BALLBAR TESTING TUNE-UP METHOD FOR MACHINE TOOL

Abstract

A ballbar testing tune-up method for machine tool includes the steps of letting a machine tool system execute a ballbar test; obtaining a phase characteristic and a peak-value characteristic; creating a Lagrange interpolation polynomial and inputting a servo controller parameter, a phase characteristic and a peak-value characteristic of the machine tool system each time when executing the ballbar test, and obtaining a proposed servo parameter. This method is simple and easy without incurring additional equipment costs, but just using existing equipment to find the proposed servo parameter quickly and input it into a machine tool system, so as to improve the response issue of a servo system and reduce manufacturing contour error to enhance the working precision of the machine tool system.

Claims

1. A ball bar testing tune-up method for machine tool, comprising the steps of: letting a machine tool system execute a ballbar test; obtaining a phase characteristic and a peak-value characteristic according to the result of the ballbar test; creating a Lagrange interpolation polynomial, increasing an interpolation order thereof according to the number of ballbar tests, and inputting a corresponding servo controller parameter of the machine tool system each time when executing the ballbar test, and at least one of the phase characteristic and the peak-value characteristic to obtain a proposed servo parameter; and inputting the proposed servo parameter to the machine tool system.

2. The ballbar testing tune-up method for machine tool according to claim 1, wherein the phase characteristic is an average value of the difference between the radius sampled at a position of the X-axis and Y-axis with a contour error fixed cycle in the ballbar test result and an average radius of the ballbar test.

3. The ballbar testing tune-up method for machine tool according to claim 1, wherein the peak-value characteristic is the difference of peak values at the X-axis and Y-axis in the ballbar test result.

4. The ballbar testing tune-up method for machine tool according to claim 3, wherein the peak-value characteristic is defined by defining a sampling time based on the neighborhood of the peak values of the X-axis and Y-axis and using the sampling time as a filter range to calculate an average value of the peak values to perform a filtering, and using the difference between the peak values of the X-axis and Y-axis after the filtering as the peak-value characteristic.

5. The ballbar testing tune-up method for machine tool according to claim 1, wherein the machine tool system comprises a servo controller having a position loop, and the proposed servo parameter is inputted as a position controller parameter to the position loop.

6. The ballbar testing tune-up method for machine tool according to claim 5, wherein the proposed servo parameter is obtained by inputting the phase characteristic into the Lagrange interpolation polynomial.

7. The ballbar testing tune-up method for machine tool according to claim 1, wherein the machine tool system comprises a servo controller having a velocity loop, and the proposed servo parameter is inputted as a controller parameter into the position loop.

8. The ballbar testing tune-up method for machine tool according to claim 7, wherein the proposed servo parameter is obtained by inputting the phase characteristic and the peak-value characteristic into the Lagrange interpolation polynomial.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

[0020] FIG. 1 is a flow chart of the present invention;

[0021] FIG. 2 is a key to the arrangement of the partial views of FIG. 2a and FIG. 2b.

[0022] FIG. 2a is a part of a block diagram showing a model of a virtual feed shaft system of the present invention;

[0023] FIG. 2b is another part of a block diagram showing a model of a virtual feed shaft system of the present invention;

[0024] FIG. 3a is a polar coordinate graph showing the impact of phase error produced by the present invention, and the phase of Y-axis is ahead of the phase of X-axis;

[0025] FIG. 3b is a polar coordinate graph showing the impact of phase error produced by the present invention, and the phase of Y-axis is behind the phase of X-axis;

[0026] FIG. 4a is a polar coordinate graph showing the impact of gain error produced by the present invention, and the gain of Y-axis is greater than the gain of X-axis;

[0027] FIG. 4b is a polar coordinate graph showing the impact of gain error produced by the present invention, and the gain of Y-axis is smaller than the gain of X-axis;

[0028] FIG. 5 is a polar coordinate graph of a ballbar test before making adjustment in accordance with an empirical embodiment of the present invention;

[0029] FIG. 6 is a polar coordinate graph of a ballbar test before making adjustment and turning off a feedforward controller in accordance with an empirical embodiment of the present invention;

[0030] FIG. 7a is a polar coordinate graph of a ballbar test before adjusting a position loop parameter in accordance with an empirical embodiment of the present invention;

[0031] FIG. 7b is a polar coordinate graph of a ballbar test after adjusting a position loop parameter in accordance with an empirical embodiment of the present invention;

