CN103801982A - Error-control-based smooth interpolation method for five-axis NC (numerical control) system - Google Patents

Abstract

The invention relates to a five-axis machining technology in the technical field of NC (numerical control), in particular to an error-control-based smooth interpolation method for a five-axis NC system. According to the method, a rotary shaft of the five-axis NC system is interpolated in a tool vector interpolation mode based on detection of singular points; a linear shaft of the five-axis NC system is interpolated in a linear interpolation mode based on the ideal trajectory of cutter location points. In a vector interpolation process, over-large nonlinear errors nearby the singular points and over-large motion of the rotary shaft are avoided through tool shaft vectors of an inclined midpoint position for a machining interval in a singularity area; the linear shaft is interpolated in a mode based on the ideal trajectory of the cutter location points at an interval with over-large trajectory nonlinear errors, so that trajectory errors can be effectively reduced. Compared with single linear interpolation and single vector interpolation, an error-control-based smooth interpolation strategy has the advantages that the machining accuracy is improved, and the machining stability of a machine tool is improved as well.

Description

A kind of level and smooth interpolating method of five axle NC systems based on error control

Technical field

The present invention relates to five axle process technologies in a kind of fields of numeric control technique, specifically a kind of level and smooth interpolating method of five axle NC systems based on error control.

Background technology

Five-shaft numerical control processing, by changing cutter axis orientation, can effectively be avoided the interference of cutter and part, better mates cutter how much and curve surface of workpiece, control the region that cutter participates in cutting, adjust cutting force and reduce tool wear, thereby improve working (machining) efficiency, improve machined surface quality.But the appearance of rotating shaft has also brought the more difficult control of cutter-orientation, problem that nonlinearity erron is larger.CNC mainly contains two kinds of modes for the interpolation of kinematic axis in interlock is controlled at present: linear interpolation mode and vector interpolation mode.Linear interpolation mode is calculated easy, and the time of implementation is shorter.But owing to only relying on a series of mini line segments to carry out the ideal interlock track of the each kinematic axis of discrete approximation lathe, therefore, after linear interpolation, between the actual interlock track of each axle and theory locus, inevitably there is nonlinearity erron.On the other hand, owing to there is non-linear conversion relation between generating tool axis vector (i, j, k) and rotating shaft, therefore cutter shaft can depart from the plane that adjacent vector forms in linear Interpolation Process, causes cutter shaft attitude error.Vector interpolation is to carry out vector interpolation in the plane forming in adjacent generating tool axis vector, then according to interpolation vector, each axle is carried out to interpolation calculating.Therefore vector interpolation greatly reduces cutter appearance error, but vector interpolation can cause the discontinuous and rotation rapidly of rotating shaft in the time approaching singular point, machine tool capability is difficult to meet now acceleration and deceleration and the rotating speed requirement of rotating shaft, very easily destroys workpiece, even damages machine tool component.Therefore how guaranteeing the continuously level and smooth of moving interpolation, effectively control cutter appearance error and trajectory error simultaneously, is the critical problem that five axle NC systems need to solve.

Existing nonlinearity erron control method or only for the synthetic trajectory error of each axle, or only for cutter shaft attitude error, consider that these two kinds of errors are all that five axles processing nonlinear motions cause, all can impact processing.

Summary of the invention

For above shortcomings part in prior art, the present invention proposes a kind of level and smooth interpolating method of five axle NC systems based on error control, difference and contact between trajectory error and cutter appearance error are analyzed, two kinds of interpolation modes are combined, interpolation algorithm based on error control is proposed, thereby two kinds of errors are all limited in allowed band, and avoid the motion sudden change of machine spindle.

The technical scheme that the present invention adopted is for achieving the above object: a kind of level and smooth interpolating method of five axle NC systems based on error control, comprises the following steps:

Adopt the cutter vector interpolation mode detecting based on singular point to carry out interpolation to five-axle numerical control system rotating shaft;

Adopt the linear interpolation mode based on desirable cutter location track to carry out interpolation to five-axle numerical control system linear axes.

