3.1 Unloaded experiment of the spindle system
Under non-loaded conditions, the spindle was running continuously at different speeds with temperature monitored. The continuous experiment contains five rotating speed stages: 0rpm, 500rpm, 1000rpm, 1500rpm, and 2000rpm. Each stage has a running time of 1 hour to ensure that the temperature change of the spindle at each rotating speed can be stabilized. The result is shown in Fig. 4.
It can be seen from the temperature monitoring graph that, in addition to the ambient temperature, each part of the spindle system will have an obvious initial temperature rise after the experiment is turned on, even if the rotating speed is 0 rpm. The temperature of each measuring point on the spindle shows a stepped upward trend with the increase of the rotating speed. We extracted the oil temperature difference of the front bearing, the rear bearing and the motor part of the spindle system, and made the curve shown in Fig. 5, which can further reveals the law of temperature rise in each part of the spindle.
Figures 5(a), 5(b), and 5(c) respectively represent the data of the temperature difference between oil inflow and outflow at the position of the front bearing, the rear bearing and the motor part. The results show that the different characteristic temperature rising in different areas of the spindle. The temperature difference in the front bearing responds relatively rapid, which can be fitted as a quadratic curve with the rotating speed. On the contrary, the temperature change in the rear bearing is closer to a linear growing. The temperature difference between the inlet and outlet of the motor's cooling oil is lower than that of the bearing, but it also shows a linear growing with the increase in rotating speed.
3.2 Axial thermal error of the spindle
In the experiment, the temperature data and displacement data were collected at a specific rotating speed. The axial thermal displacement with temperature data of the spindle at speed of 1000rpm, 2000rpm, and 3000rpm were recorded respectively, as shown in Fig. 6:
The experiment was carried out for one and a half hours in each speed group until the temperature of the spindle stabilized. The thermal displacement data is collected every three minutes with the laser displacement sensor at a sampling rate of 1000Hz, as shown in Fig. 6 (a), Fig. 6 (b), and Fig. 6 (c). Overall, displacement data at 3000rpm corresponds to the largest thermal error in the equilibrium state, where the axial thermal error reaches 40µm. The thermal error at the rotating speed of 1000rpm is the smallest, which is 8µm.
In order to explore the influence of the temperature change on the thermal error of the spindle system, also to find the linear or non-linear relationship between the key temperature data and the thermal error of the spindle, it is necessary to establish a prediction of the thermal error of the machine tool spindle with high accuracy, strong generalization ability, and small calculation amount. Common thermal error modeling methods include: multiple linear regression (MLR), artificial neural network (ANN), gray prediction model (GM), support vector machine (SVM), etc.[18–20]
Here we have chosen the SVM regression model with Gaussian kernel, and utilized the experimental data of the spindle at a rotating speed of 1000rpm, 2000rpm, and 3000rpm as the input of the training data set, and the corresponding thermal displacement as the output. Therefore, there are 88 sets of temperature-thermal displacement data in the training set in total.
Subsequently, by inputting the experimental data of the spindle at a rotating speed of 2500rpm into the trained model, the thermal displacement prediction curve can be obtained, as shown in Fig. 6(d). It can be seen that the model has a certain thermal error prediction effect, whose maximum prediction error is 2µm. Therefore, in the case of small batches of data obtained under experimental conditions, SVM regression model can obtain sufficiently accurate thermal error predictions.
3.3 Preloaded experiment of the spindle system
In this section, we have carried out experiments on the temperature difference evolution of the hydrostatic spindle under the load of torque and radial force under simulated working conditions, and explored the effect of different loading parameters to the temperature rising.