[0032] FIG. 7c is a table of DBB measurement results after making adjustment in accordance with an empirical embodiment of the present invention;

[0033] FIG. 7d is a graph of DBB measurement results after making adjustment in accordance with an empirical embodiment of the present invention;

[0034] FIG. 8a is a table of DBB measurement results when the feed rate is 1000 mm/min in accordance with an empirical embodiment of the present invention;

[0035] FIG. 8b is a graph of DBB measurement results when the feed rate is 1000 mm/min in accordance with an empirical embodiment of the present invention;

[0036] FIG. 8c is a table of DBB measurement results when the feed rate is 3000 mm/min in accordance with an empirical embodiment of the present invention;

[0037] FIG. 8d is a graph of DBB measurement results when the feed rate is 3000 mm/min in accordance with an empirical embodiment of the present invention;

[0038] FIG. 8e is a table of DBB measurement results when the feed rate is 8000 mm/min in accordance with an empirical embodiment of the present invention; and

[0039] FIG. 8f is a graph of DBB measurement results when the feed rate is 8000 mm/min in accordance with an empirical embodiment of the present invention.

DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0040] The technical characteristics of the present invention will become apparent with the detailed description of preferred embodiments accompanied with the illustration of related drawings.

[0041] With reference to FIG. 1 for a ballbar testing tune-up method for machine tool in accordance with the present invention, the method includes the following steps:

[0042] S001: analyzing and calibrating a response error of a machine tool system, wherein sufficient data are required for the analysis, so that a virtual feed shaft model is created in an embodiment and used to consider the impact of the response error occurred in the system to create a ballbar test signal and sufficient data for the analysis, and the virtual feed shaft model includes a feed drive control system, and a feedforward controller system, whose configuration and model are prior arts, and thus will not be described here. In the feed system model of the present invention, the CNC servo loop comprises, a current loop, a velocity loop and a position loop arranged from inside to outside. To simplify the current loop of the present invention, the control block diagram of the model is as shown in FIG. 2a and FIG. 2b, wherein K.sub.v = K.sub.vi/s + K.sub.vp is the velocity loop of the proportional integral (PI) controller, K.sub.vi and K.sub.vp are the parameters of the servo controller, s is a Laplace operator, K.sub.p is the position loop of the proportional (P) controller,

[00001]$\frac{1}{M_{i}s+C_i}$

and

[00002]$\frac{-1}{M_b{s}^2+C_{b}s+K_b}$

are the vibration models of the work table and base of the machine tool system respectively,

[00003]$\frac{1}{M_{m}s+B_m}$

is the linear motor model with non-linear phenomenon (friction, backlash),

[00004]$VF`AF$

are the velocity and acceleration of the feedforward control system; and the modular machine tool system includes loop gains of each shaft, a linear controller, and a feedforward controller; wherein the virtual feed shaft system changes and adjusts the parameters to avoid serious damages to the machine tool system caused by the wrong controller parameters during the experiment and establish a rare single influence phenomenon in a real machine measurement, while effectively eliminating unnecessary influences and greatly reducing the cost of collecting measurement signal sampled. Therefore, the virtual feed shaft system as shown in FIG. 2a and FIG. 2b is provided for creating sufficient databases to analyze the influence of servo mismatch.

[0043] Then, the machine tool system executes the ballbar test. Since the servo mismatch comes from a response error between the X-axis and Y-axis of the machine tool system, and the frequency domain analysis can be used to know if there is a change of gain and phase in the system response, so that a ballbar test is executed in accordance with an embodiment of the present invention, and the original equipped optical ruler of the machine tool system is provided to perform the ballbar test. In the ballbar test, the gain difference and the phase difference between the two axes will cause a contour error of the time domain trajectory, and the control parameter of the PI controller will influence the changes of gain and phase of the feed system, so that if the gains or phases of the two axes are not consistent, then we can observe the contour error from the circular tracking. The circular tracking commands for the X-axis and Y-axis are given in the following Equations 1 and 2 respectively:

[00005]$x=Rc\text{}os\left(\omega t\right)$

[00006]$y=Rs\text{}in\left(\omega t\right)$

[0044] Wherein, R and ω are the radius and angular velocity of a ballbar test path respectively, and the angular velocity can be converted by the feed rate, and t is the measurement time of the ballbar test, and the time domain tracking of the machine tool system is given in the following Equations 3 and 4:

