Backlash Error Research Articles

A feedforward kinematic error controller with an angular positioning deviations model for backlash compensation of industrial robots

The accuracy of industrial robots, typically on the order of several millimeters, has inhibited their adoption in advanced aerospace manufacturing applications, such as robotic machining. For this reason, extensive investigations have been conducted to develop solutions to improve their accuracy. These solutions can be categorized into offline and online compensation strategies, both of which have advantages and limitations. Offline compensation has been shown to improve the accuracy of industrial robots by two to three orders of magnitude; however, the sensitivity of these solutions to environmental changes and external disturbances can degrade their performance. In contrast, online compensation, which utilizes real-time measurement and compensation, is robust to these changes; however, the performance of these solutions is limited by the causality of time, preventing them from compensating fast changing errors such as backlash. In this work, a novel kinematic modeling strategy, which models the robot’s angular positioning deviations to predict when backlash will occur, is integrated into a novel online kinematic error compensation framework to leverage the advantages of both solutions. By integrating the proposed kinematic model into the online compensation framework, backlash errors can be predicted and preemptively compensated to improve performance. The performance of the combined system was evaluated using ball bar measurements, where it was shown to improve the circularity of the ball bar motion by 25 %.

Physics-informed and data-driven hybrid method for transmission accuracy design optimization of planetary roller screw mechanism

The planetary roller screw mechanism (PRSM) faces an ever-increasing precision transmission demand in current advanced equipment. The relationship between machining errors and transmission accuracy remains elusive due to the over-simplified physical models and small-sample experimental datasets. This work proposes a physics-informed and data-driven hybrid strategy for PRSM transmission accuracy evaluation and tolerance optimization. In the physical model, a PRSM transmission accuracy model is developed to calculate transmission error that considers 16 machining errors in eccentric, nominal diameter, pitch, flank angle, and roller consistency. In the dataset establishment, thread profile measurements and dynamic leadscrew inspections are conducted for the machining error and transmission accuracy data acquisition. A data augmentation approach combining the physical model with the generative adversarial network is utilized to predict travel deviation, variations, and axial backlash and estimate machining error contribution with the small-sample experimental dataset. It is firstly found that the roller consistency of nominal diameter significantly affects PRSM travel variation V2π with a 17.3 % importance value. With the developed framework, the key tolerances for screw, roller, nut, and roller consistency are optimized toward a typical precision transmission requirement using the non-dominated sorting genetic algorithm. It also provides a tolerance grade recommendation table with PRSM transmission accuracy level in engineering practice.

Dynamic Characteristics Analysis of the DI-SO Cylindrical Spur Gear System Based on Meshing Conditions

The dual-input single-output (DI-SO) cylindrical spur gear system possesses advantages such as high load-carrying capacity, precise transmission, and low energy loss. It is increasingly becoming a core component of power transmission systems in maritime vessels, aerospace, marine engineering, and construction machinery. In practical operation, the stability of the DI-SO cylindrical spur gear system is influenced by complex excitations. These excitations lead to nonlinear vibration, meshing instability, and noise, which affect the performance and reliability of the entire equipment. Hence, the dynamic performance of the DI-SO cylindrical spur gear system is thoroughly investigated in this research. The impact of excitations and nonlinear factors on the dynamic characteristics was investigated comprehensively. A comparative analysis of the gear system was conducted by establishing a bending–torsional coupling vibration analysis model under synchronous and asynchronous meshing conditions. Nonlinear factors such as periodic time-varying meshing stiffness, meshing damping, friction coefficient, friction arms, load sharing ratio, comprehensive transmission error, and backlash were considered in the proposed model. Then, the effect laws of excitations and nonlinear factors such as meshing frequency, driving load fluctuation, backlash, and comprehensive transmission error were analyzed. The results indicate that the dynamic characteristics exhibited staged stable and unstable states under different meshing frequencies and meshing conditions. At the medium-frequency meshing stage (0.96 × 104~1.78 × 104 Hz), alternating phenomena of multi-periodic, quasi-periodic, and chaotic motion states were observed. Moreover, the root mean square value (RMS) of the dynamic transmission error (DTE) in the asynchronized gear system was generally higher than that in the synchronized gear system. It was found that selecting the appropriate meshing condition could effectively reduce the amplitude of the DTE. Additionally, the dynamic performance could be significantly improved by adjusting control parameters such as driving load fluctuation (0~179 N), backlash (0.8 × 10−4~0.9 × 10−4 m), and comprehensive transmission error (7.9 × 10−4~9.4 × 10−4 m). The research results provide a theoretical guidance for the design and optimization of the DI-SO cylindrical spur gear system.

