Thermal behavior on motorized spindle considering bearing thermal deformation under oil-air lubrication
Introduction
The performance of the motorized spindle directly affects the working state of the machine tool. The bearing is the core components of the motorized spindle, and its dynamic characteristics are mainly affected by the thermal behavior of the motorized spindle, which has a great influence on machining accuracy [1,2]. Since the second half of the 20th century, the influence of thermal behavior on machining accuracy and service life has been a hot research topic.
The angular contact ball bearing is usually used on the motorized spindle to meet the working environment of light load and high speed [3,4]. And when the motorized spindle is working, the motor and the bearing are heating simultaneously, so it is necessary to study the thermal interaction behavior between different parts in the motorized spindle. Further, there is a mutual influence and coupling relationship between the thermal behavior and the mechanical structure. As analyzed above, to model the thermal characteristics of the motorized spindle is complex and essential [5].
Many scholars have done an enormous amount of research on the thermal characteristics of the bearing and spindle. Bossmanns et al. [6,7] established a thermal model of the motorized spindle by using Finite Difference Method (FDM), and analyzed the thermal behavior of the spindle by regulating the preload and speed; Aleksandar et al. [8] used Finite Element Method to divide the bearing into several regions, and established the temperature field of the spindle and bearing while the contact thermal resistance is considered; Chien et al. [9] and Liang et al. [10] modeled and analyzed the helical cooling water pipeline installed into the motorized spindle, and the results showed that the cooling effect of the water is obvious; Zhang et al. [11], Lee et al. [12], and Wu et al. [13] established the finite element model for the motorized spindle by considering the simulation boundary conditions, and analyzed the temperature distribution and the thermal deformation, Finally, they verified the feasibility of the theoretical scheme through experiments; Xiang et al. [14] proposed a spindle model for predicting thermal deformation combined with experimental correction, and studied the relationship between axial deformation and speed; Yan et al. [15] studied the changing characteristics of the spindle temperature, and proposed a new method for the spindle thermal error model; Deng et al. [16] built a mathematical model of spindle bearing system by Heat Source Method, and compared the model by Finite Element Method. Lastly, the paper proved the application value of the model in thermal analysis by the experiment; Li et al. [17] discussed the heat generation characteristics of tilt bearing and the influence on its performance parameters; Cui et al. [18] determined the thermal contact resistances among the mechanism components and established an accurate thermo-mechanical coupling simulation model. And then, the influence of thermal contact resistance on heat distribution was quantitatively analyzed. Lastly, through the experiment, it was found that the test values are in good agreement with the simulation results; Chen et al. [19] integrated the state model, shaft model, bearing model and thermal model into a complete electro-thermo-dynamic model, and then analyzed and tested the thermal performance and dynamic characteristics of the model. The results showed that the model has a good prediction behavior; Based on a biogeography optimization theory, Zhang et al. [20] improved the heat transfer coefficient and established a model for predicting the thermal deformation of motorized spindle; Li et al. [4] analyzed the thermo-mechanical coupling model and studied the influence of bearing configuration on thermo-mechanical-dynamic behavior of high speed spindle. Finally, the results showed that the influence of the bearing orientation on the spindle stiffness is obvious; Liu et al. [21] analyzed the thermal error of the motorized spindle by combining the analytical method with the finite element method, and the experiment showed that the scheme is effective in the design and development of motorized spindle; Alfares et al. [22] used the thermal network method to model the thermal characteristics of the spindle bearing system, and studied the influence of preload, speed, and other variables on the system temperature and heat production.
From the introduction above, the thermo-mechanical coupling model of motorized spindle is mainly analyzed by Finite Element Method. The advantage of this method is that it avoids complicated numerical simulation, while its main drawback is that the description for the mechanism is not deep enough and the simulation time is relatively long. In addition, the bearing is an important heat source of motorized spindle, and its thermal deformation is lack of analytical calculation. In response to these problems, combined with the characteristics of heat generation and heat transfer of motorized spindle as shown in Fig. 1, this paper intended to solve the coupled model and get the analytical solution by using the thermal network method. Simultaneously, according to the characteristics of bearing heating and heat dissipation, the optimization for the thermo-mechanical coupling model was proposed, and the scheme to improve its heat dissipation was also devised.
Section snippets
Previous analysis of displacement model considering thermal expansion
In previous studies about the thermal deformation analysis of angular contact ball bearings, the thermal expansions of the ball and rings were considered and the displacement graph was established as shown in Fig. 2. From the graph, the factor which the radius increases as the ball expands was noticed. However, the groove curvature radius about the rings also changes under thermal analysis, and yet this fact was not considered in the model.
Improvement of displacement model considering groove curvature variation and oil film thickness
There is a layer of oil film between the ball and
Heat generation in bearing
The calculation of friction torque of bearing proposed by Palmgren [26] is written as:where M0 is the friction torque associated to lubricant hydrodynamic loss, and the expression is as below:
M1 is related to the load on bearing, and it is given as:
Here, f0 is the coefficient related to lubrication method and bearing type; ν denotes the oil kinematic viscosity; n represents the speed. f1 depends on bearing type and preload while P1
Axial heat conduction resistance
The axial resistance of the bearing ring and the spindle shell is expressed as follows [32]:where L means the length of conduction; λ indicates thermal conductivity; S denotes the conduction cross section area.
Radial heat conduction resistance
The radial resistance of the bearing ring and the spindle shell is listed as [33]:where re/ri is the radius; L illustrates the length.
Heat conduction resistance of ball
The resistance of the ball in bearing can be written by [34]:
Heat contact resistance
The structural feature between the
Establishment of thermal network model
The thermal network method was applied in this investigation to get the node temperature as shown in Fig. 10, and the thermal network nodes in bearing were set up in accordance with Fig. 6. The model of the front bearing is 7008UCG/GNP4 while the model of the rear bearing is 7007UCG/GNP4, and the bearing adopts the strategy of constant pressure preload. In addition, there are U-shaped water pipes on the shell for cooling. The following assumptions are proposed to simplify the calculation of the
Validation and discussion
The temperature rise test of the motorized spindle was executed to verify the accuracy of the coupled model, and the test bed is demonstrated in Fig. 26. The instruments and sensors used in the test are listed in Table 3, and the temperature sensors are fixed on the shell surface and bearing outer ring. Through the speed, cooling water flow rate, and compressed air flow rate variables, we studied the characteristics of temperature rise on motorized spindle.
Conclusions
The accuracy and life of motorized spindle depend on the bearing dynamic characteristics to a great extent, while the bearing dynamic characteristics are directly affected by the thermal behavior. Therefore, the bearing dynamic and temperature characteristics under the condition of thermal-mechanical coupling were studied in this investigation.
The curvature radius of bearing inner/outer ring was first analyzed and modeled, and with the combination by considering the oil film thickness, a new
Declaration of competing interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Acknowledgments
This study is supported by National Natural Science Foundation of China (No. 51775277). The authors would like to express sincere gratitude to all those who helped us during the writing of this thesis as well as all anonymous reviewers for their constructive suggestions.
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