can be obtained: $Z_h\left(x_i\right)=\stackrel{\‾}{A}\sin \left(2\mathrm{\πf\Δx}(i-1)\right)---\left(6\right),$ △ x=1/40f wherein, i=1,2 ..., N, N=L/ △ x, then the surface roughness that causes of equivalent simple harmonic oscillation is: ${\mathrm{Ra}}_h=\frac{1}{N}\underset{i=1}{\overset{N}{\mathrm{\Σ}}}|Z_h\left(x_i\right)-\stackrel{\‾}{Z_h\left(x_i\right)}|---\left(7\right),$ The relative vibration equivalence is that two to vibrate the surface roughness that causes identical for the principle of simple harmonic oscillation between cutter and workpiece, i.e. Ra _h=Ra _m(8);

Equivalent amplitude is found the solution in step 3 (four), through type (4), (7) and (8)

Value,

Be in the actual processing amplitude information of Relative Vibration between cutter and workpiece;

Step 4, calculate expansion ratio, expansion ratio is the ratio that expands the height of the residual region after the effect and do not expand the residual region height of effect, namely

H in the formula _RiThe residual height of i tool margin after expanding effect on the finished surface, H _cThe theoretical residual height that does not expand the effect tool margin, i=1 wherein, 2 ..., n;

Step 5, calculate the contour curve expand finished surface after the effect, the height that expands tool margin residual region in the contour curve of finished surface after the effect is H _cSP;

Step 6, find corresponding equivalent amplitude by particular process material and the speed of mainshaft, thereby obtain the equivalent Relative Vibration curve between cutter, workpiece, the equivalent Relative Vibration curve between cutter, workpiece is:

Step 7, superpose and to obtain new surface outline curves expanding in the contour curve of finished surface after the effect and the step 6 equivalent Relative Vibration curve in the step 5 by matlab software, new curve is carried out data process and calculate surface roughness.

The invention has the beneficial effects as follows: the present invention extracts the Relative Vibration information of cutter and Tool Room from machined surface, and the impact of consideration bulking effect effects on surface roughness, the concept of expansion ratio is proposed, thereby Effective Raise the precision of prediction of surface roughness, the average forecasting error of Ra value is 5.1%.

Description of drawings

Fig. 1 extracts nose profile curve and data from machined surface, Fig. 2 is that (a represents to occur the finished surface after elasticity is recovered for the impact of bulking effect effects on surface roughness, b represents to occur the finished surface behind the Plastic Flow, c representation theory finished surface), Fig. 3 is the theoretical finished surface (amount of feeding of s-revolution, R-cutter radius of corner, Rt-is the residual height of tool margin ideally), Fig. 4 is the flow chart of Roughness Model, Fig. 5 is the ideal surfaced under the machined parameters among the embodiment one, Fig. 6 is the detection surface of NiP, Fig. 7 is the detection surface of Cu, Fig. 8 is to be 1000r/min in the speed of mainshaft, back engagement of the cutting edge is 2 μ m, under the different feed speeds, (dotted line is predicted value in the contrast of caluclate table surface roughness and real surface roughness, solid line is predicted value), Fig. 9 is to be 1000r/min in the speed of mainshaft, feed speed is 40mm/min, under different back engagement of the cutting edge, (dotted line is predicted value in the contrast of caluclate table surface roughness and real surface roughness, solid line is predicted value) Figure 10 is that to be radial diameter maximum place set up X as initial point for outermost take the processing work end face, (wherein A is cutting direction to the Z coordinate system, B is direction of feed, C is cutter, the workpiece Relative Vibration, D is workpiece, and E is diamond cutter).

The specific embodiment

The specific embodiment one: shown in Fig. 1-10, the establishment step of the described a kind of single-point diamond turning machined surface roughness Forecasting Methodology of present embodiment is as follows:

Step 1, choose typical workpiece for measurement material, change feeding rotating speed, the speed of mainshaft and back engagement of the cutting edge contrived experiment scheme, carry out in advance single-point diamond machining experiment at ultra-precision machine tool;

Step 2, the surface outline curves that adopts the prediction of contact pin type contourgraph to process typical workpiece for measurement;

Step 3, extract the process amplitude information of Relative Vibration between cutter and workpiece from the testing result of machined surface, the amplitude information of Relative Vibration obtains by the following method between described cutter and workpiece:

