Multi-body System Theory Research Articles

Characterizing machine tool spatial stiffness and predicting accuracy

As a typical precision machine, the machine tool has complex structure and changeable working conditions, which leads to huge calculation data and low analysis efficiency when using traditional finite element method to obtain stiffness information. General test methods often have discrete values and cannot obtain stiffness information comprehensively and systematically. In this paper, a method for characterizing the stiffness of machine tool processing space based on multi-body system topology is proposed. Based on the matrix condensation theory, a method for constructing the equivalent condensation model of the stiffness of machine tool components is proposed. The stiffness characterization model of the components is established by using the stiffness equivalent condensation method. Based on the multi-body system theory, the stiffness distribution model of machine tool machining space is established, which can quickly and intuitively characterize the machining stiffness information of machine tool. Finally, based on the stiffness distribution model of the machining space of the machine tool, the machining accuracy of the S-shaped test specimen is predicted. Combined with the experimental analysis, the measurement results are consistent with the prediction results. The accuracy, feasibility, and effectiveness of the stiffness distribution model of machine tool machining space are verified.

An Exoskeleton Design and Numerical Characterization for Children with Duchenne Muscular Dystrophy

This research addresses a feasibility study for validating an exoskeleton with kinematic considerations. The designed exoskeleton will be used for children with congenital disorders, especially for a case study characterized by Duchenne muscular dystrophy (DMD). The research core focuses on virtual simulations carried out through the multibody systems theory under an MSC Adams software environment, with an exoskeleton constructive solution. The designed exoskeleton mechanism is characterized by simplicity, low-cost, and easy-operation features criteria. The results obtained through a numerical processing analysis validate the feasibility study of the proposed prototype.

Load torque estimation for cable failure detection in cable-driven parallel robots: a machine learning approach

AbstractThis paper proposes a method for cable failure detection in cable-driven parallel robots (CDPRs) with arbitrary architecture, which is based on the estimates of the motor load torques, together with machine learning algorithms. By just exploiting the dynamic model of each actuator in the conditions of no load, an open-loop load torque observer is designed for each motor to estimate the presence of a load coupled through a cable. Since such a load instantaneously goes to zero for the motor with a broken cable, a simple but effective and robust signature of failure can be inferred to provide reliable detection even in the case of various model mismatches. Additionally, the load torque observer is not computationally demanding since just motor measurements are required, thus avoiding any direct measurement (and a dynamic model as well) on the end-effector. The detection of a failure is made through supervised classification algorithms based on artificial intelligence. The training of the machine learning algorithm is based on a “hybrid” approach: the dataset includes several failure cases, which are numerically generated through a system digital twin developed through the multibody system theory, together with measurements of the real system in nonfailing conditions. Different classification algorithms are considered, together with different sets of input variables to be fed to the classifier. Four numerical examples are proposed by showing the method capability in handling both fully actuated and redundantly actuated CDPRs under cable failure, both rigid and flexible cables, and also evaluating the response in the presence of cable slackness.

Research on positioning accuracy of the swivel head of milling and turning complex machining center

Abstract This article focuses on the swivel head of a milling-turning complex machining center and establishes a geometric error model between the rotary axes based on the multi-body system theory and the homogeneous coordinate transformation method. The double ball bar (DBB) is used to identify the geometric errors of the machine tool swivel head position-independent by measuring circular trajectories. The impact of PIGEs on the measurement trajectory is simulated. The swivel head is rotated at four angles (B0°, B45°, B90°, B-15°), and the laser tracker is used to analyze and study the linear axis straightness, perpendicularity, and the center coordinates and plane errors of the swivel head movement along the XZ plane. A swivel head rotation accuracy test fixture is designed to correct the positioning accuracy of a swivel head with a 45° inclination of the rotation axis. The research results show that the fluctuation of the center plane degree of freedom of the swivel head moving along the XZ plane is small, and the maximum value is 0.0086mm. Under the 45° angle posture of the swivel head, both the center coordinate error value and the plane error value are the largest. The simulation results of the swivel head position error are fairly consistent with the center coordinate error of the swivel head plane movement. A backward tilt displacement of 0.01mm~0.015mm of the machine column during assembly can reduce the influence of the weight of the swivel head on the perpendicularity and straightness of the vertical reciprocating motion, and adding auxiliary support near the base of the swivel head zero position can reduce machine straightness error.

