A dual-motor anti-backlash control method and system based on nonlinear mesh stiffness

Abstract

This invention relates to the field of servo control technology, and particularly to a dual-motor backlash elimination control method and system based on nonlinear meshing stiffness. The method first acquires the system parameters of the dual-motor drive system and establishes a three-loop control architecture. Based on the reducer transmission ratio coefficient, bidirectional parameter value conversion is performed within the three-loop control architecture to form a bidirectional mapping closed loop. A nonlinear meshing model is constructed to determine the meshing state between the gear and rack and calculate the meshing phase, obtaining the time-varying meshing stiffness and nonlinear meshing force. The armature current of the dual motors is collected, and the offset compensation torque is calculated by combining the system parameters and the time-varying meshing stiffness, and then superimposed onto the speed loop to achieve closed-loop backlash elimination control. The dual-motor backlash elimination control method and system based on nonlinear meshing stiffness provided by this invention can effectively suppress vibrations caused by commutation impact and stiffness fluctuations in the transmission system, significantly improving control accuracy and stability under variable load and high dynamic conditions.

Description

Technical Field

[0001] This invention relates to the field of servo control technology, and in particular to a dual-motor backlash elimination control method and system based on nonlinear meshing stiffness. Background Technology

[0002] Dual-motor backlash elimination control is a key technology for solving problems such as decreased positioning accuracy, sluggish dynamic response, and reversing impact caused by tooth backlash in gear and rack transmissions in large and medium-sized CNC machine tools. Its core principle is to apply opposite preload torques to two cooperating drive motors, ensuring that the two transmission gears constantly press against the two opposite meshing surfaces of the rack, thereby establishing continuous tension in the transmission chain to eliminate backlash-induced idle errors.

[0003] Despite continuous technological improvements, control accuracy and stability still face bottlenecks when dealing with the extreme operating conditions of heavy machine tools under high dynamics and variable loads. The fundamental reason lies in the oversimplification of the dynamic model of the transmission system in existing methods, and the failure to fully utilize system parameters to form an accurate closed-loop mapping. This manifests in the following two major shortcomings:

[0004] 1. Existing technologies typically model the reducer connecting the motor and gears simply as a fixed transmission ratio coefficient, used only for unidirectional conversion of speed or position. This simplification ignores the crucial role of this coefficient in system modeling and feedback. The failure to reuse the transmission ratio coefficient in multiple stages, such as position loop setting, load torque calculation, and actual position and torque feedback, leads to deviations in parameter mapping between the motor and load ends, limiting model accuracy.

[0005] 2. The meshing stiffness of gears and racks is not a constant value, but exhibits significant time-varying nonlinear characteristics due to the alternation of single-tooth and double-tooth meshing zones, the movement of the meshing point position, and factors such as manufacturing errors and wear. Current technologies generally treat gear-rack pairs as equivalent linear models with a fixed "dead zone," compensating only for the "dead zone" while completely ignoring the dynamic deformation and force transmission errors caused by fluctuations in meshing stiffness within the effective meshing region. This lack of modeling prevents the control system from fundamentally compensating for the following errors caused by stiffness variations, severely limiting the system's ultimate performance under high speed and heavy loads. Summary of the Invention

[0006] (a) Technical problems to be solved

[0007] This invention provides a dual-motor backlash elimination control method and system based on nonlinear meshing stiffness, which overcomes the problems of insufficient system model accuracy and limited transmission accuracy and stability under high dynamic variable load conditions caused by the simplification of the transmission characteristics model of the reducer, insufficient utilization of the transmission ratio coefficient feedback, and complete neglect of the time-varying nonlinear characteristics of the gear and rack meshing stiffness in the existing technology.

[0008] (II) Technical Solution

[0009] To achieve the above objectives, the present invention provides a dual-motor backlash elimination control method based on nonlinear meshing stiffness, comprising the following steps:

[0010] Step S1: Obtain the system parameters of the dual-motor drive system, and establish a three-loop control architecture for the dual-motor drive system based on the system parameters. The three-loop control architecture includes: position loop, speed loop and current loop.

[0011] Step S2: Based on the reducer transmission ratio coefficient in the system parameters, perform bidirectional parameter value conversion on several signal nodes in the three-loop control architecture to form a bidirectional parameter mapping closed loop between the motor end and the load end.

[0012] Step S3: Construct a nonlinear meshing model based on the system parameters and the bidirectional mapping closed loop of the parameters. The nonlinear meshing model is used to determine the meshing state based on the relative displacement between the gear and the rack. In the meshing state, the meshing phase is calculated based on the gear geometric parameters, and the time-varying meshing stiffness and nonlinear meshing force are calculated based on the meshing phase.

