Thermal network model and experimental validation for a motorized spindle including thermal–mechanical coupling effect

Abstract

Thermal deformation caused by temperature rise have an influence on the dynamic performance of a motorized spindle. In turn, the change in the dynamic performance will affect the temperature rise and thermal deformation of the system. However, the latter was rarely focused on in the previous literature. Therefore, a thermal network model of motorized spindle is enhanced by considering the thermal-mechanical coupling effect. Then, an iterative method is presented to solve the coupled equations, and a temperature test rig of the motorized spindle is set up to verify the proposed model. The relative error between the predicted and experimental results at two test points decreases by 9.56% and 3.44% after considering the thermal-mechanical coupling effect. The comparison with the experimental results shows that the proposed model with thermal-mechanical coupling effect can obtain a more accurate temperature field than the previous model. Key words: Motorized spindle; Thermal network model; Thermal-mechanical coupling; Temperature field IntroductionMotorized spindle is a core functional component of computer numerical control (CNC). High transmission accuracy is implemented by the spindle system because the spindle is driven by the motor directly. However, the thermal deformation of the spindle system, caused by uneven temperature rise, reduces machining precision and reliability of a motorized spindle [1]. Temperature affects not only the execution accuracy of the mechanical system [2], but also the machining accuracy of the machine tool [3]. To compensate for the error induced by the thermal deformation, an accurate temperature field prediction model of the motorized spindle is essentially studied.The temperature rise of the spindle system usually focuses on thermal characteristics. To date, considerable efforts have been dedicated on the thermal characteristics of the spindle system. As the bases of calculation for the temperature in the spindle system, a thermal-dynamic model of bearings was established by Palmgren [4] and the frictional heat of bearings was calculated by Jones [5]. Thereafter, the thermal characteristics of the spindle system have attracted increasing attention. The temperature in the spindle system was determined through the finite difference model (FDM) by Harris [6], but the thermal deformation of the spindle system was not included in their model. Later, a thermal characteristic model with thermal deformation was developed [7]. The finite element method (FEM) was also used to predict the temperature field of the spindle system [8][9][10].Recently, motorized spindles as a core part of CNC have been concerned. A finite difference model with heat transfer mechanism of motorized spindle was proposed by Bossmanns [11], and the temperature at several locations matched the measured values. Chen et al. [12] developed a thermal error model of motorized spindle and found that spindle temperature has the characteristics of time-varying, nonlinearity, and strong dependence on rotation speed. Affected by...

An accurate and efficient implicit thermal network method for the steady-state temperature field

“…where A is the square matrix, whose elements are all the function of the steady-state temperature of each node; T is the vector which consists of the steady-state temperature at each node; and B is the vector composed of the constant number. Finally, Newton's method in optimization for unconstrained problems is used to solve equation (6). In this method, the objective function F(T) = AT À B can be built first.…”

“…It can not only affect mechanical properties of materials [1][2][3] but cause changes in dynamic and static characteristics of the structure. [4][5][6] To avoid these adverse effects of the temperature variation on the service performance, the performance in the steady-state temperature is regarded as a key criterion. Therefore, the accurate and efficient prediction of the temperature field is very important in the product development stage.…”

Thermal Behavior Modeling Based on BP Neural Network in Keras Framework for Motorized Machine Tool Spindles

“…Many researchers have applied the finite element method (FEM) [ 4 , 5 , 6 , 7 , 8 , 9 , 10 , 11 , 12 ], the finite difference method (FDM) [ 13 , 14 ], or the finite difference element method (FDEM) [ 15 , 16 , 17 ] to obtain the numerical solution of temperature field of the spindle or of the entire machine tool. On the other hand, the temperature field of the spindle can be obtained by using the thermal network [ 18 , 19 , 20 , 21 ] or bond graph method [ 22 ], whereby, thermal balance equations can be solved by the Newton–Raphson method.…”

Temperature measurement point optimization and experimental research for bi-rotary milling head of five-axis CNC machine tool

“…In addition to finite element simulation, many scholars also conduct thermal network analysis based on the mechanism or build a neural network prediction model to predict thermal error. Zhou et al [8] combined the thermal-mechanical coupling effect to strengthen the thermal network model of the motorized spindle based on thermal resistance, and the average relative error of the prediction results was less than 8%. Ke et al [9] combined the thermal network method for thermal transient analysis of the main shaft and considered time-varying parameters and thermal-structural coupling.…”