CN101907876B

CN101907876B - Command point shaping, compressing and interpolating method suitable for numerical control device

Info

Publication number: CN101907876B
Application number: CN 201010185807
Authority: CN
Inventors: 于东; 张晓辉; 耿聪; 洪海涛; 郑飂默; 韩文业
Original assignee: SHENYANG HIGH-END COMPUTER NUMERICAL CONTROL TECHNOLOGY Co Ltd; Shenyang Institute of Computing Technology of CAS
Current assignee: Shenyang Zhongke Cnc Technology Co ltd
Priority date: 2010-05-28
Filing date: 2010-05-28
Publication date: 2012-01-04
Anticipated expiration: 2030-05-28
Also published as: CN101907876A

Abstract

The invention relates to a command point shaping, compressing and interpolating method suitable for a numerical control device. The method comprises the following steps of: inserting an arc which has a distance with the middle point of a tolerance set by the numerical control device and is tangential with segments of adjacent command points to the middle point of every three adjacent command points when a numerical control processing procedure judges that any three adjacent command points on a processed curve surface meet a continuous processing condition, wherein the tangential points are used as interpolation points; trimming the interpolation points to reduce calculation errors and rounding errors in the process of reckoning the interpolation points; selecting a characteristic interpolation point through judging the bending directions of processing paths of all the interpolation points; fitting by using a continuous polynomial spline curve with a second derivative to generate a smooth curve; approximately calculating the interpolation points of a current interpolation period and sending the positions of the interpolation points to a servo system of the numerical control device; and driving a servo motor to move. The invention furthest improves the processing efficiency and reduces the influences of the calculation errors and the rounding errors on the processing precision and the processed surface smoothness.

Description

Instruction point shaping, compressing and interpolating method suitable for numerical control device

Technical Field

The invention relates to a numerical control machining technology of a complex molded surface, in particular to an instruction point shaping, compressing and interpolating method suitable for a numerical control device.

Background

Complex surfaces are widely used in the design of mold cavities, automotive coverings and aerospace components, however, high speed, high precision and high surface quality machining of complex surfaces has been a difficult point of research. In the numerical control machining, in order to mill a complete complex surface and detect collision in real time, a cam (computed tomography) system generally uses a large number of micro-planes to approximate the complex surface generated by the design of a cad (computer aided design) system, as shown in fig. 1, and covers the polyhedrons with a series of tool paths within a specific tolerance range, so as to finally generate a numerical control machining program consisting of a large number of command points.

When the numerical control device adopts a traditional interpolation method, namely interpolation is carried out on a straight line segment formed by adjacent instruction points, frequent jump of acceleration and extension of processing time are inevitably caused. In addition, in the conventional interpolation method, the command points obtained by the numerical control device are all assumed to be exactly located on the tool path curve (hereinafter, referred to as a desired curve) desired by the CAM system, and are processed. In practice, however, in order for a CAM system to increase the step size and avoid successive over-or under-cut points, the command points typically are not all exactly on the desired tool path curve, but rather are within the inner and outer tolerance bands of the desired curve, as shown in FIG. 2. In addition, the CAM system has a calculation error and a rounding error in the process of generating the instruction point, so that the high-speed and high-precision machining of a complex profile is difficult to realize by adopting the conventional interpolation method.

Disclosure of Invention

Aiming at the problem that the prior art cannot meet the high-speed and high-precision machining requirements of a complex profile, the invention aims to provide the instruction point shaping, compressing and interpolating method which is high in machining efficiency and machining precision and is suitable for the numerical control device.

In order to solve the technical problems, the invention adopts the technical scheme that:

the invention relates to an instruction point shaping, compressing and interpolating method suitable for a numerical control device, which comprises the following steps of:

identification of continuous tiny line segment processing area: judging whether any three adjacent instruction points on the processed curved surface meet continuous processing conditions according to the read numerical control processing program;

estimation of interpolation point: when any adjacent three instruction points on the processed curved surface meet the continuous processing condition, inserting an arc which has a distance with the middle point which is a set tolerance of the numerical control device and is tangent with a line segment between the adjacent instruction points into the middle point of every adjacent three instruction points, wherein the tangent point is used as an interpolation point which is closer to the expected curve than the instruction point;

trimming of interpolation points: trimming the interpolation points obtained in the steps to reduce the calculation error and the rounding error in the interpolation point presumption process and enable the processing path to be smoother;

selecting characteristic interpolation points: selecting characteristic interpolation points by judging the bending direction of the processing path at each interpolation point of the processing path;

fitting of spline curve: fitting a continuous polynomial spline curve having a second derivative to the characteristic interpolation points to generate a smooth curve;

interpolation of spline curve: and (4) approximately calculating the interpolation point of the current interpolation period on the smooth curve, and sending the position of the interpolation point to a servo system of the numerical control device to drive a servo motor to move.