[0013] Step S4: Collect the armature current of the dual motors, calculate the offset compensation torque based on the armature current, system parameters and time-varying meshing stiffness, and superimpose the offset compensation torque onto the speed loop to form closed-loop backlash elimination control.

[0014] Preferably, the system parameters of the dual-motor drive system include: reducer transmission ratio coefficient, tooth backlash, and initial meshing phase.

[0015] Preferably, the signal nodes in step S2 include: a position loop input port, a current loop output port, and a load feedback port.

[0016] Preferably, the bidirectional parameter value conversion in step S2 includes:

[0017] Step S21: Convert the rack displacement and motor rotation angle in the positive direction at the position loop input port, and convert the motor torque and gear torque in the positive direction at the current loop output port;

[0018] Step S22: At the load end feedback port, the actual position of the rack is reversed with the motor rotation angle feedback, and the torque on the gear end is reversed with the feedback torque at the motor end.

[0019] Preferably, step S3, constructing the nonlinear meshing model, includes:

[0020] Step S31: Calculate the relative displacement Δx between the gear and rack based on the motor shaft speed at the motor output end;

[0021] Step S32, by comparing the relative displacement Δx with the tooth flank clearance b l The quantitative relationship determines the contact state between the gear and the rack;

[0022] If |Δx|≤b l / 2 If the gear rotation does not fill the tooth backlash, the gear and rack are in a non-contact state. (Set contact status indicator c) f =0, engagement position indicator m p =0, no meshing stiffness calculation is performed;

[0023] If |Δx|>b l / 2 indicates that the gear and rack tooth surfaces are in close contact, and a contact status indicator c is set. f =1, perform meshing stiffness calculation.

[0024] Preferably, the calculation of the meshing phase m p Calculate and normalize using the following formula:

[0025] m p =(θ g ×r b / p b )+i p

[0026] Where, where θ g For the gear rotation angle, r b p is the radius of the base circle. b As a base section, i p This is the initial engagement phase.

[0027] Preferably, the calculation of time-varying meshing stiffness and nonlinear meshing force in step S3 includes:

[0028] Step S33: The bending stiffness, shear stiffness and axial stiffness of the gear teeth are calculated by the potential energy method, and the bending stiffness, shear stiffness and axial stiffness of the gear teeth are connected in series to obtain the comprehensive stiffness of a single gear tooth.

[0029] Step S34: Calculate the tooth base stiffness based on the meshing point position, tooth root circle radius, and inner hole radius. Connect the single gear tooth composite stiffness with the tooth base stiffness in series to obtain the gear side composite stiffness kt. gear ;

[0030] Step S35: Calculate the rack tooth stiffness kt using the potential energy method. rack The contact stiffness k between the gear and rack is calculated based on Hertzian contact theory. h ;

[0031] Step S36, using the formula: k pair =1 / (1 / k h +1 / kt gear +1 / kt rack Calculate the combined stiffness of a single pair of teeth, based on the meshing phase m. p Determine the number of meshing tooth pairs;

[0032] When it is determined to be single-tooth meshing, the k pair For time-varying meshing stiffness;

[0033] When it is determined to be double-tooth meshing, the two sets of k pair The time-varying meshing stiffness is obtained by performing parallel accumulation.

[0034] The present invention also provides a dual-motor backlash elimination control system based on nonlinear meshing stiffness, comprising: a master-slave motor three-loop control module, a reducer transmission conversion module, and a nonlinear meshing model construction and calculation module;

[0035] The master-slave motor three-loop control module is used to establish and execute a three-loop control architecture including a position loop, a speed loop, and a current loop. The reducer transmission conversion module is connected to the master-slave motor three-loop control module and is used to perform bidirectional parameter value conversion on several signal nodes in the three-loop control architecture based on the reducer transmission ratio coefficient, so as to form a bidirectional parameter mapping closed loop between the motor end and the load end.

[0036] The nonlinear meshing model construction and calculation module is connected to the reducer transmission conversion module and is used to construct the nonlinear meshing model;

[0037] The master-slave motor three-loop control module and the nonlinear meshing model construction and calculation module are respectively connected to the dynamic torque compensation module. The dynamic torque compensation module is used to calculate the offset compensation torque and superimpose the offset compensation torque onto the speed loop.

[0038] Preferably, the master-slave motor three-loop control module includes: a position loop control unit, a speed loop control unit, and a current loop control unit, which are connected in sequence to form the three-loop control architecture.

[0039] Preferably, the reducer transmission conversion module includes: a forward conversion unit and a reverse conversion and feedback unit;

[0040] The forward conversion unit is used to perform a forward conversion at the position loop input port to convert rack displacement into motor rotation angle, and at the current loop output port to perform a forward conversion to convert motor torque into gear torque;

[0041] The reverse conversion and feedback unit is used to perform reverse conversion at the load-side feedback port to convert the actual position of the rack into motor rotation angle feedback, and to convert the torque applied to the gear end into the feedback torque at the motor end.

