Spindle thermal error compensation method insensitive to cooling system disturbance

Abstract

A spindle thermal error compensation method which is insensitive to the disturbance of the cooling system is provided, belonging to the technical field of error compensation in numerical control machine tools. First, the spindle model coefficient identification test, based on multi-state speed variable, is performed; after which, based on the correlation analysis between temperature and thermal error, the temperature measurement point, significantly correlated with the axial thermal error of the spindle, is determined. Next, a spindle thermal error model is established, which is insensitive to the cooling system disturbance. In addition, the coefficients in the model are identified under constraint condition, according to the nonlinear quadratic programming algorithm. Finally, based on the OPC UA communication protocol, the compensation value, as calculated by the model, is input to the numerical control system, in order to realize the compensation of the spindle thermal error.

Claims

1. A spindle thermal error compensation method that is against a disturbance of a cooling system, first, a spindle model coefficient identification test, based on multi-state speed variable, is performed; after which, based on a correlation analysis between temperature and thermal error, a temperature measurement point, a greatest correlated with an axial thermal error of the spindle, is determined; next, a spindle thermal error model is established, which is insensitive to a cooling system disturbance; in addition, coefficients in a model are identified under constraint condition, according to a nonlinear quadratic programming algorithm; finally, based on an OPC UA communication protocol, a compensation value, as calculated by the spindle thermal error model, is input to a numerical control system, in order to realize a compensation of the spindle thermal error; wherein, the steps are as follows: 1) test of coefficient identification of the spindle thermal error model four temperature sensors are arranged on a surface of a spindle at specific positions: a first temperature sensor and a fourth temperature sensor are respectively attached to positions of a rear bearing and a front bearing; a second temperature sensor and a third temperature sensor are evenly distributed between the rear bearing and the front bearing, wherein the second temperature sensor is adjacent to the rear bearing, the third temperature sensor is close to the front bearing; a detecting rod is mounted on the spindle, through a shank interface on the spindle; a displacement sensor is fixed on a working table; a fifth temperature sensor is arranged on a bed frame; the spindle runs at a range of speed values, where multiple states include rising speed, decreasing speed and starting or stopping; during this process, the first temperature sensor, the second temperature sensor and the third temperature sensor are simultaneously recorded, as well as measurement values of the fourth temperature sensor, the fifth temperature sensor, and the displacement sensor; 2) definition of spindle temperature measurement point correlation analysis is carried out, between collected temperature data of each position and the thermal error of the spindle; a correlation coefficient, between the temperature of each point and the thermal error of the spindle, is calculated as follows: $\begin{array}{cc}{\rho }_{T_j,E_Z}=\frac{\underset{i=1}{\overset{m}{.Math.}}{T}_j\left(i\right)E_z\left(i\right)-\frac{\underset{i=1}{\overset{m}{.Math.}}{T}_j\left(i\right)\underset{i=1}{\overset{m}{.Math.}}{E}_z\left(i\right)}{m}}{\sqrt{\left(\underset{i=1}{\overset{m}{.Math.}}{T}_j^2\left(i\right)-\frac{{\left(\underset{i=1}{\overset{m}{.Math.}}{T}_j\left(i\right)\right)}^2}{m}\right)\left(\underset{i=1}{\overset{m}{.Math.}}{E}_z^2\left(i\right)-\frac{{\left(\underset{i=1}{\overset{m}{.Math.