[00007]$x=K_x\cdot Rcos\left(\omega t+{\phi }_x\right)$

[00008]$y=K_y\cdot Rsin\left(\omega t+{\phi }_y\right)$

[0045] Wherein, K.sub.x and K.sub.y are the system gain values of the X-axis and Y-axis respectively, and φ.sub.x and φ.sub.y are the system phase values of the X-axis and Y-axis respectively, so that the circular measured radius

[00009]$r\left(t\right)$

can be calculated by the following Equation 5:

[00010]$r\left(t\right)=R\sqrt{K_x{}^2{\left(Rcos\left(\omega t+{\phi }_x\right)\right)}^2+K_y{}^2{\left(Rsin\left(\omega t+{\phi }_y\right)\right)}^2}$

[0046] Based on the X-axis, the servo mismatch of the machine comes from the gain difference Δφ and the phase difference ΔK of the two axes, which can be calculated by the following Equations 6 and 7.

[00011]$\Delta \phi ={\phi }_y-{\phi }_x$

[00012]$\Delta K=K_y-K_x$

[0047] If the phase difference Δφ is greater than zero, the Y-axis phase is ahead of X-axis phase, so that we know from Equation 5 that when the cycle is t′, the counterclockwise tracking radius is greater than an average radius R̅; and the track has a clockwise radius smaller than the average radius as shown in FIG. 3 and the following Equation 8:

[00013]$0>t^{\prime }>\frac{\pi }{2\omega },\pi >t^{\prime }>\frac{3\pi }{2\omega }$

[0048] If Δφ is greater than zero, it is as shown in the following Equation 9:

[00014]$r_{ccw}\left(t^{\prime }\right)>\overline{R},r_{cw}\left(t^{\prime }\right)<\overline{R}$

[0049] If Δφ is smaller than zero, it is as shown in the following Equation 10:

[00015]$r_{ccw}\left(t^{\prime }\right)<\overline{R},r_{cw}\left(t^{\prime }\right)>\left(\overline{R}\right)$

[0050] Therefore, if the gain difference ΔK is greater than zero, indicating that when the Y-axis gain value is greater than the X-axis gain value, we will be able to know from Equation 5 that if the cycle is from

[00016]$\frac{\pi }{4\omega }$

to

[00017]$\frac{3\pi }{4\omega },$

then the measurement track

[00018]$r\left(t\right)$

will be greater than

[00019]$\overline{R}$

, and if the cycle is from

[00020]$\frac{5\pi }{4\omega }$

to

[00021]$\frac{7\pi }{4\omega },$

then the measurement track

[00022]$r(t)$

will be smaller than

[00023]$\overline{R}$

; and if ΔK is smaller than zero, the conditions will be opposite as shown in FIG. 4.

[0051] S002: analyzing the servo mismatch to find the key impact and then avoiding errors caused by defective data by eliminating the low-impact segments, and calculating the important characteristics of major high-impact measurement segments. In the present invention, a phase characteristic and a peak-value characteristic can be obtained according to the ballbar test result.

[0052] In an embodiment, the phase characteristic is defined as an important segment of the ballbar test result obtained when X- and Y-axis phases are inconsistent to each other, causing a contour error synchronously outputted in the fixed cycle t′ of the two axes, and the phase characteristic has better significance. When the phase error shows up, which axis is ahead or behind can be shown immediately. When R̂ is greater than zero, it indicates that the Y-axis is ahead of X-axis, so that the counterclockwise measured radius is greater than an average radius in the cycle t′; and when R̂ is smaller than zero, it indicates that the Y-axis is behind the X-axis, so that the counterclockwise measured radius is smaller than the average radius in the cycle t′. Δt is the controller sampling time and N.sub.R is the number of characteristic calculations of segment sampling time; so that an average of the differences between the radius of contour errors occurred in the fixed cycle of the X-axis and Y-axis and the average radius of the ballbar test can be calculated according to the following Equations 11 to 13:

[00024]$t^{\prime }=\frac{\pi }{6\omega }\sim \frac{\pi }{3\omega }$

[00025]$N_R=\frac{\frac{\pi }{3\omega }-\frac{\pi }{6\omega }}{\Delta t}$

[00026]$\widehat{R}=\frac{.Math.\left(r\left(t^{\prime }\right)-\overline{R}\right)}{N_R}$

