Modeling and application of thermal contact resistance of ball screws

Aiming at determining the thermal contact resistance of ball screws,a new analytical method combining the minimum excess principle with the MB fractal theory is proposed to estimate thermal contact resistance of ball screws considering microscopic fractal characteristics of contact surfaces.The minimum excess principle is employed for normal stress analysis.Moreover,the MB fractal theory is adopted for thermal contact resistance.The effectiveness of the proposed method is validated by self-designed experiment.The comparison between theoretical and experimental results demonstrates that thermal contact resistance of ball screws can be obtained by the proposed method.On this basis,effects of fractal parameters on thermal contact resistance of ball screws are discussed.Moreover,effects of the axial load on thermal contact resistance of ball screws are also analyzed.The conclusion can be drawn that the thermal contact resistance decreases along with the fractal dimension D increase and it increases along with the scale parameter G increase,and thermal contact resistance of ball screws is retained almost constant along with axial load increase before the preload of the right nut turns into zero in value.The application of the proposed method is also conducted and validated by the temperature measurement on a self-designed test bed.

A high-efficiency regenerative shock absorber considering twin ball screws transmissions for application in range-extended electric vehicles

Renewable energy technologies,particularly in electric vehicles(EVs),have received significant attention in re-cent years.The wasted energy in a vehicle’s shock absorber can be converted into an alternative energy source by regenerative shock absorbers.In this paper,a high-efficiency regenerative shock absorber considering twin ball screws transmissions is proposed for application in range-extended electric vehicles.The proposed regenerative shock absorber can convert vibrational kinetic energy,which is traditionally dissipated as heat in suspension systems,into electricity.The proposed system is divided into four modules:suspension vibration input module,transmission module,generator module and power storage module.Induced by road roughness,the irregular linear oscillations of the suspension are transmitted to the suspension vibration input module.The reciprocating vibrations are converted into unidirectional rotation of the generator by a pair of ball screws,gears,and two overrun clutches in the transmission module.The utilisation of different screw pitches leads to different damping coefficients for upward and downward progress,enabling the shock absorber to fully utilise elastic elements to im-prove vehicle comfort when compressed and quickly absorb vibrations when stretched.The electricity produced by the generator is stored in supercapacitors to charge the battery and extend the range of EVs.The mechanical properties of the full-scaled fabricated prototype were studied by utilising a mechanical testing and sensing fix-ture.An average power output of 3.701 W in 1Hz-3 mm sinusoidal vibration input and a peak efficiency of 51.1%and average efficiency of 36.4%were achieved in a bench tests.The range can be approximately extended by 1 mile per 100 miles when EV is driving on the road of class B with a speed of 60 km/h,demonstrating that the proposed high-efficiency regenerative shock absorber is beneficial for harvesting renewable energy,and practical and significant for extending the range of EVs.

Research and experimental analysis of precision degradation method based on the ball screw mechanism

As a key transmission component in computer numerical control(CNC) machine tools,the ball screw mechanism(BSM) is usually investigated under working load conditions. Its accuracy degradation process is relatively long,which is not conducive to the design and development of new products. In this paper,the normal wear depth of the BSM nut raceway is calculated under the variable speed operation condition using the fractal wear analysis method and the BSM’s accelerated degradation proportional wear model. Parameters of the acceleration degradation model of the double-nut preloaded ball screw pair are calculated based on the physical simulation results. The accelerated degradation test platform of the BSM is designed and manufactured to calculate the raceway wear model when the lubrication condition is broken under the variable-speed inertial load and the boundary lubrication condition under the uniform speed state. Three load forces and two samples are selected for the accelerated degradation test of the BSM. The measured friction torque of the BSM is employed as the evaluation index of the accuracy degradation test. In addition,the life cycle of the accuracy retention is accurately calculated by employing the parameters of the physical simulation model of the BSM. The calculations mentioned above can be used to estimate BSM’s accuracy performance degradation law under normal operating conditions. The application of the proposed model provides a new research method for researching the precision retention of the BSM.

Three-dimensional Modeling for Predicting the Vibration Modes of Twin Ball Screw Driving Table

As a redundant drive mechanism, twin ball screw feed system has the advantage of high stiffness and little yaw vibration in the feeding process, while leads to increased difficulty with vibration characteristics analysis and structure optimization. Only low-dimensional structure and dynamics parameters are considered in the existing research, the complete and effective model for predicting the table＇s vibrations is lacked. A three-dimensional（3D） mechanical model of twin ball screw driving table is proposed. In order to predict the vibration modes of the table quantitatively, an analytical formulation following a comprehensive approach is developed, where the drive system is modeled as a lumped mass-spring system, and the Lagrangian method is used to obtain the table＇s independent and coupled axial, yaw, and pitch vibration modes. The frequency variation of each mode is studied for different heights of the center of gravity, nut positions and table masses by numerical simulations. Modal experiment is carried out on the Z-axis feed table of the horizontal machining center MCH63. The results show that for each mode, the error between the estimated and the measured frequencies is less than 13%. The independent and coupled vibration modes are in accordance with the experimental results, respectively The proposed work can serve a better understanding of the table＇s dynamics and be beneficial for optimizing the structure parameters of twin ball screw drive system in the design stage.