}}{E}_z\left(i\right)\right)}^2}{m}\right)}}& \left(1\right)\end{array}$ where, ρ.sub.T.sub.j.sub.,E.sub.z is the correlation coefficient between the measured value of a j.sup.th temperature sensor and the thermal error of the spindle, T.sub.j(i) is a temperature value measured by the j.sup.th temperature sensor at time instance i, E.sub.z(i) is a value of the spindle thermal error, measured by the displacement sensor at time instance i, m is an amount of data, measured by the displacement sensor; based on the four temperature sensors on the spindle, a maximum thermal resistance coefficient of the spindle is determined, as well as the spindle temperature measurement point, while a temperature measurement value is set to the spindle temperature T.sub.sp; 3) establishment of spindle thermal error model let the temperature value, measured by a fifth temperature sensor 12, be T.sub.e, while a calculation formula of the spindle temperature and a difference T.sub.sp-e is as follows:
T.sub.sp-e(i)=(T.sub.sp(i)−T.sub.sp(1))−(T.sub.e(i)−T.sub.e(1))  (2) where, T.sub.sp-e(i) is a difference between T.sub.sp and T.sub.e at time instance i, T.sub.sp(i) is a measured spindle temperature at the measurement point at time instance i, T.sub.e(i) is a measured value of the fifth temperature sensor 12 at time instance i; a variation of T.sub.sp-e ΔT.sub.sp-e is calculated as follows:
ΔT.sub.sp-e(i)=T.sub.sp-e(i)−T.sub.sp-e(i−1)  (3) where, ΔT.sub.sp-e(i) is a fluctuation of T.sub.sp-e at time instance i; the spindle thermal error model is as follows: $\begin{array}{cc}{E}_{ez}\left(i\right)=\left(1-{\theta }_1\right)\times E_{ez}\left(i-1\right)+{\theta }_3\times {\theta }_1\times \left(\Delta T_{\mathrm{sp}\text{-}e}\left(i-1\right)+\frac{\Delta T_{\mathrm{sp}\text{-}e}\left(i\right)-\Delta T_{\mathrm{sp}\text{-}e}\left(i-1\right)}{{\theta }_2}\right)& \left(4\right)\end{array}$ where, E.sub.ez(i) is a calculated value of the spindle thermal error at time instance i, θ.sub.1, θ.sub.2 and θ.sub.3 are coefficients; 4) identification of model coefficients based on a nonlinear quadratic programming algorithm, coefficients θ.sub.1, θ.sub.2 and θ.sub.3 of the spindle thermal error model are identified under constraints; a objective function F(θ.sub.1,θ.sub.2,θ.sub.3) is as follows: $\begin{array}{cc}\min \left[F\left({\theta }_1,{\theta }_2,{\theta }_3\right)\right]=\min \left[\underset{i=1}{\overset{m}{.Math.}}\left(E_z\left(i\right)-E_{\mathrm{ez}}\left(i\right)\right)\right]{\theta }_{1min}\le {\theta }_1\le {\theta }_{1\mathrm{ma}x}{\theta }_{2min}\le {\theta }_2\le {\theta }_{2\mathrm{ma}x}{\theta }_{3min}\le {\theta }_3\le {\theta }_{3\mathrm{ma}x}& \left(5\right)\end{array}$ where, θ.sub.1min, θ.sub.2min and θ.sub.3min are lower limit values of the coefficients θ.sub.1, θ.sub.2 and θ.sub.3 respectively, while θ.sub.1max, θ.sub.2max and θ.sub.3max are upper limit values of the constraints, for coefficients θ.sub.1, θ.sub.2 and θ.sub.3, respectively; 5) thermal error compensation based on OPC UA the spindle thermal error model runs on a compensator, the compensator sends a compensation value, as calculated by the model, to a numerical control system, using the OPC UA communication protocol, the numerical control system compensates the spindle thermal error, according to the calculated compensation value.

Description

DESCRIPTION OF THE DRAWINGS

(1) FIG. 1 is a schematic diagram of the spindle temperature measuring points arrangement and thermal error testing.

(2) FIG. 2 is a flow chart of the spindle thermal error compensation.

(3) FIG. 3(a) is the spindle thermal error curve, before compensation.

(4) FIG. 3(b) is the compensated spindle thermal error curve.

(5) In the figures: 1 spindle; 2 spindle rear bearing; 3 first temperature sensor; 4 second temperature sensor; 5 third temperature sensor; 6 spindle rear bearing; 7 fourth temperature sensor; 8 detecting rod; 9 displacement sensor; 10 working table; 11 bed frame; 12 fifth temperature sensor; 13 shank interface.