[0053] In the peak-value characteristic, the time domain peak values of the two axes are inconsistent with each other since the gains of the two axes are different, so that when ΔK is greater than zero, the motion trajectory in the ballbar test is as shown in FIG. 4. In the cycle from

[00027]$\frac{\pi }{4\omega }$

to

[00028]$\frac{3\pi }{4\omega },$

the measured radius track is greater than an average radius. The difference between the peak values of the X-axis and Y-axis is used as the peak-value characteristic

[00029]${\widehat{P}}_e$

. To reduce the impact of machine vibration and signal conversion,

[00030]$N_p$

sampling time is obtained from the neighborhood of the peak value and used as a filter range

[00031]$t_f$

in an embodiment, and the average value is calculated for filtering, and the difference between the peak values of the two axes is used as the peak-value characteristic

[00032]${\widehat{P}}_e$

. When

[00033]${\widehat{P}}_e$

is greater than zero, it indicates that the gain value of the Y-axis is greater than the gain value of the X-axis; when

[00034]${\widehat{P}}_e$

is smaller than zero, it indicates that the gain value of the Y-axis is smaller than the gain value of X-axis; which can be calculated by the following Equations 14 to 17:

[00035]$t_f=N_p\cdot \Delta t$

[00036]$t_x{}^{\prime }=\frac{2\pi }{\omega }\pm t_f$

[00037]$t_y{}^{\prime }=\frac{\pi }{\omega }\pm t_f$

[00038]$\widehat{P_e}=\frac{\left|{\displaystyle .Math.y\left(t_y{}^{\prime }\right)}\right|-\left|{\displaystyle .Math.x\left(t_x{}^{\prime }\right)}\right|}{N_p+1}$

[0054] S003: finding an important characteristic under the system response error, and then creating a Lagrange interpolation polynomial for the calculation to obtain a proposed servo parameter and provide a proposed controller parameter to the operators. To improve the accuracy and convergence of the algorithm, the order of interpolation is increased according to the number K of performing the ballbar tests, the servo controller parameter of the machine tool system and at least one of the phase characteristic and the peak-value characteristic are inputted accordingly for the execution of the ballbar test each time, so as to obtain the proposed servo parameter, and its calculation is shown in the following Equations 18 to 20, wherein

[00039]$p_i^k$

is the servo controller parameter, and

[00040]$F_i$

is the selected characteristic.

[00041]$f\left(F_i^k\right)=p_i^{k}k=1,\mathrm{2...},n$

[00042]$\left[p_1,p_2,p_3\right]=\left[k_{pp},k_{vp},k_{vi}\right]$

[00043]$\left[F_1,F_2\right]=\left[\widehat{R},\widehat{P_e}\right]$

[0055] After the first ballbar tests of different parameters are performed, a single record of track measurement data and controller parameters have not create the Lagrange interpolation polynomial yet, so that the parameter range between

[00044]$P_{i,\max }^g$

and

[00045]$p_{i,\min }^g$

of the controller, the controller parameter

[00046]$p_i^1,$

the phase characteristic ̂R̂.sub.1 of the first ballbar test calculated after the first ballbar test are given to the position controller parameter proposed value

[00047]$p_1^2$

of the second ballbar test. The calculation method used after the first circular measurement is shown in the following Equations 21 and 22, wherein the controller parameters of the axes having the gain ahead or the phase behind are adjusted, or the controller parameters of the axes having both of the gain and phase ahead are adjusted:

[00048]$p_i^2=p_i^1+\frac{{\widehat{R}}_1}{R_{\max }-R_{\min }}\times \left(p_{i,\max }^g-p_{i,\min }^g\right)$

[00049]$p_i^2=p_i^1-\frac{{\widehat{R}}_1}{R_{max}-R_{m\text{}in}}\times \left(p_{i,m\text{}ax}^g-p_{i,m\text{}in}^g\right)$

[0056] After the second ballbar test is executed, the important characteristic F.sub.2 of the second is obtained, and the phase characteristic F.sub.3 of the next ballbar test is zero, and the third position controller parameter

[00050]$p_1^3$

is calculated. The calculation method after the second circular measurement is as shown in Equation 23:

[00051]$p_i^3=\frac{p_i^2{F}_1-p_i^1{F}_2}{F_1-F_2}$

[0057] After the controller parameter

[00052]$p_i^3$

is used in the third ballbar test to calculate

[00053]${\widehat{R}}_3$

, and

[00054]${\widehat{R}}_e$

is set to zero to calculate the fourth proposed parameter

[00055]$p_1^4.$

The calculation method after the third circular measurement is as shown in Equation 24:

[00056]$p_i^4=\frac{p_i^1{F}_2{F}_3\left(F_2-F_3\right)-p_i^2{F}_1{F}_3\left(F_1-F_3\right)+p_i^3{F}_1{F}_2\left(F_1-F_2\right)}{\left(F_1-F_2\right)\left(F_2-F_3\right)\left(F_1-F_3\right)}$

[0058] After the controller parameter

[00057]$p_1^3$

is used in the third ballbar test to obtain

[00058]$F_3$

, and

[00059]$F_4$

is set to zero to calculate the fourth proposed parameter

[00060]$p_1^4.$

The calculation method of the fourth circular measurement is as shown in Equations 25 to 29:

[00061]$p_i^5=\frac{-p_i^1{a}_1+p_i^2{a}_2-p_i^3{a}_3+p_i^4{a}_4}{\left(F_1-F_2\right)\left(F_2-F_3\right)\left(F_3-F_4\right)\left(F_1-F_3\right)\left(F_1-F_4\right)\left(F_2-F_4\right)}$

[00062]$a_1=F_2{F}_3{F}_4\left(F_2-F_3\right)\left(F_2-F_4\right)\left(F_3-F_4\right)$

[00063]$a_2=F_1{F}_3{F}_4\left(F_1-F_3\right)\left(F_1-F_4\right)\left(F_3-F_4\right)$

[00064]$a_3=F_1{F}_2{F}_4\left(F_1-F_2\right)\left(F_1-F_4\right)\left(F_2-F_4\right)$

[00065]$a_4=F_1{F}_2{F}_3\left(F_1-F_2\right)\left(F_1-F_3\right)\left(F_2-F_3\right)$

[0059] The order of the created Lagrange interpolation polynomial increases with the number k of ballbar tests, so that after the n.sup.th ballbar test, the calculation of the Lagrange interpolation polynomial is as shown in Equations 30 and 31. Assumed that the selected characteristic is set to zero, the proposed servo parameter is calculated.

[00066]$L_{n,k}(0)=\frac{\left(0-{\widehat{F}}_1\right)\left(0-{\widehat{F}}_2\right).Math.\left(0-{\widehat{F}}_{k-1}\right)\left(0-{\widehat{F}}_{k+1}\right).Math.\left(0-{\widehat{F}}_n\right)}{\left({\widehat{F}}_k-{\widehat{F}}_1\right)\left({\widehat{F}}_k-{\widehat{F}}_2\right).Math.\left({\widehat{F}}_k-{\widehat{F}}_{k-1}\right)\left({\widehat{F}}_k-{\widehat{F}}_{k+1}\right).Math.\left({\widehat{F}}_k-{\widehat{F}}_n\right)}$

[00067]$p_i^{n+1}=p_i^1{L}_{n,1}\left(0\right)+.Math.+p_i^n{L}_{n,n}\left(0\right)={\displaystyle {.Math.}_{k=1}^n{p}_i^k{L}_{n,k}\left(0\right)}$

[0060] S004: Since the machine tool system uses an AC servomotor for the control, and a position controller, a velocity controller and a feedforward controller are used for the control, therefore the selection of the servo controller parameter is very important. Therefore, the present invention can input the proposed servo parameter into the machine tool system to adjust the controller parameter, and further improve its manufacturing precision. The present invention further provides a servo adjustment method for improve the contour precision of machine tools. A ballbar test is used to obtain the track of an optical ruler, and the aforementioned method is used for the key impact measurement segment, and the Lagrange interpolation is used to obtain the proposed servo parameter, and a parameter adjustment stop condition, a position controller parameter (K.sub.pp), and a velocity controller parameter (K.sub.vp K.sub.vi) are set to improve the machine response errors.

[0061] To improve the precision of adjusting the servo machine, the following steps are carried out before adjusting the servo parameters:

[0062] 1. Determining the axis with the response behind: To avoid insufficient gain of the two axes occurred during the manufacture performed at a feed rate higher than the measured feed rate caused by a too large decrease of the frequency width of the machine after making the adjustment, it is necessary to determine the phase or gain of which axis falls behind, and adjust the servo parameter of such axis. After the parameter reaches the range of its limits, the servo controller parameter of the other axis is adjusted.

