A method for researching rigid-flexible coupling hysteresis characteristics of ball screw pair

Abstract

The application discloses a kind of ball screw pair rigid-flexible coupling hysteresis characteristic research methods.The application relates to the technical field of ball screw pair transmission, and comprises the following steps: step 1: establishing the three-dimensional model of ball screw pair, inputting the model into RecurDyn software;step 2: meshing the screw model and replacing it with FFlex flexible body;step 3: establishing the contact surface on the flexible body and adding boundary conditions;step 4: applying the contact and constraint conditions between parts;step 5: applying excitation conditions;step 6: solving the torsion angle and hysteresis;step 7: setting simulation conditions for simulation experiment.The method lays a foundation for improving dynamic transmission accuracy, and is of great significance for the dynamic characteristic research of high-precision equipment such as high-end numerical control machine tools and robot joints.

Description

Technical Field

[0001] This invention relates to the field of ball screw transmission technology, and more specifically to a method for studying the hysteresis characteristics of rigid-flexible coupling in ball screw pairs. Background Technology

[0002] A ball screw assembly is a mechanical device that converts rotary motion into linear motion, characterized by superior load-bearing capacity, stable transmission accuracy, rapid response, and long service life. Leveraging these technological advantages, ball screw assemblies occupy an important position in high-end fields such as industrial robots, CNC machining centers, rail transit equipment, medical devices, and intelligent manufacturing production lines. When constructing its system mechanical model, for low-speed or conventional load conditions, the influence of the microscopic elastic deformation of components on the macroscopic motion trajectory is negligible, and a rigid body model can be used to simplify the analysis process. However, as modern equipment evolves towards higher speeds and heavier loads, the inertial forces and elastic deformations of components caused by high-speed motion and heavy loads of the ball screw assembly superimpose, causing a deviation between the actual displacement and the commanded displacement of the nut. This results in hysteresis in the ball screw assembly feed system, leading to response lag and inconsistencies in response between forward loading and reverse unloading, which in turn significantly reduces the motion positioning accuracy and repeatability of the machine tool. Due to the hysteresis characteristics, the dynamic behavior of ball screw pairs will exhibit a significant rigid-flexible coupling effect, which makes it impossible for traditional rigid body theory to accurately describe its true dynamic characteristics.

[0003] Existing research theoretically analyzes the hysteresis characteristics of ball screw pairs based on stiffness and backlash, which differs somewhat from engineering practice. In the RecurDyn environment, a rigid-flexible coupled multibody dynamics model reflects the elastic deformation of the screw components and the nonlinearity of the contact between the balls and the screw, solving the hysteresis curve deviation problem caused by neglecting flexible deformation in traditional methods. This provides guidance for the practical application of ball screw pairs in high-precision equipment such as high-end CNC machine tools and robot joints. Therefore, designing a method for studying the rigid-flexible coupled hysteresis characteristics of ball screw pairs, performing rigid-flexible coupled multibody dynamics simulation analysis on the ball screw pairs, and calculating the influence of factors such as friction, backlash, and elastic deformation on the hysteresis characteristics of the ball screw pairs are problems that urgently need to be solved by those skilled in the art. Summary of the Invention

[0004] In view of this, the present invention provides a method for studying the hysteresis characteristics of rigid-flexible coupling of ball screw pairs, which lays the foundation for improving the dynamic transmission accuracy and is of great significance for the study of the dynamic characteristics of high-precision equipment such as high-end CNC machine tools and robot joints.

[0005] To achieve the above objectives, the present invention adopts the following technical solution: a method for studying the hysteresis characteristics of rigid-flexible coupling in ball screw pairs, comprising:

[0006] Step 1: Create a 3D model of the ball screw pair, including the screw model, ball model, and nut model. Set a rotating plate model and a baffle model at both ends of the screw model. Input the 3D model, rotating plate model, and baffle model into the multibody dynamics analysis software RecurDyn.

