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Modern tendency of machine tools design requires more accurate model to predict the system dynamics, in order to anticipate its interaction with machining process. In this paper, a comprehensive dynamic model of ball screw feed system (BSFS) considering nonlinear kinematic joints is introduced to investigate the varying dynamic characteristics when worktable is subjected to combined load from six directions. The load–deformation relationship of each kinematic joint is dealt with a set of translational and angular spring elements. The nonlinear restoring force function of each joint involving coupling displacement is calculated. Based on the lumped mass method, the analytical 18-DOF dynamic equation is formulated by the analysis of the interaction force between joints. Model verification tests are conducted. The worktable response exhibits the abundant and fascinating nonlinear phenomena arising in nonlinear joint and coupling effect. The nonlinear behavior behaves significant difference owing to the variations of excitation, platform position, screw length, preload and damping of joints. Thus, the model is promising for comprehension of machine dynamic behavior and for development of sophisticated control strategy.

In this study, a novel kinetic model is established to investigate the dynamic characteristic of the ball screw feed system by considering the thermal deformation of bearing joints, screw-nut joints and screw shaft. Based on the Hertz contact theory, the relationship between elastic restoring force and axial deformation of bearing joints and screw-nut joints is obtained, respectively. Then the dynamic characteristics of the kinetic equation are analyzed by Runge–Kutta method. The vibration characteristics of the feed system with and without thermal deformation are analyzed, and the results indicate that the amplitude becomes larger when thermal deformation is considered. The motion state of the feed system at different frequencies is analyzed, and the results show that with the change of frequency, the motion state of the system will appear period-doubling motion, quasi-periodic motion and chaotic motion. Finally, the influence of different parameters on the vibration characteristics of the system is discussed.

In order to investigate the effect of thermal expansion on the ball screw feed system (BSFS) of a precision machine tool, theoretical modeling of and experimental study on thermally induced error are focused in this paper. A series of thermal experiments are conducted on the machine tool to measure the temperature of the main heat source and measuring points of BSFS. This study is to classify the main heat sources and discuss the impact on the ball screw feed system separately. By the experimental data of ball screw system, the thermal model of screw shaft in the axial direction is analyzed and verified. Based on the heat generation and transfer analysis of ball screw system, thermal expansion of screw shaft in the axial direction is modeled mathematically. In addition, by analyzing the effects of machining parameters such as rotational speed, preloads, and lead, we get the parameter influence of BSFS’s temperature rising and thermal deformation. This work can help us reduce thermal deformation effectively and improve the precision of CNC machining.

To establish the dynamic model of machine tool structure is an important means to assess the performance of the machine tool structure during the cutting process. It is necessary to study the dynamics of the machine tools in different configurations for the sake of analyzing the dynamic behavior of the machine tools in the entire workspace. In this paper, a robust approach is presented to build an efficient and reliable dynamic model to evaluate the position-dependent dynamics of the twin ball screw (TBS) feed system. First, the TBS feed system is divided into several components, and a finite element (FE) model is built for each component. Second, the Craig-Bampton method is proposed to reduce the order of the substructures. Third, a multipoint constraints (MPCs) method was introduced to model the mechanical joint substructures of the TBS system, and the spring-damper element (SDE) is employed to connect the condensation nodes. Finally, a series experimental tests and full-order FE analysis are conducted on the self-designed TBS worktable in the four positions to validate the effectiveness of the proposed dynamic model. The results show that the proposed approach evaluates accurately the position-dependent behavior of the TBS system.

Thermal error is a common problem in machine tool processing. It is usually proposed to take the screw as a one-dimensional rod heat transfer system to solve the thermal error of the screw by establishing a thermal characteristic equation. This method regards the temperature on the nut as the temperature of the screw contact surface without considering the heat transfer distance between the screw and the mounting point on the nut. To solve this problem, this paper takes the screw-nut feed system as a two-dimensional heat transfer structure considering both the screw and nut. In addition, to solve the low convergence speed and easy fall into a local optimum problem in optimal parameter identification, the improved particle swarm optimization algorithm (IPSOA) is proposed to identify the boundary parameters of thermal characteristics equations. Finally, the temperature and thermal error of the screw-nut feed system is calculated by the identified results. Experiments under different working conditions show that the maximum prediction residual error of the two-dimensional method (TDM) is less than 7.2 μm, and the simulating prediction accuracy can reach 86.2%. Besides, compared with the one-dimensional model (ODM), TDM has a higher prediction accuracy, which verifies the effectiveness of the proposed method.

