Thermal Error Analysis of Hydrostatic Turntable System

Abstract

The thermal error caused by the temperature rise in the service condition of the hydrostatic turntable system has a significant impact on the accuracy of the machine tool. The temperature rise is mainly caused by the friction heat of the bearing and the heat of the oil pump. The amount of heat mainly depends on the working parameters, such as the oil supply pressure and the oil film gap. The unreasonable parameter setting will cause the reduction in the internal flow of the hydrostatic bearing and the increase in the oil pump power, which makes the heat of the lubricating oil increase and the heat dissipation capacity decrease during the movement. Based on the established hydrostatic turntable system, in order to explore the main influencing factors of its thermal error, the temperature field model of the component is established by calculating the thermal balance of the key components of the system. The thermal coupling analysis of the component is carried out by using the model, and the temperature rise, deformation and strain curves of the hydrostatic turntable system under different service conditions are obtained. The results show that with the increase in the temperature, the deformation and strain of the bearing increase monotonously. For every 1 °C increase, the total deformation of the bearing increases by about 0.285 $\mathsf{\mu }\mathrm{m}$. The higher the oil supply pressure, the higher the temperature rise in the system. The larger the oil film gap, the lower the temperature rise in the system. The oil supply pressure has a greater influence on the temperature rise and thermal deformation than the oil film gap. This study provides a valuable reference for reducing the thermal error generated by the hydraulic turntable of the ultra-precision lathe.

1. Introduction

As the core component of the precision CNC lathe, the hydrostatic turntable can form a supporting oil film in the clearance of the motion pair through the oil supply system and realize the fluid lubrication support and rotary motion guidance without solid direct contact [1]. Because of its advantages of a high precision, a small axial and radial runout, high stiffness and good damping characteristics, it is widely used in precision machining, optical equipment and semiconductor manufacturing [2]. Due to the limitation of the machining accuracy and the complexity of actual working conditions, the geometric error, structural error, control error and thermal error will have a significant impact on the accuracy of precision CNC machine tools [3]. The geometric and structural errors can be controlled by high-precision machining process and assembly calibration, and the control-related errors can be improved by servo system optimization and advanced algorithms [4]. In contrast, the thermal error is caused by factors such as bearing friction and motor operation heating, which is inevitable, time-varying and non-linear [5]. In order to ensure the machining accuracy of the workpiece, precision CNC machine tools generally process the workpiece in a thermally stable state. Although modern machine tools generally have independent temperature control systems, due to the influence of factors such as the thermal expansion coefficient of the workpiece and the lubrication state, it is difficult to achieve the ideal state of temperature control [6]. The resulting thermal error will directly affect the accuracy retention of the machine tool under actual machining conditions. Studies have shown that thermal errors account for 40% to 70% of the total machining errors, and they are the key factors affecting the machining accuracy [7].

Under the service condition of the hydrostatic rotary table, the heat energy generated by the bearing friction and oil pump operation will increase the temperature of the bearing and its internal lubricating oil and make the temperature field of the whole rotary table system change significantly through heat transfer and convective heat transfer [8,9,10,11]. This leads to thermal error problems such as increased thermal deformation and the decreased viscosity of the lubricating medium, which seriously affects the machining accuracy of the machine tool [12]. Therefore, it is of great significance to study the thermal error of the hydrostatic turntable to reduce its heat transfer effect and improve the machining accuracy of precision CNC machine tools [13,14].

At present, the research on the thermal error of the hydrostatic turntable system at home and abroad has achieved a series of remarkable results. Fu Yanjun et al. established a static mathematical model of the opposite oil pad of the static pressure turntable for the closed hydrostatic turntable of the PM flow meter [15]. Hu Qiu et al. proposed a corresponding improvement strategy by studying the thermal error influence mechanism of the high-torque direct-drive ultra-precision hydrostatic turntable [16]. Hu Junping et al. used the fluid–structure–thermal coupling model to study the influence of working parameters on the performance of the hydrostatic turntable [17]. Based on the idea of an equivalent oil film thickness of each sealing edge, Xiong Wanli et al. used the analytical method to study the inclined bearing characteristics of hydrostatic turntables [18]. Congbin Yang et al. introduced the concept of internal flow and used the finite difference method to evaluate the bearing performance of the oil pad inside the turntable [19]. Zhang Yanqin et al. carried out a quasi-steady-state analysis through numerical simulations and obtained the variation in performance indexes, such as the temperature and pressure of the lubricating oil film with time under different loads [20].

