Error Mesh Research Articles

The Precision Improvement of Robot Integrated Joint Module Based on a New ADRC Algorithm

This article analyzes the factors causing the precision error of the robot joint module, such as gear meshing disturbance, output elastic deformation, and load mutation. An improved active disturbance rejection control (ADRC) algorithm is proposed to overcome the uncertainty of nonlinear factors and variables of this research topic. The output precision loss of the joint module is introduced as a new input variable of ADRC, combined with the input variable of torque current of the joint module. The extended state observer is redesigned, and the online estimation of disturbance is realized. According to the disturbance estimation results, the current loop algorithm of permanent magnet synchronous motors is improved to compensate the torque disturbance of the robot joint module. The experimental results show that the improved ADRC algorithm can obviously suppress the disturbance of the joint module, weaken the meshing error and torque output deformation of the harmonic reducer gear, and improve the control accuracy of the joint module.

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.

Study on the effect of bearing position and stiffness on the dynamic behavior of output stage of CHT system based on the cylindrical gear meshing

The internal and external rotor shafts are important components to transfer power in coaxial helicopters, and bearing supports could affect the dynamic behavior of the transmission system. In order to explore the influence of bearing support structure, bearing position and support stiffness on the dynamic behavior of the output stage of coaxial helicopter transmission (CHT) system based on the cylindrical gear meshing, a rigid-flexible coupled dynamic model is established under cantilever-cantilever support structure and cantilever-simple support structure considering the flexibility of rotor shaft based on Timoshenko beam theory, and time-varying mesh stiffness (TVMS), comprehensive meshing error are also considered. Newmark-beta numerical method was applied to calculate the dynamic response. The result indicates that the load sharing performance of gear pair using cantilever-simple support structure is better than that of cantilever-cantilever structure, but the maximum vibration displacement of bull gears is reduced apparently. Simultaneously, the bearing positions and stiffness can be adjusted to achieve better performance in load distribution and maximum vibration displacement of bull gears.

Accuracy Analysis of Complex Transmission System with Distributed Tooth Profile Errors

Tooth profile errors are the internal excitations that cause gear meshing errors, which are critical error factors affecting gear transmission accuracy. In existing studies, it is usually regarded as a constant or random distribution function. However, the actual machined tooth profile error is not a constant, so this estimation is inconsistent with the actual situation, resulting in an inaccurate evaluation of transmission accuracy. This paper proposes a method for representing tooth profile errors using distribution errors (including systematic and random errors), and a mathematical model of distributed tooth profile errors is presented. The contact stresses of the complex transmission system were compared with those obtained by formulas, proving that tooth profile errors increase contact stress. A method for calculating gear meshing error is proposed to evaluate the actual output accuracy of the complex transmission system. Compared with the test, the output accuracy is reduced by 13.8% under the temperature environment and distributed tooth profile errors. The proposed methods can accurately predict the transmission accuracy of precision transmission systems at the design stage and provide theoretical support for reducing systematic and random errors at the gear machining stage.

Dynamic Effect Analysis of Cryogenic Solid-Lubricated Ball Bearings with Geometrical-Frictional Defects

The traction behavior in cryogenic solid-lubricated ball bearings (CSLBBs) of liquid rocket engines (LREs) has a significant effect on the dynamic response of the bearing–rotor system. To reveal the fault mechanism of CSLBBs, a tribo-dynamic model is proposed in this paper that considers the solid-lubricated traction, six-DOF motion of the ball and contact collisions between the ball and the cage. The modified traction model uses fan-shaped and arched sections to discretize the contact area to eliminate the meshing error. The newly developed fault model, called ‘geometrical-frictional defects’, can more realistically represent solid-lubrication coating defects. The results show that the frictional excitation can significantly increase bearing vibration by increasing the traction force on the raceway. The change in the amplitude of the bearing vibration and its derivative can be used as a reference to determine the depth of defects. The width of the defect can be diagnosed by monitoring the double-pulse time interval and spectrum of the bearing vibration signal. This research may provide some theoretical guidance for the design and condition monitoring of CSLBBs.