[0042] (III) Beneficial Effects

[0043] This invention provides a dual-motor backlash-eliminating control method and system based on nonlinear meshing stiffness. It achieves bidirectional parameter mapping closed-loop between the motor and load ends by systematically reusing the reducer transmission ratio coefficient across multiple nodes, including the position loop, current loop, and load feedback. This overcomes the shortcomings of traditional methods that simplify the reducer to a unidirectional fixed coefficient and fail to fully utilize feedback, achieving precise matching and closed-loop feedback of position and torque signals in the transmission chain. By combining the constructed nonlinear meshing model, it incorporates time-varying gear and rack meshing stiffness into the real-time control model for the first time, avoiding the oversimplification of the transmission pair as a fixed "dead zone." This fundamentally compensates for dynamic following errors caused by periodic fluctuations in meshing stiffness, making the system model closely match the actual physical process.

[0044] The meshing state is dynamically determined based on real-time calculation of relative displacement, and the time-varying meshing stiffness is calculated based on the precise geometric phase in the meshing state. Based on this real-time stiffness and the collected dual motor current, the offset compensation force is dynamically calculated. It can adaptively follow the changes in the stiffness characteristics of the transmission system itself and the load state, improve the control accuracy and stability of the system under variable load and high dynamic conditions, and effectively suppress commutation shock and vibration caused by stiffness fluctuation. Attached Figure Description

[0045] Figure 1 The flowchart of a dual-motor backlash elimination control method based on nonlinear meshing stiffness according to the present invention is shown.

[0046] Figure 2 A schematic diagram of a dual-motor backlash-eliminating control system based on nonlinear meshing stiffness is shown in this invention.

[0047] Figure 3 This diagram shows the structure of the master-slave motor three-loop control module;

[0048] Figure 4 A schematic diagram of the reducer transmission conversion module is shown.

[0049] Figure 5 A schematic diagram of gear and rack meshing stiffness during a single meshing cycle is shown.

[0050] Figure 6 A schematic diagram of gear and rack meshing stiffness during multiple meshing cycles is shown.

[0051] Figure 7 The diagram shows the gear meshing state during the backlash elimination process of the dual motors;

[0052] Figure 8 The diagram shows the meshing position of gear 1 during the backlash elimination process of the dual motors;

[0053] Figure 9 The diagram shows the meshing position of gear 2 during the backlash elimination process of the dual motors;

[0054] Figure 10 The diagram shows the meshing stiffness of gear 1 during the backlash elimination process of the dual motors;

[0055] Figure 11 The diagram shows the meshing stiffness of gear 2 during the backlash elimination process of the dual motors;

[0056] Figure 12 The diagram shows the nonlinear gear and rack meshing force during the backlash elimination process of the dual motors;

[0057] Figure 13 The diagram shows the variation in clearance between gear 1, gear 2, and the rack.

[0058] Figure 14 The input-output curves show the gap elimination effect.

[0059] The module includes: 1: Master-slave motor three-loop control module; 11: Position loop control unit; 12: Speed ​​loop control unit; 13: Current loop control unit; 2: Reducer transmission conversion module; 21: Forward conversion unit; 22: Reverse conversion and feedback unit; 3: Nonlinear meshing model construction and calculation module; 4: Dynamic torque compensation module. Detailed Implementation

[0060] The present invention will now be described in detail with reference to the accompanying drawings and embodiments. The technical solutions in the embodiments of the present invention will be clearly and completely described. 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.

[0061] In the description of this invention, it is necessary to understand that the orientations or positional relationships indicated by terms such as "upper," "lower," "left," "right," "inner," "outer," "top," and "bottom" are based on the orientations or positional relationships shown in the accompanying drawings. They are intended only to facilitate the description of this invention and to simplify the description, and are not intended to indicate or imply that the components referred to must have a specific orientation, or be constructed and operated in a specific orientation. Therefore, they should not be construed as limitations on this invention.

[0062] like Figure 1 As shown, this invention provides a dual-motor backlash elimination control method based on nonlinear meshing stiffness, comprising the following steps:

[0063] Step S1: Obtain the system parameters of the dual-motor drive system, and establish a three-loop control architecture for the dual-motor drive system based on the system parameters. The three-loop control architecture includes: position loop, speed loop and current loop.

[0064] The system parameters of the dual-motor drive system include: reducer transmission ratio coefficient, tooth backlash, and initial engagement phase;

[0065] The three-loop control architecture adopts a periodic synchronous speed mode. The position loop is configured as a PID controller, while the speed loop and current loop are both configured as PI controllers. Parameter adaptation ensures a fast and stable response of each control link.