In summary, at present, scholars at home and abroad have studied the thermal error of hydrostatic turntables, mainly through the establishment of mathematical models and a simulation analysis to explore the influence of working parameters such as the oil film pressure and oil film clearance on the thermal error of hydrostatic turntables. However, the comparative study of the comprehensive influence of these factors on the thermal error of the turntable system under multiple working conditions is not deep enough. At the same time, most of the restrictors used in the hydrostatic turntable in the above research are common orifices and capillary tubes, while there are few studies on the hydrostatic turntable using annular gap restrictors. Compared with the former two, the annular gap restrictor can control the bearing performance of the bearing by adjusting its throttling parameters during the working process.

In view of the above problems, this paper takes the constant pressure annular clearance throttling hydrostatic turntable as the research object. In the first section, through the critical analysis of the existing research, the necessity of the research on the thermal error of the hydrostatic turntable is expounded. In Section 2, the temperature field model of the component is established by simplifying the turntable model into a bearing model and calculating its thermal balance, and the maximum temperature rise in the turntable system is obtained based on the model. In Section 3, the temperature rise and total deformation of the bearing bush under different working parameters are obtained by a thermal–mechanical coupling simulation. The comprehensive influence of working parameters such as different oil supply pressures and oil film clearances on the thermal error is obtained by a comparative analysis. The accuracy of the temperature field model in Section 2 is further verified. This study provides a valuable reference for the in-depth analysis of the characteristics and variation in the thermal error of the hydrostatic turntable. The corresponding heat dissipation system and compensation system can be developed to improve the positioning accuracy and stability of the turntable. At the same time, it can also evaluate the applicability of the hydrostatic turntable under different working conditions and temperature conditions and provide technical support for different fields.

2. Temperature Field Model of Hydrostatic Turntable System

2.1. The Overall Structure of the Hydrostatic Turntable System

The main structure of the hydrostatic turntable used in this paper is shown in Figure 1. It is mainly composed of workbench 1, hydrostatic bearing 2, annular slit restrictors 3 and frame 6. Radial bearing 15 and thrust bearing 16 are symmetrically distributed on the inner and upper and lower sides of hydrostatic bearing 2, and the motor is integrated inside frame 6. When working, the hydrostatic bearing and the worktable are driven by the motor to rotate axially.

Figure 2 shows the three-dimensional model diagram of the turntable system. There are oil grooves between the contact surfaces of the radial bearing and the spindle, the thrust bearing and the workbench, which are convenient for the lubricating oil to enter and cooperate with the spindle and the workbench to support and guide the components on the turntable. Due to the continuous rotation during the operation and the large amount of heat emitted by the lubricating oil, it is the main part of the heat concentration in the hydrostatic turntable system. Therefore, it is necessary to study the main influencing factors of the thermal error generated by the system, and it is necessary to analyze the thermal error of the hydrostatic bearing.

2.2. Temperature Field Modeling of Hydrostatic Turntable

Considering that the viscosity value of the hydraulic oil is sensitive to the temperature when the hydrostatic turntable is working, it will decrease with the increase in temperature, which will reduce the bearing capacity and stiffness of the oil film, thus affecting the working ability of the whole system. Therefore, it is necessary to calculate the average temperature rise in the hydraulic oil of the hydrostatic turntable.

When the lubricating oil flows in the clearance of the hydrostatic bearing, it is a laminar flow state or a turbulent flow state, or it may be a superposition state between the two. Different flow states have different corresponding flow field characteristics and different calculation methods. Therefore, it is necessary to judge the fluid state by Formula (1). If the calculated Reynolds number is less than 2000, the fluid is considered to be in a laminar flow. When the Reynolds number is greater than 4000, the fluid is considered to be in a turbulent state; when the Reynolds number is between 2000 and 4000, the fluid is considered to be in the transition stage between the laminar flow and turbulent flow [21].

$$\mathrm{Re}={\displaystyle \frac{\rho vl}{\mu }}$$

(1)

where $\rho$ is the density of the hydraulic oil, v is the flow rate of the fluid, $l$ is the equivalent radius through the interface and $\mu$ is the dynamic viscosity of hydraulic oil.

Since the turntable uses No.32 lubricating oil, the hydraulic support surface clearance is 40 $\mathsf{\mu }\mathrm{m}$, and the fluid flow rate is assumed to be 20 $\mathrm{m}/\mathrm{s}$; the calculated Reynolds number is 225, which is much smaller than 2000. Therefore, it can be considered that the fluid in the hydrostatic bearing is in a laminar flow state, and the static performance can be used to calculate the temperature rise.

