Research on temperature rise characteristics of grease lubricated ball screw pair

Aerospace ball screws cannot be lubricated for maintenance and replacement, so they use grease that can run for a long time and keep the performance. Under high speed and high load conditions, the ball screw will be warmed up rapidly, and the temperature has a great effect on the capability of the grease. In this paper, we deduce the formula for calculating the screw temperature, establish a thermodynamic simulation of the ball screw model to get its temperature under different conditions, and set up a test bench to try out the screw temperature rise to investigate thermal properties in the grease lubrication conditions.


Introduction
In the aerospace field, grease is commonly used in the lubrication of ball screws, and the performance of the grease has a great influence on the friction torque and start-up torque during ball screw transmission [1] .Friction will inevitably generate heat, and the increase in temperature will not only lead to accelerated aging and decomposition of the grease inside the ball screw sub but also reduce the friction performance and thermal conductivity of the grease, and set up to lead to the complete failure of the grease.
At present, domestic and foreign scholars studied the thermal characterization of ball screws mainly through the friction torque, heat generation, and thermal convection formula to calculate the heat of each heat source and convective heat transfer coefficient, and then imported into the ABQUS software to get the simulation thermal field.G. Palazzo [2] has investigated the heat transfer in the working process of CNC machine tools and proposed a modeling method to study the thermal equilibrium of machine tools.Li Y [3] developed a finite difference method-based thermal properties model for a ball screw feed drive system considering moving heat sources, which can better predict the temperature change of the ball screw sub-system.Li T [4] established a new adaptive mobile thermal model with a moving heat source and different operating modes based on heat transfer theory, and the model quickly predicted the thermal error of the ball screw sub with high robustness.

Calculation of heat generation
The internal and external heat sources of a ball screw are largely composed of motor heat, bearing friction heat, and internal raceway friction heat of the ball screw.For studying the temperature rise characteristics of the ball screw sub, the heat generation from these three heat sources needs to be calculated.

2.1.1
Servo motor heat generation.The motor's heat production due to the friction of the internal structure in the process of transmitting power is transmitted from the shaft end of the ball screw sub using heat conduction.Since the heat is mainly related to the rotational speed, the transmission efficiency of the motor, and the size of the input torque, the heat is calculated as follows.Therefore, the formula for calculating the heat is as follows.
n ( 1) 9550 In the formula, Qd is heat generation for the motor; Md is input torque for the motor; d  is motor efficiency.

Bearing heat generation.
The type of support bearing for the ball screw vice is a rolling bearing, and its heat generation is mainly the friction heat produced by the internal structural elements of the bearing that hinder its movement when the inner and outer rings of the bearing rotate.Therefore, the heat generated by the friction of the bearing is not only related to the rotational speed but also related to the frictional torque of the bearing, which is calculated as follows [5][6] .
In the formula, n is speed; Mz is the frictional torque of bearings.

Internal heat generation of ball screws.
Grease lubricated Ball Screws generate a certain amount of heat due to the frictional contact of the balls with the raceways of the screws and the raceways of the nuts during the movement process.Since ball screws are similar to rolling bearings, the heat generated within the ball screw is shown as follows [7] .

Convection heat transfer and temperature rise calculations
Convective heat transfer in grease-lubricated ball screw units is the forced convection of itself unit with air.When its thermal equilibrium state, the heat loss per unit time is equal to the amount of heat generated, which is calculated as follows [8] .
In the formula, T is the real-time temperature of ball screws; TA is the initial room temperature; H1 is the coefficient of heat generation; H2 is the heat transfer coefficient; H3 is the temperature rise coefficient.
According to the principle of equation conversion, the theoretical formula for the temperature variation of ball screw sub with time is as follows.

Simulation analysis
Due to the complexity of the internal structure of the screw vice, it is difficult to correctly get its internal temperature distribution, but as long as some structural simplification and mesh delineation of the screw, it is possible to obtain a more accurate temperature value through the temperature-displacement coupled finite element simulation analysis [9][10] .The temperature-displacement coupling simulation model of the grease-lubricated ball screw vice is shown in Figure 2.

Temperature rise test
For verifying the accuracy of the theory and simulation, the temperature test is carried out on the ball screw sub-loading test bench, and the test setup is displayed in Figure 4.The test bench is mostly made up of a driving device, sensor, and loading device, which can measure a variety of performance Tests were conducted according to the working conditions required by the theoretical and simulation models, and the test results are shown in Figure 5.When the working condition is 3000 RPM-6000 N, the temperature rapidly rises to 145℃, at this time, white smoke appears in the screw, the grease melts, the lubrication state changes, and it is impossible to achieve thermal balance, so the experiment is stopped.

Analysis of Results
Comparison of temperature rise test results with theoretical calculation and analysis results, it can be seen that under the same load speed, the trend of temperature rise is consistent, but the results obtained from the test are slightly smaller than the theoretical calculation results.To reach a stable temperature condition to take the stable temperature value to calculate the error value, and to not reach a stable condition to take the cut-off position temperature value to calculate the error value are shown in Table 1.There are several reasons for the existence of error: (1) In addition to the ball screw vice, other friction in the movement process will also produce heat; (2) The theoretical analysis only considers the convective heat transfer between the screw sub and the air, but in the actual test, there is heat conduction between the ball screw sub and the test bench, which results in more temperature dissipation paths and more dissipation; (3) The melting point of grease is low in the operation process, with the temperature rise of grease properties appear to uncontrollable degradation of the state or even in the high-speed state from the inside of the raceway, resulting in lubrication tends to fail, affecting the temperature transfer and rise.

Conclusion
This paper establishes the ball screw temperature calculation formula under the thermal equilibrium state, establishes a thermodynamic model according to the performance parameters in the theoretical formula, carries out the temperature-displacement coupled finite element simulation analysis to obtain a more accurate temperature value, and finally verifies the accuracy of the theoretical and simulation models through the temperature rise test.The main results are as follows: (1) The temperature curve of the ball screw vice in the operation process is an exponential rule of change, and when it reaches the thermal equilibrium, the heat generation per unit time is equal to the heat dissipation, and the temperature reaches stability.
(2) The larger the rotation rate and load of the ball screw vice, the larger the speed of temperature rise change, and the higher the temperature when reaching thermal equilibrium.
(3) When the speed and load are low, the temperature rise of the ball screw sub is relatively smooth, and when it reaches thermal equilibrium, the grease can maintain its normal working performance; when the condition is worse, the temperature of the screw sub rises sharply and exceeds the melting point of the grease, and the grease deteriorates and melts rapidly and loses lubrication performance, which results in operation failure, so the grease lubricated ball screw sub can only run for a short time in the case of high-speed and high-load working condition.
(4) The theoretical and simulation model in this paper does not consider the performance change of grease in the process of temperature rise, which leads to errors in the temperature rise results; subsequent research can be carried out to study the effect of temperature on the performance of grease, and to establish a coupling model between the thermal characteristics of grease and the thermal characteristics of the screw, to obtain more accurate simulation results.
theory of heat transfer and the theory of temperature rise of screw sub can calculate the theoretical sub temperature rise under different working conditions, Figure1for the speed of 2000 RPM under the action of different load force temperature rise curves and the load of 6000 N under different speeds of the temperature rise curve of the screw sub.

Table 1 .
Temperature rise comparison and error calculation.