The method for judging whether any three adjacent instruction points on the processed curved surface meet the continuous processing condition adopts a double-chord high error method, which specifically comprises the following steps:

calculating the distance between any three adjacent instruction points on the processed curved surface;

calculating the double-chord height error according to the arc segment and the distance between the adjacent command points;

if the calculated double-chord height error is smaller than the maximum chord height error set by the numerical control device, the three instruction points meet continuous processing conditions;

and if the calculated double-chord height error is not smaller than the maximum chord height error set by the numerical control device, the continuous processing conditions are not satisfied among the three instruction points.

And (3) trimming the interpolation point by adopting a least square method, wherein the formula is as follows:

wherein:

Q_i(u)＝a_iu³+b_iu²+c_iu+d_i (u_i≤u≤u_i+4) (5)

a_i、b_i、c_i、d_ifor successive interpolation points Q_i、Q_i+1、Q_i+2、Q_i+3And Q_i+4Curve Q obtained by fitting with least squares penalty_iCoefficient vector of (u), u_iAnd u_i+4Are respectively interpolated points Q_iAnd Q_i+4Corresponding parameter value, O_kIs an interpolation point O_kThe corrected value.

The selection process of the characteristic interpolation point comprises the following steps:

marking the initial interpolation point O₁For the characteristic interpolation point in the current continuous tiny line segment processing area, and calculating the initial interpolation point O₁And an interpolation point O adjacent thereto₂Is processed to a pilot vector O'₁And O'₂Cross product between to obtain vector v₁₂；

Judging the subscript j of the interpolation point to be calculated and the number n of the interpolation points, if j is less than n, calculating the interpolation point O_j-1And O_jIs processed to a pilot vector O'_j-1And O'_jCross product between to obtain vector v_j-1j；

Calculating the vector v_j-2j-1And v_j-1jAngle alpha therebetween_jIf α is_jIf j is less than 90 degrees, j is j +1, and the size step of judging the subscript j of the interpolation point to be calculated currently and the number n of the interpolation points is carried out;

if α is_jNot less than 90 DEG, an interpolation point O is marked_jAs a characteristic interpolation point, j is j +1, and interpolation point O is set as_j-1As a new initial interpolation point, switching to a step of marking the initial interpolation point O1 as a characteristic interpolation point in the processed curved surface meeting the continuous processing condition;

if j is n, mark point O_jFor the feature interpolation point, the feature interpolation point selection is ended.

The method also comprises a machining precision control step between the spline curve fitting step and the spline curve interpolation step, and the process is as follows:

inputting interpolation points between two adjacent characteristic interpolation points and a spline curve formed by fitting;

calculating an interpolation point O between two adjacent characteristic interpolation points_mThe distance L between the corresponding spline curve is not greater than the distance L of the numerical control systemWhen the maximum profile deviation is set, the spline curve is explained at the interpolation point O_mThe requirement of processing precision is met;

taking and interpolating point O_mAdjacent next interpolation point O_m+1Judging whether all interpolation points are completely taken;

if all the interpolation points are taken out, judging all the interpolation points O_m+1Whether the requirements of machining precision are met;

if the distance L does not meet the machining precision requirement, finding out an interpolation point O corresponding to the maximum value in the distance L_sTaking the interpolation point as a new characteristic interpolation point between the two adjacent characteristic interpolation points;

fitting a new spline curve by using the new characteristic interpolation points to replace the original spline curve, and continuously inputting interpolation points between two adjacent characteristic interpolation points and the spline curve to be synthesized;

if the interpolation points are not completely taken, the calculation is switched to the calculation of the interpolation point O between two adjacent characteristic interpolation points_mA distance L step from the corresponding spline curve;

when L is larger than the maximum contour deviation preset by the numerical control system, the spline curve is shown at the interpolation point O_mIf the position does not meet the machining precision requirement, recording the serial number of the current interpolation point and the distance from the current interpolation point to the spline curve, and continuously taking the interpolation point O_mAdjacent next interpolation point O_m+1And (5) carrying out the following steps.

The invention has the following beneficial effects and advantages:

1. the processing efficiency is high. The calculation of the interpolation points of the method is carried out on the smooth curve, so that the switching speed between the adjacent interpolation points is greatly improved, the time required by processing is greatly shortened, and the processing efficiency is improved to the maximum extent.

2. The processing precision is high. The method of the present invention can reduce the influence of the tolerance between the command point and the desired curve on the machining accuracy by presuming the interpolation point closer to the desired curve than the command point, and can reduce the influence of the calculation error and the rounding error on the machining accuracy and the machined surface finish by trimming the interpolation point.