[0007] Step 2: Mesh the lead screw model and replace the rigid bodies in the lead screw model with FFlex flexible bodies;

[0008] Step 3: Create a contact surface in the FFlex flexible body and add boundary conditions at each point in the mesh of the contact surface;

[0009] Step 4: Apply contact and constraint conditions between the lead screw, ball bearings, nut, rotating plate, and baffle in the multibody dynamics analysis software RecurDyn;

[0010] Step 5: Based on step 4, apply excitation conditions in RecurDyn;

[0011] Step 6: Based on Step 5, solve for the torsion angle of the lead screw and the hysteresis of the nut in RecurDyn;

[0012] Step 7: Based on step 6, set the simulation conditions in RecurDyn and conduct the simulation experiment.

[0013] Preferably, the contact surfaces in step 3 include the contact surface between the rotating plate and the lead screw, the contact surface between the lead screw and the ball bearing, and the contact surface between the baffle and the lead screw.

[0014] Preferably, the constraints applied in the multibody dynamics analysis software RecurDyn in step 4 include: the nut moving axially, and a Translate joint being added between the nut and the Ground to move the screw axially; the rotating plate model rotating about the screw axis, and a Revolute joint being added between the rotating plate model and the Ground; and the baffle model rotating about the screw axis, and a Revolute joint being added between the baffle model and the Ground.

[0015] Preferably, the parameters of the RecurDyn contact in step 4 include: stiffness coefficient, damping coefficient, friction coefficient, stiffness index, and penetration depth.

[0016] Preferably, the stiffness coefficient is determined by the material of the part, and the stiffness coefficient e is 1.3 to 1.5; the penetration depth is 0.01 mm; the damping coefficient is 0.1% to 1% of the stiffness value; the friction coefficient includes static friction coefficient and dynamic friction coefficient, which are 0.02 and 0.01 respectively.

[0017] Preferably, the excitation conditions in step 5 include: applying a step rotational speed on the turntable and adding an axial step load to the nut.

[0018] Preferably, a step speed of 1000 rpm is applied to the rotating plate, and a step load of 3000 N is added to the nut.

[0019] Preferably, the torsion angle of the lead screw in step 6 is calculated using the following formula:

[0020]

[0021] in, The deformation effect generated by the axial torque transmission of the lead screw under load conditions is characterized by the dynamic angular displacement difference between the lead screw rotor and the baffle. This represents the angular displacement of the rotating plate around the axis of the leadscrew. This represents the angular displacement of the baffle around the axis of the lead screw.

[0022] Preferably, the hysteresis of the nut in step 6 is calculated using the following formula:

[0023] Δδ=p*n*tL

[0024] Where Δδ represents the offset between the actual displacement and the commanded displacement of the nut, p is the ball screw lead, and L is the displacement of the nut along the screw axis.

[0025] Preferably, the specific process of step 7 includes: clicking Dynamic / KinematicAnalysis in Analysis, setting End Time to 0.1S, Step to 1000, Maximum Time Step to 0.00001, and clicking Simulate to start the simulation.

[0026] As can be seen from the above technical solution, compared with the prior art, the present invention discloses a method for studying the hysteresis characteristics of rigid-flexible coupling of ball screw pairs, which has at least the following technical effects:

[0027] (1) The rigid-flexible coupling hysteresis characteristic analysis method proposed in this invention, by constructing a multibody dynamics model that considers the flexible deformation of the ball screw, has for the first time achieved accurate characterization of the hysteresis characteristics of the ball screw pair under high speed and heavy load conditions, providing a reference for the engineering application of ball screw pairs in high speed and heavy load.

[0028] (2) Based on three-dimensional modeling software, finite element analysis and RecurDyn dynamic analysis software, the present invention completes the three-dimensional modeling of the ball screw pair in the three-dimensional modeling software, makes the screw flexible in the finite element analysis software, and accurately reflects the elastic deformation of the screw component and the nonlinearity of the contact between the ball and the screw through the rigid-flexible coupling multibody dynamic model in the RecurDyn environment. This solves the problem of hysteresis curve deviation caused by neglecting flexible deformation in traditional methods, and lays the foundation for studying the hysteresis characteristics of the ball screw pair and improving the dynamic transmission accuracy.