The described vector interpolation mode detecting based on singular point comprises the following steps:

By the instruction of adjacent two NC axles

be converted to respectively corresponding cutter location coordinate by direct kinematics: (u _{w, n}, q _w,n) and (u _{w, n+1}, q _{w, n+1}); Wherein, (x _{m, n}, y _{m, n}, z _{m, n}) and (x _{m, n+1}, y _{m, n+1}, z _{m, n+1}) instruction of expression lathe linear axes,

with

represent rotary axis of machine tool instruction, u _w,nand u _{w, n+1}for cutter heart point position vector, q _w,nand q _{w, n+1}cutter axis orientation vector;

Ask the cutter axis orientation vector of two cutter location coordinate midpoint

if q _{w, 0.5}' be in singular regions, solve the rotating shaft coordinate of adjacent two NC axle instruction midpoint

corresponding cutter axis orientation vector q is tried to achieve in direct kinematics conversion by Digit Control Machine Tool self _{w, 0.5}; By q _{w, 05}' to q _{w, 0.5}inclination ε _allowangle, obtains the generating tool axis vector that midpoint is new

wherein ε _allowthe machete appearance error allowing for machining accuracy; The rotating shaft in subinterval, mid point left and right is adopted respectively to vector interpolation;

If q _{w, 0.5}' be in outside singular regions, cutter shaft does not tilt to process, and whole interval rotating shaft adopts vector interpolation.

The described linear interpolation mode based on desirable cutter location comprises the following steps:

Calculate the trajectory error δ of adjacent two NC axle instruction midpoint _non-linearif, δ _non-linear≤ δ _allow, linear axes directly adopts linear interpolation; If δ _non-linear> δ _allow, count m by u according to interpolation cycle _w,nand u _{w, n+1}between straightway m decile, the rotating shaft coordinate at the each point place simultaneously obtaining in conjunction with vector interpolation, obtains the linear axes coordinate at each interpolated point place by the inverse kinematics conversion of Digit Control Machine Tool self; δ _allowfor maximum allows trajectory error.

The trajectory error δ of described adjacent two NC axle instruction midpoint _non-linearcomputational methods be:

Solve the machine spindle coordinate of adjacent two NC axle instruction midpoint

Convert conversion by direct kinematics and solve corresponding cutter heart point position vector (x _{w, 0.5}, y _{w, 0.5}, z _{w, 0.5});

According to the cutter heart point position vector (x of starting point and destination county _{w, n}, y _{w, n}, z _w,n) and (x _{w, n+1}, y _{w, n+1}, z _{w, n+1}) solve desirable mid point cutter heart point vector

Try to achieve the trajectory error of adjacent two NC axle instruction midpoint by following formula:

${\mathrm{\δ}}_{\mathrm{non}-\mathrm{linear}}=\sqrt{{(\frac{x_{w,n}+x_{w,n+1}}{2}-x_{w,0.5})}^2+{(\frac{y_{w,n}+y_{w,n+1}}{2}-y_{w,0.5})}^2+{(\frac{z_{w,n}+z_{w,n+1}}{2}-z_{w,0.5})}^2}$

The present invention has following beneficial effect and advantage:

1 for reducing cutter appearance error, and this method adopts vector interpolation to rotating shaft.But in vector Interpolation Process, to the processing interval in singular regions, avoid near excessive nonlinearity erron singular point and the excessive movements of rotating shaft by the generating tool axis vector of inclination point midway.

2 in the excessive interval of track nonlinearity erron, and this method adopts the interpolation mode based on desirable Path to linear axes, can effectively reduce trajectory error.

3 with single linear interpolation with vector interpolation compare, the level and smooth interpolation strategy based on error control had both improved machining accuracy, had improved again the stability of machine tooling.

Accompanying drawing explanation

Fig. 1 is the two turntable five-axis machine tool schematic diagrames of the AC of the inventive method application;

Fig. 2 is the two turntable five-axis machine tool kinematic chains of AC;

Fig. 3 vector interpolation schematic diagram;

Fig. 4 is the inventive method flow chart.