[0066] The gear ratio coefficient of the reducer is used to establish the parameter mapping relationship between the motor end and the load end, providing a conversion benchmark for subsequent bidirectional parameter value conversion at the position loop input port, current loop output port and load end feedback port. The tooth backlash is used to determine the meshing state of the gear and rack, serving as a quantitative threshold to distinguish between disengagement and meshing states. The initial meshing phase is located in the calculation of the subsequent meshing phase. Combined with the gear geometric parameters, it accurately identifies the relative position of the current contact point in the meshing zone, providing a phase benchmark for the calculation of time-varying meshing stiffness.

[0067] Step S2: Based on the reducer transmission ratio coefficient in the system parameters, perform bidirectional parameter value conversion on several signal nodes in the three-loop control architecture to form a bidirectional parameter mapping closed loop between the motor end and the load end.

[0068] The reducer has a fixed transmission ratio coefficient, which is used to realize the digital modeling of the transmission characteristics between the motor shaft and the gear shaft. By converting the parameter values ​​at multiple signal nodes, a precise parameter mapping relationship between the motor end and the load end is established, forming a two-way feedback closed loop of position and torque, thereby making up for the defects of traditional simplified models in mapping accuracy.

[0069] The signal nodes in step S2 include: position loop input port, current loop output port and load feedback port;

[0070] The bidirectional parameter value conversion in step S2 includes:

[0071] Step S21: At the position loop input port, the rack displacement and motor rotation angle are positively converted; at the current loop output port, the motor torque and gear torque are positively converted.

[0072] The rack position setting value is converted into the motor end rotation angle setting value through the transmission ratio coefficient, clarifying the correspondence between rack displacement and motor rotation angle to provide a reference for position control. The driving torque corresponding to the motor armature output current signal is converted into the torque at the drive gear end through the transmission ratio coefficient, realizing the torque matching between the motor output and the gear drive requirements.

[0073] Step S22: At the load end feedback port, the actual position of the rack is reversed with the motor rotation angle feedback, and the torque on the gear end is reversed with the torque fed back to the motor end;

[0074] The actual position of the rack is converted into the motor end rotation angle feedback value through the transmission ratio coefficient to complete the signal matching of the position closed loop. The torque on the gear end is converted into the motor end feedback torque in reverse through the transmission ratio coefficient to form the torque closed loop feedback.

[0075] By performing bidirectional parameter value conversion at the position loop input port, current loop output port, and load feedback port, the reducer model is deeply integrated with the three-loop control framework. Relying on the bidirectional feedback mechanism formed by forward and reverse conversion, the convenience of simplifying the reducer model into a transmission ratio coefficient is retained, while the shortcomings of traditional simplified models in mapping accuracy are made up for, thereby improving the accuracy of the system model from the source of control.

[0076] like Figure 5-6 As shown, in step S3, a nonlinear meshing model is constructed based on the system parameters and the bidirectional mapping closed loop of the parameters. The nonlinear meshing model is used to determine the meshing state based on the relative displacement between the gear and the rack. In the meshing state, the meshing phase is calculated based on the gear geometric parameters, and the time-varying meshing stiffness and nonlinear meshing force are calculated based on the meshing phase.

[0077] Step S3, which constructs the nonlinear meshing model, includes:

[0078] Step S31: Calculate the relative displacement Δx between the gear and rack based on the motor shaft speed at the motor output end;

[0079] By acquiring the speed signals of the master / slave motors and using the parameter mapping relationship established in step S2 based on the transmission ratio coefficient of the reducer, the motor speed is integrated and the signal is calibrated and converted to obtain the relative displacement Δx between the gear and rack in the meshing line direction. This Δx is a direct physical quantity for determining whether the gear and rack pair has effective contact and is in a free or meshing state.

[0080] Step S32, by comparing the relative displacement Δx with the tooth flank clearance b l The quantitative relationship determines the contact state between the gear and the rack;

[0081] If |Δx|≤b l / 2 If the gear rotation does not fill the tooth backlash, the gear and rack are in a non-contact state. (Set contact status indicator c) f =0, engagement position indicator m p = 0, no meshing stiffness calculation is performed;

[0082] If |Δx|>bl / 2 indicates that the gear and rack tooth surfaces are in close contact, and a contact status indicator c is set. f =1, perform meshing stiffness calculation;

[0083] The calculation of the meshing phase m p Calculate and normalize using the following formula:

[0084] m p =(θ g ×r b / p b )+i p

[0085] Where, where θ g For the gear rotation angle, r b p is the radius of the base circle. b As a base section, i p For the initial engagement phase, m p It is a cyclic value between 0 and 1.

[0086] The calculation of time-varying meshing stiffness and nonlinear meshing force in step S3 includes:

[0087] Step S33: The bending stiffness, shear stiffness and axial stiffness of the gear teeth are calculated by the potential energy method, and the bending stiffness, shear stiffness and axial stiffness of the gear teeth are connected in series to obtain the comprehensive stiffness of a single gear tooth.