Dynamic research on winding and capturing of tensegrity flexible manipulator

With the rapid development of social intelligence, flexible manipulator has become a typical representative of the intelligent era. However, due to the strong nonlinearity brought about by the high flexibility of the flexible manipulator, as well as the nonsmooth problems it faces during operation such as cable slacking and contact, it poses challenges to its modeling and dynamic analysis. Considering the above difficulties, this article first proposes a modeling strategy for flexible manipulator based on the theory of tensegrity, which can establish a highly flexible manipulator model. Then, based on the theory of nonsmooth multibody systems, a nonsmooth mathematical formula for cable slacking and contact is established to address the nonsmooth phenomena. Finally, a variable cross-section tensegrity flexible manipulator is designed, and the dynamic characteristics of winding and capturing are analyzed. Numerical results validate the effectiveness of the proposed method.

Geometric error modeling and compensation for high precision composite optical measurement systems

Composite optical measurement systems are widely used in the field of precision measurement due to their combination of inspection with high accuracy, speed, wide range, real-time, and other advantages. Whereas errors are prevalent in measurements, in order to improve detection accuracy, the systems must be compensated for geometric errors in three-dimensional space. Aiming at the complex situation of multi-probes and multi-zooms in the composite optical measurement system, the current error modelling methods are difficult to be directly applied, so this paper establishes a unified three-dimensional volumetric error model based on the theory of multi-body system and combined with the principle of geometric optics, performs the error verification through the direct measurement method, and finally realises the compensation of geometric error in the continuous space of the whole measurement range. Eventually, the accuracy of the proposed error model and the effectiveness of the error compensation method were verified by a laser interferometer and standard objects to be measured, and the integrated geometric error of the system was decreased by 76.55%, which effectively improved the accuracy of the system. The error modelling and compensation method proposed in this paper provides a new idea for the error compensation of the zoom measurement system, and at the same time, it is universal for the measurement systems of different structures and motion forms, which can be widely used in the field of precision measurement.

An approach for optimal tolerance allocation of five-axis machine tools by simultaneously considering volumetric error and processing simplicity index

Optimal tolerance allocation (OTA) is one of the most effective ways to improve the machining precision of machine tools. However, the existing OTA methods have the problem that tolerance-cost models are particularly vulnerable to subjective factors, which lead to tolerance allocation scheme with poor applicability and reliability. For this reason, a novel OTA method that simultaneously considers volumetric error and processing simplicity index (PSI) is proposed in this paper. Based on the multi-body system theory and homogeneous transform matrix, the volumetric error prediction model based on tolerance of machine tools’ key parts is firstly established by taking the geometric error as a bridge between tolerance and volumetric error of machine tools. Then, the weight coefficient of each tolerance parameter is calculated based on sensitivity analysis method. Moreover, PSI, which denotes the degree of processing simplicity to reach the required tolerance value, is innovatively proposed to replace manufacturing cost. And the tolerance-PSI model is established to replace tolerance-cost model. Then, an OTA model is established by minimizing volumetric error and maximizing PSI. The NSGA-II is employed to obtain OTA scheme. Finally, simulations and experiments are conducted to validate the feasibility and effectiveness of the presented method.

Vibration characteristics of the rotary table of large spin coater and its influencing factors

The rotary table vibration of the spin coater directly impacts the quality of the spin coating film. In view of the unclear vibration characteristics of the rotary table during operation, the rotary table vibration characteristics and its influencing factors considering the spindle system are studied. Based on the elastic contact theory and multi-body system theory, the rotary table vibration characteristics of the rotary table when the parts of the rotary table are flexible are analyzed by establishing the rotary table multi-rigid body and flexible coupling dynamics models, respectively. By comparing with the rotary table vibration measurement results, it is found that the flexible treatment of the load tray is more consistent with the actual vibration characteristics. The study further analyzes the effects of the unbalance of the rotary table, the rotary table speed, the coaxiality of the load tray and the spindle, and the perpendicularity of the load tray and the spindle on the vibration characteristics. The results show that the influence of the spin coater rotary table under the actual working conditions is from the highest to the lowest degree of influence on the unbalance of the load tray, the coaxiality of the load tray and the spindle, the perpendicularity of load tray and the spindle, and the rotational speed of the rotary table. This study provides a reliable theoretical and experimental basis for the vibration characteristics analysis and structural design of the spin coater rotary table.