The specific embodiment

Below in conjunction with drawings and Examples, the present invention is described in further detail.

The present embodiment, take the two turntable five-axis machine tools of AC as research object, as shown in Figure 1, is the two turntable five-axis machine tool structural representations of AC used in the inventive method.Fig. 2 is the type machine tool motion chain.Interpolating method based on error control comprises the following steps: set up Machine kinematics Direct/Reverse kinematical equation; Judge that whether the generating tool axis vector of consecutive points midpoint is in singular regions, the mid point generating tool axis vector in singular regions is tilted to process; Calculate midpoint nonlinearity erron, if exceed allowable error, linear axes is adopted to the interpolation mode based on desirable Path.

For the processing interval of adjacent cutter spacing data composition, interpolation flow process as shown in Figure 4.

Step 1) set up the Direct/Reverse kinematical equation of the two turntable five-axis machine tools of AC.

If the workpiece coordinate system origin of coordinates is O _w, the tool position vector under workpiece coordinate system is u _w=(x _wy _wz _w) T, tool orientation vector is q _w=(ij is k) ^t; Lathe coordinate system initial point is O _m, lathe linear axes is X, Y, Z, corresponding linear movement vector is u _m=(x _my _mz _m) ^t, rotary axis of machine tool is A and C, corresponding lathe corner is respectively α and γ.

$\left(\begin{array}{cc}i& x_w\\ j& y_w\\ k& z_w\\ 0& 1\end{array}\right)=T(t_x,t_y,t_z)R_Z(-\mathrm{\γ})R_X(-\mathrm{\α})$ (1)

$T(x_m-t_x,y_m-t_y,z_m-t_z)\left(\begin{array}{cc}0& 0\\ 0& 0\\ 1& 0\\ 0& 1\end{array}\right)$

(t in formula _x, t _y, t _z) representing the offset vector of workpiece coordinate system initial point to AC axle pivot, R represents the homogeneous coordinate transformation matrix of gyration, T represents the homogeneous coordinate transformation matrix of translational motion, R _m(Ω) represent around M axle rotation Ω angle.

The inverse kinematics equation that obtains the two turntable five-axis machine tools of AC by formula (1) as the formula (2).

$\left\{\begin{array}{c}{x}_m=(x_w-t_x)\cos \left(\mathrm{\&gamma;}\right)-(y_w-t_y)\sin \left(\mathrm{\&gamma;}\right)+t_x\\ y_m=(x_w-t_x)\cos \left(\mathrm{\&alpha;}\right)\sin \left(\mathrm{\&gamma;}\right)+(y_w-t_y)\cos \left(\mathrm{\&alpha;}\right)\cos \left(\mathrm{\&gamma;}\right)\\ -(z_w-t_z)\sin \left(\mathrm{\&alpha;}\right)+t_y\\ z_m=(x_w-t_x)\sin \left(\mathrm{\&alpha;}\right)\sin \left(\mathrm{\&lambda;}\right)+(y_w-t_y)\sin \left(\mathrm{\&alpha;}\right)\cos \left(\mathrm{\&lambda;}\right)\\ +(z_w-t_z)\cos \left(\mathrm{\&alpha;}\right)+t_z\\ \mathrm{\&alpha;}=\arccos \left(k\right),(0\&le;\mathrm{\&alpha;}\&le;\mathrm{\&pi;})\\ \mathrm{\&gamma;}=\arctan 2(i,j),(-\mathrm{\&pi;}<\mathrm{\&gamma;}\&le;\mathrm{\&pi;})\end{array}\right.---\left(7\right)$

Step 2) read adjacent NC code, convert and be converted to corresponding cutter location coordinate by direct kinematics: (u _{w, n}, q _{w, n}) and (u _{w, n+1}, q _{w, n+1}), next ask the generating tool axis vector of midpoint,

${q_{w,0.5}}^{\&prime;}=\frac{0.5\&times;(q_{w,n}+q_{w,n+1})}{|0.5\&times;(q_{w,n}+q_{w,n+1})|}---\left(3\right)$

Then according to q _{w, 0.5}' each component judge that processing is whether in singular regions.For the two turntable lathes of AC, q _{w, 0.5}' k component more approach 1 cutter shaft and approach unusual attitude, therefore judge q _{w, 05}' k component whether be greater than permissible value.