3. The surface processing quality is high. The method can fit the instruction points in the continuous tiny line segment processing area into a smooth curve with C2 continuity, thereby eliminating the break angle between adjacent line segments and improving the processing quality of the surface of the workpiece.

Drawings

FIG. 1 is a schematic diagram illustrating the conversion of an original curved surface and an approximate curved surface in the prior art;

FIG. 2 is a diagram illustrating a desired curve and internal and external tolerances in the prior art;

FIG. 3 is a flow chart of the method of the present invention;

FIG. 4 is a schematic diagram of double chord height error determination;

FIG. 5 is a schematic diagram of interpolation point estimation;

FIG. 6 is a schematic diagram illustrating interpolation point crossing;

FIG. 7 is a diagram of feature interpolation point selection;

FIG. 8 is a flow chart of a feature interpolation point selection process;

FIG. 9 is a schematic radial plot of a fit of feature interpolated points;

FIG. 10 is a flow chart of machining accuracy control;

FIG. 11 is a path diagram of a curved surface to be processed;

FIG. 12a is a velocity map of a process using a conventional interpolation method;

FIG. 12b is a velocity map of a process using a smooth interpolation algorithm;

FIG. 12c is a graph of processing speed using the method of the present invention;

FIG. 13a is a comparison of a conventional interpolation method with an original model;

FIG. 13b is a comparison of the original model with the smooth interpolation algorithm;

FIG. 13c is a graph comparing the method of the present invention with the original model;

FIG. 14a is a diagram illustrating the surface effect of a sample machined by a conventional interpolation method;

FIG. 14b is a drawing of the effect of the machined surface of the sample using the smooth interpolation algorithm;

FIG. 14c is a diagram showing the surface effect of the sample workpiece processed by the method of the present invention.

Detailed Description

The method of the present invention will be described in further detail with reference to the accompanying drawings.

As shown in fig. 3, the command point shaping, compressing and interpolating method for a numerical control device according to the present invention includes the steps of:

fitting of spline curve: fitting the n characteristic interpolation points by using an n-1 section polynomial spline curve with continuous second derivative to generate a smooth curve;

Step one, the specific process of analyzing the processing path is as follows:

for a given numerical control machining program, whether continuous machining conditions are met between any three adjacent instruction points is judged through a double-chord height error method, and therefore the instruction points in the numerical control machining program are divided into a discontinuous micro-line segment machining area and a continuous micro-line segment machining area. As shown in FIG. 4, for three instruction points P in arbitrary order_i-1、P_iAnd P_i+1，L_i-1iAnd L_ii+1Are respectively an instruction point P_i-1And P_iAnd P_iAnd P_i+1Distance between, δ₁And delta₂Are respectively over-command points P_i-1、P_iAnd P_i+1Arc segment and line segment P_i-1P_iAnd P_iP_i+1The generated double chord height error is R which is three command points P_i-1、P_iAnd P_i+1The radius of the determined circle is determined,

is three instruction points P_i-1、P_iAnd P_i+1Two command points P on the determined circle_i-1、P_iHalf of the central angle corresponding to the middle minor arc,

is three instruction points P_i-1、P_iAnd P_i+1Two command points P on the determined circle_i、P_i+1Half of central angle corresponding to middle minor arc, theta is vector

Andthe included angle therebetween. The value can be calculated by the following formula:

if the calculated double chord height error delta₁And delta₂Are all smaller than the maximum chord height error delta set by the numerical control device_cmaxThen, the instruction point P is described_i-1、P_iAnd P_i+1The continuous processing condition is met; if the calculated double chord height error delta₁And delta₂One is larger than the maximum chord height error delta set by the numerical control device_cmaxThen, the instruction point P is described_i-1、P_iAnd P_i+1The condition of continuous processing is not satisfied. Therefore, the instruction points in the numerical control machining program can be divided into a discontinuous micro-line segment machining area and a continuous micro-line segment machining area by judging every three adjacent instruction points.

Step two, the specific process of estimating the interpolation point is as follows:

for any one continuous micro-line segment processing area, at the middle point formed by continuous three instruction points, an arc which has a tolerance set for the numerical control system and is tangent to two line segments with the adjacent instruction points is inserted to estimate an interpolation point which is closer to the expected curve than the instruction point. As shown in fig. 5, from the instruction point P_i-1、P_iAnd P_i+1Two adjacent small line segments P_i-1P_iAnd P_iP_i+1At the corner of which a distance corner command point P is inserted_iTo a tolerance delta_tmaxSize and line segment P_i-1P_iAnd P_iP_i+1Tangent to point Q_iAnd Q_i+1After the arc, the following equation can be obtained according to the geometrical knowledge:

wherein L is a tangent point and an instruction point P_iBeta is a vector of

Andthe included angle therebetween. Under the condition that the set tolerance of the numerical control system is certain, the tangent point Q can be found by combining the graph 2 and the graph 5_iAnd Q_i+1Ratio instruction point P_iCloser to the desired curve. Therefore, after the numerical control system sets the tolerance, the point Q can be taken off_iAnd Q_i+1As a point of instruction P_iThe corresponding interpolation point. At this time, tangent point Q_iAnd Q_i+1The coordinates of (a) can be written as:

\{\begin{matrix} Q_{i} = \frac{L}{L_{i - 1 i}} P_{i - 1} + \frac{L_{i - 1 i} - L}{L_{i - 1 i}} P_{i} \\ Q_{i + 1} = \frac{L_{ii + 1} - L}{L_{ii + 1}} P_{i} + \frac{L}{L_{ii + 1}} P_{i + 1} \end{matrix} - - - (3)

wherein L is_i-1iAnd L_ii+1Are respectively line segment P_i-1P_iAnd P_iP_i+1Length of (2)And a point P of instruction_i-1、P_iAnd P_i+1The coordinates of (a) can be obtained from a numerical control machining program. As shown in FIG. 6, to prevent the intersection of the interpolation points corresponding to the adjacent command points due to the too short line segment, the tangent point and the command point P_iThe distance L between the adjacent line segments should be constrained by the length of the adjacent line segments, in addition to the tolerance set by the system:

at this time, the interpolation point corresponding to each of the remaining instruction points except the first and last instruction points in the continuous minute line segment processing area can be calculated by the above-described method, and the first and last instruction points can take themselves as the interpolation points corresponding thereto.

Step three, the trimming of the interpolation point specifically comprises the following steps:

the interpolation points are estimated from the tolerances set by the command points and numerical control system, and therefore, the distance from each interpolation point to a desired curve is much larger than the distances from other interpolation points to desired curves. Therefore, it is obviously undesirable to generate a smooth curve machining path directly by fitting the interpolated points. In order to reduce the calculation error and rounding error in the interpolation point estimation process and to make the curve fitted to the interpolation points smoother, the present embodiment uses a least square method based on cubic polynomial to trim every five consecutive interpolation points.

Before trimming the interpolation points, each interpolation point needs to be parameterized to ensure that each interpolation point has a corresponding parameter value. In order to enable the parameter value corresponding to each interpolation point to reflect the turning condition of the line segment formed by the interpolation points, the method adopts a centripetal parameterization method to parameterize the interpolation points.

After parameterizing each interpolation point, take u³，u²U, 1 as a set of orthogonal basis functions of a cubic polynomial space, at which arbitrary five successive interpolation points Q are present_i、Q_i+1、Q_i+2、Q_i+3And Q_i+4Fitted curve Q between_i(u) can be written as:

Q_i(u)＝a_iu³+b_iu²+c_iu+d_i(u_i≤u≤u_i+4) (5)

wherein a is_i、b_i、c_i、d_iIs a fitted curve Q_iCoefficient vector of (u) (vector dimension is same as number of motion axes), u_iAnd u_i+4Interpolation of points Q_iAnd Q_i+4The corresponding parameter value. At this time, the point Q is interpolated_i、Q_i+1、Q_i+2、Q_i+3、Q_i+4To Q_iHaving a parameter value u on (u)_i、u_i+1、u_i+2、u_i+3、u_i+4Point Q of_i(u_i)、Q_i(u_i+1)、Q_i(u_i+2)、Q_i(u_i+3) The sum of the squares Ji of the distances between can be written as:

wherein,

in the formula, Q_ix(u_k)、Q_iy(u_k)、Q_ix(u_k) Are respectively Q_iHaving a parameter value u on (u)_kPoint Q of_i(u_k) Coordinate values in the X, Y, Z directions, X_k、Y_k、Z_kAre respectively interpolated points Q_kCoordinate values in the X, Y, Z directions, J_ix、J_iy、J_izAre respectively interpolated points Q_i、Q_i+1、Q_i+2、Q_i+3、Q_i+4To curve with parameter value u_i、u_i+1、u_i+2、u_i+3、u_i+4Point Q of_i(u_i)、Q_i(u_i+1)、Q_i(u_i+2)、Q_i(u_i+3) The sum of the squares of the distances in the X, Y, Z directions. It can be found from equations (6) and (7) that J is to be expressed_iTo minimize, J should be_ix、J_iyAnd J_izAre all minimal. To this end, J_ix、J_iyAnd J_izThe partial derivatives of (c) must satisfy the following condition:

<math><mrow> <mfenced open='{' close=''> <mtable> <mtr> <mtd> <mfrac> <msub> <mrow> <mo>&PartialD;</mo> <mi>J</mi> </mrow> <mi>ix</mi> </msub> <msub> <mrow> <mo>&PartialD;</mo> <mi>a</mi> </mrow> <mi>ix</mi> </msub> </mfrac> <mo>=</mo> <mfrac> <msub> <mrow> <mo>&PartialD;</mo> <mi>J</mi> </mrow> <mi>ix</mi> </msub> <msub> <mrow> <mo>&PartialD;</mo> <mi>b</mi> </mrow> <mi>ix</mi> </msub> </mfrac> <mo>=</mo> <mfrac> <msub> <mrow> <mo>&PartialD;</mo> <mi>J</mi> </mrow> <mi>ix</mi> </msub> <msub> <mrow> <mo>&PartialD;</mo> <mi>c</mi> </mrow> <mi>ix</mi> </msub> </mfrac> <mo>=</mo> <mfrac> <msub> <mrow> <mo>&PartialD;</mo> <mi>J</mi> </mrow> <mi>ix</mi> </msub> <msub> <mrow> <mo>&PartialD;</mo> <mi>d</mi> </mrow> <mi>ix</mi> </msub> </mfrac> <mo>=</mo> <mn>0</mn> </mtd> </mtr> <mtr> <mtd> <mfrac> <msub> <mrow> <mo>&PartialD;</mo> <mi>J</mi> </mrow> <mi>iy</mi> </msub> <msub> <mrow> <mo>&PartialD;</mo> <mi>a</mi> </mrow> <mi>iy</mi> </msub> </mfrac> <mo>=</mo> <mfrac> <msub> <mrow> <mo>&PartialD;</mo> <mi>J</mi> </mrow> <mi>iy</mi> </msub> <msub> <mrow> <mo>&PartialD;</mo> <mi>b</mi> </mrow> <mi>iy</mi> </msub> </mfrac> <mo>=</mo> <mfrac> <msub> <mrow> <mo>&PartialD;</mo> <mi>J</mi> </mrow> <mi>iy</mi> </msub> <msub> <mrow> <mo>&PartialD;</mo> <mi>c</mi> </mrow> <mi>iy</mi> </msub> </mfrac> <mo>=</mo> <mfrac> <msub> <mrow> <mo>&PartialD;</mo> <mi>J</mi> </mrow> <mi>iy</mi> </msub> <msub> <mrow> <mo>&PartialD;</mo> <mi>d</mi> </mrow> <mi>iy</mi> </msub> </mfrac> <mo>=</mo> <mn>0</mn> </mtd> </mtr> <mtr> <mtd> <mfrac> <msub> <mrow> <mo>&PartialD;</mo> <mi>J</mi> </mrow> <mi>iz</mi> </msub> <msub> <mrow> <mo>&PartialD;</mo> <mi>a</mi> </mrow> <mi>iz</mi> </msub> </mfrac> <mo>=</mo> <mfrac> <msub> <mrow> <mo>&PartialD;</mo> <mi>J</mi> </mrow> <mi>iz</mi> </msub> <msub> <mrow> <mo>&PartialD;</mo> <mi>b</mi> </mrow> <mi>iz</mi> </msub> </mfrac> <mo>=</mo> <mfrac> <msub> <mrow> <mo>&PartialD;</mo> <mi>J</mi> </mrow> <mi>iz</mi> </msub> <msub> <mrow> <mo>&PartialD;</mo> <mi>c</mi> </mrow> <mi>iz</mi> </msub> </mfrac> <mo>=</mo> <mfrac> <msub> <mrow> <mo>&PartialD;</mo> <mi>J</mi> </mrow> <mi>iz</mi> </msub> <msub> <mrow> <mo>&PartialD;</mo> <mi>d</mi> </mrow> <mi>iz</mi> </msub> </mfrac> <mo>=</mo> <mn>0</mn> </mtd> </mtr> </mtable> </mfenced> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>8</mn> <mo>)</mo> </mrow> </mrow></math>

interpolating point Q_i、Q_i+1、Q_i+2、Q_i+3And Q_i+4And a parameter value u corresponding to the coordinate value_i、u_i+1、u_i+2、u_i+3And u_i+4After substituting equation (8), the calculation is performedCurve Q_i(u) coefficient vectors in the X, Y and Z directions, respectively. In calculating Q_iAfter the expression (u), there is a parameter value u_i、u_i+1、u_i+2、u_i+3And u_i+4And the first and second derivatives at that point can be written as:

in the formula, O_kIs an interpolation point O_kThe corrected value. If there are n interpolation points in the current continuous tiny line segment processing area, divide the first three interpolation points Q₁、Q₂、Q₃And the last three interpolation points q_n-2、Q_n-1Q_nThe trimmed new interpolation point and the first and second derivative vectors at the point need to be considered separately, and the trimmed new interpolation points and the first and second derivative vectors at the point of the rest interpolation points can be taken as the average values of the point with the parameter value corresponding to the interpolation point and the first and second derivative vectors at the point on the middle three of the five curves approximating the interpolation point.