Effect of contact angle and helix angle on slide-roll ratio under the accelerated motion state of ball screw mechanism

To study the effect of the contact angle and helix angle on slide-roll ratio at the ball contact points under the accelerated motion state of ball screw mechanisrm(B S M),the curve theory in differential geometry a d the homogeneous transformation matrix ae used to establish the acceleration kinematics model of BSM.The model can be used to describe the accelerated motion relationships among the screw,balls and nut,calculate the acceleration of relative motion at the contact points between the balls and raceways,and analyze five accelerated motion rules between the balls and raceways.It also conducts a simulation analysis of the slide-roll ratio relationship between the accelerations at the ball center and the contact point of ball under different contact angles and helix angles.As shownby the analysis,with the increase in the BSM’s contact angle,the slide-roll ratio at the contact points decreases,and the contact angle has a relatively significant effect on the slide-roll ratio.However,with the decrease in the BSM’helix angle,the slide-roll ratio at the contact points decreases,and the helix angle has a relatively insignificant effect on the slide-roll ratio.By measuring the accelerations of both the screw and nut under the accelerated motion state,it also verifies the existence of the slide-roll mixed motion at the ball contact point A between the ball and the screw racewayand pure rolling at the ball contact point B between the ball and the nut raceway during the accelerated motion.

Integral sliding mode control for flexible ball screw drives with matched and mismatched uncertainties and disturbances

The design of servo controllers for flexible ball screw drives with matched and mismatched disturbances and uncertainties is focused to improve the tracking performance and bandwidth of ball screw drives.A two degrees of freedom mass model is established based on the axial vibration characteristics of the transport ball screw,and the controller of an adaptive integral sliding mode is proposed combining the optimal design of state feedback gain matrix K to restrain the vibration and the matched disturbances and uncertainties.Then for the counteraction of the mismatched disturbances and uncertainties,a nonlinear disturbance observer is also developed.The trajectory tracking performance experiments and bandwidth analysis were conducted on experimental setup with the proposed control method.It is proved that the adaptive integral sliding mode controller has a high tracking performance and bandwidth especially for the axial vibration characteristics model of ball screw drives.And the ball screw tracking accuracy also has a considerable improvement with the application of the proposed nonlinear disturbance observer.

Acceleration-Dependent Analysis of Vertical Ball Screw Feed System without Counterweight

The distinguishing feature of a vertical ball screw feed system without counterweight is that the spindle system weight directly acts on the kinematic joints.Research into the dynamic characteristics under acceleration and deceleration is an important step in improving the structural performance of vertical milling machines.The magnitude and direction of the inertial force change significantly when the spindle system accelerates and decelerates.Therefore,the kinematic joint contact stiffness changes under the action of the inertial force and the spindle system weight.Thus,the system transmission stiffness also varies and affects the dynamics.In this study,a variable-coefficient lumped parameter dynamic model that considers the changes in the spindle system weight and the magnitude and direction of the inertial force is established for a ball screw feed system without counterweight.In addition,a calculation method for the system stiffness is provided.Experiments on a vertical ball screw feed system under acceleration and deceleration with different accelerations are also performed to verify the proposed dynamic model.Finally,the influence of the spindle system position,the rated dynamic load of the screw-nut joint,and the screw tension force on the natural frequency of the vertical ball screw feed system under acceleration and deceleration are studied.The results show that the vertical ball screw feed system has obviously different variable dynamics under acceleration and deceleration.The influence of the rated dynamic load and the spindle system position on the natural frequency under acceleration and deceleration is much greater than that of the screw tension force.

Structure design and characteristics analysis of a cylindrical giant magnetostrictive actuator for ball screw preload

In order to achieve automatic adjustment of the double-nut ball screw preload, a magnetostrictive ball screw preload system is proposed. A new cylindrical giant magnetostrictive actuator （CGMA）, which is the core component of the preload system, is developed using giant magnetostrictive material （GMM） with a hole. The pretightening force of the CGMA is determined by testing. And the magnetic circuit analysis method is introduced to calculate magnetic field intensity of the actuator with a ball screw shaft. To suppress the thermal effects on the magnetostrictive outputs, an oil cooling method which can directly cool the heat source is adopted. A CGMA test platform is established and the static and dynamic output characteristics are respectively studied. The experimental results indicate that the CGMA has good linearity and no double-frequency effect under the bias magnetic field and the output accuracy of the CGMA is significantly improved with cooling measures. Although the output decreased with screw shaft through the actuator, the performance of CGMA meets the design requirements for ball screw preload with output displacement more than 26 μm and force up to 6200 N. The development of a CGMA will provide a new approach for automatic adjustment of double-nut ball screw preload.

