The proposed hybrid optimization algorithm integrates particle swarm optimizatio(PSO)with Ant Colony Optimization(ACO)to improve a number of pitfalls within PSO methods traditionally considered and/or applied to indus...The proposed hybrid optimization algorithm integrates particle swarm optimizatio(PSO)with Ant Colony Optimization(ACO)to improve a number of pitfalls within PSO methods traditionally considered and/or applied to industrial robots.Particle Swarm Optimization may frequently suffer from local optima and inaccuracies in identifying the geometric parameters,which are necessary for applications requiring high-accuracy performances.The proposed approach integrates pheromone-based learning of ACO with the D-H method of developing an error model;hence,the global search effectiveness together with the convergence accuracy is further improved.Comparison studies of the hybrid PSO-ACO algorithm show higher precision and effectiveness in the optimization of geometric error parameters compared to the traditional methods.This is a remarkable reduction of localization errors,thus yielding accuracy and reliability in industrial robotic systems,as the results show.This approach improves performance in those applications that demand high geometric calibration by reducing the geometric error.The paper provides an overview of input for developing robotics and automation,giving importance to precision in industrial engineering.The proposed hybrid methodology is a good way to enhance the working accuracy and effectiveness of industrial robots and shall enable their wide application to complex tasks that require a high degree of accuracy.展开更多
This study aimed to identify and compensate for the geometric errors of the double swiveling axes in a five-axis computer numerical control(CNC)machining center.Hence,a three-dimensional coordinate calculation algorit...This study aimed to identify and compensate for the geometric errors of the double swiveling axes in a five-axis computer numerical control(CNC)machining center.Hence,a three-dimensional coordinate calculation algorithm for a measured point with additional rotational rigid body motion constraints is proposed.The motion constraints of the rotational rigid body were analyzed,and a mathematical model of the measured point algorithm in the swiveling axes was established.The Levenberg-Marquard method was used to solve the nonlinear superstatically determined equations.The spatial coordinate error was used to separate the spatial deviation of the measured point.An identification model of the position-independent and position-dependent geometric errors was established.The three-dimensional coordinate-solving algorithm of the measured point in the swiveling axis and geometric error identification method based on the Monte Carlo method were analyzed numerically.Geometric error measurement and cutting experiments were performed on a VMC25100U five-axis machining center,which integrated two swiveling axes.Geometric errors of the A-and B-axes were identified and measured experimentally.The angular positioning errors before and after compensation were measured using a laser interferometer,which verified the effectiveness of the proposed algorithm.A cutting experiment of a round table part was performed.The shape and position accuracy of the processed part before and after compensation were detected using a coordinate measuring machine.It verified that the geometric error of the swiveling axis was effectively compensated by the algorithm proposed herein.展开更多
Accuracy allocation is crucial in the accuracy design of machining tools.Current accuracy allocation methods primarily focus on positional deviation,with little consideration for tool direction deviation.To address th...Accuracy allocation is crucial in the accuracy design of machining tools.Current accuracy allocation methods primarily focus on positional deviation,with little consideration for tool direction deviation.To address this issue,we propose a geometric error cost sensitivity-based accuracy allocation method for five-axis machine tools.A geometric error model consisting of 4l error components is constructed based on homogeneous transformation matrices.Volumetric points with positional and tool direction deviations are randomly sampled to evaluate the accuracy of the machine tool.The sensitivity of each error component at these sampling points is analyzed using the Sobol method.To balance the needs of geometric precision and manufacturing cost,a geometric error cost sensitivity function is developed to estimate the required cost.By allocating error components affecting tool direction deviation first and the remaining components second,this allocation scheme ensures that both deviations meet the requirements.We also perform numerical simulation of a BC-type(B-axis and C-axis type)five-axis machine tool to validate the method.The results show that the new allocation scheme reduces the total geometric error cost by 27.8%compared to a uniform allocation scheme,and yields the same positional and tool direction machining accuracies.展开更多