Step four, selecting the characteristic interpolation points specifically comprises the following steps:

for the same continuous tiny line segment processing area, if the processing path designated by a plurality of interpolation points is bent along the same direction, the requirement of processing precision can be met only by an expected curve formed by fitting the geometric information of the first and last interpolation points of the processing path. Therefore, for the purpose of compressing the number of interpolation points and reducing the number of times of fitting, it is possible to find an interpolation point where the bending direction of the processing path changes in advance before fitting the interpolation points, and define such an interpolation point as a characteristic interpolation point.

As shown in fig. 7 and 8, n corrected interpolation point values O₁、O₂...、O_n-1And O_nAnd finding out a characteristic interpolation point where the bending direction of the processing path changes by the constructed continuous tiny line segment processing area through the following steps:

(1) marking the initial interpolation point O₁For the characteristic interpolation point in the current continuous tiny line segment processing area, and calculating the initial interpolation point O₁And an interpolation point O adjacent thereto₂Is processed to a pilot vector O'₁And O'₂Cross product between to obtain vector v₁₂；

(2) Judging the subscript j of the interpolation point to be calculated and the number n of the interpolation points, if j is less than n, calculating the interpolation point O_j-1And O_jIs processed to a pilot vector O'_j-1And O'_jCross product between to obtain vector v_j-1j；

(3) Calculating the vector v_j-2j-1And v_j-1jAngle alpha therebetween_jIf α is_jIf j is less than 90 degrees, j is j +1, and the step (2) is carried out to judge the size of the subscript j of the interpolation point to be calculated currently and the number n of the interpolation points;

(4) if α is_jNot less than 90 DEG, an interpolation point O is marked_jAs a characteristic interpolation point, j is j +1, and interpolation point O is set as_j-1As a new initial interpolation point, go to step (1) to mark the initial interpolation point O₁Characteristic interpolation points in the processed curved surface which meet continuous processing conditions;

(5) if j is n, mark point O_jFor the feature interpolation point, the feature interpolation point selection is ended.

Step five, the fitting process of the characteristic interpolation points is as follows:

for N characteristic interpolation points in any continuous tiny line segment processing area, fitting can be carried out by using an N-1-segment quintic polynomial spline curve with continuous second derivative so as to achieve the purpose of generating a smooth curve. As shown in FIG. 9, the point O is interpolated for any two adjacent features_iAnd O_jBetween them by an interpolated point O_i+1、...、O_j-1Specified broken lineMachining path and passing feature interpolation point O_iAnd O_jSmooth curve O formed by fitting geometric information_k(u) wherein the curve O is smoothed_kThe expression of (u) can be written as:

O_k(u)＝A_ku⁵+B_ku⁴+C_ku³+D_ku²+E_ku+F_k(u∈[u_i，u_j]) (10)

wherein A is_k、B_k、C_k、D_k、E_kAnd F_kIs O_kCoefficient vector of (u) (vector dimension equals number of motion axes), u_iAnd u_jRespectively being characteristic interpolation points O_iAnd O_jThe corresponding parameter value. O is_k(u) there are 6 coefficient vectors, so 6 boundary conditions are needed to determine these coefficient vectors. To ensure O_k(u) passing the characteristic interpolation point O_iAnd O_jAnd satisfies C2 continuity with adjacent curves at the characteristic interpolation point, optionally the characteristic interpolation point O_iAnd O_jThe coordinate value and the first and second lead vectors are used as a spline curve O_k(u) boundary conditions, these boundary conditions being taken into O_k(u) the following equation is obtained:

interpolating features by a point O_iAnd O_jCoordinate value of (d), corresponding parameter value u_iAnd u_jAnd a calculated first derivative vector O'_iAnd O'_jAnd a second derivative vector O ″)_iAnd O ″)_jWith the formula (11), the spline curve O can be calculated_kCoefficient of (u).

Step six, the calculation of the interpolation points comprises the following specific processes:

for the fitted curve O (u), a second-order Taylor expansion method is adopted to approximately calculate a parameter value u corresponding to the interpolation point of the ith interpolation period_iAt this time u_iThe formula of (c) can be expressed by the following formula:

wherein u is_i-1The parameter value corresponding to the interpolation point of the i-1 th interpolation period, T is the interpolation period of the numerical control system, V_i-1And A_i-1The machining speed and acceleration, O' (u), planned for the i-1 th interpolation period, respectively_i-1) And O' (u)_i-1) Are each O (u) at u_i-1The first and second derivative vectors of (c) can be calculated by their expressions. Introducing the planned processing speed and accelerationThe formula (12) can calculate the parameter value corresponding to the interpolation point of the current interpolation period, and the calculated parameter value is substituted into the expression of the expected curve to obtain the interpolation point of the current interpolation period.