[0063] 2. Turning of the feedforward controller: Since the feedforward controller will have impact on the system response, therefore it is necessary to turn off the feedforward controller first, and then turn on the feedforward controller after the system adjustment has been made, in order to avoid any wrong proposed parameter calculated by the poor servo system adjustment method of the feedforward controller.

[0064] For the adjustment of the position loop parameter, in the first stage, K.sub.pp has a larger impact on the system phase and gain, so that the characteristic

[00068]$\widehat{R}$

with better convergence and significant phase is selected, and the aforementioned Lagrange interpolation is used to obtain the proposed servo parameter for adjusting the position controller parameter K.sub.pp, and the goals are to minimize the phase characteristic to obtain better response performance and improve the servo mismatching issue. Since the phase characteristic R̂ uses segment average for the calculation, therefore some gain errors may remain in the final convergence, and the radius measurement segment is symmetrically oriented at 45 degrees, thus leading to the result of

[00069]$\widehat{R}$

being close to zero.

[0065] For the adjustment of the velocity loop parameter, the gain characteristic

[00070]${\widehat{P}}_e$

is used in the second stage, and the aforementioned Lagrange interpolation is used to obtain the proposed servo parameter to adjust the velocity controller parameter K.sub.vp, and improve the system gain error; and then the velocity controller parameter K.sub.vi is adjusted. To avoid an unstable system resulted from a too-small change of the system response caused by the velocity controller parameter K.sub.vi and a too-large error of the calculation of the Lagrange difference, a phase characteristic

[00071]$\widehat{R}$

with better convergence is used as the calculation characteristic and the abovementioned adjustment is made.

Stop Condition

[0066] To shorten the system adjustment time and avoid the occurrence of wrong controller parameters that may cause huge vibration and damage to the machine tool system, the stop condition of the algorithm is set as follows:

[0067] 1. Parameter Convergence: If the proposed controller parameter is equal to the control parameter of the previous ballbar test rounded up to an integer, the system is considered to be convergent, and the current adjustment of the servo parameter is completed.

[0068] 2. Achieving the Goal of System Adjustment: The goal of system adjustment is set, and if the roundness after the ballbar test is smaller than 10 .Math.m, then the goal is considered to be adjusted, and the servo system adjustment is completed and in compliance with the industrial system adjustment standards.

[0069] 3. Reaching the parameter adjustment limits: During the process of adjusting physical systems, the system response error is not only due to the impact of the servo controller parameter, but when there is a possibility of having another error source that affects the calculation of the algorithm and results in a proposed control parameter exceeding the proposed range of the parameter. These situations indicate that the adjustment of the machine tool system parameter has reached its limit, so that the value closest to the proposed control parameter is selected from the parameter proposed range as the proposed control parameter.

Empirical Embodiment

[0070] In the present invention, the proposed servo parameter obtained from the aforementioned method and the created servo system adjustment system are applied to physical machines such as the CHMER three-axis machine tool for the calibration of servo parameters of the physical systems, and the experiment form is shown in the following Table 1, and a Double Ball Bar (DBB) measuring instrument is provided for the measurement verification before and after adjusting the parameter.

TABLE-US-00001 Measured Plane Plain XY Measured feed rate 3000 mm/min Measured radius 100 mm

[0071] Since the feedforward controller will reduce the impact of the parameters to the response of the system, and a wrong feedforward controller parameter will cause system response errors, therefore the feedforward controller does not adjust its parameter. Before making a servo adjustment, the feedforward controller parameter is turned off to reduce the impact to the system response, and then a circular measurement is carried out to draw a polar coordinate image as shown in FIG. 6, and the machine adjustment is performed according to the adjusting procedure to improve the response matching of the internal loops of the controller. After the machine adjustment is completed, the feedforward controller is turned on as shown in FIG. 7a to FIG. 7d to perform DBB verification with different feed rates as shown in FIG. 8a to FIG. 8f. Since the machine tool system has other errors that impact the roundness. However, we still can see the effect of servo mismatch is close to zero under different feed rates, thereby proving the effectiveness of the present invention.

[0072] While the invention has been described by means of specific embodiments, numerous modifications and variations could be made thereto by those skilled in the art without departing from the scope and spirit of the invention as set forth in the claims.