Geometric error,mainly due to imperfect geometry and dimensions of machine components,is one of the major error sources of machine tools.Considering that geometric error has significant effects on the machining qualit...Geometric error,mainly due to imperfect geometry and dimensions of machine components,is one of the major error sources of machine tools.Considering that geometric error has significant effects on the machining quality of manufactured parts,it has been a popular topic for academic and industrial research for many years.A great deal of research work has been carried out since the 1970s for solving the problem and improving the machining accuracy.Researchers have studied how to measure,detect,model,identify,reduce,and compensate the geometric errors.This paper presents a thorough review of the latest research activities and gives an overview of the state of the art in understanding changes in machine tool performance due to geometric errors.Recent advances in measuring the geometrical errors of machine tools are summarized,and different kinds of error identification methods of translational axes and rotation axes are illustrated respectively.Besides,volumetric geometric error modeling,tracing,and compensation techniques for five-axis machine tools are emphatically introduced.Finally,research challenges in order to improve the volumetric accuracy of machine tools are also highlighted.展开更多
Laser tracers are a three-dimensional coordinate measurement system that are widely used in industrial measurement.We propose a geometric error identification method based on multi-station synchronization laser tracer...Laser tracers are a three-dimensional coordinate measurement system that are widely used in industrial measurement.We propose a geometric error identification method based on multi-station synchronization laser tracers to enable the rapid and high-precision measurement of geometric errors for gantry-type computer numerical control(CNC)machine tools.This method also improves on the existing measurement efficiency issues in the single-base station measurement method and multi-base station time-sharing measurement method.We consider a three-axis gantry-type CNC machine tool,and the geometric error mathematical model is derived and established based on the combination of screw theory and a topological analysis of the machine kinematic chain.The four-station laser tracers position and measurement points are realized based on the multi-point positioning principle.A self-calibration algorithm is proposed for the coordinate calibration process of a laser tracer using the Levenberg-Marquardt nonlinear least squares method,and the geometric error is solved using Taylor’s first-order linearization iteration.The experimental results show that the geometric error calculated based on this modeling method is comparable to the results from the Etalon laser tracer.For a volume of 800 mm×1000 mm×350 mm,the maximum differences of the linear,angular,and spatial position errors were 2.0μm,2.7μrad,and 12.0μm,respectively,which verifies the accuracy of the proposed algorithm.This research proposes a modeling method for the precise measurement of errors in machine tools,and the applied nature of this study also makes it relevant both to researchers and those in the industrial sector.展开更多
A systematic geometric model has been presented for calibration of a newly designed 5-axis turbine blade grinding machine. This machine is designed to serve a specific purpose to attain high accuracy and high efficien...A systematic geometric model has been presented for calibration of a newly designed 5-axis turbine blade grinding machine. This machine is designed to serve a specific purpose to attain high accuracy and high efficiency grinding of turbine blades by eliminating the hand grinding process. Although its topology is RPPPR （P： prismatic; R： rotary）, its design is quite distinct from the competitive machine tools. As error quantification is the only way to investigate, maintain and improve its accuracy, calibra- tion is recommended for its performance assessment and acceptance testing. Systematic geometric error modeling technique is implemented and 52 position dependent and position independent errors are identified while considering the machine as five rigid bodies by eliminating the set-up errors of workpiece and cutting tool. 39 of them are found to have influential errors and are accommodated for finding the resultant effect between the cutting tool and the workpiece in workspace volume. Rigid body kinematics techniques and homogenous transformation matrices are used for error synthesis.展开更多
Assembly geometric error as a part of the machine tool system errors has a significant influence on the machining accuracy of the multi-axis machine tool.And it cannot be eliminated due to the error propagation of com...Assembly geometric error as a part of the machine tool system errors has a significant influence on the machining accuracy of the multi-axis machine tool.And it cannot be eliminated due to the error propagation of components in the assembly process,which is generally non-uniformly distributed in the whole working space.A comprehensive expression model for assembly geometric error is greatly helpful for machining quality control of machine tools to meet the demand for machining accuracy in practice.However,the expression ranges based on the standard quasistatic expression model for assembly geometric errors are far less than those needed in the whole working space of the multi-axis machine tool.To address this issue,a modeling methodology based on the Jacobian-Torsor model is proposed to describe the spatially distributed geometric errors.Firstly,an improved kinematic Jacobian-Torsor model is developed to describe the relative movements such as translation and rotation motion between assembly bodies,respectively.Furthermore,based on the proposed kinematic Jacobian-Torsor model,a spatial expression of geometric errors for the multi-axis machine tool is given.And simulation and experimental verification are taken with the investigation of the spatial distribution of geometric errors on five four-axis machine tools.The results validate the effectiveness of the proposed kinematic Jacobian-Torsor model in dealing with the spatial expression of assembly geometric errors.展开更多
