Planetary Roller Screw Research Articles

Dynamic Model of Planetary Roller Screw Mechanism with Considering Torsional Degree of Freedom

To predict accurately the dynamics performance of planetary roller screw mechanism, it is necessary to establish its streamline and engineering-compliant dynamic model, which is the basis of mechanical design and precision control of the system. In this paper, the relative displacement between roller and ring gear along the line of action is deduced and the relationship between nature frequencies and the number of rollers is discussed. Considering the torsional stiffness of all components and the thread mesh stiffness based on the Hertzian contact theory, the purely torsional model for planetary roller screw mechanism is presented to reveal the natural frequencies and vibration mode characteristics of the system. The results show that the natural properties of undamped system in planetary roller screw mechanism are mainly reflected by two typical vibration modes: rotational mode and roller mode.

PECULIARITIES OF THE DEVELOPMENT AND MANUFACTURING OF THE PROTOTYPE OF GAPLESS PLANETARY ROLLER SCREW MECHANISM

Known designs of gapless planetary roller screw mechanisms (PRSM) are highly accurate and rigid, but have low load capacity and short life. To eliminate these shortcomings, a new design of a gapless PRSM was developed and patented using a one-piece thin-walled nut. Due to radial deformation of the nut, the gaps between the threaded parts of the mechanism are chosen. The previous works have described the design of a new gapless PRSM and theoretically proved the possibility of a significant increase in load capacity and life using this mechanism. To confirm the theoretical results and conclusions, it is necessary to conduct experimental studies for which a prototype of the new gapless PRSM was made. The work presented describes a new technology for manufacturing threaded parts of this mechanism. In contrast to the traditional technology of grinding screw surfaces of the PRSM parts, which require special expensive equipment, it is proposed to grind and bore the screw surfaces of the parts with special plates on CNC turning machines. The metrological control has established that the dimensions of all parts of the prototype, including the threaded parts, did not go beyond the fields of the calculated or assigned tolerances.

Study on jamming mechanism of the planetary roller screw mechanism

This paper explores if there exists jamming phenomena in the planetary roller screw mechanism. Three kinds of jamming phenomena, such as mechanical jamming, dead point jamming, and self-locking jamming, are elaborated by using static analysis of the planetary roller screw mechanism. The results show that mechanical jamming and dead point jamming won’t happen in the planetary roller screw mechanism under the condition of high strength materials, high post-treatment hardness and without regard to error. And when the nut bears unbalanced loads or when the nut and the roller may self-lock in small pitch, the variation of input torque and output velocity is analysed by dynamics simulations. The fact that the planetary roller screw mechanism will not be self-locking jamming is verified.

Mixed-lubrication analysis of planetary roller screw

Abstract The mixed-lubrication model of the planetary roller screw is proposed considering contact load, contact geometry of thread, surface roughness and transient effects. The influences of rotational speed of the screw, axial load and surface roughness on lubrication are discussed. Increasing rotational speed has a significant effect on the lubrication of contact areas. As the speed increases, the film thickness increases while the friction coefficient and contact-area ratio decrease, and the lubrication mode changes from mixed to full-film. As the load increases, the film-thickness ratio decreases while the friction coefficient and maximum subsurface von Mises stress increase. High-precision machining can improve lubrication by properly reducing the roughness of the machined surface, which would increase film thickness and decrease the contact-area ratio.

Local contact characteristics of threaded surfaces in a planetary roller screw mechanism

This study investigates the local contact characteristics of the threaded surface meshing of a planetary roller screw mechanism (PRSM). First, according to the threaded surface structure and threaded surface meshing characteristics, expressions for the principal curvature and principal direction of the contact ellipse at a contact point are derived based on the differential geometry theory. Next, based on a force analysis and threaded surface equations, an analytical model is established to calculate the dimensions and principal vector direction of contact ellipses on threaded surfaces. The elastic deformation and maximum contact stress are determined using Hertz elastic contact theory. Then, finite element (FE) numerical models for a single pair of threads at the screw–roller interface and the roller–nut interface are developed to calculate the contact area and maximum contact stress. The results are compared with those of the analytical model to demonstrate the validity of the analytical model. Finally, based on the analytical model proposed in this article, the local contact characteristics of threaded surfaces with various thread pitches, flank angles, and profile radii of roller threads are analyzed in detail.