Study on Nonlinear Dynamic Characteristics of RV Reducer Transmission System

Rotate vector (RV) reducers have widely been used in high-performance precision drives for industrial robots. However, the current nonlinear dynamic studies on RV reducers are not extensive and require a deeper focus. To bridge this gap, a translational–torsional nonlinear dynamic model for an RV reducer transmission system is proposed. The gear backlash, time-varying mesh stiffness, and comprehensive meshing errors are taken into account in the model. The dimensionless vibration differential equations of the system were derived and solved numerically. By means of bifurcation diagrams, phase trajectories, Poincaré sections, and the power spectrum, the motion state of the system was studied with the bifurcation parameters’ variation, including excitation frequency and meshing damping. The results demonstrate that this system presents enriched nonlinear dynamic characteristics under different parameter combinations. The motion state of the system is more susceptible to change at lower frequencies. Increasing the meshing damping coefficient proves effective in suppressing the occurrence of chaos and reducing vibration amplitudes, significantly enhancing the stability of the transmission system.

Deep Spectral Meshes: Multi-Frequency Facial Mesh Processing with Graph Neural Networks

With the rising popularity of virtual worlds, the importance of data-driven parametric models of 3D meshes has grown rapidly. Numerous applications, such as computer vision, procedural generation, and mesh editing, vastly rely on these models. However, current approaches do not allow for independent editing of deformations at different frequency levels. They also do not benefit from representing deformations at different frequencies with dedicated representations, which would better expose their properties and improve the generated meshes’ geometric and perceptual quality. In this work, spectral meshes are introduced as a method to decompose mesh deformations into low-frequency and high-frequency deformations. These features of low- and high-frequency deformations are used for representation learning with graph convolutional networks. A parametric model for 3D facial mesh synthesis is built upon the proposed framework, exposing user parameters that control disentangled high- and low-frequency deformations. Independent control of deformations at different frequencies and generation of plausible synthetic examples are mutually exclusive objectives. A Conditioning Factor is introduced to leverage these objectives. Our model takes further advantage of spectral partitioning by representing different frequency levels with disparate, more suitable representations. Low frequencies are represented with standardised Euclidean coordinates, and high frequencies with a normalised deformation representation (DR). This paper investigates applications of our proposed approach in mesh reconstruction, mesh interpolation, and multi-frequency editing. It is demonstrated that our method improves the overall quality of generated meshes on most datasets when considering both the L1 norm and perceptual Dihedral Angle Mesh Error (DAME) metrics.

Study on the vibration characteristics of worm helical gear drive

The application of worm helical gear in smart car, smart home and other fields can significantly reduce the weight of products. Accordingly, the requirements for vibration and noise are also increased. In this paper, the lumped mass method is used to establish the dynamic model of point contact bending-twisting shaft meshing coupling worm helical gear drive. In this model, the contact ellipse is transformed into an equivalent rectangle, and the nonlinear factors such as time-varying meshing stiffness, tooth meshing error and meshing damping are considered. The vibration characteristics of worm helical gear drive in three directions and at meshing point are obtained for the first time. Machining accuracy, tooth surface modification and assembly errors are transformed into the error in the dynamic model respectively, and their effects on the vibration characteristics are analyzed. The closed vibration and noise performance test bench of worm helical gear drive is built, and the influence of three kind of errors on the vibration characteristics of worm helical gear drive are tested to verify the correctness of the dynamic model and its numerical analysis results. Both the theoretical analysis and the experimental results show that machining accuracy, tooth surface modification and the assembly error have a great influence on the vibration characteristics.

The development of a modular design workflow for 3D printable bioresorbable patient-specific bone scaffolds to facilitate clinical translation

ABSTRACT A streamlined design workflow that facilitates the efficient design and manufacture of patient-specific scaffolds independently applied by the surgical team has been recognised as a key step in a holistic approach towards the envisioned routine clinical translation of scaffold-guided bone regeneration (SGBR). A modular design workflow was developed to semi-automatically fill defect cavities, ensure patient specificity and ideal surgical scaffold insertion for a given surgical approach, add fixation points to secure the scaffolds to the host bone and generate scaffold based on Voronoi, periodic lattice and triply periodic minimal surface pore architectures. The adopted functional representation modelling technique produces models free from 3D printing mesh errors. It was applied to a clinical case of a complicated femoral bone defect. All models were free from mesh errors and the patient-specific fit and unobstructive insertion were validated via digital inspection and physical investigation by way of 3D printed prototypes. The real-time responsiveness of the workflow to user input allows the designer to receive real-time feedback from the surgeon, which is associated with reducing the time to finalise a patient-specific scaffold design. In summary, an efficient workflow was developed that substantially facilitates routine clinical implementation of SGBR through its ability to streamline the design of 3D printed scaffolds.