In order to improve the process precision of an XY laser annealing table, a geometric error modeling, and an identification and compensation method were proposed. Based on multi-body system theory, a geometric error m...In order to improve the process precision of an XY laser annealing table, a geometric error modeling, and an identification and compensation method were proposed. Based on multi-body system theory, a geometric error model for the laser annealing table was established. It supports the identification of 7 geometric errors affecting the annealing accuracy. An original identification method was presented to recognize these geometric errors. Positioning errors of 5 lines in the workspace were measured by a laser interferometer, and the 7 geometric errors were identified by the proposed algorithm. Finally, a software-based error compensation method was adopted, and a compensation mechanism was developed in a postprocessor based on LabVIEW. The identified geometric errors can be compensated by converting ideal NC codes to actual NC codes. A validation experiment has been conducted on the laser annealing table, and the results indicate that positioning errors of two validation lines decreased from ±37 μm and ±33 μm to ±5 μm and ±4.5 μm, respectively. The geometric error modeling, identification and compensation method presented in this work can be straightforwardly extended to any configurations of 2-dimensional worktable.展开更多
The methods of identifying geometric error parameters for NC machine tools are introduced. According to analyzing and comparing the different methods, a new method-displacement method with 9 lines is developed based o...The methods of identifying geometric error parameters for NC machine tools are introduced. According to analyzing and comparing the different methods, a new method-displacement method with 9 lines is developed based on the theories of the movement errors of multibody system (MBS). A lot of experiments are also made to obtain 21 terms geometric error parameters by using the error identification software based on the new method.展开更多
A finite element model was established for analyzing the geometric errors in turning operations and a two-step analyzing process was proposed. In the first analyzing step, the cutting force and the cutting heat for th...A finite element model was established for analyzing the geometric errors in turning operations and a two-step analyzing process was proposed. In the first analyzing step, the cutting force and the cutting heat for the cutting conditions were obtained using the AdvantEdge. Also, the deformation of a workpiece was estimated in the second step using the ANSYS. The deformation was analyzed for a 150 mm-long workpiece at three different measuring points, such as 10, 70 and 130 mm from a reference point, and the amounts of the deformation were compared through experiments. /n the results of the comparison and analysis, the values obtained from these comparison and analysis represent similar tendencies. Also, it is verified that their geometric errors increase with the increase in temperature. In addition, regarding the factors that affect the deformation of a workpiecc, it can be seen that the geometric error in the lathe is about 15%, the error caused by the cutting force is about 10%, and the deformation caused by the heat is about 75%.展开更多
Rotary tables are equipments in precision machinery applied in five-axis Machine Tools and CMM （Coordinate Measuring Machines）, offering rotational （C-axis） and tilting motion （A-axis）, allowing the obtaining of...Rotary tables are equipments in precision machinery applied in five-axis Machine Tools and CMM （Coordinate Measuring Machines）, offering rotational （C-axis） and tilting motion （A-axis）, allowing the obtaining of several configurations for manufacturing or inspection of parts with complex geometries. The demand for high accuracy, high efficiency and fewer errors in the positioning of the part in precision machines increases every day, thus ensuring their high confidence and the use of aerostatic bearings enable constructive innovations to the equipment. In this context, this work presents the mechanical design, the development and error analysis of a prototype of an aerostatic rotary table. This study emphasizes the analysis of a prototype that uses the air as a working principle for reducing friction between moving parts, increasing the mechanical efficiency, and its influence of motion error is also discussed based on the experimental results. For the geometrical errors analysis, experimental tests were realized in laboratory using a DBB （Double Ballbar）. The tests are performed with only one axis moving, observing the behavior of the system for different feedrate at the C-axis.展开更多