In order to improve the processing precision, the method of the invention designs a processing precision control step between the step 5) and the step 6), and the specific process is as follows:

the method judges whether the spline curve formed by fitting meets the requirement of machining precision at the interpolation point by calculating the distance between the interpolation point and the corresponding curve point (the point of the expected curve with the parameter value corresponding to the interpolation point) in real time. And for the interpolation points which do not meet the machining precision requirement, the curve segment shape of the spline curve at the interpolation points is adjusted by adding new characteristic interpolation points, so that the fitted spline curve meets the machining precision requirement at all the interpolation points.

Interpolation points O for two adjacent features shown in FIG. 9_iAnd O_jThe processing precision of the spline curve at the interpolation point can be controlled by the following process, and the specific flow is shown in fig. 10:

(1) calculating a characteristic interpolation point O_iAnd O_jInterpolation point O between_m(m starting from i + 1) to the corresponding spline O_k(u_m) A distance L between u_mIs an interpolation point O_mThe corresponding parameter value. When L is less than or equal to e_maxWhen (e)_maxThe maximum profile deviation preset for the system) is transferred to the process (2); when L > e_maxWhen the process is finished, the process (3) is switched to;

(2)L≤e_maxillustrates a spline curve O_k(u) at the interpolation point O_mMeets the requirement of processing precision. Judging the sizes of m and j, if m is less than j, describing the characteristic interpolation point O_iAnd O_jIf all interpolation points between the m and the m are not judged completely, adding 1 to the m and then switching to the process (1); if m is j, the characteristic interpolation point O is described_iAnd O_jAfter all interpolation points are judged, the process is switched to the process (4);

(3)L＞e_maxdescription curve segment O_k(u) at the interpolation point O_mThe processing precision requirement is not met. And recording the value of m and the distance L, and judging the sizes of m and j. If m < j, the characteristic interpolation point O is specified_iAnd O_jIf all interpolation points between the m and the m are not judged completely, adding 1 to the m and then switching to the process (1); if m is j, the characteristic interpolation point O is described_iAnd O_jAfter all interpolation points are judged, the process is switched to the process (4);

(4) and judging whether an m value is recorded. If no m value is recorded, curve segment O is illustrated_k(u) at a characteristic interpolation point O_iAnd O_jAll the interpolation points between the two points meet the requirement of the processing precision, and the processing precision control is finished; if m is recorded, the curve segment O is illustrated_k(u) at a characteristic interpolation point O_iAnd O_jFinding out the interpolation point O corresponding to the maximum value in L when the interpolation point does not meet the processing precision_s(and curve segment O)_k(u) interpolation point farthest away) and takes the interpolation point as a characteristic interpolation point O_iAnd O_jInterpolating points with new features, and going to the process (5);

(5) by interpolation of points O by features_iAnd O_sAnd O_sAnd O_jFitting a new spline curve O_s-1(u) and O_s(u) instead of O_k(u) as a characteristic interpolation point O_iAnd O_jThe new curve segment is formed, and the machining precision control is carried out again according to the process until the characteristic interpolation point O_iAnd O_jThe curve segment between meets the machining precision requirement at all the interpolation points.

The invention has the following execution effects:

the executing mechanism of the method adopts an Anduan Mechatolin-III bus and a sigma-2 servo and motor, the control machine tool is a three-axis numerical control milling machine, and the main parameters of the device are as follows:

CPU Pentium M-1.6GHz memory 512M hard disk 40G

The feed rate F is 3000m/min

Interpolation period T1 ms

Maximum acceleration A_max＝500mm/s^-2

Chord height error delta_cmax＝0.01mm

Tolerance delta_tmax＝0.01mm

Error of contour e_max＝0.01mm

In order to verify the effectiveness of the method, the complex profile shown in fig. 11 is actually processed by respectively adopting a traditional interpolation method, a smooth interpolation algorithm and the method, a processing path is generated by CAD/CAM software UG under the condition that the internal and external tolerance is set to be 0.03mm, as shown in fig. 11, and comparison and analysis are respectively carried out on the processing speed, the processing precision and the surface processing quality. Fig. 12a, 12b, and 12c show comparison graphs of the processing speeds of the above three methods, and fig. 13a, 13b, and 13c show comparison graphs of interpolation points and original models generated in the actual processing process of the above three methods; FIGS. 14a, 14b, and 14c are comparative graphs showing the machined surfaces of the sample pieces in the above three methods.

From the three figures above, it can be seen that:

1. compared with the traditional interpolation method, the method can greatly reduce the time required by the complex profile processing, and the processing time required by adopting the text algorithm and the smooth interpolation algorithm is not greatly different, as shown in fig. 12a, 12b and 12 c. The invention is mainly characterized in that when the method and the smooth interpolation algorithm are adopted, the calculation of interpolation points is carried out on a smooth curve, so that the switching speed between adjacent interpolation points is greatly improved, and the time required by processing is greatly shortened.