[0029] (3) When setting parameters, this invention can not only set the material parameters of the ball screw FFlex flexible body model, such as Young's modulus and Poisson's ratio, but also set the contact parameters between various components, such as the friction coefficient and the ball radius. In addition, the rotational speed and load can also be set according to the actual engineering situation. It can solve the hysteresis characteristics of the ball screw pair under the influence of multiple factors such as elastic deformation, friction and backlash, and provide a reference for the engineering application of the ball screw pair. Attached Figure Description

[0030] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on the provided drawings without creative effort.

[0031] Figure 1 This is a flowchart provided for the present invention;

[0032] Figure 2 This is an assembly drawing of a simplified ball screw assembly with rotating plates and baffles at both ends, provided by the present invention.

[0033] Figure 3 This is a mesh generation model diagram of the lead screw provided by the present invention in finite element software;

[0034] Figure 4 This is the rigid-flexible coupling assembly diagram of the RecurDyn ball screw pair provided by the present invention;

[0035] Figure 5 This is a diagram showing the contact surface arrangement of the lead screw FFlex flexible body provided by the present invention;

[0036] Figure 6 This is a boundary condition setting diagram for the lead screw FFlex flexible body provided by the present invention;

[0037] Figure 7 This is a diagram showing the contact and constraint conditions between various components of the RecurDyn rigid-flexible coupling model of the ball screw pair provided by this invention.

[0038] Figure 8 This is the contact parameter setting provided by the present invention;

[0039] Figure 9 This is the torsion angle calculation formula provided by the present invention;

[0040] Figure 10 This invention provides a formula for calculating the hysteresis of nut transmission.

[0041] Figure 11 This is a simulation parameter setting diagram provided by the present invention;

[0042] Figure 12 This is a diagram showing the calculation results of the torsion angle provided by the present invention;

[0043] Figure 13 This is a graph showing the calculation results of the nut transmission hysteresis provided by the present invention;

[0044] Specifically, 1. rotating plate, 2. lead screw, 3. ball bearing, 4. nut, 5. baffle. Detailed Implementation

[0045] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0046] like Figure 1 As shown in the figure, this invention discloses a method for studying the hysteresis characteristics of rigid-flexible coupling in ball screw pairs, including:

[0047] Step 1: Create a 3D model of the ball screw pair, including the screw model, ball model, and nut model. Set a rotating plate model and a baffle model at both ends of the screw model. Input the 3D model, rotating plate model, and baffle model into the multibody dynamics analysis software RecurDyn.

[0048] Step 2: Mesh the lead screw model and replace the rigid bodies in the lead screw model with FFlex flexible bodies;

[0049] Step 3: Create a contact surface in the FFlex flexible body and add boundary conditions at each point in the mesh of the contact surface;

[0050] Step 4: Apply contact and constraint conditions between the lead screw, ball bearings, nut, rotating plate, and baffle in the multibody dynamics analysis software RecurDyn;

[0051] Step 5: Based on step 4, apply excitation conditions in RecurDyn;

[0052] Step 6: Based on Step 5, solve for the torsion angle of the lead screw and the hysteresis of the nut in RecurDyn;

[0053] Step 7: Based on step 6, set the simulation conditions in RecurDyn and conduct the simulation experiment.

[0054] In another specific embodiment, such as Figure 2 As shown, a three-dimensional model of the ball screw pair is established, and based on the actual structure, three-dimensional models of rotating plate 1 and baffle 5 are established at both ends of the screw model respectively. The material of each part is selected as steel, and the model is imported into the multibody dynamics analysis software RecurDyn.

[0055] In step 1, the 3D model is simplified based on the actual structure of the ball screw assembly and designed using Solidworks. It is understood that the components described here include the screw 2, balls 3, and nut 4 of the ball screw assembly.

[0056] In another specific embodiment, such as Figure 3-4 As shown, the three-dimensional model of the established lead screw 2 is imported into the finite element analysis software ANSYS, and the three-dimensional model is meshed and output as a cdb file in the finite element software. The output cdb file is then imported into the RecurDyn software to replace the rigid body in the three-dimensional model of the lead screw with an FFlex flexible body.