The dual-drive feed system can significantly reduce the effects of nonlinear friction. However, due to the numerous heat sources in its system, the thermal responsive mechanism is still unclear. The reason restricts the realization of high-precision micro-feed. Moreover, the existing thermal simulated model of the machine tool oversimplifies the calculation process of thermal contact resistance (TCR), resulting in a significant error in simulation. Therefore, a full-state TCR calculation model is proposed, and based on the model, a high-precision thermal behavior model of the dual-drive feed system is established. Firstly, the entire deformation process of the asperities is characterized by using fractal theory, and the TCR between the joint parts of the feed system is calculated by considering the thermal resistance of air or grease. A thermal simulated model of the dual-drive feed system is developed based on the solved heat generation and the heat transfer coefficients. Then, the temperature rise characteristics of the dual-drive feed system and the responsive mechanism of thermal deformation under different working conditions are analyzed. The influence of TCR on temperature field distribution and deformation field is discussed. Finally, the experiments on temperature rise and thermal deformation are conducted on the dual-drive feed system. The results of the simulated analysis and experiments show that the accuracy of the simulation can be significantly improved by using the full-state TCR model. The error of the thermal model based on the full-state TCR is much smaller than that of the general TCR model and the without TCR. The accurate description of the TCR has an essential impact on the accuracy of the simulated model, and the obstruction of the heat flow by air or grease cannot be neglected.

Taking the ball screw feed system as the research object, the two degree of freedom axial dynamic model of the system is constructed firstly. Based on Hertz contact theory, when the ball screw pair adopts variable lead self-preloading to eliminate the assembly clearance between the ball and raceway, considering the nonlinear segmented axial elastic recovery force generated by the uneven contact deformation between the ball and raceway under the action of external excitation force, further derive the nonlinear dynamic equation group of the system. Next, the fourth-order Runge-Kutta method was used to numerically solve the equation system, obtaining the system’s two and three-dimensional phase diagrams, Poincaré sections, time-domain waveform diagrams, frequency spectra, and bifurcation diagrams. Then, the effects of damping constant, initial contact angle between ball and raceway in ball screw pairs, and number of balls on the system’s response characteristics were analyzed, and the influence of external excitation forces on system stability was further studied. Finally, it was verified through experiments that the axial vibration of the system is indeed nonlinear vibration, providing a theoretical basis for the study of the dynamic characteristics of the ball screw feed system.

Currently, due to the rare consideration on the coupling of the various rolling joints and their directional dynamic parameters, and the constraints of the traditional modeling methods, the dynamic modeling precision of the ball screw feed system and the dynamic parameters identification accuracy of the rolling joints are difficult to be further improved. In this paper, a novel method to identify the dynamic parameters of rolling joints based on the digital twin dynamic model of the assembled ball screw feed system is proposed. Firstly, synchronizing information of the physical entity, the geometric model is constructed. Then the finite element analysis (FEA) model is constructed which can simultaneously consider multiple rolling joints and their dynamic parameters at multiple directions. Based on the FEA modal data, the deep neural network (DNN) model is constructed to reflect the mapping between the dynamic parameters and the natural frequencies. Thus, the digital twin dynamic model can be established by fusion of these sub-models. Combining the digital twin-driven and experimental natural frequencies, the optimization model is built, and the dynamic parameters can be identified by particle swarm optimization (PSO) algorithm. Finally, the relative error of dynamic parameters identification is less than 3%, which indicates that the proposed method is feasible, effective, and has greater accuracy.

Variations in running conditions cause fluctuation in the temperature field of precision machine tools, which inevitably results in thermal errors. To meet the demands of dynamic and time-varying temperature control capability, an active temperature control (ATC) method based on time grating principle is proposed, and the ATC system is developed. The ATC system contains main-loop and sub-loops. The oil target temperature in the sub-loop is determined according to the running parameters and the matching principle of the generalized heat generation–dissipation power. In accordance with the time grating principle, dynamic and differential oil temperature control of each sub-loop is achieved via the inlet time regulation of high-temperature (H-t) or low-temperature (L-t) oil in the main-loop. The main-loop H-t and L-t oil target temperatures are determined by the target range of the sub-loop temperature. The dynamic distribution of the refrigeration capacity and proportional heating mode is adopted to control the temperatures of H-t and L-t oil. By focusing on the feed system of precision machine tool, we carry out both dynamic simulation study and verification experiments, and the results show that the ATC method and system can effectively regulate the temperature field of precision machine tools, thus improving the thermal accuracy of the precision machine tool.

Vibration in state-of-the-art machining impacts accuracy by diminishing the machine’s dynamic precision and the workpiece surface quality. The dependability of the cutters and productivity becomes a severe problem for optimizing the computer numerical control machine tools’ (CNCMT) efficiency. Therefore, investigating the twin ball screw drive system vibration properties as well as its corresponding control measures is vital. This paper thoroughly reviews the recent works on methods of analyzing and controlling vibration for dual-driven feed systems (DDFS). The research on vibration control technologies, parameter identification, and system modeling are identified and summarized; the merits and drawbacks of various methods are discussed for comparative purposes. Furthermore, the asymmetrical relation between DDFS and single-driven feed systems are thoroughly discussed based on their dynamic properties. Finally, based on existing studies, related research prospects are described systematically, and these research directions are sure to markedly contribute to developing methods for dampening vibrations on DDFS of CNCMT.