[0088] For a single-sided gear tooth, based on the current meshing point position, a mechanical model of its bending deformation, shear deformation, and axial compression deformation is established using the potential energy method, and the corresponding bending stiffness, shear stiffness, and axial stiffness are calculated. Since these three deformations are in series along the force transmission path, they can be combined using the equivalent stiffness formula to obtain the comprehensive deformation stiffness of a single gear tooth at the meshing point.

[0089] Step S34: Calculate the tooth base stiffness based on the meshing point position, tooth root circle radius, and inner hole radius. Connect the combined stiffness of this single gear tooth with the tooth base stiffness in series to obtain the combined stiffness kt on the gear side. gear ;

[0090] Step S35: Calculate the rack tooth stiffness kt using the potential energy method. rack The contact stiffness k between the gear and rack is calculated based on Hertzian contact theory. h ;

[0091] Step S36, using the formula: k pair =1 / (1 / k h +1 / kt gear +1 / kt rack Calculate the combined stiffness of a single pair of teeth, based on the meshing phase m. pDetermine the number of meshing tooth pairs;

[0092] When it is determined to be single-tooth meshing, use this k pair The time-varying meshing stiffness, the total meshing stiffness k total =k pair ;

[0093] When it is determined to be double-tooth meshing, the two sets of k pair The time-varying meshing stiffness is obtained by parallel accumulation, and the total meshing stiffness k is... total =k pair1 +k pair2 .

[0094] Step S4: Collect the armature current of the dual motors, calculate the offset compensation torque based on the armature current, system parameters and time-varying meshing stiffness, and superimpose the offset compensation torque onto the speed loop to form closed-loop backlash elimination control.

[0095] By using current sensors installed on the main motor and slave motor drivers, the armature current signals of the two motors are collected in real time and synchronously to ensure the stability and anti-interference of the control signals. The collected raw current signals need to be filtered to remove high-frequency noise and switching harmonics, so as to obtain current feedback values ​​that can be used for accurate calculation.

[0096] like Figure 2-4 As shown, the present invention also provides a dual-motor backlash elimination control system based on nonlinear meshing stiffness, including: a master-slave motor three-loop control module 1, a reducer transmission conversion module 2, and a nonlinear meshing model construction and calculation module 3;

[0097] The master-slave motor three-loop control module 1 is used to establish and execute a three-loop control architecture including a position loop, a speed loop, and a current loop. The reducer transmission conversion module 2 is connected to the master-slave motor three-loop control module 1 and is used to perform bidirectional parameter value conversion on several signal nodes in the three-loop control architecture based on the reducer transmission ratio coefficient, so as to form a bidirectional parameter mapping closed loop between the motor end and the load end.

[0098] The nonlinear meshing model construction and calculation module 3 is connected to the reducer transmission conversion module 2 and is used to construct the nonlinear meshing model, thereby realizing the deep coupling between the mechanical transmission chain and the electrical control system.

[0099] The nonlinear meshing model construction and calculation module 3 receives the speed signal from the motor end, calculates the relative displacement of the gear and rack in the meshing line direction through integration and transmission ratio conversion, compares the relative displacement with the tooth backlash in the system parameters and determines the meshing state, calculates the meshing phase and the total time-varying meshing stiffness of the system in the meshing state, and calculates and outputs the nonlinear meshing force acting on the gear shaft in real time based on the calculated total time-varying meshing stiffness and the elastic deformation between the gear and rack. This nonlinear meshing force is fed back to the reverse conversion unit of the reducer transmission conversion module 2 and is finally fed back to the motor end as a load disturbance, thus truly reflecting the stiffness characteristics of the transmission chain in the system model.

[0100] The master-slave motor three-loop control module 1 and the nonlinear meshing model construction and calculation module 3 are respectively connected to the dynamic torque compensation module 4. The dynamic torque compensation module 4 is used to calculate the offset compensation torque and superimpose the offset compensation torque onto the speed loop, thereby dynamically adjusting the output torque difference between the two motors so that the drive gear is always pressed against the target working tooth surface of the rack with an adaptively variable preload.

[0101] The master-slave motor three-loop control module 1 includes: a position loop control unit 11, a speed loop control unit 12, and a current loop control unit 13. The position loop control unit 11, speed loop control unit 12, and current loop control unit 13 are connected in sequence to form the three-loop control architecture.