Modelling of static contact with friction of threaded surfaces in a planetary roller screw mechanism

This paper investigates the nature of the contact with friction between the threaded surfaces in a planetary roller screw mechanism (PRSM). Contact analyses are applied to both the screw/roller interface and roller/nut interface. Prior work has neglected to take a fundamental approach towards understanding the contact characteristics of threaded surfaces under the combined action of normal pressure and tangential friction forces. Accordingly, in this paper, coordinate transformations and meshing equations of threaded surfaces are used to establish the contact locations of components. The relative velocities at the screw/roller and roller/nut interfaces are derived, and it is shown that the main contact mode of the screw/roller is sliding contact due to the relative velocity in the axial direction is not equal to zero, whereas rolling contact is the main contact mode at the roller/nut interface. Then, based on the contact mechanics, after the velocities of the contact points in the contact ellipse are derived, the normal pressure and friction force distributions and the components of the displacement and stress are also derived. Lastly, a verification model is developed by finite element method (FEM) to illustrate how the developed theory may be used to perform sensitivity analyses for improved parameter designs.

Thermal characteristics analysis and experimental study of the planetary roller screw mechanism

The thermal characteristics of the planetary roller screw mechanism (PRSM) under various working conditions are investigated both analytically and experimentally. Firstly, thermal boundary conditions including the thermal contact resistance, thermal constriction resistance, conductive and convective resistance are particularly characterized and formulated, based on the fractal theory and heat transfer theory. Secondly, a thermal model based on the thermal network method (TNM), is established to predict the PRSM temperature evolution. The thermal balance equation set is solved by considering the influence of lubricant viscosity drop and the change of heat generation. Thirdly, the main factors affecting the thermal characteristics of the PRSM system, such as the external load, screw speed, and lubricating grease, are discussed and analyzed. The correlation between the experimental data and the calculated values confirms the validity of the proposed thermal model for the transient thermal analysis. Results indicate that the external load, operating speed, and lubricant consistency have a significant influence on the temperature rise level, even leading to the thermal failure of the PRSM. This study provides an in-depth understanding of the thermal behavior and heat transfer mechanism of the PRSM, and thus can be applied to its design and development.

Modelling of transmission accuracy of a planetary roller screw mechanism considering errors and elastic deformations

Based on the motion principle of a planetary roller screw mechanism (PRSM) converting the rotary motion into linear motion, a calculation model of the transmission error under free load is established considering the error and clearance, as well as a transmission error model under different working loads considering the elastic deformation. The error is mainly concerned with PRSM manufacturing errors and assembly errors, the theoretical transmission error curve obtained by measuring the accumulative error and flank angle of the thread, the coaxial error of the screw thread, and the deviation error and eccentric error. Besides, an error analysis and measurement of the experimental system is performed to verify that the system meets the experimental requirements and is conducive to obtain accurate experimental results. Lastly, the transmission error experiment of the PRSM prototype under free load and different working loads are further conducted. The experimental data of the transmission error are compared with the analytical solution presented in this paper, and the results show that the difference is 20.1% under the free load condition and is less than 15% under different working loads.