If q _{w, 0.5}' be in singular regions, take following mode to process generating tool axis vector: first to use the rotating shaft coordinate of asking midpoint according to the linear interpolation mode of the kinematic axis shown in formula (2), wherein t=0.5.Convert the generating tool axis vector q while trying to achieve linear interpolation by direct kinematics _{w, 0.5}.By q _{w, 0.5}' to q _{w, 0.5}inclination ε _allowangle, obtains new mid point generating tool axis vector

(ε _allowfor maximum allows cutter appearance error).Wherein, linear interpolation mode is as follows:

If the machine coordinates that adjacent cutter location is corresponding (comprising linear axes and rotating shaft) is MC _nand MC _n+1.Linear interpolation is pressed with a series of small straightway discrete approximation finished surfaces, and the value of machine coordinates each moment t in centre is

MC _t=(MC _n+1-MC _n)*t+MC _n(0≤t≤1) (4)

Step 3) is calculated the trajectory error δ of midpoint _non-linear, several situations below of dividing are carried out interpolation to the axle motion between consecutive points.

If δ _non-linear≤ δ _allow(δ _allowfor maximum allows trajectory error), midpoint cutter shaft is through tilting to process, and whole interval rotating shaft adopts vector interpolation, and linear axes directly adopts linear interpolation; If δ _non-linear≤ δ _allow, midpoint cutter shaft is through tilting to process, and the rotating shaft in subinterval, left and right adopts vector interpolation, and linear axes is according to linear interpolation; If δ _non-near> δ _allow, midpoint cutter shaft, through tilting, is not first counted m by u according to interpolation cycle _w,nand u _{w, n+1}between straightway m decile, rotating shaft is carried out to vector interpolation simultaneously, then converts by inverse kinematics the machine spindle coordinate that obtains each interpolated point place; If δ _non-near> δ _allow, midpoint cutter shaft, will u through tilting _{w, n}and u _{w, n+1}between straightway m decile, the rotating shaft in subinterval, left and right is adopted to vector interpolation simultaneously, last inverse kinematics conversion solves the machine spindle coordinate at each interpolated point place.

Wherein the mode of rotation axis vector interpolation is as follows:

As shown in Figure 3, establishing initial cutter vector is q _{w, n}, terminal generating tool axis vector is for being q _{w, n+1}.With the initial point O of former coordinate system _was the initial point of new coordinate system, with not coplanar vector e _y=q _w,n, e _z=(q _{w, n}× q _{w, n+1})/| q _w,n× q _{w, n+1}|, e _x=(e _y× e _z)/| e _y× e _z| as one group of base of new coordinate system, form x axle, y axle and the z axle of new coordinate system.Obviously, due in new coordinate system, q _w,nrotate to q around its z axle _{w, n+1}, the transition matrix that is tied to new coordinate system due to former coordinate is E=[e _x ^t, e _y ^t, e _z ^t], therefore the solution formula of the desirable generating tool axis vector in t moment is:

${q_{w,t}}^{\&prime;}=E\left[\begin{array}{ccc}\cos \left(\mathrm{t\&omega;}\right)& -\sin \left(\mathrm{t\&omega;}\right)& 0\\ \sin \left(\mathrm{t\&omega;}\right)& \cos \left(\mathrm{t\&omega;}\right)& 0\\ 0& 0& 1\end{array}\right]\left[\begin{array}{c}0\\ 1\\ 0\end{array}\right](0\&le;t\&le;1)---\left(5\right)$

Wherein, ω=arccos (q _{w, n}q _{w, n+1}).