[0102] The reducer transmission conversion module 2 includes: a forward conversion unit 21 and a reverse conversion and feedback unit 22;

[0103] The forward conversion unit 21 is used to perform a forward conversion at the position loop input port to convert rack displacement into motor rotation angle, and at the current loop output port to perform a forward conversion to convert motor torque into gear torque;

[0104] The conversion and feedback unit 22 is used to perform reverse conversion at the load-side feedback port to convert the actual position of the rack into motor rotation angle feedback, and to convert the torque applied to the gear end into the feedback torque at the motor end.

[0105] This invention also provides an embodiment of a dual-motor backlash elimination control method and system based on nonlinear meshing stiffness applied to the X-axis of a heavy-duty upright floor-type milling and boring machine, specifically including:

[0106] This embodiment uses the X-axis drive control system of a heavy-duty, upright, floor-type milling and boring machine as the application object. The X-axis of this machine tool adopts gear and rack transmission and uses dual motors for coordinated drive to achieve backlash elimination. The core steps and system construction of applying the method and system of this invention are as follows:

[0107] Obtain the key system parameters of this dual-motor drive system, including: the fixed transmission ratio coefficient of the reducer i=90, and the tooth backlash b. l =0.2mm, initial engagement phase i p =0 (calibrated by gear installation positioning), the main motor and slave motor have the same model and parameters, including motor rotational inertia of 0.0206 kg·m², rated current of 15A, and back electromotive force coefficient of 2.78V·s / rad; the load mass is 35000 kg, and the compensation bias torque is 10N. Based on this, a three-loop control architecture including a position loop, a speed loop, and a current loop is established. The position loop uses a PID controller (parameter K). p1 =1、K i1 =0、K d1 =-0.01), both the speed loop and current loop use PI controllers (speed loop parameter is K). p2 =3.5, K i2 =0, current loop parameter is K p3 =20、K i3 =0), and adopts a periodic synchronous speed mode to ensure coordinated control of the master and slave motors;

[0108] Based on the reducer transmission ratio coefficient i=90, bidirectional parameter value conversion is performed at multiple signal nodes in the three-loop control architecture to form a bidirectional parameter mapping closed loop between the motor end and the load end (gear and rack end):

[0109] Input comparison and contact determination: Calculate the current rack position x. r With gear rotation angle θ g The difference Δx on the meshing line. If the absolute value of this displacement difference Δx is less than or equal to the tooth flank clearance b. l If the rotational speed is half of the required value, it indicates that the gear's rotational speed has not yet "filled" the tooth flank clearance, and the gear and rack are not effectively meshing, remaining in a "free play" or "disengagement" state. At this point, the contact state is c. f Set to 0, engagement position m p The value is 0. If the absolute value of Δx is greater than b. l If half of the gear's rotation has overcome the backlash and made contact with the other side of the rack's teeth, it enters a "meshing" state. At this point, c f It is set to 1. During the specific control process, the change in the meshing state of the two gears is as follows: Figure 7 As shown;

[0110] Meshing position calculation: Further calculate the position of the line of engagement under meshing conditions, using the base circle radius r. b and base section p b These two parameters are directly related to the involute geometry of the gear. Gear rotation angle θ g Multiply by the base circle radius r bThe displacement L along the meshing line is obtained, representing the distance the tooth contact point moves along the theoretical meshing line. This position is removed with respect to the base pitch p. b And superimposed with the initial engagement phase i p This will give you a repeating decimal m between 0 and 1. p It precisely identifies the relative phase of the engagement zone where the current contact point is located. This m p This is a crucial input for subsequent calculations of time-varying meshing stiffness. Meshing stiffness varies with m. p The stiffness varies periodically between the single-tooth meshing region (lower stiffness) and the double-tooth meshing region (higher stiffness). Since the nonlinear meshing stiffness values ​​are discrete data, they are determined based on m... p One-dimensional interpolation is performed on the magnitude of the stiffness to obtain the precise stiffness value at the current meshing position. In the specific control process, the meshing position changes as follows: Figures 8-9 As shown;

[0111] The numerical calculation of discrete nonlinear meshing stiffness includes:

[0112] Based on the meshing point location, the bending stiffness, shear stiffness and axial stiffness of the gear teeth are calculated using the potential energy method, and the tooth stiffness is obtained by connecting them in series.

[0113] Based on the meshing point location, tooth root circle radius, and inner hole radius, the tooth base stiffness is calculated. The gear tooth stiffness and tooth base stiffness are then connected in series to obtain the gear side comprehensive stiffness kt. gear ;

[0114] The rack and pinion tooth stiffness kt is calculated using the potential energy method based on the meshing point location. rack The contact stiffness k of gear and rack is calculated based on Hertzian contact theory. h ;

[0115] via k pair =1 / (1 / k h +1 / kt gear +1 / kt rack Calculate the comprehensive stiffness of a single pair of teeth on the meshing line. Based on the number of moving tooth pairs corresponding to the meshing position, obtain the total nonlinear meshing stiffness through parallel accumulation. In the specific control process, the time-varying meshing stiffness is as follows: Figures 10-11 As shown. The nonlinear meshing force obtained through the nonlinear gear and rack meshing module is as follows: Figure 12 As shown;