Load distribution over threads of planetary roller screw mechanism with pitch deviation

A model is proposed to calculate load distribution over threads of planetary roller screw mechanism (PRSM) with pitch deviation. Firstly, four kinds of machining errors of threads including pitch deviation, deviation of thread angle, division error of multiple threads and deviation of pitch diameter are analyzed, and the relationships among them are investigated. After analyzing the relationships among the errors, pitch deviation is chosen to be the main machining error to investigate because it can reflect the effects of other machining errors, and is the most influential machining error on the contact condition and deformation compatibility relationship, i.e. the load distribution of PRSM. Based on the proposed model, the effects of pitch deviation on the load distribution of PRSM are studied through numerical analyses, and load distributions under different machining precisions are analyzed. In order to experimentally verify the investigation, two PRSM samples are measured and tested under the same experimental conditions. The experimental results show that load distributions over threads will fluctuate because of the existence of pitch deviations. The pitch deviations, load distributions over threads and wear depths of threads in the samples show obvious accordance, which indirectly demonstrates the effects of pitch deviation on load distribution.

Transient thermal analysis of standard planetary roller screw mechanism based on finite element method

The thermal behavior of the standard planetary roller screw mechanism needs to be investigated since the large amount of heat generated by the friction torque on multiple contact points during the transmission process. In this article, a simplified transmission system model of standard planetary roller screw mechanism is first established for the finite element analysis. Second, the friction torque of standard planetary roller screw mechanism is calculated and the boundary conditions of thermal analysis are deduced. Then, the transient thermal analysis of the standard planetary roller screw mechanism based on finite element method is conducted by considering the moving heat source and thus temperature field distribution at any time and the temperature rise curve at different positions of the standard planetary roller screw mechanism can be obtained. Finally, the correlation between the experimental data and the calculated values confirms the validity of the proposed thermal model for the transient thermal analysis.

Design and bearing characteristics of planetary roller screws based on aerospace high-load conditions

Under the background of the rapid development of today’s aerospace industry, the bearing characteristics of planetary roller screw drive under high overload conditions are studied. Designing a high-load, high-performance precision planetary roller screw drive is of practical and significant. An axially spaced RV type planetary roller screw with a single nut is designed under aerospace conditions. Under the conditions of the aerospace working load and efficiency, the parameters and structures of the planetary roller screw are completed. Based on this, the bearing characteristics of the planetary roller screw are studied and the equivalent finite element model of the planetary roller screw is analyzed. Those analyses include stress and strain, elastic–plastic properties, transmission efficiency, and dynamic load capacity. The results show that the design of planetary roller screw meets the design requirements for aerospace conditions. And the results can provide a basis for the design and manufacture of planetary roller screws under high loads.

Электромеханический привод с планетарным роликовинтовым механизмом для электрохимического станка с вибрирующим электродом

Электромеханический привод с планетарным роликовинтовым механизмом для электрохимического станка с вибрирующим электродом

Thread Modification Method for Load Balance on Planetary Roller Screw Mechanism

Based on the relationship between the load distribution and the load deformation of the thread of the planetary roller screw mechanism (PRSM), a modification method of the roller thread is proposed. The nut side and the screw side of the roller thread are modified by different amount of modification, and the modified thread load distribution is calculated and analyzed. The results show that the effects of roller thread modification on the load distribution are significant, and the sensitivity of the load capacity of the nut and screw to the modification is different. Through the study of the influence of roller thread modification on thread load distribution, the optimal value of the roller thread modification on the nut side and the screw side is obtained under the PRSM parameters given in this paper, which provides a theoretical guidance for the future PRSM load balancing design.

Investigation on the uncertain factors of the elastic–plastic contact characteristics of the planetary roller screw mechanism

The scatter of uncertain factors of the planetary roller screw mechanism, which originated from the manufacturing process, has a significant influence on its serving performance. However, this influence remains insufficiently studied. Further, the elastic–plastic contact analysis of the planetary roller screw mechanism with considering the uncertainties needs large numbers of repetitive calculations by traditional finite element method, which is labor intensive and often impractical. In this paper, an uncertain model of the planetary roller screw mechanism, including parameterization and finite element calculation, is established to conduct the elastic–plastic contact analysis automatically. Besides, the finite element method results can be also obtained automatically with the self-compiled flow program and the secondary development platform using the design of experiment method. Then, a mathematic model is applied to value the influence of the uncertain factors on the contact characteristics. The Pareto graphs are plotted to clearly show this sequence of the percent effects of all the uncertain factors. The present work, for the first time, developed an automatic modeling method for analyzing efficiently the uncertain factors of planetary roller screw mechanism, which is worthy in industrial application.