The CNC machine tool is the fundamental equipment of the manufacturing industry,particularly in sectors where achieving high levels of accuracy is crucial.Geometric accuracy design is an important step in machine tool...The CNC machine tool is the fundamental equipment of the manufacturing industry,particularly in sectors where achieving high levels of accuracy is crucial.Geometric accuracy design is an important step in machine tool design and plays an essential role in determining the machining accuracy of the workpiece.Researchers have extensively studied methods to model,extract,optimize,and measure the geometric errors that affect the geometric accuracy of machine tools.This paper provides a comprehensive review of the state-of-the-art approaches and an overview of the latest research progress associated with geometric accuracy design in CNC machine tools.This paper explores the interrelated aspects of CNC machine tool accuracy design:modeling,analysis and optimization.Accuracy analysis,which includes geometric error modeling and sensitivity analysis,determines a machine tool’s output accuracy through its volumetric error model,given the known accuracy of its individual components.Conversely,accuracy allocation designs the accuracy of the machine tool components according to given output accuracy requirements to achieve optimization between the objectives of manufacturing cost,quality,reliability,and environmental impact.In addition to discussing design factors and evaluation methods,this paper outlines methods for verifying the accuracy of design results,aiming to provide a practical basis for ensuring that the designed accuracy is achieved.Finally,the challenges and future research directions in geometric accuracy design are highlighted.展开更多
A new instrument for checking the quality of elevator guide rails is introduced.With this instrument,the general geometric errors such as straightness,flatness,squareness,twist,thickness and height can be measured aut...A new instrument for checking the quality of elevator guide rails is introduced.With this instrument,the general geometric errors such as straightness,flatness,squareness,twist,thickness and height can be measured automatically,simultaneously in a short time with high accuracy.It is very useful for elevator guide rail factories to improve their work efficiency and the quality of their products.展开更多
The cutter runout effect has significant influence on the shape of cutter swept surface and the machining surface quality. Hence,it is necessary to integrate the cutter runout effect in cutter swept surface modeling,g...The cutter runout effect has significant influence on the shape of cutter swept surface and the machining surface quality. Hence,it is necessary to integrate the cutter runout effect in cutter swept surface modeling,geometric error prediction and tool path optimization for five-axis flank machining. In this paper,an envelope surface model considering cutter runout effect is first established,and geometric errors induced by runout effect are derived based on the relative motion analysis between the cutter and part in machining. In the model,the cutter runout is defined by four parameters,including inclination angle,location angle,offset value and the length of cutter axis. Then the runout parameters are integrated into the rotation surface of each cutting edge that is used to form the final cutter envelope surface for the five-axis machining process. Thus,the final resulting geometric errors of the machined surface induced by cutter runout can be obtained through computing the deviations from the nominal cutter swept surface. To reduce these errors,an iterative least square method is used to optimize the tool paths for five-axis flank machining. Finally,a validation example is given for a specific ruled surface. Results show the effectiveness and feasibility of the analytical model of geometric errors induced by cutter runout,and also show that the geometric errors can be reduced significantly using the proposed tool path planning method.展开更多
This paper considers geometric error control in the parabola-blending linear interpolation method(Zhang,et al.,2011).Classical model of chord error by approximation with contact circle on the parabolas leads to incorr...This paper considers geometric error control in the parabola-blending linear interpolation method(Zhang,et al.,2011).Classical model of chord error by approximation with contact circle on the parabolas leads to incorrect result.By computing the geometric error directly without accumulating the approximation error and chord error,the authors realize correct geometric error control by establishing inequality constraints on the accelerations of the motion.展开更多
We propose a novel spatial phase-shifting interferometry that exploits a genetic algorithm to compensate for geometric errors. Spatial phase-shifting interferometry is more suitable for measuring objects with properti...We propose a novel spatial phase-shifting interferometry that exploits a genetic algorithm to compensate for geometric errors. Spatial phase-shifting interferometry is more suitable for measuring objects with properties that change rapidly in time than the temporal phase-shifting interferometry. However, it is more susceptible to the geometric errors since the positions at which interferograms are collected are different. In this letter, we propose a spatial phase-shifting interferometry with separate paths for object and reference waves. Also, the object wave estimate is parameterized in terms of geometric errors, and the error is compensated by using a genetic algorithm.展开更多