DETAILED DESCRIPTION

(6) In order to make the objectives, technical solutions and advantages of the present invention more apparent, the present invention is described in detail below with reference to the accompanying drawings.

(7) An embodiment of the present invention will be described in detail, by taking as an example a vertical machining center spindle. The maximum spindle speed of the machining center is 12000 r/min. The spindle is equipped with a water cooling device.

(8) The first step is the parameter identification test of the spindle thermal error model.

(9) Four temperature sensors are arranged on the surface of the spindle 1, where specifically, the first temperature sensor 3 and the fourth temperature sensor 7 are attached to the positions of the rear bearing 2 and the front bearing 6, respectively; the second temperature sensor 4 and the third temperature sensor 5 are evenly distributed between the rear bearing 2 and the front bearing 6, wherein the second temperature sensor 4 is close to the rear bearing 2 and the third temperature sensor 5 is close to the front bearing 6; the detecting rod 8 is mounted on the spindle, through the shank interface; the displacement sensor 9 is fixed on the table 10 by a magnetic table seat; the fifth temperature sensor 12 is arranged on the bed frame 11.

(10) Let the spindle run in the order shown in Table 1.

(11) TABLE-US-00001 TABLE 1 Spindle operation sequence table Serial number Spindle speed (r/min) Operation hours (mm) 1 1000 30 2 4000 20 3 6000 10 4 8000 30 5 2000 60 6 0 120 7 4000 70 8 10000 60 9 0 20

(12) The measured values from temperature sensors (3, 4, 5, 7 and 12) and the displacement sensor 9 are simultaneously recorded, during the operation of the spindle.

(13) The second step, the spindle temperature measurement point is determined.

(14) Correlation analysis is carried out, between the collected temperature data of each position and the thermal error of the spindle. The correlation coefficient, between the temperature of each point and the thermal error of the spindle, is calculated as follows:

(15) $\begin{array}{cc}{\rho }_{T_j,E_Z}=\frac{\underset{i=1}{\overset{m}{.Math.}}{T}_j\left(i\right)E_z\left(i\right)-\frac{\underset{i=1}{\overset{m}{.Math.}}{T}_j\left(i\right)\underset{i=1}{\overset{m}{.Math.}}{E}_z\left(i\right)}{m}}{\sqrt{\left(\underset{i=1}{\overset{m}{.Math.}}{T}_j^2\left(i\right)-\frac{{\left(\underset{i=1}{\overset{m}{.Math.}}{T}_j\left(i\right)\right)}^2}{m}\right)\left(\underset{i=1}{\overset{m}{.Math.}}{E}_z^2\left(i\right)-\frac{{\left(\underset{i=1}{\overset{m}{.Math.}}{E}_z\left(i\right)\right)}^2}{m}\right)}}& \left(1\right)\end{array}$
where, ρ.sub.T.sub.j.sub.,E.sub.z is the correlation coefficient between the measured value of the j.sup.th temperature sensor and the thermal error of the spindle, T.sub.j(i) is the temperature value measured by the j.sup.th temperature sensor at time instance i, E.sub.z(i) is the spindle thermal error value, measured by the displacement sensor 9 at time instance i, m is the amount of data measured by the displacement sensor 9.

(16) The correlation coefficient between the measured values of the temperature sensors 3, 4, 6, and 7 and the measured values of the displacement sensor 9 is calculated according to the Eq. (1). The specific results are shown in Table 2.

(17) TABLE-US-00002 TABLE 2 Correlation coefficient between temperature and thermal error of the spindle Temperature Sensor Correlation coefficient First Temperature Sensor 3 0.9145 Second Temperature Sensor 4 0.9546 Third Temperature Sensor 6 0.9039 Fourth Temperature Sensor 7 0.7880

(18) The second temperature sensor 4, having the largest correlation coefficient with the thermal error, is selected as the spindle temperature measuring point, while its temperature measurement value is set as the spindle temperature T.sub.sp.