The temperature rise in the hydraulic oil in the hydrostatic rotary table is mainly caused by the internal friction power, and the internal friction power depends on the factors such as the linear velocity of the bearing. The following assumptions need to be made when calculating the temperature rise in the hydraulic oil:

(1)

Ignoring the heat transfer between the hydraulic oil and the bearing parts; that is, the heat generated by the internal friction of the hydrostatic bearing under the working condition of the hydrostatic rotary table is all used to increase the temperature of the hydraulic oil;

(2)

The convective heat transfer coefficient of the fluid of the lubricating medium and the external air does not change with the temperature;

(3)

The power consumed by the turntable motor is all converted into heat and absorbed by the lubricating oil;

(4)

The process of the hydraulic oil temperature rising caused by the internal friction power follows the law of the conservation of energy.

2.2.1. Temperature Rise Calculation of Radial Bearing

The power consumption of the hydrostatic rotary table mainly includes the power consumption of the liquid friction and the oil supply system when the bearing and the spindle are sliding relatively. When the spindle rotates, the relative rotation between the spindle and the bearing bush will cause the shear friction of the lubricating oil in the gap to heat up, and the consumed energy is the spindle liquid friction power $N_f$, as shown in Formula (2).

$$N_f=n\cdot f\cdot v_1$$

(2)

where $n$ is the number of oil chambers, $v_1$ is the spindle speed and $f$ is the friction force in a single oil chamber of the journal bearing. The calculation is shown in Formula (3).

$$f=\mu v_1\left({\displaystyle \frac{A_1}{h_0}}+{\displaystyle \frac{A_2}{h_0+z_1}}\right)$$

(3)

where $A_1$ is the area of the hydraulic support surface of a single oil chamber, $A_2$ is the area of the hollowing part of a single oil chamber, $h_0$ is the oil film gap and $z_1$ is the depth of the oil chamber.

The energy consumed in the process of pumping the lubricating oil through the bearing of the oil supply system is the pumping power, as shown in Formula (4).

$$N_p=p_s\cdot Q=p_s\cdot n\cdot q$$

(4)

where $P_s$ is the oil supply pressure, $Q$ is the total flow rate of the radial bearing and $q$ is the flow rate flowing out of the single oil cavity of the radial bearing.

The oil chamber of the radial bearing is shown in Figure 3. The size of the oil chamber is very small relative to the bearing diameter, so it can be equivalent to a rectangular oil chamber for calculation. From the continuity equation of the liquid flow, it can be seen that the flow rate $q$ of the single oil cavity of the bearing flowing outward at no load is as shown in Formula (5).

$$q={\displaystyle \frac{R{h}_0^3}{6\mu l_1}}\left({\displaystyle \frac{l{l}_1}{R{b}_1}}+2{\theta }_1\right)p_0$$

(5)

The parameters of the radial bearing can be calculated by Formula (6), and the specific parameter values are shown in

Table 1. Radial bearing parameter table.

Symbol	Definition	Parameter Values
n	Number of oil chambers	4
$\mu$	Dynamic viscosity of lubricating oil	28.8 × 10−3 Pa·s
v1	Spindle speed	0.39 m/s
A1	The area of the hydraulic support surface of a single oil chamber	2148.90 mm2
A2	The area of the hollowing part of a single oil chamber	2285.91 mm2
h0	Oil film gap	$20 \mathsf{\mu }\mathrm{m}$
$z_1$	The depth of the oil chamber	2 mm
$P_s$	Oil supply pressure	$2 \mathrm{M}\mathrm{P}\mathrm{a}$
R	Average radius of oil cavity	75 mm
$P_0$	Pressure of oil chamber	1 MPa
L	Bearing length	111.81 mm
l	Oil chamber length	93.81 mm
l1	Axial sealing surface length	9 mm
B	Bearing width	36 mm
b	Oil chamber width	20 mm
b1	Circumferential sealing surface width	8 mm
b2	Width of oil return tank	6 mm
$c$	Specific heat capacity of lubricating oil	$2120 \mathrm{J}/\mathrm{k}\mathrm{g} \cdot \mathrm{℃}$
$\rho$	Lubricating oil density	$0.9 \mathrm{g}/{\mathrm{c}\mathrm{m}}^3$

.