Nonlinear dynamic characteristics analysis method of planetary gear train torsional vibration considering meshing oil film force

Planetary gear train is an important part of automatic transmission. The oil film between teeth is one of the key factors affecting the torsional vibration of planetary gear train. Selecting the appropriate oil film stiffness is of great significance for analyzing the nonlinear dynamic characteristics of planetary gear train. A method for analyzing the nonlinear dynamic characteristics of planetary gear system torsional vibration considering the oil film force between teeth is proposed in this paper. A 3-DOF torsional vibration model of planetary gear train considering oil film is established. In this model, the oil film between teeth is equivalent to a time-varying nonlinear spring-damper element, and nonlinear factors such as backlash and meshing error are also considered. The effects of meshing oil film thickness on oil film stiffness and damping are analyzed, and the torsional vibration characteristics of planetary gear train under different meshing stiffness, meshing damping ratio, and rotational speed are analyzed based on bifurcation diagrams. The results show that in one meshing cycle, the meshing oil film thickness first becomes larger and then becomes smaller. When the meshing oil film thickness increases, the meshing oil film stiffness and the equivalent meshing oil film damping become smaller. The torsional vibration of planetary gear train can be effectively reduced by increasing meshing stiffness, damping ratio, rotational speed within a certain range. This method provides technical support for reducing torsional vibration of planetary gear train and realizing stable transmission of planetary gear train.

A prediction method for the backlash error of robot precision reducers based on optimal assembly

Abstract The kinematic accuracy and service life of robot precision reducers are directly affected by their assembly accuracy, and the backlash error is one of the most important performance indicators for evaluating the assembly accuracy. A prediction method for the backlash error of robot precision reducers is proposed, which can quickly and accurately calculate the backlash error of the optimal assembly reducers. Based on the optimal assembly process, the sensitive relationship between the errors of the crucial components and the assembly accuracy of the reducer is analysed, and the crucial errors affecting the backlash error are identified. The cumulative backlash of the crucial error along the dimensional chain is clarified, and the corresponding relationship between the backlash and the backlash error is determined. On this basis, backlash prediction models are established for the involute planetary gear and cycloidal-pin gear transmission parts, respectively. The mapping relationship between dimensional errors and backlash is also derived. Furthermore, the backlash error of the reducer is obtained by calculating the backlash error caused by each error term of the high-speed stage and low-speed stage transmission parts. Finally, the effectiveness and correctness of the prediction method are verified by the optimal assembly of RV reducers and the measurement of the backlash error. The theory and method proposed in this paper can quickly and accurately predict the backlash error of the reducer for robots, effectively predict the assembly accuracy of the selective reducers, significantly improve the assembly efficiency of the reducers, and then provide theoretical guidance and technical support for enhancing the assembly quality and kinematic accuracy of robot reducers.