Thermo-mechanical coupling–based finite element analysis of the load distribution of planetary roller screw mechanism

In this article, 3D or three-dimensional finite element analysis is used to simulate and evaluate the load distribution characteristics of a planetary roller screw mechanism under thermo-mechanical coupling. The finite element model takes into account the installation modes of the planetary roller screw mechanism, which is verified by comparison with theoretical models for a certain load magnitude in four installation modes. In addition, the effects of the installation mode, load magnitude, and temperature condition on the load distribution are also systematically analyzed. The numerical results reveal a phenomenon of threads separating from the meshing, which indicates that the influence of thermo-mechanical coupling on the load distribution cannot be ignored. Furthermore, the influence of the installation mode on the screw–roller interface is larger than that on the nut–roller interface. Compared with the screw–roller interface, the temperature difference is one of the main conditions affecting the load distribution of the planetary roller screw mechanism and has a significant effect on the nut–roller interface. In addition, the influences of the screw rotational speed and the load magnitude on the load distribution on the screw–roller interface are larger than those on the nut–roller interface for the four installation modes.

An improved thermal estimation model of the inverted planetary roller screw mechanism

The inverted planetary roller screw mechanism has recently become competitive in the electro-mechanical actuation system due to its high load-carrying capacity and small assembly size. However, a significant amount of heat at the frictional contact interfaces and power loss inside the electrical machine can be naturally generated in a compact and high-load inverted planetary roller screw mechanism system. The conductive heat leads to the temperature rise of inverted planetary roller screw mechanism components that subsequently results in thermal drift and error as well as the actuation accuracy degradation. An analytical approach is applied to calculate the friction torque of the contact pairs and support bearings in the inverted planetary roller screw mechanism system. As the thermal load, heat generation is derived from the friction in nut-roller-screw section and bearings. Then, the heat generation and convection boundary conditions are formulated to facilitate thermal behavior analysis. Finally, using the finite element method, steady-state and transient thermal-mechanical coupling analyses are performed to estimate the temperature distribution and thermal expansion of the inverted planetary roller screw mechanism components. Computational results reveal that operating conditions of rotation speed and external load have significant influence on the thermal characteristics of the inverted planetary roller screw mechanism. This study can serve as a foundation for modeling temperature field and analyzing coupled thermal-mechanical response of inverted planetary roller screw mechanism in electro-mechanical actuation system, which can be useful in determining thermal error compensation.

Development of Increased Load Capacity Structures of Planetary Roller Screw Mechanisms (Determination of Inter-axial Distance Increment)

One of the trends in development of mechanical engineering is that there is an inreasing load capacity of machines. For aerospace industry it is desirable to implement this increase without growing mass of an aircraft, which consists of aggregates, mechanisms, units and machine parts. Among the mechanisms, those that convert rotational motion into translational one account for a sizable proportion. The most promising of them are planetary roller screw mechanisms (PRSM). To increase the load capacity of the PRSM with the same mass is possible due to decreasing α angle of the turn profile of the threaded parts for these mechanisms (see the earlier published paper).The PRSMs have a number of features, one of which is the inequality of the helix angles of the screw and the roller in the contact area, because of which it is necessary to increase the inter-axial distance by increment value. In traditional PRSMs α=90º, and for them, as for a particular case with α=90º, the techniques to determine Δαw have been developed.For the general case, when α angle value is arbitrary (α<90° for increasing the load capacity), a technique to determine Δαw increment (see the second paper earlier published) and a technique for calculating dimensions of the PRSM main parts and their tolerance bands have been developed (see the third paper earlier published), in which Δαw increment is used. Hence, this increment is a key parameter. To determine Δαw a numerical method and a computer calculation program have been developed.This paper presents numerous results of Δαw increment computer calculation according to the developed technique. The Δαw increment value calculated by the developed technique has coincided with Δαw increment value, which was determined for traditional PRSM with the angle α=90º.The paper analyses an effect of various structural parameters on Δαw increment value. It has been found that the radius by which a profile of the roller turns is circumscribed essentially has no effect on Δαw value.The α angle of the profile of turns and the thread pitch of the PRSM parts significantly affect the Δαw value. The paper presents the graphs constructed to determine the coordinates of the point of initial contact of the mating thread turns of the screw and the rollers as well as the graphs to determine the distance from the point of initial contact to the edge of the turn of the screw and the roller. All the information presented can be used to design the PRSMs, including those with increased load capacity.

