Analysis of beam non-touching error of CNC lathe track operation in full speed supplementary modality
According to the measurement principle of the ballbar meter, the ballbar recorder records the coordinates of each sampling point and the radius error information at the point when performing the measurement.
If the coordinate information of the sampling point Pk(Xk, Yk) can be separately recorded by two laser interferometers, we can obtain: Rk=X2k+Y2k-R, and use the angle information of the point k=(2mkN), k is the nth At the sampling point, N is the total number of sampling points, and m is the coefficient related to the sampling interval. In the actual measurement, two strip-shaped plane mirrors are fixed on the main shaft, and two laser measuring instruments are mounted on the table. The directions of the laser beams are directed to the X and Y axes, respectively, and the reflected beam is always consistent with the incident beam. Obviously, when the machine tool performs circular interpolation motion, the X-direction laser interferometer outputs a sinusoidal curve, and the Y-direction laser interferometer outputs a cosine curve, which is shown as a measurement diagram.
The steps of the non-contact measurement method are as follows: (1) to establish the functional equation <6> of each individual error element of the machine tool; 2 integrate these single-term error functions and substitute them into the ballbar measurement principle formula (1) to establish the mathematics of non-contact measurement. Model; 3 Solve the obtained mathematical model, substitute the measured data, and use the analysis software to obtain each individual error.
Since the laser interferometer is a non-contact measurement method, it avoids the shortage of the ballbar instrument, so it can be used for the precision detection of the numerical control machine during high-speed feed, and obtains the individual error elements of the machine tool.
There are many error elements in the analysis and processing of single error elements. This paper mainly discusses the measurement of machine tool volume error and servo gain error.
Geometric error element modeling As shown, when the slide moves along the guide rail, the slide has a total of 6 error elements in space, where: xx, yx, zx are the positioning error, horizontal and vertical straightness error respectively (first 1st The mark indicates the direction of the error, the second subscript indicates the direction of motion), x(x), y(x), and z(x) are the roll error, yaw and pitch error <7> (subscript error) Direction). In addition to the six error elements of each translational axis, there is also a verticality error between any two axes. Therefore, the three-axis machining center has 21 error elements in space.
The function equation of the positioning error When establishing the measurement mathematical model, the linear displacement errors x(x), y(y) and z(z) are expressed by polynomial functions, as follows: x(x)=ni=1dxxiXRiy(y)= Ni=1dyyiYRiz(z)=ni=1dzziZRi(2) where: X/R, Y/R and Z/R are the relative coordinates of the X, Y, and Z axes, respectively; dxxi, dyyi, and dzzi are the coefficients of the polynomial.
The function equations of yaw, pitch and straightness error are analyzed. The yaw and pitch errors and the corresponding straightness error have approximate derivative relationship. After the actual measurement, it is found that when the polynomial function of the straightness error takes more than two coefficients, The measurement results are more accurate.
The following functional equation can be obtained: y(X)=ni=2dyxiXRiEy(X)=-ni=1idzxi(X/R)i-1Rz(X)=ni=2dzxiXRiEz(X)=ni=1idyxi(X/R)i -1R(3) can also obtain the mathematical equation (omitted) of the corresponding error elements of the Y and Z axes. Where dyxi, dzxi are the coefficients of the equation.
The rolling error error elements Ex(X), Ey(Y), Ez(Z) have a very complicated influence on the accuracy of the machining center. It is difficult to accurately model. In order to improve the practicability of the mathematical model, this paper does not Consider the effects of roll error.
The function equation of the verticality error element is the perpendicularity error between the XY, YZ and ZX axes, and the displacement errors caused by them are: x=ZR, y=XR, z=YR(4) geometric error comprehensive mathematics In general, geometric errors account for 30% and 50% of the total error of the machining center. Therefore, monitoring the magnitude of the geometric error is very important to maintain machine accuracy. The linear superposition of the individual geometric error element function equations for each axis constitutes a mathematical model of the geometric error of the machining center. In this paper, a vertical three-axis machining center is taken as an example to establish a mathematical model of the geometric error elements of the machining center. The size effect of the tool was not considered during the modeling process.
The function equation of the servo gain mismatch error element When the servo gain of the linear axis of the machine does not match, the following error and contour error occur when the arc contour is interpolated at high speed.
The positioning errors of the X, Y and Z axes of the measurement results are: x(X)=4.2my(Y)=6.3mz(Z)=3.7m Straightness error: y(X)=-1.9mz(X) =2.4mx(Y)=5.8mz(Y)=-7.5mx(Z)=-1.5my(Z)=4.3mX, Y and Z axis yaw and pitch errors are: Ey(X)=-12radEz (X)=11radEx(Y)=-50radEz(Y)=-31radEx(Z)=8radEy(Z)=5rad Verticality error: =4rad=61rad=23rad Measurement results analysis The above measurement results are repeated measurements One of them is compared with the result of the machine tool with the ballbar instrument (machine accuracy history detection database): 1 under the same measurement conditions, the non-contact method measurement feed rate is much larger than the contact method feed rate. At the speed (6 times), the former has higher precision, so it is more suitable for the precision detection of modern high-speed machine tools. 2 The measurement range of the non-contact method is relatively large. In theory, by expanding the scale of the mathematical model, all the geometry can be measured. Errors and most errors associated with servo systems.
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