Engineering design and testing of rotary joints’ driving systems for the CFETR multi-purpose overload robot

This study focuses on the engineering design and testing of the rotary joints' driving systems for the China Fusion Engineering Test Reactor (CFETR) Multi-Purpose Overload Robot (CMOR). CMOR is a critical component in the CFETR. The CFETR tokamak serves as an engineering test reactor in China for magnet confinement fusion research. CMOR, a 7-DOF manipulator, is specifically designed for internal maintenance within the CFETR. This poses significant challenges in the design of the joint driving systems. The joint types of CMOR are categorized into three, comprising one translation joint, two swing joints, and four rotary joints. Using rotary joint J6 of CMOR as an example, this paper provides a detailed exploration of the engineering design and testing of the rotary joints' driving systems, offering a comprehensive explanation of their design specifications and principles. Specification and strength assessments are conducted on the engineering design results, meeting all requirements. Furthermore, the paper delves into the testing methods of the driving systems, including the assessment of transmission error and backlash error, two crucial indicators for the driving system. This research contributes valuable insights for future joint designs and testing of the CMOR heavy-load manipulator.

Multi-Objective Optimization Design of Cycloid-Pin Gears Based on RV Reducer Precision Transmission Performance

This paper aims to realize multi-objective optimization of cycloid-pin gears to improve the positioning accuracy and load-carrying capacity of the rotary vector (RV) reducer, via the consideration of backlash, transmission error, and torsional stiffness. Initially, the analytical models of the RV transmission backlash and transmission error are developed by using both purely geometrical and equivalent model methods individually. Based on the generalized Hooke’s law, a torsion angle model is established to characterize the torsional stiffness of the system, utilizing methods such as Hertzian contact theory and bearing stiffness models. Subsequently, employing the Monte Carlo method, extremum method, and quality loss function, mapping objective functions for dimensional accuracy (tolerance) and transmission performance (backlash, transmission error, and torsional stiffness) are constructed. The geometry dimensions, dimensional accuracy, and modification of the cycloid-pin gear are considered as design variables to create a multi-objective optimization model. The improved Parallel Adaptive Genetic Algorithm using Deferential Evolution (PAGA-DE) is used for multi-objective solutions. Through example calculations, the impact of cycloid-pin gear parameters on transmission performance before and after optimization is determined. The reliability of backlash after optimization within 1.5′ reaches 99.99%, showing an increase of 8.24%. The reliability of transmission error within 1′ reaches 98.52%, demonstrating an increase of 1.35%. The torsional angle is reduced by 8.9% before optimization. The results indicate that the proposed multi-objective optimization design method for cycloid-pin gears can achieve the goal of improving the transmission performance of the RV reducer.

Modelling and dynamic behaviours of a high-contact-ratio spur-gear system considering rough surface

The dynamic characteristics of a high-contact-ratio (HCR) spur-gear system having rough surfaces generated by shot peening (SP) were studied, with specific emphasis on characterisation of the gear-surface topography as well as modelling of the gear backlash and static transmission error. Accordingly, a four-degree-of-freedom dynamic model was established. Simulation experiments were then conducted using surface roughness, rotational velocity, input torque, and shaft-bearing stiffness as the variables. The results show that the dynamic characteristics of the gear system tend toward instability with increasing surface roughness. The models developed in this study outline a method for building indirect relationships between the vibration, dynamics, and tooth-surface microscopic features. This research thus provides a theoretical basis for designing the tooth-surface topography of HCR gears in the future.

Ball Screw Health Monitoring With Inertial Sensors

In industrial applications, the mechanical wear on ball screw components can lead to a loss of positioning accuracy that reduces the operational reliability and reproducibility of production systems. Existing monitoring solutions are impractical for real industrial settings or are unable to provide quantifiable estimates of the magnitude of degradation. To address this, the proposed method strategically applies a two-phase data collection with inertial sensors to perform both health monitoring and fault magnitude estimation. The first, online phase offers a practical, non-intrusive means of monitoring the ball screw degradation during normal production operations. As deemed necessary by the first phase, the second, offline phase is implemented outside the production routine to physically quantify the detected fault. The combined methods offer a balanced approach that provides detailed information while still considering the requirements of a production environment. To validate the performance of this proposed strategy, a run-to-failure experiment was performed on a linear axis testbed. Validation results indicate that the method is a pragmatic and promising approach for incipient fault detection and absolute backlash error measurement in a linear axis.