The Axial Nonlinear Vibration Analysis of Ball-screw about Machine Tool Feeding System

The forced state of the ball-screw of machine tool feeding system is analyzed. The ball-screw is simplified as Timoshenko beam and the differential equation of motion for the ball-screw is built. To obtain the axial vibration equation,the differential equation of motion is simplified using the assumed mode method. Axial vibration equation is in form of Duffing equation and has the characteristics of nonlinearity. The numerical simulation of Duffing equation is proceeded by MATLAB / Simulink. The effect of screw length,exciting force and damping coefficient are researched,and the axial vibration phase track diagram and Poincare section are obtained. The stability and period of the axial vibration are analyzed. The limit cycle of phase track diagram is enclosed. Axial vibration has two type-center singularity distributions on both sides of the origin. The singularity attracts vibration to reach a stable state,and Poincare section shows that axial vibration appears chaotic motion and quasi periodic motion or periodic motion. Singularity position changes with the vibration system parameters,while the distribution doesn’ t change. The period of the vibration is enhanced with increasing frequency and damping coefficient. Test of the feeding system ball-screw axial vibration exists chaos movement. This paper provides a certain theoretical basis for the dynamic characteristic analysis of machine feeding system ball-screw and optimization of structural parameters.

Precision loss of ball screw mechanism under sliding-rolling mixed motion behavior

The sliding-rolling mixed motion behavior degrades the ball screw’s precision at different levels.Based on the sliding-rolling mixed motion between ball and screw/nut raceway,the ball screw’s precision loss considering different given axial loading and rotational speed working conditions was investigated.Since creep and lubrication relate to sliding and rolling motion wear,the creep and lubrication characteristics are analyzed under different working conditions.Besides,the precision loss was calculated considering the sole influence of sliding behavior between ball and screw and compared with the results from other current models.Finally,research on precision loss owing to the sliding-rolling mixed motion behavior was realized under given working conditions,and suitable wear tests were carried out.The analytical results of precision loss are in good agreement with the experimental test conclusions,which is conducive to better predicting the law of precision loss in stable wear period.

Development of Chinese large-scale space end-effector

In order to achieve large tolerance capture and high stiffness connection for space payload operations,a Chinese large-scale space end-effector (EER) was developed.Three flexible steel cables were adopted to capture the payload with large capture allowance.Ball screw transmission mechanism and plane shape-constraint four bar linkage mechanism were utilized to connect the payload with high stiffness.The experiments show that capture tolerances in X,Y,Z,Pitch,Yaw,Roll directions are 100 mm,100 mm,120 mm,10.5°,10.5°,12°,respectively.The maximum connection stiffness is 4 800 N·m.The end-effector could meet the requirements for space large tolerance capture and high stiffness connection in the future.

Measurement and Simulation of Energy Consumption of Feed Drive Systems

In this study, in order to investigate the power consumption of feed drive system, mathematical models for the single-axis experimental apparatus are developed. This apparatus can be driven by either of ball screw or linear motor and it is possible to change the mechanical properties of such as grease viscosity of the table. Then, the power consumption is simulated by proposed method based on the mathematical model of feed drive systems and the simulated results are compared with the measured results of the experimental apparatus to confirm the validity of the proposed method. In addition, it is clarified that the energy usages of the feed drive system. The energy losses of the feed drive system are divided into the loss of each part and these energy losses are calculated by the proposed method. Then, it is investigated that the influence of the velocity and friction to the energy consumption of feed drive system. As the results, it is confirmed that proposed method can accurately predict the power consumption of the ball-screw feed drive system. It is also clarified that the energy usage for both of ball-screw and linear motor drive systems.

Thermal error regression modeling of the real-time deformation coefficient of the moving shaft of a gantry milling machine

This paper describes a novel modeling method for determining the thermal deformation coefficient of the moving shaft of a machine tool.Firstly,the relation between the thermal deformation coefficient and the thermal expansion coefficient is expounded,revealing that the coefficient of thermal deformation is an important factor affecting the precision of moving shaft feed systems.Then,thermal errors and current boundary and machining conditions are measured using sensors to obtain the first set of parameters for a thermal prediction model.The dynamic characteristics of the positioning and straightness thermal errors of the moving axis of a machine tool are analyzed under different feed speeds and mounting modes of the moving shaft and bearing.Finally,the theoretical model is derived from experimental data,and the axial and radial thermal deformation coefficients at different time and positions are obtained.The expressions for the axial and radial thermal deformation of the moving shaft are modified according to theoretical considerations,and the thermal positioning and straightness error models are established and experimentally verified.This modeling method can be easily extended to other machine tools to determine thermal deformation coefficients that are robust and self-correcting.