Dynamic modelling of an armoured face conveyor considering the curved chains

PurposeDue to the structural layout, mining process, and working environment, curved chains such as horizontal and vertical bends inevitably exist in the armoured face conveyor (AFC). With the increasing power, conveying capacity, and distance of the AFC, the dynamic influence of these curved chains should be highly emphasized. This paper establishes a dynamic model of the AFC by multi-body system theory and finite segment method, in which the curved chains can be fully considered.Design/methodology/approachThe scraper chains are firstly grouped into the straight, horizontal bend, vertical convex and concave bend sections. Each bend section running in a circle is simplified as an ideal arc. Through solving its differential equilibrium equation and using Newton's second law, its running resistance is derived. Then the grouped chains are discretized into finite control elements according to the Kelvin model, and the governing equation of each control element is established. The dynamic model of the AFC is obtained by assembling these equations, and the corresponding simulation model is developed by using MATLAB/Simulink.FindingsCase studies with real scenarios are provided, and simulations are carried out. The results show that the running resistance contributed by the curved chains is larger than the traditional empirical value.Originality/valueThe work in this paper helps the dynamic performance design of AFC, with a deep understanding of the curved chains.

Gear evaluation deviations-based crucial geometric error identification of five-axis CNC gear form grinding process

The gear form grinding accuracy is significantly affected by crucial geometric errors. The gear form grinding process is a special line contact forming method. There are exclusive evaluation standards for gear grinding accuracy. While the existing sensitivity analysis for spatial point errors cannot meet the final gear report requirements. Hence, a novel method for analysis of geometric error influence on the key gear evaluation deviations (GED) is proposed. First, the actual digital tooth surface considering geometric errors and gear form grinding mechanism was constructed according to the homogeneous transformation matrix (HTM) and multi-body system theory (MBS). Second, the GED of the digital tooth surface was gained according to the modified gear meshing equations. Third, the analytic mapping relationship between the GED and machine tool geometric errors was first established. Then, the crucial geometric errors affecting the GED were identified based on a proposed Morris method. Finally, the identification results were compared to the existing publications, and the compensation discussions of crucial errors were demonstrated to validate the advantages of the proposed method. It can be found that the compensation results of GED-oriented key errors are better than those of the traditional methods, which is beneficial to the improvement of evaluation reports.

Dynamics modeling and flight characteristics of folded multi-body aircraft

This paper studies the dynamic modeling method of fold-able multi-body aircraft based on the dynamics theory of multi-body system. Considering the multi-body aircraft as a complete multi-rigid body system, the dynamic model for the free unfolding process of the multi-body aircraft after horizontal launch is established. On the basis of the multi-body dynamics model, the coil spring moment model and the damping moment model for the flexible connection between the flight units are added. Taking a certain type of fold-able three-section wing aircraft as an example, the numerical simulation calculation is carried out. The influence of the flexible connection stiffness coefficient between the flight unit on the dynamic characteristics of the fold-able multi-body aircraft in the free deployment process and the relationship between the stiffness of the flexible connection and the maximum initial folding angle are studied. Finally, the stability envelope between the stiffness coefficient of the flexible connection and the maximum initial folding angle is determined.