Step 3 (one), according to the surface outline curves and the data that detect, being radial diameter maximum place take the outermost of processing work end face sets up X, Z coordinate system as initial point, extract point of a knife and radially representing in the actual process Relative Vibration between cutter and workpiece with respect to the profile of workpiece in radially reflection, X-direction is the tool feeding direction, Z-direction is cutter cutting-in direction, and then radially the number of cutter profile is:

Wherein L is for radially detecting length, and s is the amount of feeding of cutter revolution, and the number that extracts data from the detection curve of machined surface also is N;

Coordinate is x on the X-axis of step 3 (two), extraction data _i=x ₁+ (i-1) △ x=x ₁+ (i-1) s(2), i=1 wherein, 2 ..., N, thus the point of a knife coordinate data that can obtain extracting is (x _i, Z _i(x _i)), the contour curve of Relative Vibration is between the cutter that extracts from machined surface and workpiece: Z _m(x _i)=Z _i(x _i)-min (Z _i(x _i)) (3), i=1 wherein, 2 ..., N-1, the surface roughness that the contour curve of above-mentioned Relative Vibration causes: ${\mathrm{Ra}}_m=\frac{1}{N}\underset{i=1}{\overset{N}{\mathrm{\Σ}}}|z_m\left(x_i\right)-\frac{\underset{i=1}{\overset{N}{\mathrm{\Σ}}}{Z}_m\left(x_i\right)}{N}|---\left(4\right),$ I=1 wherein, 2 ..., N;

Step 3 (three), the Relative Vibration between cutter and workpiece equivalence is simple harmonic oscillation, the equation of establishing its simple harmonic oscillation is: $Z_h\left(x\right)=\stackrel{\‾}{A}\sin \left(2\mathrm{\πfx}\right)---\left(5\right),$ Its discretization can be obtained: $Z_h\left(x_i\right)=\stackrel{\‾}{A}\sin \left(2\mathrm{\πf\Δx}(i-1)\right)---\left(6\right),$ △ x=1/40f wherein, i=1,2 ..., N, N=L/ △ x, then the surface roughness that causes of equivalent simple harmonic oscillation is: ${\mathrm{Ra}}_h=\frac{1}{N}\underset{i=1}{\overset{N}{\mathrm{\Σ}}}|Z_h\left(x_i\right)-\stackrel{\‾}{Z_h\left(x_i\right)}|---\left(7\right),$ The relative vibration equivalence is that two to vibrate the surface roughness that causes identical for the principle of simple harmonic oscillation between cutter and workpiece, i.e. Ra _h=Ra _m(8);

Equivalent amplitude is found the solution in step 3 (four), through type (4), (7) and (8)

Value,

Be in the actual processing amplitude information of Relative Vibration between cutter and workpiece;

Step 4, calculate expansion ratio, expansion ratio is the ratio that expands the height of the residual region after the effect and do not expand the residual region height of effect, namely

H in the formula _RiThe residual height of i tool margin after expanding effect on the finished surface, H _cThe theoretical residual height that does not expand the effect tool margin, i=1 wherein, 2 ..., n;

Step 5, calculate the contour curve expand finished surface after the effect, the height that expands tool margin residual region in the contour curve of finished surface after the effect is H _cSP;

Step 6, find corresponding equivalent amplitude by particular process material and the speed of mainshaft, thereby obtain the equivalent Relative Vibration curve between cutter, workpiece, the equivalent Relative Vibration curve between cutter, workpiece is:

Step 7, superpose and to obtain new surface outline curves expanding in the contour curve of finished surface after the effect and the step 6 equivalent Relative Vibration curve in the step 5 by matlab software, new curve is carried out data process and calculate surface roughness.

The software of matlab described in the present embodiment is main in the face of science is calculated, the high-tech computer software of visual and programming of interactive by U.S. mathworks company issue.