Research on Acceleration Segmented Compensation Strategy for Backlash of CNC Machine Tools

For the problem of backlash in the semi-closed-loop linear feed servo system of CNC machine tools, which seriously affects the accuracy of machine tools, an acceleration segmentation backlash compensation strategy is proposed. In the reverse motion of the servo motor, the servo motor is controlled to compensate for the backlash error during a period of accelerated motion and a period of decelerated motion. Based on the established backlash transmission model, the parameters of the compensated motion process are calculated. In order to ensure accurate and quick compensation of the gap compensation value for the transmission gap, the backpropagation method is used to backpropagate the acceleration calculation based on whether the acceleration process time is an integer multiple of the servo interpolation period. Finally, the feasibility of the method is verified through experiments, and the results show that the method improves the positioning accuracy of machine tools.

High-Precision Tribometer for Studies of Adhesive Contacts

Herein, we describe the design of a laboratory setup operating as a high-precision tribometer. The whole design procedure is presented, starting with a concept, followed by the creation of an exact 3D model and final assembly of all functional parts. The functional idea of the setup is based on a previously designed device that was used to perform more simple tasks. A series of experiments revealed certain disadvantages of the initial setup, for which pertinent solutions were found and implemented. Processing and correction of the data obtained from the device are demonstrated with an example involving backlash and signal drift errors. Correction of both linear and non-linear signal drift errors is considered. We also show that, depending on the research interests, the developed equipment can be further modified by alternating its peripheral parts without changing the main frame of the device.

Study on multi-clearance nonlinear dynamic characteristics of herringbone gear transmission system under optimal 3d modification

The tooth surface 3d modification technology is the most effective method to realize the reduction of vibration and noise of gear system (GS) by comprehensively considering tooth profile modification and axial modification. Moreover, the system nonlinear factors such as backlash and bearing clearance will make the motion of GS have complex variability. Therefore, we will combine 3d modification technology with contact performance and dynamic characteristics to optimize the meshing characteristics of herringbone gear pair through tooth contact analysis technology, loaded tooth contact analysis technology and antlion optimizer with error minimum amplitude as optimization objective, determine three nonlinear dynamic model of herringbone gear for numerical solution. Finally, this paper studies the influence of different system parameters on the system nonlinear dynamic characteristics under 3d modification and non-modification from both local vibration characteristics on the diagrams of time history, phase, spectrum and Poincare map and global vibration characteristics on the diagrams of system bifurcation and maximum Lyapunov exponent. The results show: After optimizing modification, the system vibration is obviously reduced. With the increase of input power, input speed, backlash and static transmission error (STE), the system has jump, while there is no jump with the change of bearing clearance and damping ratio. Compared with other parameters, the changes of input speed and STE make system have complex bifurcation characteristics. The 3d modification can eliminate the jump and make system motion more regular.

Analytical Investigation on Load Sharing Performance of Planetary Gear Transmission under Loop Maneuver

In order to explore the influence of airframe space motion on the load sharing performance (LSP) of planetary gear transmission (PGT) inside an aircraft, the combined influence of the rotation of the carrier (internal non-inertial system, INIS) and space motion of the fuselage (external non-inertial system, ENIS) is considered. Firstly, the motion equations of PGT members under the airframe loop maneuver are derived, and then the time-varying meshing stiffness, backlash, and tooth profile error are considered; a system-level dynamics model of PGT with casing is established and solved by numerical integration. The results show that the loop maneuver intensifies the fluctuation of the dynamic meshing force in the time domain and does not change its spectral distribution, but it will affect the peak value of the low frequency part. After considering the loop maneuver, there are differences in the load sharing coefficient (LSC) of each branch, and the fluctuation range of LSC increases. The interactive influence of working conditions, bearing stiffness, manufacturing eccentricity errors and loop motion parameters on the LSP is investigated and compared in depth. This research can be utilized to guide the design of aircraft’s drivetrain.