Projecting robot dynamics onto trajectories

AbstractMachines and mechanisms realize processes, from the shaping process of a milling machine and the motion process of an automotive system to the trajectory realization of a robot. The dynamics of a machine generated by a properly chosen set of constraints in combination with an appropriate drive system is designed to meet the prescribed requirements of the process, which is done by projecting the machine equations of motion on the process dynamics. We get a set of nonlinear relations, which represent the machine motion in terms of the required process motion. A well-known example is the projection of arbitrary many robot degrees of freedom (DOFs) on a given path resulting in a set of nonlinear equations with one DOF only, the path coordinate s. Application of this idea can be used to construct a mobility space $(\ddot{s}, \dot{s}, s)$ for any combination of coordinates and constraints. The paper presents a corresponding approach for n-link robots by applying multibody system theory. Method might be interesting for layout of machines and mechanisms. Practical aspects are discussed, and an example is given.

Dynamic Simulation of Multiple Launch Rocket System Marching Fire Based on the Fuzzy Adaptive Sliding Mode Control

This paper presents a servo control method for the multiple launch rocket system (MLRS) launcher during marching fire operations. The MLRS, being a complex nonlinear system, presents challenges in designing its servo controller. To address this, we introduce the fuzzy adaptive sliding mode control (FASMC) approach. The permanent magnet synchronous motor (PMSM) and controller of the MLRS were simulated in the MATLAB/Simulink environment. The dynamic model of the MLRS during marching fire was established using multi-body system theory, vehicle mechanics, and launch dynamics. The dynamic model was then integrated with the FASMC-based controller using the Adams/View module. Numerical calculations were performed to demonstrate the control performance and the effectiveness and applicability of the proposed approach were validated through a comparison experiment between FASMC and other common control methods.

A method of sensitivity analysis and precision prediction for geometric errors of five-axis machine tools based on multi-body system theory

A method of sensitivity analysis and precision prediction for geometric errors of five-axis machine tools based on multi-body system theory

Optimal Design Method for Static Precision of Heavy-Duty Vertical Machining Center Based on Gravity Deformation Error Modelling

Due to the large size and large span of heavy-duty machine tools, the structural deformation errors caused by gravity account for a large proportion of the static errors, and the influence of gravity deformation must thus be considered in the machine tool precision design. This paper proposes a precision design method for heavy-duty vertical machining centers based on gravity deformation error modelling. By abstracting the machine tool into a multibody system topology, the static error model of the machine tool is established based on the multibody system theory and a homogeneous coordinate transformation. Assuming that the static error of each motion axis is composed of two parts, i.e., the manufacturing-induced geometric error and the gravity deformation error, the machine tool stiffness model of the relationship between gravity and deformation error is developed using the spatial beam elements. In the modelling process, the stiffness coefficients and volume coefficients of the components are introduced to fully consider the influences of structural parameters on machine tool precision. Taking the machine tool static precision, the component stiffness coefficients and the volume coefficients as the design variables, based on the use of the worst condition method, error sensitivity analysis and global optimization algorithm, the optimal allocation of the static error budget of the machine tool and the structural design requirements of each component are determined, providing a valuable guide for the detailed structure design and manufacture processing of the machine tool components.

Sensitivity analysis of geometric error for a novel slide grinder based on improved Sobol method and its application

In order to improve both the accuracy and efficiency of grinding slide, this paper designs a novel grinder with dual-lead-dual-head. Since the geometric error is one of the major contributors causing machine inaccuracies, the sensitivity analysis is performed to identify the critical geometric error terms, and an application to accuracy self-test is also given. The volumetric model of the grinder with 38 geometric errors is built using the homogeneous transformation matrix (HTM) and multi-body system (MBS) theory. An improved Sobol method with quasi-Monte-Carlo algorithm is utilized to perform the global sensitivity analysis (GSA) in the entire workspace. The particular sensitivity analysis is further carried out on the basis of the machining characteristics of a typical slide. All sensitivity analysis results are validated through the error compensation simulations. Besides that, some discussions are given to determine the total critical errors of the grinder considering both entire workspace and particular machining requirements. Finally, the pitch and yaw errors between the dual-grinding-head are investigated, and based on the sensitivity analysis results, a quick accuracy self-test approach is proposed to reduce the measurement load in practice.