2. Compared with the traditional interpolation method and the smooth interpolation algorithm, the method can greatly reduce the number of over-cut points and under-cut points, as shown in fig. 13a, 13b and 13c, wherein the points with darker color gray levels are the over-cut points, and the points with lighter color gray levels are the under-cut points, and can effectively eliminate break angles between adjacent line segments and make the processed surface smoother, as shown in fig. 14a, 14b and 14 c. This is because the method generates a smooth curve by fitting an interpolation point closer to the CAM expected curve than the command point, thereby reducing the influence of the deviation between the command point and the expected curve on the machining accuracy and improving the workpiece surface machining accuracy.

Claims

1. A command point shaping, compressing and interpolating method suitable for a numerical control device is characterized by comprising the following steps:

estimation of interpolation point: when any three instruction points on the processed curved surface meet the continuous processing condition, inserting an arc which has a distance with the middle point which is a set tolerance of the numerical control device and is tangent with a line segment between the adjacent instruction points into the middle point of every adjacent three instruction points, wherein the tangent point is an interpolation point which is closer to the expected curve than the instruction point;

trimming of interpolation points: trimming the interpolation points obtained in the steps, reducing calculation errors and rounding errors in the interpolation point presumption process, and enabling the machining path to be smoother;

interpolation of spline curve: calculating the interpolation point of the current interpolation period approximately to the smooth curve, and sending the position of the interpolation point to a servo system of the numerical control device to drive a servo motor to move;

the method for judging whether any three adjacent instruction points on the processed curved surface meet the continuous processing condition or not adopts a double-chord height error method, which specifically comprises the following steps:

if the calculated double-chord height error is not smaller than the maximum chord height error set by the numerical control device, the three instruction points meet continuous processing conditions;

wherein:

Q_i(u)＝a_iu³+b_iu²+c_iu+d_i(u_i≤u≤u_i+4) (5)

a_i、b_i、c_i、d_ifor successive interpolation points Q_i、Q_i+1、Q_i+2、Q_i+3And Q_i+4Curve Q obtained by fitting_iCoefficient vector of (u), u_iAnd u_i+4Are respectively interpolated points Q_iAnd Q_i+4Corresponding parameter value, O_kTo an interpolation point Q_kA corrected value;

marking the initial interpolation point O₁For the characteristic interpolation point in the current continuous tiny line segment processing area, and calculating the initial interpolation point O₁And always adjacent interpolation point O₂Is processed to a pilot vector O'₁And O'₂Cross product between to obtain vector v₁₂；

Judging the subscript of the interpolation point to be calculated at present as j and the number n of the interpolation points, if j is less than n, calculating the interpolation point O_j-1And O_jIs processed to a pilot vector O'_j-1And O'_jCross product between to obtain vector v_j-1j；

if α is_jNot less than 90 DEG, an interpolation point O is marked_jAs a characteristic interpolation point, j is j +1, and interpolation point O is set as_j-1As a new initial interpolation point, the mark is shifted to the initial interpolation point O₁Interpolating points for the features in the processed curved surface satisfying the continuous processing conditions;

2. The command point shaping, compressing and interpolating method for a numerical control device as set forth in claim 1, wherein: the method also comprises a machining precision control step between the kernel of the spline curve and the interpolation step of the spline curve, and the process is as follows:

calculating an interpolation point O between two adjacent characteristic interpolation points_mThe distance between the point and the corresponding spline curve is L, and when L is not more than the maximum contour deviation preset by the numerical control system, the interpolation point O with the spline curve is indicated_mThe requirement of processing precision is met;

if all the interpolation points are taken out, judging all the next interpolation points O_m+1Whether the requirements of machining precision are met;

and fitting a new spline curve by using the new characteristic interpolation points to replace the original spline curve, and continuously inputting interpolation points between two adjacent characteristic interpolation points and the spline curve formed by fitting.

3. The command point shaping, compressing and interpolating method for a numerical control device as set forth in claim 2, wherein: if the interpolation points are not completely taken, the calculation is switched to the calculation of the interpolation point O between two adjacent characteristic interpolation points_mAnd L, distance between the corresponding spline curves.

4. The command point shaping, compressing and interpolating method for a numerical control device as set forth in claim 2, wherein:

when L is larger than the maximum profile difference preset by the numerical control system, the spline curve is shown at the interpolation point O_mIf the position does not meet the machining precision requirement, recording the serial number of the current interpolation point and the distance from the current interpolation point to the spline curve, and continuously taking the interpolation point O_mAdjacent next interpolation point O_m+1And (5) carrying out the following steps.