Ball Screw Feed Research Articles

Stiffness matching method for the ball screw feed drive system of machine tools

The static stiffness of machine tools plays an important role in ensuring the performance of machine tools and improving the machining accuracy. In the design stage, stiffness matching provides a theoretical basis for determining the stiffness of each component. This study proposed a stiffness matching design method for machine tools. First, the deformation model of machine tools is established on the basis of the state space model. Through force analysis, the relationships between the deformations and stiffness of each part are determined. Second, the stiffness model of the machine tool is established by combining these relationships with the deformation model. Third, the objective function is determined by performing sensitivity analysis after obtaining the stiffness range. The stiffness matching design results are obtained through multi-objective linear programming. Lastly, the stiffness simulations, theoretical model, and experimental results are analyzed. The maximum errors among the experimental, simulation, and theoretical results (18.8 % and 19.9 %) are within the acceptable range. In conclusion, the proposed method is suitable for designing ball screw feed drive systems that requires rigidity.

Temperature simulation and thermal equilibrium analysis of the ball screw feed drive system under various working conditions

As one of the most important part of the machine tool, thermal behaviors of the ball screw feed drive system has great effect on the positioning accuracy and machining accuracy. Finite element method is widely used for simulating the temperature of the ball screw under various working conditions. In this paper, in order to improve the simulation accuracy, the moving heat loads are considered in the finite element model, and the response surface methodology is proposed to optimize the boundary conditions. The correctness and effectiveness of the method are verified by experimental data. In addition, according to the temperature simulation results of the ball screw feed drive system, thermal equilibrium is defined and the factors which have influenced on it are analyzed.

Design and implementation of speed fluctuation reduction for a ball screw feed system at low-speed operation

Abstract. In the high-precision servo feed system, when the permanent magnet synchronous motor (PMSM) is operated at low speed in the classical drive feed system (CDFS), the speed fluctuation caused by the motor torque harmonics seriously affects the speed smoothness of the servo system. In this paper, a novel double-drive differential feed system (DDFS) is proposed to effectively suppress the effect of torque harmonics of PMSM on speed fluctuation of the linear feed system at low-speed operation. Firstly, the effect of motor torque harmonics on motor speed for the DDFS is analyzed by the sensitivity function of the servo system, which indicates that the torque harmonics have little effect on the motor speed at high-speed operation. Then, in the DDFS, we make two motors rotate in the same direction at high speed and differentially synthesize at the ball screw to obtain low-velocity linear motion. Compared with the CDFS, the DDFS can suppress the effect of motor torque harmonics on speed fluctuation of the table and improve speed smoothness at low-speed operation.

Dynamic characteristics and reliability analysis of ball screw feed system on a lathe

For ball screw feed system on a lathe, the randomness of geometric parameters deriving from the inevitable manufacturing and assembly errors significantly affected the system dynamic characteristics and turning accuracy. In this study, a novel lumped dynamic model accounting for the analytical piecewise restoring force function involving the overall axial deformation is proposed. The equivalent mechanical model of bearing joints including the change of nominal contact angle is made a reasonable simplification to facilitate acquisition of the system analytical equation of motion. Additionally, the approximate analytical solution of the proposed equation is obtained by the modified Lindstedt–Poincaré method (MLP). The advanced first order second moment method (AFOSM) is employed to evaluate the reliability of dynamic response error. Furthermore, the numerical simulation aims to demonstrate the capabilities of the MLP and AFOSM method in the practical applications. Eventually, the effects of external excitation, sliding platform position, and nominal contact angles on the dynamic response are discussed and the reliability and sensitivity analysis in accordance with actual turning accuracy level is presented.