[0116] The current of the two motors is collected in real time by current sensors. Combined with the real-time meshing position information of the gears and rack, and based on the electromechanical coupling relationship of nonlinear meshing stiffness, the driving torque of the two motors is dynamically distributed. A current compensation algorithm is used to offset the transmission error caused by meshing backlash, achieving backlash-eliminating control that considers nonlinear meshing stiffness. In this specific control process, the change in backlash between gear 1, gear 2, and the rack is as follows: Figure 13As shown;

[0117] The specific backlash elimination effect of this embodiment on a certain sine command control of the X-axis is as follows: Figure 14 As shown.

[0118] It is understood that the various embodiments mentioned above in this invention can be combined with each other to form combined embodiments without violating the principle and logic. Due to space limitations, this invention will not elaborate further.

[0119] Those skilled in the art will understand that, in the above-described method of the specific implementation, the order in which each step is written does not imply a strict execution order and does not constitute any limitation on the implementation process. The specific execution order of each step should be determined by its function and possible internal logic.

[0120] This invention provides a dual-motor backlash-eliminating control method and system based on nonlinear meshing stiffness. By systematically reusing the reducer transmission ratio coefficient at multiple nodes, including the position loop, current loop, and load feedback end, a bidirectional parameter mapping closed loop between the motor end and the load end is constructed. This overcomes the shortcomings of traditional methods that simplify the reducer to a unidirectional fixed coefficient and have insufficient feedback utilization, achieving precise matching and closed-loop feedback of position and torque signals on the transmission chain. By combining the constructed nonlinear meshing model, time-varying gear and rack meshing stiffness is incorporated into the real-time control model for the first time, abandoning the oversimplification of the transmission pair to a fixed "dead zone." This fundamentally compensates for the dynamic following error caused by periodic fluctuations in meshing stiffness, making the system model closely match the actual physical process.

[0121] The meshing state is dynamically determined based on real-time calculation of relative displacement, and the time-varying meshing stiffness is calculated based on the precise geometric phase in the meshing state. Based on this real-time stiffness and the collected dual motor current, the offset compensation force is dynamically calculated. It can adaptively follow the changes in the stiffness characteristics of the transmission system itself and the load state, improve the control accuracy and stability of the system under variable load and high dynamic conditions, and effectively suppress commutation shock and vibration caused by stiffness fluctuation.

[0122] The various embodiments of the present invention have been described above. These descriptions are exemplary and not exhaustive, nor are they limited to the disclosed embodiments. Many modifications and variations will be apparent to those skilled in the art without departing from the scope and spirit of the described embodiments. The terminology used herein is chosen to best explain the principles, practical application, or technical improvements to the embodiments in the market, or to enable others skilled in the art to understand the embodiments disclosed herein.

Claims

1. A dual-motor backlash elimination control method based on nonlinear meshing stiffness, characterized in that, Includes the following steps: Step S1: Obtain the system parameters of the dual-motor drive system, and establish a three-loop control architecture for the dual-motor drive system based on the system parameters. The three-loop control architecture includes: position loop, speed loop and current loop. Step S2: Based on the reducer transmission ratio coefficient in the system parameters, perform bidirectional parameter value conversion on several signal nodes in the three-loop control architecture to form a bidirectional parameter mapping closed loop between the motor end and the load end. Step S3: Construct a nonlinear meshing model based on the system parameters and the bidirectional mapping closed loop of the parameters. The nonlinear meshing model is used to determine the meshing state based on the relative displacement between the gear and the rack. In the meshing state, the meshing phase is calculated based on the gear geometric parameters, and the time-varying meshing stiffness and nonlinear meshing force are calculated based on the meshing phase. Step S4: Collect the armature current of the dual motors, calculate the offset compensation torque based on the armature current, system parameters and time-varying meshing stiffness, and superimpose the offset compensation torque onto the speed loop to form closed-loop backlash elimination control.

2. The dual-motor backlash elimination control method based on nonlinear meshing stiffness according to claim 1, characterized in that, The system parameters of the dual-motor drive system include: reducer transmission ratio coefficient, tooth backlash, and initial meshing phase.

3. The dual-motor backlash elimination control method based on nonlinear meshing stiffness according to claim 1, characterized in that, The signal nodes in step S2 include: a position loop input port, a current loop output port, and a load feedback port.

4. The dual-motor backlash elimination control method based on nonlinear meshing stiffness according to claim 3, characterized in that, The bidirectional parameter value conversion in step S2 includes: Step S21: Convert the rack displacement and motor rotation angle in the positive direction at the position loop input port, and convert the motor torque and gear torque in the positive direction at the current loop output port; Step S22: At the load end feedback port, the actual position of the rack is reversed with the motor rotation angle feedback, and the torque on the gear end is reversed with the feedback torque at the motor end.