$$\left\{\begin{array}{l}{l}_1={\displaystyle \frac{L-l}{2}}\hfill \\ b_1={\displaystyle \frac{B-b}{2}}\hfill \\ {\theta }_1={\displaystyle \frac{\pi }{4}}-\left({\displaystyle \frac{b_1}{R}}+{\displaystyle \frac{b_2}{2R}}\right)\hfill \end{array}\right.$$

(6)

The accurate calculation of the temperature rise remains challenging, as it is not only directly associated with heat sources but also influenced by the ambient conditions, heat dissipation structures and operational duration. The following temperature rise calculation formula is developed based on the law of energy conservation. By assuming that the frictional power of the spindle fluid and the oil pump power are completely converted into thermal energy absorbed by the lubricating oil, the maximum temperature rise ∆T of the lubricating oil between the bearing outlet and inlet is derived as shown in Formula (7). Substituting the corresponding parameters, the maximum temperature rise in the radial bearing is 1.29 °C.

$$\Delta T={\displaystyle \frac{\left(N_f+N_p\right)}{c\rho Q}}$$

(7)

2.2.2. Temperature Rise Calculation of Thrust Bearing

The single oil chamber of the thrust bearing is shown in Figure 4. The friction power of the thrust bearing is calculated as Formulas (8) and (9) by splitting and integrating the sum, where P_zi is the friction power of each region of the single oil chamber of the thrust bearing, 1, 2, 3 and 5 are different sealing surface areas of a single oil chamber, and 4 is the oil chamber area.

$$N_f=n{\displaystyle \sum _{i=1}^5{P}_{zi}}$$

(8)

$$\left\{\begin{array}{l}{P}_{z1}=P_{z2}={{\displaystyle \int }}_{R_1}^{R_4}\mu {\left({\displaystyle \frac{2\pi nR}{60}}\right)}^2{\displaystyle \frac{R{\alpha }_1}{h_0}}dR\hfill \\ P_{z3}={{\displaystyle \int }}_{R_3}^{R_4}\mu {\left({\displaystyle \frac{2\pi nR}{60}}\right)}^2{\displaystyle \frac{R{\alpha }_2}{h_0}}dR\hfill \\ P_{z4}={{\displaystyle \int }}_{R_2}^{R_3}\mu {\left({\displaystyle \frac{2\pi nR}{60}}\right)}^2{\displaystyle \frac{R{\alpha }_2}{h_0+z_1}}dR\hfill \\ P_{z5}={{\displaystyle \int }}_{R_1}^{R_2}\mu {\left({\displaystyle \frac{2\pi nR}{60}}\right)}^2{\displaystyle \frac{R{\alpha }_2}{h_0}}dR\hfill \end{array}\right.$$

(9)

The flow q flowing into a fan-shaped oil chamber of the bearing through the annular gap restrictor at no load can be calculated by Formula (10).

$$q={\displaystyle \frac{h_0^3}{3\mu }}\left({\displaystyle \frac{l}{B-b}}+{\displaystyle \frac{b}{L-l}}\right)p_0$$

(10)

The approximate calculation formulas of the rectangular oil chamber and fan-shaped oil chamber are shown in Formula (11), and the parameters of the thrust bearing are shown in

Table 2. Thrust bearing parameter table.

Symbol	Definition	Parameter Values
$\mu$	Dynamic viscosity of lubricating oil	28.8 × 10−3 Pa·s
R1		77 mm
R2		86 mm
R3		101 mm
R4		110 mm
${\alpha }_1$		0.082 rad
${\alpha }_2$		1.351 rad
$h_0$	Oil film gap	$20 \mathsf{\mu }\mathrm{m}$
$z_1$	The depth of the oil chamber	2 mm
$P_s$	Oil supply pressure	$2 \mathrm{M}\mathrm{P}\mathrm{a}$
$P_0$	Pressure of oil chamber	$1 \mathrm{M}\mathrm{P}\mathrm{a}$
n	Number of oil chambers	8
$c$	Specific heat capacity of lubricating oil	$2120 \mathrm{J}/\mathrm{k}\mathrm{g} \cdot \mathrm{℃}$
$\rho$	Lubricating oil density	$0.9 \mathrm{g}/{\mathrm{c}\mathrm{m}}^3$

.

$$\left\{\begin{array}{l}B=R_4-R_1\hfill \\ b=R_3-R_2\hfill \\ L={\displaystyle \frac{\left(R_1+R_4\right)({\alpha }_2+2{\alpha }_1)}{2}}\hfill \\ l={\displaystyle \frac{\left(R_2+R_3\right){\alpha }_2}{2}}\hfill \end{array}\right.$$

(11)

By substituting the outcomes of Formula (10) into Formula (4), the pumping power Np of the thrust bearing is derived. Subsequently, by integrating Formulas (7) and (8), the calculated maximum temperature rise in the thrust bearing is determined to be 1.77 °C.