Among them, the detail of the radial loading unit is shown in Fig. 7, including a pair of piezoelectric actuators, pressure sensors, charge amplifiers and signal collector. Piezoelectric ceramics are set for sinusoidal excitation with no bias voltage. The pressure load signal is collected by a pressure sensor preloaded in series with the piezoelectric actuators. The spindle torque is loaded by the magnetic powder brake. At the rotating speed of 100rpm. The magnetic powder brake with 600w rated power corresponds to a maximum torque output of 57.3Nm, so the maximum torque output of 60Nm can be used for loading, since the empirical value of the grinding wheel torque is usually 20-70Nm. Before each test, the spindle system has been warmed up till the temperature is stabilize. The output torque of the magnetic powder brake is set from 0Nm to 60Nm, while the temperature rising information of the spindle under the corresponding working conditions is collected.
By analyzing the temperature difference between the inlet and outlet oil, as shown in Fig. 7(a), it is promising to infer that under the condition of a fixed rotating speed, the temperature rise of the spindle under different torques is mainly reflected in the motor, and the bearing temperature change is not greatly affected by the torque loading. Since the motor heat is directly proportional to the output power, and the output power will increase with the increase of the load torque, the temperature difference between the oil input and output of the motor will increase stepwise under different torque loads. The overall temperature rise curve of the motor also shows a step-like upward trend, as shown in Fig. 7(b).
In the experiment, the temperature rise trend of the motor basically conforms to the quadratic curve fitting, and the temperature rise curve is basically the same under different radial force loading as long as the torque loading condition remains the same, which indicated that the radial force has little effect on the motor temperature rise within the usual range, while torque is the main source of thermal power.
3.4 Experiment of hydrostatic guideway system
In this experiment, nine temperature measurement points are set up at both the hydrostatic guideway and the hydraulic station, including: rail oil inlet, rail oil outlet, rail base, workbench, hydraulic station oil outlet, hydraulic station oil inlet, and cooler outlet, cooler inlet, the air. A temperature sensor is arranged at each point for data collection during the experiment. The time set for the experiment is 5.5 hours, and the temperature change is monitored during the experiment. The laser aligner is used to measure the motion straightness of the workbench when starting up and then every half an hour. The progress has been set at a feed speed of 500mm/min. The data collected during the experiment is shown in Fig. 8 below.
We extracted the temperature data of 4 key measuring points to make the curve as shown in Fig. 8(a), T1-T4 respectively represent the guide rail oil inlet, the guide rail oil outlet, the workbench, and the guide rail base. The experimental results indicated that the oil inlet temperature rises rapidly after starting up to about 24℃, which is 4℃ higher than the average temperature of room temperature (20℃), that may become the main source of thermal errors in the feed system. While the measured temperature of the guide rail base and the worktable shows a very slow rise. The low temperature of the oil outlet indicates that the heat energy of the oil is almost completely transferred to the inside of the guide rail.
The change of the motion straightness of the hydrostatic guideway in the whole experiment is shown in Fig. 8(b). Figure 8(c) shows the comparison curve of the vertical error of the hydrostatic rail before and after the experimental progress. It can be indicate from the figure that with the loading process of thermal stress from the oil, the vertical motion error of the workbench which is carried by the hydrostatic guideway increases across the board, due to the thermal deformation of the rail’s surface. The vertical motion straightness presents a shape with low ends and high middle. It also shows that the amplitude of motion straightness increases with time, but the shape remains unchanged.
Considering the temperature change data of the experimental process in Fig. 8(a), it is reasonable to believe that the thermal stress of the hydrostatic guideway has a direct effect on the accuracy of the machine tools, and the heat source mainly comes from the temperature rise of the hydraulic oil. With the continuous increase of the running time of the feed system, the oil film temperature of the hydrostatic guideway continues to rise, resulting in a continuous decrease in the straightness accuracy of the moving workbench. Within 5.5 hours of progressing time, under the effect of thermal deformation, the motion straightness of the workbench increased from 1.91µm to 6.11µm, as shown in Fig. 8(d). The overall motion accuracy is reduced by about 4µm, so that the straightness of the hydrostatic guideway cannot be maintained within a suitable accuracy range. There have been many studies on the relationship between the motion accuracy of the hydrostatic rail and the surface profile of the rail, but it is not the focus of this article. The thermal effect of the motion error will be explained with more details in out other research results.