Variable stiffness-based vibration prediction for full coupling model of gearbox

Vibration is a problem worthy of attention in gearbox design. In the case of high speed and heavy load, vibration may be more significant, so some methods are needed to predict the vibration of the gearbox. At present, most vibration prediction methods have the problems of few research parameters, low fidelity and a large amount of calculation. In this paper, a fully coupled finite method model of variable stiffness gearbox based on lumped parameter method (LPM) is proposed, and the vibration prediction of gearbox housing is carried out considering time-varying meshing stiffness (TVMS), transmission error and other factors. Firstly, a new stiffness calculation method was proposed based on finite element theory and potential energy method, which can accurately solve the TVMS of fault gear. At the same time, the comprehensive meshing error of gear was solved. At then, the TVMS and comprehensive meshing error of the healthy gear and fault gear were brought into the dynamic equation of two-stage spur gear to obtain meshing force. After that, the meshing force was used as an excitation to solve the vibration of the gearbox housing. Finally, the vibration regularity of the health gearbox and fault gearbox was compared. The sensitivity of each gear shaft to the vibration caused by fault and the vibration regularity of different bearing seats of the same gear shaft was explored. The effectiveness of the simulation results was verified by experiments.

Dynamic characteristics of a spur gear pair under the coupled effects of angular misalignment fault and tooth modification

Angular misalignment is a common fault in gearbox manufacturing and installation, which directly affects the meshing characteristics of the gear pair. Tooth axial modification is considered to be a useful way to suppress angular misalignment. However, accurate determination of contact characteristics, e.g., contact stiffness and friction, caused by the coupled effects of angular misalignment and tooth modification is difficult. To settle this problem, this article put forward a method on the strength of the slice coupling and nonlinear Hertzian contact calculation. With the proposed model, the meshing errors caused by angular misalignment and tooth axial modification are derived. Then the influence of nonlinear Hertzian contact and friction on time-varying mesh stiffness (TVMS) is considered in each sliced tooth. In addition, an iterative computation method is proposed to calculate the proposed analytical model. Further, a dynamic model is developed to study the influences of angular misalignment and tooth axial modification on gear dynamic characteristics. Finally, the analytic model is validated by an experimental setup for a spur gear pair with ideal installation, misalignment and tooth axial modification. Results show that the proposed model is effective and efficient for predicting the dynamic response of the spur gear pair under the coupled effects of angular misalignment and tooth modification.

Monitoring gear wear with transmission error

The use of transmission error (TE) in gear diagnostics has recently become more feasible. TE is a parameter that describes the meshing error between two gears, i.e., the deviation in angular position from the theoretically perfect, rigid involute case, and can be measured very accurately using shaft encoders installed on the unloaded part of the input and output shafts. It is hence one of the measurements closest to the source – the internal excitation from the gearmesh. Wear induces geometric deviations on gear tooth profiles, which will manifest as a geometric TE (GTE). To perform effective gear wear monitoring, one requires reliable sensors or measurements that are sensitive to anomalies due to wear, especially when wear is at an early stage and hard to detect. Vibration, which is usually measured on the gearbox casing, tends to be affected by the complex transfer path from the source to the measurement point and thus poses challenges in monitoring wear. Conventional wear analysis techniques, including image acquisition and characterisation of worn gear surfaces, often involve disruption of the operation and offline analysis, causing some delay. TE, as a measurement much closer to the source, has considerable benefits compared to vibration as well as traditional wear analysis.This paper demonstrates a comparative study on TE measured from dry and lubricated wear experiments, offering new insights on the effect of different wear mechanisms on TE signals. The results show that TE is sensitive to the evolution of gear wear and could be used to perform trending effectively. Such a powerful measurement with good trending ability could revolutionise gear prognostics. With the embedded sensor trend associated with Industry 4.0 and Internet of Things, the use of inbuilt encoders will likely become more prevalent in industry, allowing the use of TE measurements in practical gear monitoring.