Converted by inverse kinematics again, the generating tool axis vector in t moment is converted to rotating shaft coordinate.

Claims (4)

1. the level and smooth interpolating method of five axle NC systems based on error control, is characterized in that, comprises the following steps:

Adopt the cutter vector interpolation mode detecting based on singular point to carry out interpolation to five-axle numerical control system rotating shaft;

Adopt the linear interpolation mode based on desirable cutter location track to carry out interpolation to five-axle numerical control system linear axes.

2. a kind of level and smooth interpolating method of five axle NC systems based on error control according to claim 1, is characterized in that, the described vector interpolation mode detecting based on singular point comprises the following steps:

By the instruction of adjacent two NC axles

be converted to respectively corresponding cutter location coordinate by direct kinematics: (u _{w, n}, q _w,n) and (u _{w, n+1}, q _{w, n+1}); Wherein, (x _{m, n}, y _{m, n}, z _{m, n}) and (x _{m, n+1}, y _{m, n+1}, z _{m, n+1}) instruction of expression lathe linear axes,

with

represent rotary axis of machine tool instruction, u _w,nand u _{w, n+1}for cutter heart point position vector, q _w,nand q _{w, n+1}cutter axis orientation vector;

Ask the cutter axis orientation vector of two cutter location coordinate midpoint

if q _{w, 0.5}' be in singular regions, solve the rotating shaft coordinate of adjacent two NC axle instruction midpoint

corresponding cutter axis orientation vector q is tried to achieve in direct kinematics conversion by Digit Control Machine Tool self _{w, 0.5}; By q _{w, 0.5}' to q _{w, 05}inclination ε _allowangle, obtains the generating tool axis vector that midpoint is new wherein ε _allowthe machete appearance error allowing for machining accuracy; The rotating shaft in subinterval, mid point left and right is adopted respectively to vector interpolation;

If q _{w, 0.5}' be in outside singular regions, cutter shaft does not tilt to process, and whole interval rotating shaft adopts vector interpolation.

3. a kind of level and smooth interpolating method of five axle NC systems based on error control according to claim 2, is characterized in that, the described linear interpolation mode based on desirable cutter location comprises the following steps:

Calculate the trajectory error δ of adjacent two NC axle instruction midpoint _non-linearif, δ _non-linear≤ δ _allow, linear axes directly adopts linear interpolation; If δ _non-linear> δ _allow, count m by u according to interpolation cycle _{w, n}and u _{w, n+1}between straightway m decile, the rotating shaft coordinate at the each point place simultaneously obtaining in conjunction with vector interpolation, obtains the linear axes coordinate at each interpolated point place by the inverse kinematics conversion of Digit Control Machine Tool self; δ _allowfor maximum allows trajectory error.

4. a kind of level and smooth interpolating method of five axle NC systems based on error control according to claim 3, is characterized in that the trajectory error δ of described adjacent two NC axle instruction midpoint _non-linearcomputational methods be:

Solve the machine spindle coordinate of adjacent two NC axle instruction midpoint

Convert conversion by direct kinematics and solve corresponding cutter heart point position vector (x _{w, 0.5}, y _{w, 0.5}, z _{w, 0.5});

According to the cutter heart point position vector (x of starting point and destination county _{w, n}, y _{w, n}, z _w,n) and (x _{w, n+1}, y _{w, n+1}, z _{w, n+1}) solve desirable mid point cutter heart point vector

Try to achieve the trajectory error of adjacent two NC axle instruction midpoint by following formula:

${\mathrm{\&delta;}}_{\mathrm{non}-\mathrm{linear}}=\sqrt{{(\frac{x_{w,n}+x_{w,n+1}}{2}-x_{w,0.5})}^2+{(\frac{y_{w,n}+y_{w,n+1}}{2}-y_{w,0.5})}^2+{(\frac{z_{w,n}+z_{w,n+1}}{2}-z_{w,0.5})}^2}$

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