[0057] In this step, the 3D model of the ball screw assembly is first imported into finite element analysis software for flexibility testing. This finite element analysis software can be, for example, Ansys. The 3D model of the ball screw assembly is imported into Ansys Workbench. After meshing the imported 3D model of the ball screw 2 using the Static Structural module, the Write input File option is selected in Static Structural (A5) to output a .dat file. This .dat file is then imported into APDL, and the CDWRITE command is entered. A .cdb file is generated in the working directory. The specific format of the CDWRITE command is: CDWRITE,db,Fname,cdb.

[0058] Specifically, the contact surfaces in step 3 include the contact surface between the rotating plate and the lead screw, the contact surface between the lead screw and the ball bearing, and the contact surface between the baffle and the lead screw.

[0059] In another specific embodiment, such as Figure 5-6As shown, in this step, the specific method for establishing the contact surface and boundary conditions of the FFlex flexible body of the lead screw 2 is as follows: Enter the volume editing mode of the FFlex flexible body model of the lead screw 2, and use the Patch Set function to establish the contact surfaces of the ball 3 and the raceway of the lead screw 2, the contact surfaces of the rotating plate 1 and the lead screw 2, and the contact surfaces of the baffle 5 and the lead screw 2 respectively. When applying the boundary conditions at each point, use the BC function of the volume editing mode to select all nodes at both ends of the lead screw 2, and check the X, Y, Z, RX, RY options to restrict the corresponding degrees of freedom of the selected nodes; select all nodes in the raceway part of the lead screw 2, and check the X, Y, RX, RY options to restrict the corresponding degrees of freedom of the selected nodes.

[0060] Specifically, such as Figure 7 As shown, the constraints applied in the multibody dynamics analysis software RecurDyn in step 4 include: the nut moving axially, adding a Translate joint for the axial movement of the lead screw between the nut and the Ground; the rotating plate model rotating around the lead screw axis, adding a Revolute joint between the rotating plate model and the Ground; and the baffle model rotating around the lead screw axis, adding a Revolute joint between the baffle model and the Ground.

[0061] Specifically, the parameters of the RecurDyn contact in step 4 include: stiffness coefficient, damping coefficient, friction coefficient, stiffness index, and penetration depth.

[0062] Specifically, such as Figure 8 As shown, the stiffness coefficient is determined by the material of the part, and the stiffness coefficient e is 1.3 to 1.5; the penetration depth is 0.01 mm; the damping coefficient is 0.1% to 1% of the stiffness value; the friction coefficient includes the static friction coefficient and the dynamic friction coefficient, which are 0.02 and 0.01 respectively.

[0063] In another specific embodiment, the contacts between the components include: adding GeoSphere contact between the lead screw 2 and the ball 3; adding Sphere-to-Sphere contact between the ball 3; adding GeoSphere contact between the ball 3 and the nut 4; adding GeoSurface contact between the rotating plate 1 and the lead screw 2; and adding GeoSurface contact between the baffle 5 and the lead screw 2. Specifically, when applying constraints, the nut 4 moves axially, and a sliding joint is added between the nut 4 and the ground; the rotating plate 1 rotates, and a revolute joint is added between the rotating plate and the ground; the baffle 5 rotates, and a revolute joint is added between the baffle and the ground.

[0064] Specifically, the excitation conditions in step 5 include: applying a step speed on the turntable and adding an axial step load to the nut;

[0065] Specifically, in order to simulate the real physical process, make the rotation speed and load transition smoothly, and control the stability and convergence of the simulation, a step speed of 1000 rpm is applied to the rotating plate, and a step load of 3000 N is added to the nut.

[0066] Specifically, such as Figure 9 As shown, the torsion angle of the lead screw in step 6 is calculated using the following formula:

[0067]

[0068] in, The deformation effect generated by the axial torque transmission of the lead screw under load conditions is characterized by the dynamic angular displacement difference between the lead screw rotor and the baffle, with the dimension in radians. This represents the angular displacement of the rotating plate around the axis of the leadscrew. This represents the angular displacement of the baffle around the axis of the lead screw.