Vibration signal modeling of planetary gearbox based on dynamics and finite element method for tooth crack diagnosis

Planetary gear set contains many kinds of nonlinear factors, such as time-varying meshing stiffness, bearing support, backlash, and comprehensive transmission error, which will deeply affect the gearbox response behaviors and vibration characteristics. During the operation of planetary gear set, there are several gear pairs meshing simultaneously, which will lead to multiple vibration sources and complicate vibration transmission. The revolution of the planet gears makes the meshing force of the gear pairs vary periodically, and the continuous motion of the meshing point also changes the length of vibration transmission path. This study aims to establish a hybrid model that can simulate the vibration signals of gearbox measuring points through fusing the dynamic model of planetary gear set and the transmission path model. Through the simulation analysis, the vibration characteristics of the measuring point signal of the planetary gearbox are revealed, and the crack fault of the planet gear tooth is effectively isolated. Finally, the availability and validity of the presented model are experimentally verified, and the magnitude match is up to 78%. The model can not only provide a theoretical basis for data-driven fault diagnosis methods, but also solve the pain point of diagnostic samples scale and balance by simulation means.

The global behavior evolution of non-orthogonal face gear-bearing transmission system

The nonlinear global behavior evolution process of the non-orthogonal face gear-bearing system was studied in this paper. Firstly, a multi-degree-of-freedom coupled vibration model of the non-orthogonal face gear-bearing system was established, which took into account factors such as time-varying meshing stiffness, tooth backlash, bearing clearance, and transmission error. Then the cell mapping method was used to calculate the phase trajectory of each cell on the Poincaré section to 1000 steps, and observed the influence of the initial state of the system on the dynamic behavior of the system after a long time history. This paper used the global bifurcation diagram, the global behavior diagram obtained by the cell mapping method, the multi-initial value phase diagram and the Poincaré section to illustrate the evolution process of the global behavior of the system with the excitation frequency, meshing damping and load fluctuation. The research results show that with the change of control parameters, the system gradually changed from periodic response to chaos after a long time history, and presented complex phenomena such as the coexistence of multiple periodic responses and the coexistence of periodic responses and chaotic responses in the evolution process.

Research on nonlinear dynamic performance of the central bevel gear transmission system in aero-engine with complex excitation

For the requirement of the vibration control and fault diagnosis of the central bevel gear transmission system in an aero-engine, this paper proposes a 12-degree-of-freedom dynamic model for the first time in order to investigate nonlinear dynamic behavior of the central bevel gear transmission system considering the internal and external excitations. The dynamic model is developed by the use of lumped parameter modeling. Time-varying meshing stiffness, gear backlash and gear transmission error are included in the internal excitations, the input power of the central bevel gear transmission system, the speed fluctuation of the driven shaft and the high-pressure rotor unbalance excitation are included in the complex external excitations. Using the bifurcation diagram, the largest Lyapunov exponent, time domain diagram, frequency domain diagram, phase diagram and Poincaré map, the effects of input power change, driven shaft speed fluctuation excitation and high-pressure rotor unbalance excitation on the complex nonlinear dynamic behavior of the central bevel gear transmission system are analyzed. The increase of input power, reduction of speed fluctuation and control of high-pressure rotor unbalance are beneficial to expand the stable area of the system.

Nonlinear dynamic analysis of the central bevel gear transmission system in aero engine subjected to internal and external excitation

The research on the nonlinear dynamic characteristics of the central bevel gear transmission system was carried out for the requirement of the vibration control and fault diagnosis of the central bevel gear transmission system in an aero engine. This paper proposes the dynamic model for the first time in order to investigate nonlinear dynamic behavior of the central bevel gear transmission system, and the internal and external excitations are taken into account by using lumped parameter modeling. Time-varying meshing stiffness, gear backlash, and gear transmission error is included in the internal excitations, and the input power, the speed fluctuation of the driven shaft and the high-pressure rotor unbalance excitation are included in the external excitations. The effects of the external excitations on the complex nonlinear dynamic behavior of the system are studied. The results show that reasonable control of input power, speed fluctuations, and high-pressure rotor mass imbalance can improve engine vibration.