Dynamic Analysis of a Combined Spiral Bevel Gear and Planetary Gear Set in a Bucket Elevator with High Power Density

A combined spiral bevel gear and planetary gear set was designed for bucket elevators to reduce the system’s complexity and improve the system’s efficiency. The dynamic model of a combined spiral bevel gear and a 2K-H planetary gear train was developed by using the lumped mass method, where the time-varying mesh stiffness and comprehensive mesh error were introduced. Then, the equations of motion of the system were solved with the Newmark numerical integration method, and the dynamic transmission error and mesh force of the gear pairs were obtained. The influences of different input rotational speeds and power on the dynamic response of the system were analyzed. The dynamic responses of the bearings between the bevel gears, planet carrier, and box were calculated. It was found that the dynamic mesh force gradually decreased with an increase in speed, and it increased with an increase in power. For low-speed and heavy-load transmission systems, the influence of power on the mesh force was more significant. It could also be found that the efficiency of the transmission system composed of a spiral bevel gear and a planetary gear was improved compared with that of the traditional system. Finally, the effectiveness of the dynamic model was validated through a comparison of the test signals. The results of the analysis in this study can be used to guide the design of vibration and noise reduction.

Vibration Performance of Traction Gearbox of a High-Speed Train: Theoretical Analysis and Experiments

The gearbox is the key component of the traction drive system of a high-speed train. At the same time, the traction gearbox can easily experience a box housing failure due to bearing internal excitation from gear meshing and external excitation from motor torque fluctuation, the wheel polygon, and so on. In order to analyze the vibration and noise of the gearbox, a dynamic model of a high-speed train gear transmission system was established under the conditions of time-varying meshing stiffness and time-varying meshing error. A frequency spectrum analysis of the vibration at the key nodes of the model that changed with the speed was carried out. A test rig for a traction gearbox of a high-speed train was built, and a testing method for the vibration and noise of a high-speed train traction gearbox was put forward. The testing of and research on the traction gearbox under various working conditions were carried out, and the dynamic evaluation indexes of acceleration, vibration intensity, and air noise at different measuring points of the high-speed train traction gearbox were obtained. The study provided a test reference and a basis for the dynamic performance optimization design and fault diagnosis of a high-speed railway traction gearbox system.

Isogeometric boundary element method for isotropic damage elastic mechanical problems

In this work, a complex isotropic damage mechanics structural model is developed using the isogeometric method to study the strain displacement and influence factors in isotropically damaged elastics. The proposed modeling method can be constructed dynamically by introducing control points and weight coefficients, which improves the accuracy and eliminates mesh errors, and the boundary element method is used for theoretical analysis and calculation of damage mechanics. For the description of irregular geometric models, the isogeometric method has unparalleled superiority. The isogeometric method can seamlessly connect the geometry generated by the advantages of CAD and CAE, and the combination of the two methods is very useful for the future extension of IGABEM to practical engineering applications. At the same time, we use the source point isolation method to establish the boundary-domain integral equations and use the radial integration method to solve the domain integrals. Compared with the traditional boundary element method, the isogeometric boundary element method makes the construction of complex models simple. The numerical results show that the numerical method has good stability and robustness, which provides strong support for further software integration.

Deep Neural Network Regression of MANO from a Single Image

In order to improve the precision and efficiency of estimating the pose and shape of the 3D human hand from a monocular RGB image and accelerate 3D reconstruction, combining the efficiency of deep neural networks and accuracy of traditional optimization, DeepMANO is proposed. First, a DNN model is used to extract sparse features from image, then using these features to regress MANO model parameters. The regressed parameters are then used to initialize the iterative optimization routine which fits MANO to 3D joints. Finally, the parameters obtained by the routine are employed to supervise the network. Two large hand motion datasets, FreiHand and ObMan, are utilized to train the network. The approach assumes a weak perspective model. Experimental results show that the hand pose error is reduced by 52% and mesh error is reduced by 59% compared with state-of-the-art (SOTA) methods. The running time is about three times faster than SOTA methods.