Kinematic modeling and error parameter identification of automated fiber placement machine based on measured data

This paper presents a novel kinematic modeling and error parameter identification method for a six-axis gantry automated fiber placement (AFP) machine. Multi-body system theory is used to model the kinematics of the AFP machine, and then use the homogeneous transformation matrix to represent the transfer relationship of the coordinate system. Based on 54 geometric errors of the AFP machine, a volumetric error transfer model is established. To eliminate the training bias caused by sampling randomness, 10-fold cross-validation combined with the Levenberg–Marquardt method is used to train the kinematic model of the AFP machine. Based on the coordinates of random points in space measured by a laser tracker, all the position-dependent geometric errors and position-independent geometric errors of the linear and rotary axes can be identified simultaneously. After the error parameters are identified, the average error of the random points in the X-direction is reduced from 0.72 to 0.08 mm, a drop of 88.9%. Corresponding experiments are carried out on the body diagonals and the winglet placement path. The experimental results show that the volumetric error transfer model and error parameter identification method proposed in the article can accurately predict the volumetric errors of the AFP machine, and can also meet the requirements of the AFP machine placement accuracy.

Investigation on Structural Mapping Laws of Sensitive Geometric Errors Oriented to Remanufacturing of Three-Axis Milling Machine Tools

Three-axis milling machine tools are widely used in manufacturing enterprises, and they have enormous potential demands for remanufacturing to improve their performance. During remanufacturing a three-axis milling machine tool, the structure needs to be reconstructed, so it is necessary to identify sensitive geometric errors of the remanufactured machine tool. In the traditional sensitive geometric error identification method, complex error modeling and analysis must be conducted. Therefore, professional knowledge is required, and the process of the identification is cumbersome. This paper focused on the quick identification of sensitive geometric errors for remanufacturing of three-axis milling machine tools. Firstly, sensitive geometric errors of a three-axis milling machine tool were identified based on the multi-body system theory and partial differential method. Then, mapping laws between the sensitive geometric errors and the machine tool structure were firstly presented. According to the proposed mapping laws, the sensitive geometric errors can be identified quickly and easily without complex error modeling and analysis. Finally, the simulation and experiment show that the straightness error of milling is improved up to 0.007 mm by compensating the sensitive geometric errors identified by the proposed mapping laws. The table lookup method based on the mapping laws can quickly identify the sensitive geometric errors of three-axis milling machine tools, which is beneficial for the efficiency and precision of remanufacturing of machine tools.

Error Model and Frequency Modulation Characteristics Analysis of Laser Processing Platform for Micro Crystal Resonator

Laser processing platform for micro crystal resonator (MCR) frequency modulation is an important piece of equipment to apply laser etching technology to the MCR frequency modulation process. The positioning accuracy of the laser processing platform has an important influence on frequency modulation characteristics. In order to improve the precision and efficiency of the laser processing platform for MCR frequency modulation, the error model of the laser processing platform for MCR frequency modulation is established based on the multi-body system theory. According to the Monte Carlo simulation method, the influence of laser processing platform error for MCR on frequency modulation characteristics is analyzed. Considering the requirements of the MCR frequency modulation process, the laser processing platform for MCR frequency modulation is built, and the frequency deviation and frequency modulation performance are verified to meet the engineering requirements.

Dynamic modeling and parameter identification for a gantry-type automated fiber placement machine

Dynamic models play a critical role in the design of model-based controllers, which has a significant effect on the dynamic characteristics of motion equipment. This paper mainly focuses on the dynamic modeling and parameter identification for a gantry-type automated fiber placement (AFP) machine. First, a dynamic modeling process combining prismatic axes and revolute axes is conducted by Newton-Euler method, in which the effects of friction and hydraulic balance system are also considered. Then, as the convenience for parameter identification and the application in linearity control, the methods of dynamic model linearization and determination of minimum inertial parameters based on the multi-body system (MBS) theory are proposed, with which a dynamic model in the form of linearized minimum inertial parameters is consequently established. To identify the parameters in the model, key issues regarding excitation trajectory, filtering, and identification algorithm are discussed in detail. Finally, corresponding experiments are performed on the AFP machine, and experimental results show that there is a good agreement between the prediction of the model and the measurement in actuality. Data analysis shows that except for Z-axis, the relative error rates of the others are not greater than 5%, which proves the effectiveness of the established dynamic model and the identified parameters.