(19) The third step is to establish the spindle thermal error model.

(20) Let the temperature value measured by the fifth temperature sensor 12 be T.sub.e, while the calculation formula of the spindle temperature and the difference T.sub.sp-e is as follows:
T.sub.sp-e(i)=(T.sub.sp(i)−T.sub.sp(1))−(T.sub.e(i)−T.sub.e(1))  (2)
where, T.sub.sp-e(i) is the difference between T.sub.sp and T.sub.e at time instance i, T.sub.sp(i) is the measured value of the spindle temperature at the measurement point at time instance i, T.sub.e(i) is the measured value of the fifth temperature sensor 12 at time instance i.

(21) The variation of Tsp-e ΔTsp-e is calculated as follows:
ΔT.sub.sp-e(i)=T.sub.sp-e(i)−T.sub.sp-e(i−1)  (3)
where, ΔT.sub.sp-e(i) is the amount of change of T.sub.sp-e at time instance i.

(22) The spindle thermal error model formula is as follows:

(23) $\begin{array}{cc}{E}_{ez}\left(i\right)=\left(1-{\theta }_1\right)\times E_{ez}\left(i-1\right)+{\theta }_3\times {\theta }_1\times \left(\Delta T_{\mathrm{sp}\text{-}e}\left(i-1\right)+\frac{\Delta T_{\mathrm{sp}\text{-}e}\left(i\right)-\Delta T_{\mathrm{sp}\text{-}e}\left(i-1\right)}{{\theta }_2}\right)& \left(4\right)\end{array}$
where, E.sub.ez(i) is the calculated value of the spindle thermal error at time instance i, θ.sub.1, θ.sub.2 and θ.sub.3 are coefficients.

(24) The fourth step is about the identification of model coefficients.

(25) Based on the nonlinear quadratic programming algorithm, the coefficients θ.sub.1, θ.sub.2 and θ.sub.3, in the above thermal error model, are identified under constraints. The objective function F(θ.sub.1,θ.sub.2,θ.sub.3) is as shown in the following equation.

(26) $\begin{array}{cc}\min \left[F\left({\theta }_1,{\theta }_2,{\theta }_3\right)\right]=\min \left[\underset{i=1}{\overset{m}{.Math.}}\left(E_z\left(i\right)-E_{\mathrm{ez}}\left(i\right)\right)\right]{\theta }_{1min}\le {\theta }_1\le {\theta }_{1\mathrm{ma}x}{\theta }_{2min}\le {\theta }_2\le {\theta }_{2\mathrm{ma}x}{\theta }_{3min}\le {\theta }_3\le {\theta }_{3\mathrm{ma}x}& \left(5\right)\end{array}$
where, θ.sub.1min, θ.sub.2min θ.sub.3min are the lower bounds of the coefficients θ.sub.1, θ.sub.2 and θ.sub.3 respectively, while θ.sub.1max, θ.sub.2max and θ.sub.3max are the upper limit values of the coefficients θ.sub.1, θ.sub.2 and θ.sub.3, respectively.

(27) The spindle thermal error model is established according to Eqs. (2) to (4). According to Eq. (5), the parameters in the model are identified, while the identification result is: θ.sub.1=7.5×10.sup.−5, θ.sub.2=9.8×10.sup.−3, θ.sub.3=408.1 μm/□.

(28) The fifth step is thermal error compensation based on OPC UA

(29) The spindle thermal error model is implemented on the compensator, while the compensation value, as calculated by the model, is sent to the numerical control system, using the OPC UA communication protocol. The numerical control system compensates for the thermal error of the spindle, according to the received compensation value. The compensation process is shown in FIG. 2.

(30) FIG. 3(a) and FIG. 3(b) illustrate the comparison result, before and after thermal error compensation, of the vertical machining center spindle, as obtained by the aforementioned steps. FIG. 3(a) is the thermal error curve of the spindle, before compensation, while FIG. 3(b) is the thermal error curve of the spindle, after compensation.