Thermal error modeling method for ball screw feed system of CNC machine tools in x-axis

The feed system of CNC machine tool has the characteristics of multiple heat sources and strong time-varying heat generation rate of each heat source. However, previous studies have paid little attention to the time-varying heat generation rate of each heat source, so it is difficult to accurately predict the temperature rise and thermal error of the lead screw. In this paper, Monte Carlo (MC) simulation-integrated FEM method was used to capture the heat generation rate of each heat source in the feed system. Consequently, relationship of the ratio of each heat source to the total heat generation rate of the system with the running time was obtained. Then, based on heat ratios of the heat sources, the torque current of the servo motor in the feed system was proposed to calculate the heat generation rate of each heat source. Finally, based on the finite difference method of one-dimensional heat conduction equation, numerical prediction model for thermal error of the lead screw was put forward. Finally, the accuracy and validity of the calculation model were verified by comparing with the experimental results.

Thermal characteristic analysis of ball screw feed drive system based on finite difference method considering the moving heat source

Thermal characteristic analysis of ball screw feed drive system based on finite difference method considering the moving heat source

Heat Source Forecast of Ball Screw Drive System Under Actual Working Conditions Based on On-Line Measurement of Temperature Sensors.

In view of the time-varying complexity of the heat source for the ball screw feed system, this paper proposes an adaptive inverse problem-solving method to estimate the time-varying heat source and temperature field of the feed system under working conditions. The feed system includes multiple heat sources, and the rapid change of the moving heat source increases the difficulty of its identification. This paper attempts to develop a numerical calculation method for identifying the heat source by combining the experiment with the optimization algorithm. Firstly, based on the theory of heat transfer, a new dynamic thermal network model was proposed. The temperature data signal and the position signal of the moving nut captured by the sensors are used as input to optimize the solution of the time-varying heat source. Then, based on the data obtained from the experiment, finite element software parametric programming was used to optimize the estimate of the heat source, and the results of the two heat source prediction methods are compared and verified. The other measured temperature points obtained by the experiment were used to compare and verify the inverse method of this numerical calculation, which illustrates the reliability and advantages of the dynamic thermal network combined with the genetic algorithm for the inverse method. The method based on the on-line monitoring of temperature sensors proposed in this paper has a strong application value for heat source and temperature field estimation of complex mechanical structures.

Precision loss modeling method of ball screw pair

Abstract A precision loss modeling method of the ball screw pair was proposed by introducing an effective contact coefficient to consider the intermittent contact between the balls and screw grooves and the parameter in the precision loss model was modified by establishing a multiscale contact mechanics model. The multiscale contact mechanics model between two rough curved surfaces was established by considering the elastic, elastic-plastic, and plastic deformations of contacting asperities to compute such contact parameters as the total actual contact area and contact load. A surface contact coefficient was introduced into the multiscale contact mechanics model to modify the contact parameters by taking the rough curved surfaces of balls and screw grooves into account. The microtopographies of rough surfaces of screw grooves and balls were characterized by the fractal geometry theory, and then the characterization of the microtopography of screw groove surfaces and the multiscale contact mechanics model were unified in the precision loss modeling. Then the relative sliding distance was calculated according to the kinematic analysis of the ball screw. Finally, the precision loss model of the ball screw pair was established by the above analysis. To verify the effectiveness of the precision loss model, the wear test was conducted on a dual-drive ball screw feed drive system under different working conditions. The predicted results agree well with the experimental data in the stable wear stage and the predictive accuracy of the model is much higher than that of previous studies. The effects of such parameters as the axial load and the feed rate on the precision loss were discussed. It is shown that the precision loss increases with the axial load and the feed rate.

Hybrid Multi-Domain Analytical and Data-Driven Modeling for Feed Systems in Machine Tools

Position error-compensation control in the servo system of computerized numerical control (CNC) machine tools relies on accurate prediction of dynamic tracking errors of the machine tool feed system. In this paper, in order to accurately predict dynamic tracking errors, a hybrid modeling method is proposed and a dynamic model of the ball screw feed system is developed. Firstly, according to the law of conservation of energy, a complete multi-domain system analytical model of a ball screw feed system was established based on energy flow. In order to overcome the uncertainties of the analytical model, then the data-driven model based on the back propagation (BP) neural network was established and trained using experimental data. Finally, the data-driven model was coupled with the multi-domain analytical model and the hybrid model was developed. The model was verified by experiment at different velocities and the results show that the prediction accuracy of the hybrid model reaches high levels. The hybrid modeling method combines the advantages of analytical modeling and data-driven modeling methods, and can significantly improve the feed system’s modeling accuracy. The research results of this paper are of great significance to improve the compensation control accuracy of CNC machine tools.