[0069] Specifically, such as Figure 10 As shown, the hysteresis of the nut in step 6 is calculated using the following formula:

[0070] Δδ=p*n*tL

[0071] Where Δδ represents the deviation between the actual displacement and the commanded displacement of the nut, i.e., the loss of movement of the ball screw pair; p is the lead of the ball screw; and L is the displacement of the nut along the screw axis.

[0072] In another specific embodiment, the torsion angle of the lead screw and the hysteresis of the nut are solved in RecurDyn by selecting the Expression method in the Scope post-processing tool to solve the torsion angle of the lead screw 2 and the hysteresis of the nut 4.

[0073] Specifically, the Expression mode in the Scope post-processing tool allows users to input any valid mathematical or logical expression to obtain results and update the graph in real time. This allows for debugging, optimization, and anomaly detection during simulation, improving debugging efficiency.

[0074] Specifically, such as Figure 11As shown, the specific simulation process in step 7 includes: clicking Dynamic / Kinematic Analysis in Analysis, setting the End Time to 0.1s for short-time simulation to avoid redundant calculations, setting the Step to 1000 steps to save results at an interval of 0.0001s (0.1s / 1000) to provide sufficiently dense data points for later curve plotting, and setting the Maximum Time Step to 0.00001 to limit the maximum step size of the simulation, which can improve the convergence of the system simulation of high-stiffness systems and nonlinear problems. In addition, the RecurDyn software uses a variable step size algorithm, allowing the solver to moderately increase the step size during the steady phase and automatically reduce the step size during critical events (such as collisions), balancing efficiency and stability. Finally, click Simulate to start the simulation.

[0075] In another specific embodiment, such as Figure 12-13 As shown, the calculation results of the torsion angle and the nut transmission hysteresis are obtained based on the simulation process. The following conclusions can be drawn:

[0076] (1) The rigid-flexible coupling hysteresis characteristic analysis method proposed in this invention, by constructing a multibody dynamics model that considers the flexible deformation of the ball screw, has for the first time achieved accurate characterization of the hysteresis characteristics of the ball screw pair under high speed and heavy load conditions, providing a reference for the engineering application of ball screw pairs in high speed and heavy load.

[0077] (2) This invention is based on 3D modeling software, finite element analysis, and RecurDyn dynamic analysis software. The 3D model of the ball screw assembly is completed in the 3D modeling software, the screw is made flexible in the finite element analysis software, and the elastic deformation of the screw components and the nonlinearity of the contact between the balls and the screw are accurately reflected through a rigid-flexible coupled multibody dynamic model in the RecurDyn environment. The inertial force and elastic deformation of the components caused by the high-speed motion and heavy load of the ball screw assembly superimpose, causing a deviation between the actual displacement and the commanded displacement of the nut. This results in hysteresis in the ball screw assembly feed system, with response lag and inconsistent responses between forward loading and reverse unloading. Consequently, this significantly reduces the motion positioning accuracy and repeatability of the machine tool. This invention solves the problem of hysteresis curve deviation caused by neglecting flexible deformation in traditional methods, laying the foundation for studying the hysteresis characteristics of ball screw assemblies and improving dynamic transmission accuracy.

[0078] (3) When setting parameters, this invention can not only set the material parameters of the ball screw FFlex flexible body model, such as Young's modulus and Poisson's ratio, but also set the contact parameters between various components, such as the friction coefficient and the ball radius. In addition, the rotational speed and load can also be set according to the actual engineering situation. It can solve the hysteresis characteristics of the ball screw pair under the influence of multiple factors such as elastic deformation, friction and backlash, and provide a reference for the engineering application of the ball screw pair.

[0079] The various embodiments in this specification are described in a progressive manner, with each embodiment focusing on its differences from other embodiments. Similar or identical parts between embodiments can be referred to interchangeably. For the apparatus disclosed in the embodiments, since they correspond to the methods disclosed in the embodiments, the description is relatively simple; relevant parts can be referred to the method section.