Dynamic Modeling and Analysis of Nonlinear Compound Planetary System

In the vehicle composite planetary gear transmission system, nonlinear excitations such as time-varying meshing stiffness, backlash and comprehensive error would lead to large vibration and noise, uneven load distribution, unstable operation and other problems. To address these issues, this work focuses on compound planetary gears and develops the bending-torsion coupling nonlinear dynamic model of the system based on the Lagrange equation. There are internal and external multi-source excitations applied to the system. This model is used to study the bending-torsion coupling meshing deformation relationship of each meshing pair along with the translational and torsional directions. The natural frequencies and vibration modal characteristics of the system are extracted from the model, and the influence of rotational inertia and meshing stiffness on the inherent characteristics of the system are studied. The coupling vibration characteristics of the system under operating condition are analyzed in terms of the inherent characteristics and time–frequency characteristics of the system. The simulation results exhibit that the planetary gear system has three modes. The change in natural frequency trajectory has two phenomena: modal transition and trajectory intersection. The main frequencies include engine rotating frequency, meshing frequency and its double frequency, and the rotation frequency and harmonic frequency of the engine have a great influence on the vibration response of the system. Finally, the virtual prototype of the composite planetary system is used to verify the accuracy of the established model from speed, inherent characteristics, meshing force and frequency composition.

Adaptive Neural Network Control of an Uncertain Nuclear Refueling Machine With Input Backlash and Asymmetric Output Constraint

This paper studies the control problem of an uncertain nuclear refueling machine (RM) system in the presence of uncertainty, external disturbance, input backlash and asymmetric output constraint. Taking into account the effects of external disturbance and input backlash, the RM system with fuel rod is modeled as a copling partial differential equation-ordinary differential equation (PDE-ODE). Using the backstepping method, an adaptive neural network control scheme is designed to drive the RM and bridge to the desired positions and simultaneously reduce the vibration of fuel rod. A novel asymmetric tangent-type barrier Lyapunov function (Tan-BLF) is constructed to restrict the position tracking error into the given range. The formulation of backlash nonlinearity is transformed into the expected input and nonlinear error. Then the combination of input backlash error and boundary disturbance is defined as a disturbance-like item. Applying the robust control strategy and adaptive technique, two auxiliary input signals are proposed to offset the impact of the disturbance-like item. The adaptive neural network (NN) is employed to compensate for the system uncertainty. The practical stability of the RM system with the proposed control is demonstrated via the theoretical Lyapunov analysis. Simulation verifies the performance of the designed control scheme.

A New Control Method for Backlash Error Elimination of Pneumatic Control Valve

Backlash is a commonly non-linear phenomenon, which can directly degrade the control accuracy of a pneumatic control valve. To explain the cause and law of backlash error, and to propose an effective method, many research works on the modeling of a pneumatic control valve system have been carried out. The currently model of a control valve system can be classified as a physical model, data-driven model, and semi-physical model. However, most models only consider the force-displacement conversion process of a pneumatic diagram actuator in a pneumatic control valve system. A physical model based on the whole workflow of the pneumatic control valve system is established and a control method to eliminate the backlash error is proposed in this paper. Firstly, the physical model of the pneumatic control valve system is established, which is composed of three parts: pneumatic diaphragm actuator model, nozzle-flapper structure model and electromagnetic model. After that, the input–output relationship of the pneumatic control valve system can be calculated according to the established physical model, and the calculation results are consistent with the experimental result. Lastly, a self-calibration PID (SC-PID) control method is proposed for backlash error elimination. The proposed method can solve valve stem oscillation caused by backlash during valve control.