Kinematic Model of Planetary Roller Screw Mechanism With Run-Out and Position Errors

A kinematic model of the planetary roller screw mechanism (PRSM) is proposed, which accounts for the run-out errors of the screw, roller, nut, ring gear, and carrier, and the position errors of the nut and the pinhole in the carrier. The roller floating region, which contains all the possible positions of the roller inside the pinhole, is obtained by analyzing the axial clearances between mating thread surfaces and the radial clearance between the roller and carrier. The proposed model is based on the constraint that the set of roller floating region is not empty. Then, the additional rigid-body movement on the nut is derived and the path of motion transfer from the screw to the nut is obtained. According to the fundamental property of rigid-body kinematics, the axial velocity of the nut is derived and the transmission error of the PRSM is calculated. The proposed model is verified by comparing the calculated transmission error with experimental one. The results show that the transmission error of the PRSM with run-out and position errors is cyclic with a period corresponding to the rotation period of the screw and the magnitude of the transmission error can be much larger than the lead error of the screw. Besides, due to the run-out and position errors, the roller can move radially or transversally inside the pinhole of the carrier when the elements in the PRSM are regarded as rigid bodies.

A nonlinear six degrees of freedom dynamic model of planetary roller screw mechanism

A nonlinear six degrees of freedom (DOFs) dynamic model to determine the motion and internal forces acting on the moving parts of the planetary roller screw mechanism (PRSM) is proposed in this paper. A load distribution coefficient is assumed and introduced to describe the load distribution among threads of the screw, roller and nut. The friction forces at the screw-roller, nut-roller and ring gear-carrier interfaces are calculated by using the Coulomb friction, rolling contact and Couette flow principles, respectively. Because the friction and contact forces acting on the screw, roller, nut and carrier constitute a spatial force system, the equations of motion for the PRSM, which are derived by using Newton's second law, relate the forces to the six DOFs of those parts. The transient and steady-state behaviors of the PRSM under a heavy or light external load and the sinusoid motion of the mechanism are simulated and discussed. The results show that the load conditions have great influence on the motion and internal forces of the PRSM.

Bond graph-based dynamic model of planetary roller screw mechanism with consideration of axial clearance and friction

To reveal the dynamic characteristics of planetary roller screw mechanism, a dynamic model of planetary roller screw mechanism is developed in this study, which is based on the bond graph theory that accounts for friction, axial clearance, and screw stiffness. First, the bond graph models of friction, axial clearance, and load distribution are presented. Then, a bond graph model of the entire planetary roller screw mechanism for the dynamic analysis is established using the 20-sim software package, and the dynamic equations are solved using the Runge–Kutta–Fehlberg algorithm. Finally, the axial speed, axial acceleration, and contact force of the components are derived under different axial loads and with different axial clearances. Furthermore, the dynamic friction characteristics at different angular velocities of the screw and the dynamic stiffnesses for different axial clearances are also obtained. The results can provide a theoretical basis for planetary roller screw mechanism design with consideration of dynamic characteristics.