In this section, through the analysis of the internal structure of the hydrostatic turntable system, the turntable system is simplified as a bearing to establish a temperature field model. After judging that the lubricating oil in the bearing is in a laminar flow state, under the assumption of the temperature rise, the bearing is divided into the radial bearing and thrust bearing to calculate the temperature rise in the lubricating oil, and the maximum temperature rise in the radial bearing and thrust bearing is 1.29 and 1.77 °C, respectively.

3. Finite Element Analysis of Thermal Characteristics of Turntable System

3.1. Finite Element Analysis of Temperature Field of Bearing Bush

In order to explore the temperature field distribution of the bearing under service conditions, a steady-state thermal simulation was carried out in ANSYS 2022 R1. Considering the simulation speed and accuracy, the automatic method is used for meshing. The specific meshing scheme is shown in

Table 3. Grid division scheme table.

Grid Division Scheme	Overall Meshing Density (mm)	Local Meshing Density (mm)
a	8	2
b	5	2
c	2	2

, and the model after meshing is shown in Figure 5 [22].

The boundary conditions of the steady-state thermal simulation are shown in

Table 4. Steady-state thermal simulation boundary condition setting value.

Boundary Conditions	Parameter Values
Inlet pressure	2 MPa
Oil chamber pressure	1 MPa
Oil outlet pressure	0 MPa
Materials	Structural steel
Heat flow of radial bearing	10.21 W
Heat flow of thrust bearing	19.95 W
Ambient temperature	22 °C

. The radial and axial heat flow settings of the bearing model are shown in Figure 6, which correspond to the sum of the liquid friction power N_p and the oil pump power N_f of the radial bearing and the thrust bearing, respectively. The bearing material is structural steel. Because the radial and axial end faces of the bearing bush are in contact with the liquid film and bear the dynamic pressure of the liquid film on the end face, the radial and axial end faces of the bearing bush are set as the fluid–solid coupling surface in the calculation. The axial displacement constraint is added to the axial downward side of the bearing bush, and the heat conduction type is set to coupled heat transfer, ignoring the thermal radiation. The lubricating oil is set to a laminar flow state, and the energy equation and viscous dissipation equation are turned on. The solver solution format selects a high-order solution mode to ensure the accuracy and reliability of the solution.

The steady-state thermal simulation results under different meshing schemes are shown in

Table 5. Error comparison table of different meshing schemes.

Grid Division Scheme	Overall Meshing Density (mm)	Local Meshing Density (mm)	Maximum Temperature Rise (°C)	Error (Relative to b-Meshing Scheme)
a	8	2	1.616	2.5%
	6.5	2	1.590	0.8%
b	5	2	1.577	0
	3.5	2	1.575	0.1%
c	2	2	1.576	0.02%

, and the temperature field distribution of the bearing under the (b) meshing scheme is shown in Figure 7. It can be seen from Table 5 and Figure 7 that the relative errors of different meshing schemes compared with scheme (b) are all below 5%, and the calculation results of the three meshing schemes (a–c) are similar. The average temperature rise in the bearing is about 0.26 °C, the oil chamber is the heat concentration part and the maximum temperature rise is about 1.577 °C. There is a significant increasing trend from the edge of the bearing to the axial end, which is in line with the actual situation. Considering the simulation speed and accuracy, the (b) scheme is used for meshing.

3.2. Thermal Deformation Analysis of Bearing Bush Under Different Working Conditions

After solving the temperature field of the bearing, the temperature field is imported into the statics module to calculate the thermal deformation of the turntable. The finite element analysis results of the thermal deformation of the bearing bush under the condition of the oil supply pressure of 2 MPa and the oil film gap of 20 $\mathsf{\mu }\mathrm{m}$ are shown in Figure 8.

It can be seen from Figure 8 that in the process of thermal–mechanical coupling, the thermal deformation of the bearing bush is not uniform, and it shows an obvious increasing trend from the edge of the bearing to the axis end. The deformation at the edge of the bearing bush is the smallest, about 0.093 $\mathsf{\mu }\mathrm{m}$; the average total deformation of the bearing is 0.14 $\mathsf{\mu }\mathrm{m}$; the deformation at the oil sealing surface of the bearing is the largest, about 0.278 μm; and the maximum stress reaches 5.3 MPa. It is the main deformation zone of the bearing, which mainly affects the axial runout accuracy of the turntable. The results are in good agreement with the actual situation, which further verifies the accuracy of the temperature field model.