The specific embodiment two

Be 1000r/min at rotating speed, back engagement of the cutting edge 2 μ m, feed speed is under the condition of 25mm/min, for NiP, extracts the Relative Vibration amplitude information

Be 5nm, for Cu, extract the Relative Vibration amplitude information

Be 15nm, by $Z_h\left(x\right)=\stackrel{\‾}{A}\sin \left(2\mathrm{\πfx}\right)---\left(5\right)$ Calculate equivalent Relative Vibration;

Shown in Fig. 5-7, calculate expansion ratio SP, under this processing conditions, the expansion ratio SP of NiP is that the expansion ratio SP of 1.3, Cu is 0.65, calculates the contour curve that expands finished surface after the effect;

To expand the contour curve of finished surface after the effect and equivalent Relative Vibration by matlab software and superpose and carry out data and process can be calculated and predict the outcome, predict the outcome with actual result to such as Fig. 8 and Fig. 9;

Shown in Fig. 8-9, NiP and Cu process under the same conditions, identical lathe, identical cutter, identical machined parameters, different places are properties of materials, and actual processing result all has certain departing from for theoretical value, and main cause just is that bulking effect has changed the size of theoretical roughness of surface, under the identical condition, the surface roughness of NiP and Cu differs larger, and this shows in the Prediction of Surface Roughness method, must consider the impact of bulking effect.

Claims (1)

1. the Forecasting Methodology of a surface roughness in single-point diamond turning, it is characterized in that: the establishment step of the Forecasting Methodology of described a kind of surface roughness in single-point diamond turning is as follows:

Step 1, choose typical workpiece for measurement material, change feeding rotating speed, the speed of mainshaft and back engagement of the cutting edge contrived experiment scheme, carry out in advance single-point diamond machining experiment at ultra-precision machine tool;

Step 2, the surface outline curves that adopts the detection of contact pin type contourgraph to process typical workpiece for measurement;

Step 3, extract the process amplitude information of Relative Vibration between cutter and workpiece from the testing result of machined surface, the amplitude information of Relative Vibration obtains by the following method between described cutter and workpiece:

Step 3 (one), according to the surface outline curves and the data that detect, being radial diameter maximum place take the outermost of processing work end face sets up X, Z coordinate system as initial point, extract point of a knife and radially representing in the actual process Relative Vibration between cutter and workpiece with respect to the profile of workpiece in radially reflection, X-direction is the tool feeding direction, Z-direction is cutter cutting-in direction, and then radially the number of cutter profile is:

Wherein L is for radially detecting length, and s is the amount of feeding of cutter revolution, and the number that extracts data from the detection curve of machined surface also is N;

Coordinate is x on the X-axis of step 3 (two), extraction data _i=x ₁+ (i-1) Δ x=x ₁+ (i-1) s (2), i=1 wherein, 2 ..., N, thus the point of a knife coordinate data that can obtain extracting is (x _i, Z _i(x _i)), the contour curve of Relative Vibration is between the cutter that extracts from machined surface and workpiece: Z _m(x _i)=Z _i(x _i)-min (Z _i(x _i)) (3), i=1 wherein, 2 ..., N-l, the surface roughness that the contour curve of above-mentioned Relative Vibration causes:

I=1 wherein, 2 ..., N;

Step 3 (three), the Relative Vibration between cutter and workpiece equivalence is simple harmonic oscillation, the equation of establishing its simple harmonic oscillation is:

Its discretization can be obtained:

Δ x=1/40f wherein, f represents the frequency of simple harmonic oscillation, i=1,2 ..., N, N=L/ Δ x, then the surface roughness that causes of equivalent simple harmonic oscillation is:

The relative vibration equivalence is that two to vibrate the surface roughness that causes identical for the principle of simple harmonic oscillation between cutter and workpiece, i.e. Ra _h=Ra _m(8);

Equivalent amplitude is found the solution in step 3 (four), through type (4), (7) and (8)

Value,

Be in the actual processing amplitude information of Relative Vibration between cutter and workpiece;

Step 4, calculate expansion ratio, expansion ratio is the ratio that expands the height of the residual region after the effect and do not expand the residual region height of effect, namely

H in the formula _Ri, be the residual height of i tool margin after expanding effect on the finished surface, H _cThe theoretical residual height that does not expand the effect tool margin, i=1 wherein, 2,, n;

Step 5, calculate the contour curve expand finished surface after the effect, expand the height of tool margin residual region in the contour curve of finished surface after the effect for being H _cSP;

Step 6, find corresponding equivalent amplitude by particular process material and the speed of mainshaft, thereby obtain the equivalent Relative Vibration curve between cutter, workpiece, the equivalent Relative Vibration curve between cutter, workpiece is:

Step 7, superpose and to obtain new surface outline curves expanding in the contour curve of finished surface after the effect and the step 6 equivalent Relative Vibration curve in the step 5 by matlab software, new curve is carried out data process and calculate surface roughness.

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