Workspace analysis and trajectory tracking of a planar hybrid manipulator with ball screw feed drive

The hybrid manipulators have benefits of both serial as well as parallel manipulators. In this paper, a planar hybrid manipulator with six degrees-of-freedom is proposed; it consists of two parallel manipulators each having three degrees-of-freedom. The models for forward and inverse dynamic analysis of this manipulator are presented with bond graph approach. The actuators of the manipulator have ball screw feed drive mechanism to convert rotary motion into linear motion. There are basically three problems addressed in the paper. First, the models are simulated for trajectory tracking of a semi-circular path traced by the lower manipulator initially and then tracking of another semi circular path by upper manipulators. The second problem addressed is to develop the bond graph model of the hybrid manipulator with proportional control to reach a desired position from an initial position with an unity slope after few seconds. Finally, workspace analysis for given semi-circular trajectory is done with calculation of area of the workspace of lower, upper and hybrid manipulators. It is observed from the simulation that the response follows the desired trajectory within the permissible limit. The result indicates that manipulator follows nearly tangential path. It is seen from the result that the desired trajectory lies within the workspace boundary.

Sensor-less estimation of positioning reversal value for ball screw feed drives

Motion accuracy of the feed drive systems deteriorate due to wear of the bearing and ball screw during the long term use. It is known that the wear makes larger positioning reversal value. In this study, a sensor-less estimation method for the positioning reversal value of ball screw driven feed drive systems based on the servo signals is proposed. The proposed method analyses the relationship between amplitude of feedback position and motor torque during swept sine wave motion. It is experimentally confirmed that the proposed method can estimate the positioning reversal values adequately.

Dynamic analysis of a ball screw feed system with time-varying and piecewise-nonlinear stiffness

In this study, a single-degree-of-freedom model is established to investigate the dynamic characteristics of a single-nut double-cycle ball screw feed system by considering the contact states of the nonlinear kinematic joints. Based on fully considering the parameters of the ball screw feed system, the axial deformations and forces of the key components are calculated to construct a set of piecewise-nonlinear restoring force functions of the system displacement and worktable position. The variations of the contact stiffnesses of the kinematic joints and transmission stiffness of the system with different boundary conditions are analyzed and the results indicate that they all have abrupt changes when the system displacement reaches a critical value. The changing law of the system transmission stiffness in the whole stoke is discussed. Additionally, the effects of excitation force, worktable position and system mass on the dynamic characteristics of the system and its correlative components are analyzed.

Cooling effect and temperature regulation of oil cooling system for ball screw feed drive system of precision machine tool

In order to investigate the cooling effect of forced fluid circulation on the ball screw feed drive system of a precision boring machine tool, theoretical modeling of and experimental study on temperature control of screw shaft along with heat generation and dissipation interactions are focused in this paper. Thermal behavior measurements are conducted on the machine tool to detect the temperature of the feed drive system equipped with oil cooling circulation real-timely. Based on the heat generation and forced convention analysis of ball screw system, temperature distribution of screw shaft in the axial direction is modeled mathematically. Relationship between the heat convection coefficient and cooling system parameters is established to formulize the surface temperature distribution considering the flowing speed of cooling medium as time-invariant. Numerical simulation was conducted showing that the geometric dimension of flow passages and the speed of cooling flows significantly influences the thermal behavior. The fuzzy PID control strategy is employed to regulate the temperature of screw shaft with the flow rate of cooling fluid adjusted by a valve controlled hydraulic system. The relations between temperature rise and flow rate are formulated indirectly while taking the heat generation under the no-cooling working condition as disturbance. Measurements with feed drive system operating at different feed rates are preformed and the proposed temperature regulation method proves to reduce about 3 °C in temperature variation through experimental results based control system simulation.