[0080] The above description of the disclosed embodiments enables those skilled in the art to make or use the invention. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of the invention. Therefore, the invention is not to be limited to the embodiments shown herein, but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A method for studying the hysteresis characteristics of rigid-flexible coupling in ball screw pairs, characterized in that, include: Step 1: Create a 3D model of the ball screw pair, including the screw model, ball model, and nut model. Set a rotating plate model and a baffle model at both ends of the screw model. Input the 3D model, rotating plate model, and baffle model into the multibody dynamics analysis software RecurDyn. Step 2: Mesh the lead screw model and replace the rigid bodies in the lead screw model with FFlex flexible bodies; Step 3: Create a contact surface in the FFlex flexible body and add boundary conditions at each point in the mesh of the contact surface; Step 4: Apply contact and constraint conditions between the lead screw, ball bearings, nut, rotating plate, and baffle in the multibody dynamics analysis software RecurDyn; Step 5: Based on step 4, apply excitation conditions in RecurDyn; Step 6: Based on Step 5, solve for the torsion angle of the lead screw and the hysteresis of the nut in RecurDyn; Step 7: Based on step 6, set the simulation conditions in RecurDyn and conduct the simulation experiment; The torsion angle of the lead screw in step 6 is calculated using the following formula: in, The deformation effect generated by the axial torque transmission of the lead screw under load conditions is characterized by the dynamic angular displacement difference between the lead screw rotor and the baffle. This represents the angular displacement of the rotating plate around the axis of the leadscrew. This represents the angular displacement of the baffle around the axis of the leadscrew. The hysteresis of the nut in step 6 is calculated using the following formula: in, Characterizes the actual displacement of the nut relative to the commanded displacement. For the ball screw lead; The displacement of the nut along the axial direction of the lead screw.

2. The method for studying the hysteresis characteristics of rigid-flexible coupling in a ball screw pair according to claim 1, characterized in that, The contact surfaces in step 3 include the contact surface between the rotating plate and the lead screw, the contact surface between the lead screw and the ball bearing, and the contact surface between the baffle and the lead screw.

3. The method for studying the hysteresis characteristics of rigid-flexible coupling in a ball screw pair according to claim 1, characterized in that, The constraints applied in the multibody dynamics analysis software RecurDyn in step 4 include: the nut moving axially, adding a Translate joint for the axial movement of the lead screw between the nut and the ground; the rotating plate model rotating around the lead screw axis, adding a Revolute joint between the rotating plate model and the ground; and the baffle model rotating around the lead screw axis, adding a Revolute joint between the baffle model and the ground.

4. The method for studying the hysteresis characteristics of rigid-flexible coupling in a ball screw pair according to claim 1, characterized in that, The parameters of the RecurDyn contact in step 4 include: stiffness coefficient, damping coefficient, friction coefficient, stiffness index, and penetration depth.

5. The method for studying the hysteresis characteristics of rigid-flexible coupling in a ball screw pair according to claim 4, characterized in that, The stiffness coefficient is determined by the material of the part, and the stiffness coefficient e is 1.3 to 1.5; the penetration depth is 0.01 mm; the damping coefficient is 0.1% to 1% of the stiffness value; the friction coefficient includes the static friction coefficient and the dynamic friction coefficient, which are 0.02 and 0.01 respectively.

6. The method for studying the hysteresis characteristics of rigid-flexible coupling in a ball screw pair according to claim 1, characterized in that, The excitation conditions in step 5 include: applying a step speed on the turntable and adding an axial step load to the nut.

7. The method for studying the hysteresis characteristics of rigid-flexible coupling in a ball screw pair according to claim 6, characterized in that, A step speed of 1000 rpm is applied to the rotating plate, and a step load of 3000 N is added to the nut.

8. The method for studying the hysteresis characteristics of rigid-flexible coupling in a ball screw pair according to claim 1, characterized in that, The specific process of step 7 includes: clicking Dynamic / Kinematic Analysis in Analysis, setting End Time to 0.1S, Step to 1000, Maximum Time Step to 0.00001, and clicking Simulate to start the simulation.

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