Nonlinear Dynamic Response Analysis of a Three-Stage Gear Train Based on Lightweight Calculation for Edge Equipment.

Bevel gears are widely used in aerospace transmission systems as well as modern mechanical equipment. In order to meet the needs and development of aerospace, high-speed dynamic vehicles, and various defense special equipment, higher and higher requirements are made for the high precision and stability of gear transmission systems, as well as the prediction and control of noise and vibration. Considering the nonlinear factors such as comprehensive gear error and tooth side clearance, a dynamic model of the three-stage gear transmission system is established. The relevant physical parameters, geometric parameters, and load parameters in the gear system are considered random variables to obtain the stochastic vibration model. When the random part of the random parameters is much smaller than the deterministic part, the vibration differential equation is expanded into a first-order term at the mean of the random parameter vector according to the Taylor series expansion theorem, and the ordering equation is solved numerically. Based on the improved stochastic regression method, the nonlinear dynamic response analysis of the three-stage gear train is carried out. This results in a relatively stable system when the dimensionless excitation frequency is in the range of 0.716 to 0.86 and the magnitude of the dimensionless integral meshing error is < 1.089.

Development and Evaluation of a Rib Statistical Shape Model for Thoracic Surgery.

Patients with advanced cancer undergoing chest wall resection may require reconstruction. Currently, rib prostheses are created by segmenting computed tomography images, which is time-consuming and labour intensive. The aim was to optimise the production of digital rib models based on a patient's age, weight, height and gender. A statistical shape model of human ribs was created and used to synthetise rib models, which were compared to the ones produced by segmentation and mirroring. The segmentation took 11.56±1.60 min compared to 0.027 ±0.009 min using the new technique. The average mesh error between the mirroring technique and segmentation was 0.58±0.25 mm (right ribs), and 0.87±0.18 mm (left ribs), compared to 1.37±0.66 mm ( ) and 1.68 ±0.77 mm ( ), respectively, for the new technique. The new technique is promising for the efficiency and ease-of-use in the clinical environment. Clinical Relevance- This is an optimised 3D modelling method providing clinicians with a time-efficient technique to create patient-specific rib prostheses, without any expertise or software knowledge required.

Nonlinear Dynamics Analysis of a Multistage Planetary Gear Transmission System

A nonlinear dynamic model for a multistage planetary gear transmission system, which consists of two-stage planetary gear plus one-stage parallel shaft gear, is proposed. The time-varying meshing stiffness, comprehensive meshing errors and backlash between gear pairs are taken into account in the model, and the connections between the gear stages are characterized by coupling stiffness. The dimensionless vibration differential equations of the system are derived and solved numerically. By means of global bifurcation diagram, largest Lyapunov exponent (LLE), phase diagram and Poincaré map, the stability of the system is studied with the bifurcation parameters variation including excitation frequency and comprehensive meshing errors. The results demonstrate that the system presents strange attractors with rich forms under different parameter combinations. With the increase of the excitation frequency, the meshing state of the system changes, showing a complex motion and indicating the sensitivity of the system to external excitation. Under the variation of the bifurcation parameter of comprehensive meshing error, the complex dynamic behavior of the system is observed, it is found that the increase of comprehensive meshing error has a negative impact on the stability of the system.

Divergence/Connection Preservation Scheme in the Curvilinear Domain with a Small Geometric Approximation Error

Additional grid points are often introduced for the higher-order polynomial of a numerical solution with curvilinear elements. However, those points are likely to be located slightly outside the domain, even when the vertices of the curvilinear elements lie within the curved domain. This misallocation of grid points generates a mesh error, called geometric approximation error. This error is smaller than the discretization error but large enough to significantly degrade a long-time integration. Moreover, this mesh error is considered to be the leading cause of conservation error. Two novel schemes are proposed to improve conservation error and/or discretization error for long-time integration caused by geometric approximation error: The first scheme retrieves the original divergence of the original domain; the second scheme reconstructs the original path of differentiation, called connection, thus retrieving the original connection. The increased accuracies of the proposed schemes are demonstrated by the conservation error for various partial differential equations with moving frames on the sphere.