A novel dynamics model of ball-screw feed drives based on theoretical derivations and deep learning

High fidelity models of feed drive are critical factors to increase positioning accuracy and decrease contour error. To predict feed drives dynamics, this paper reports a novel method for modeling dynamics of feed drive by combining advantages of theoretical derivations and deep learning. First, the paper derives a rigid-flexible-combined dynamics model (RFCDM) for feed drive from classical dynamics theory. Then parameters identification of RFCDM is accomplished by referring product manuals and conducting constant velocity experiment with different feed rates. Continuous action reinforcement learning automata (CARLA) is adopted to tune all parameters of RFCDM simultaneously. A simulation error estimation model (SEEM) is applied to approximate simulation error between models simulation position and worktables actual position. The hybrid dynamics model (HDM) of feed drives which integrates RFCDM with SEEM is validated by experiments with various trajectories. Experimental results show that the gap between HDMs prediction position and worktables actual position is on the order of magnitude of 0.01 mm which is about 1/10 of the tracking error, indicating the HDM can predict the dynamics of feed drives with safe accuracy.

Explicit modeling and investigation of friction torques in double-nut ball screws for the precision design of ball screw feed drives

Explicit friction torque model composed of an applied load and viscous friction terms is formulated for two-point contact double-nut ball screws. Precision friction torque test rig is developed to verify the model. Forward and reverse direction measurements show a small friction difference due to the asymmetric nut geometry. Experiments confirm the friction prediction accuracy of 89%. Although a large axial load is applied to a ball screw, a lower and smoother friction torque is obtained by a proper preload selection through the developed model. It is also applicable as a thermal boundary condition for the finite element analysis. Efficient, smooth and accurate feed systems are obtained through the optimization of ball screw design parameters by minimizing the friction model.

Analysis of lead screw pre-stretching influences on the natural frequency of ball screw feed system

The accurate prediction and test of the dynamic characteristics of the ball screw feed system are of great significance to the design, manufacture and improvement of the machine tool. At present, the dynamic modeling of ball screw feed system mostly ignores the influence of assembly on the dynamic characteristics of the system. In order to solve the above-mentioned problems, this paper studies the machine tool with both ends fixed ball screw, considering the influences of the pre-stretching of the lead screw on the joint of the screw and the nut. With the lead screw divided into three sections, the lumped parameter model of the ball screw feed system is established, and the influences of the lead screw pre-stretching on the natural frequency of the system are analyzed. The designed auxiliary clamping device is used to measure the frequency response of the system, which includes the translational motion and the rotational motion. The results of the experiments show that the established dynamic model can predict the dynamic characteristics of the system well. The torque wrench and the designed adaptor are used to adjust the pre-stretching of the lead screw, and the frequency response of the system are tested under different pre-stretching conditions of the lead screw. Both theoretical and experimental results show that the pre-stretching of the lead screw has a significant effect on the contact state of the screw-nut joint, which makes the natural frequency of the system change obviously.

Dynamic Characteristic Optimization of Ball Screw Feed Drive in Machine Tool Based on Modal Extraction of State Space Model