5. The dual-motor backlash elimination control method based on nonlinear meshing stiffness according to claim 4, characterized in that, Step S3, which constructs the nonlinear meshing model, includes: Step S31: Calculate the relative displacement Δx between the gear and rack based on the motor shaft speed at the motor output end; Step S32, by comparing the relative displacement Δx with the tooth flank clearance b l The quantitative relationship determines the contact state between the gear and the rack; If |Δx|≤b l / 2 If the gear rotation does not fill the tooth backlash, the gear and rack are in a non-contact state. (Set contact status indicator c) f =0, engagement position indicator m p =0, no meshing stiffness calculation is performed; If |Δx|>b l / 2 indicates that the gear and rack tooth surfaces are in close contact, and a contact status indicator c is set. f =1, perform meshing stiffness calculation.

6. The dual-motor backlash elimination control method based on nonlinear meshing stiffness according to claim 5, characterized in that, The calculation of meshing phase m p Calculate and normalize using the following formula: m p =(θ g ×r b / p b )+i p Where, where θ g r is the gear rotation angle. b p is the radius of the base circle. b For the base section, i p This is the initial engagement phase.

7. The dual-motor backlash elimination control method based on nonlinear meshing stiffness according to claim 6, characterized in that, The calculation of time-varying meshing stiffness and nonlinear meshing force in step S3 includes: Step S33: The bending stiffness, shear stiffness and axial stiffness of the gear teeth are calculated by the potential energy method, and the bending stiffness, shear stiffness and axial stiffness of the gear teeth are connected in series to obtain the comprehensive stiffness of a single gear tooth. Step S34: Calculate the tooth base stiffness based on the meshing point position, tooth root circle radius, and inner hole radius. Connect the single gear tooth composite stiffness with the tooth base stiffness in series to obtain the gear side composite stiffness kt. gear ; Step S35: Calculate the rack tooth stiffness kt using the potential energy method. rack The contact stiffness k between the gear and rack is calculated based on Hertzian contact theory. h ; Step S36, using the formula: k pair =1 / (1 / k h +1 / kt gear +1 / kt rack Calculate the combined stiffness of a single pair of teeth, based on the meshing phase m. p Determine the number of meshing tooth pairs; When it is determined to be single-tooth meshing, the k pair For time-varying meshing stiffness; When it is determined to be double-tooth meshing, the two sets of k pair The time-varying meshing stiffness is obtained by performing parallel accumulation.

8. A dual-motor backlash elimination control system based on nonlinear meshing stiffness for implementing the dual-motor backlash elimination control method based on nonlinear meshing stiffness as described in any one of claims 1-7, characterized in that, include: The master-slave motor three-loop control module (1), the reducer transmission conversion module (2), and the nonlinear meshing model construction and calculation module (3) are all included. The master-slave motor three-loop control module (1) is used to establish and execute a three-loop control architecture including a position loop, a speed loop and a current loop. The reducer transmission conversion module (2) is connected to the master-slave motor three-loop control module (1) and is used to perform bidirectional parameter value conversion on several signal nodes in the three-loop control architecture based on the reducer transmission ratio coefficient, so as to form a bidirectional parameter mapping closed loop between the motor end and the load end. The nonlinear meshing model construction and calculation module (3) is connected to the reducer transmission conversion module (2) and is used to construct the nonlinear meshing model; The master-slave motor three-loop control module (1) and the nonlinear meshing model construction and calculation module (3) are respectively connected to the dynamic torque compensation module (4). The dynamic torque compensation module (4) is used to calculate the offset compensation torque and superimpose the offset compensation torque onto the speed loop.

9. The dual-motor backlash elimination control system based on nonlinear meshing stiffness according to claim 8, characterized in that, The master-slave motor three-loop control module (1) includes: a position loop control unit (11), a speed loop control unit (12), and a current loop control unit (13). The position loop control unit (11), the speed loop control unit (12), and the current loop control unit (13) are connected in sequence to form the three-loop control architecture.

10. The dual-motor backlash elimination control system based on nonlinear meshing stiffness according to claim 9, characterized in that, The reducer transmission conversion module (2) includes: a forward conversion unit (21) and a reverse conversion and feedback unit (22); The forward conversion unit (21) is used to perform a forward conversion of rack displacement into motor rotation angle at the position loop input port and a forward conversion of motor torque into gear torque at the current loop output port; The reverse conversion and feedback unit (22) is used to perform reverse conversion at the load end feedback port to convert the actual position of the rack into the motor rotation angle feedback, and to convert the torque on the gear end into the feedback torque at the motor end.

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