Due to the different thermal deformations caused by the temperature rise in the hydrostatic rotary table under different service conditions, the oil supply pressure and the oil film gap have a great influence on the thermal error. After adding the boundary conditions corresponding to different working conditions, the results of the temperature rise and thermal deformation after the operation simulation are shown in Figure 9 and Figure 10.

The following can be observed from Figure 9 and Figure 10: (1) As the temperature increases, the deformation and strain of the hydrostatic turntable system increase monotonically. For every 1 °C increase, the total deformation of the bearing bush increases by about 0.285$\mathsf{\mu }\mathrm{m}$. (2) The temperature rise and total deformation of the hydrostatic turntable system increase with the increase in the oil supply pressure and decrease with the increase in the oil film clearance. For every 0.2 °C increase, the oil supply pressure needs to be increased by about 0.5 MPa, and the oil film gap needs to be reduced by about 15 $\mathsf{\mu }\mathrm{m}$; for every 0.1 $\mathsf{\mu }\mathrm{m}$ increase in the total deformation of the bearing, the oil supply pressure needs to increase by about 1 MPa, and the oil film gap needs to be reduced by about 15$\mathsf{\mu }\mathrm{m}$. At the same time, the slope of the thermal error curve under different oil supply pressures is obviously larger than the slope of the thermal error curve under different oil film gaps, which indicates that the oil supply pressure has a greater influence on the thermal error than the oil film gap.

In this section, after comparing and selecting the appropriate meshing scheme, the temperature rise and total deformation of the bearing bush under different working parameters are obtained by thermal–mechanical coupling simulations. Through a comparative analysis, the influence of different oil supply pressures and oil film clearances on the thermal error of the turntable is obtained; that is, for every 1 °C increase, the total deformation of the bearing bush increases by about 0.285 $\mathsf{\mu }\mathrm{m}$. The higher the oil supply pressure, the higher the temperature rise and the total deformation of the system. The larger the oil film gap, the lower the temperature rise and the total deformation of the system, and the oil supply pressure has a greater influence on the temperature rise than the oil film gap, which further verifies the accuracy of the temperature field model in Section 2.

4. Conclusions

In order to study the thermal error of the hydrostatic turntable system and improve the accuracy of the machine tool, this paper explores the main influencing factors of the thermal error of the system by thermal balance calculations and a thermal coupling analysis of the key components of the hydrostatic turntable system. The main research results are as follows:

(1)

As the temperature increases, the deformation and strain of the hydrostatic turntable system increase monotonically. For every 1 °C increase, the total deformation of the bearing increases by about 0.285 $\mathsf{\mu }\mathrm{m}$. This conclusion provides inspiration for the optimal design of the cooling system of the hydrostatic rotary table. For example, the thermal safety limit of the turntable operation can be established according to the quantitative relationship between the temperature and deformation to improve the heat dissipation accuracy of the cooling system.

(2)

The temperature rise in the hydrostatic turntable system increases with the increase in the oil supply pressure and decreases with the increase in the oil film clearance. The oil supply pressure has a greater influence on the temperature rise and thermal deformation than the oil film clearance. This conclusion is helpful for the coordinated control of the oil supply pressure and the oil film gap of the hydrostatic turntable. The flow rate can be increased by moderately increasing the oil film gap and the oil supply pressure, thereby reducing the heat generated by the oil film surface during the movement, causing a large amount of heat to be taken away by the hydrostatic oil, so as to reduce the temperature rise in the hydrostatic turntable system and improve the overall accuracy.

At present, due to the complexity of the actual working conditions of the hydrostatic turntable and the limitation of the accuracy of the measuring equipment, we have not specifically measured the actual thermal error of the turntable. After that, we plan to measure the thermal errors such as the temperature rise and total deformation of the hydrostatic turntable under different working conditions through experiments and compare them with the theoretical results, so as to further verify the accuracy of the simulation and conclusions.

In general, the results of this study provide a new perspective for the in-depth study of the thermal error influencing factors of the hydrostatic turntable, which is helpful to improve the stability and reliability of the hydrostatic turntable, and provide some ideas for the design improvement and technological innovation of the hydrostatic turntable.