The accurate prediction and research about the dynamic characteristic of machine tool during the design process are essential to develop high-performance machines. In order to consider the effect of mechanical modal characteristics on the whole dynamic performance and servo controller of ball screw feed drive fully, the modal characteristics of mechanical transmission are extracted and solved based on reduced state space matrix of ball screw feed system, which is also easy for integration with servo control model. On this basis, the step-by-step optimization method from the global to the local is proposed to optimize the servo controller and overall dynamic performance of ball screw feed drive. This step-by-step optimization method is as follows: first, the global initial optimal tuning of servo controller parameters under the influence of structure modal characteristics is originally realized through the analytic derivation of servo controller based on the extraction of state space modal characteristics. Second, the integrated model of the feed drive system is established. Finally, based on the above global optimization results, the overall dynamic performance, and the servo parameters of the feed drive system under the influence of the modal characteristics are further studied and optimized locally. Taking the ball screw feed drive studied in this paper like the example, its rise time and the settling time of step response are 0.089 and 0.104s before optimization, while these reduce to 0.038 and 0.092s after optimization. Its dynamic response performance after optimization is much better. The optimization result is also validated by the test: the rise time and the settling time by the test are 0.042 and 0.094s, which are close to that from the simulation. Also, the consistency of step response curves from experiment and simulation as well. All these show that: this prediction and optimization method of overall dynamic performance considering the modal characteristic influence of mechanical transmission fully is correct and reliable.

Dynamic axial contact stiffness analysis of position preloaded ball screw mechanism

This article establishes an axial contact stiffness model of position preloaded ball screw mechanism based on Hertz contact theory. The analysis of dynamic axial contact stiffness is one of the foundations of the research on the dynamic characteristic of the ball screw feed drive system. The model takes into account the coupling relationship between the contact angle and the normal contact force, as well as the coupling relationship between the elastic deformation and the contact deformation coefficient. The static and dynamic axial contact stiffness characteristics of the preloaded ball screw mechanism are studied. The numerical analysis result shows that the static contact stiffness of the preloaded ball screw mechanism increases with the increase in the preload and decreases with the increase in the axial load. The dynamic contact stiffness of the preloaded ball screw mechanism increases with the increase in the screw’s rotational speed. The variation range of dynamic contact stiffness increases with the increase in axial load under the same preload. And the variation range of dynamic contact stiffness decreases with the increase in preload under the same axial load. The axial contact stiffness model established in this article can be used to analyze either static or dynamic contact stiffness of position preloaded ball screw mechanism.

Thermal Performances Prediction Analysis of High Speed Feed Shaft Bearings Under Actual Working Condition

High-speed machining is a key technology for greatly improving productivity and reducing production costs. Angular contact ball bearing is the key component of ball screw feed system. Predictive analysis of bearings thermal behavior is significant to ensure the working accuracy of machine tools. Due to the continuous dynamic changes under actual working conditions, it is difficult to predict and model of the bearings heating characteristics. This paper develops a comprehensive calculation method for predicting the thermodynamic characteristics on high speed feed shaft bearings. Based on quasi-static model and thermal dynamic model, Monte Carlo optimization algorithm is used to inverse the temperature field experimental temperature data. The real heating characteristics of heat source are comprehensively predicted and analyzed, so as to accurately predict the bearing thermal dynamic performances of feed shaft bearings. The research work in this paper lays a strong foundation for the thermal error modeling and thermodynamic analysis of the ball screw feed system of machine tools.

Dynamic Modeling and Experiment Research on Twin Ball Screw Feed System Considering the Joint Stiffness

It is of great significance to study the dynamic characteristics of twin ball screw (TBS) feed system to improve the precision of gantry-type dual-driven computer numerical control (CNC) machine tools. In this paper, an equivalent dynamic model of the TBS feed system is established utilizing lumped mass method considering the stiffness of joints. Equivalent axial stiffness of screw-nut joints and bearing joints are both calculated by Hertz contact theory. Furthermore, a friction model is proposed because the friction force of the screw nut affects the stiffness of the joints. Then, the friction parameters are obtained by using the nonlinear system identification method. Meanwhile, a finite element model (FEM) is developed to assess the dynamic characteristics of TBS feed system under the stiffness of joints. Finally, validation experiments are conducted, and the results show that the positions of the nut and the velocities of worktable greatly affect the dynamic characteristics of the TBS feed system. Compared with the theoretical calculation, FEM and experiments indicate that the dynamic modeling proposed in this article can reach a higher accuracy.