In heavy duty machine tools, hydrostatic turntable is often used as a means for providing rotational motion and supporting workpiece, so the accuracy of turntable is crucial for part machining. In order to analyze the...In heavy duty machine tools, hydrostatic turntable is often used as a means for providing rotational motion and supporting workpiece, so the accuracy of turntable is crucial for part machining. In order to analyze the influence of load-indcued errors on machining accuracy, an identification model of load-induced errors based on the deformation caused by applied load of hydrostatic turntable of computerized numerical control(CNC) gantry milling heavy machine is proposed. Based on multi-body system theory and screw theory, the space machining accuracy model of heavy duty machine tool is established with consideration of identified load-induced errors. And then, the influence of load-induced errors on space machining accuracy and the roundness error of a milled hole is analyzed. The analysis results show that load-induced errors have a big influence on the roundness error of machined hole, especially when the center of the milled hole is far from that of hydrostatic turntable.展开更多
In order to improve the low output accuracy caused by the elastic deformations of the branch chains,a finite element-based dynamic accuracy analysis method for parallel mechanisms is proposed in this paper.First,takin...In order to improve the low output accuracy caused by the elastic deformations of the branch chains,a finite element-based dynamic accuracy analysis method for parallel mechanisms is proposed in this paper.First,taking a 5-prismatic-spherical-spherical(PSS)/universal-prismatic-universal(UPU)parallel mechanism as an example,the error model is established by a closed vector chain method,while its influence on the dynamic accuracy of the parallel mechanism is analyzed through numerical simulation.According to the structural and error characteristics of the parallel mechanism,a vector calibration algorithm is proposed to reduce the position and pose errors along the whole motion trajectory.Then,considering the elastic deformation of the rod,the rigid-flexible coupling dynamic equations of each component are established by combining the finite element method with the Lagrange method.The elastodynamic model of the whole machine is obtained based on the constraint condition of each moving part,and the correctness of the model is verified by simulation.Moreover,the effect of component flexibility on the dimensionless root mean square error of the displacement,velocity and acceleration of the moving platform is investigated by using a Newmark method,and the mapping relationship of these dimensionless root mean square errors to dynamic accuracy is further studied.The research work provides a theoretical basis for the design of the parameter size of the prototype.展开更多
The unsatisfied surface quality seriously impedes the wide application of incremental sheet forming(ISF)in industrial field.As a novel approach,the interpolator method is a promising strategy to enhance the surface qu...The unsatisfied surface quality seriously impedes the wide application of incremental sheet forming(ISF)in industrial field.As a novel approach,the interpolator method is a promising strategy to enhance the surface quality in ISF.However,the mechanism for the improvement of surface quality and the influence of interpolator properties on surface roughness are not well understood.In this paper,the influences of process variables(i.e.tool diameter,step size and thickness of interpolators)on the forming process(e.g.surface roughness,forming force and geometric error)are investigated through a systematic experimental approach of central composite design(CCD)in two-point incremental sheet forming(TPIF).It is obtained that the increase in thickness of interpolators decreases the surface roughness in direction vertical to the tool path while increases the surface roughness in direction horizontal to the tool path.Nevertheless,the combined influence between thickness of interpolators and process parameters(tool diameter and step size)is limited.Meanwhile,the placement of interpolator has little influence on the effective forming force of blank.In addition,the geometric error enlarges with the increase of step size and thickness of interpolator while decreases firstly and then increase with an increase in tool diameter.Finally,the influencing mechanism of the interpolator method on surface quality can be attributed to the decrease of thecontact pressure due to the increase of contact area with the unchanged contact force.Meanwhile,the interpolator method eliminates the sliding friction on the surface of blank due to the stable relative position between the blank and the interpolator.展开更多
Motivated by the definition of the machining errors induced by tool path planning methods, a mapping curve of the tool axis of a cylindrical cutter is constructed on the tool surface. The mapping curve is a typical on...Motivated by the definition of the machining errors induced by tool path planning methods, a mapping curve of the tool axis of a cylindrical cutter is constructed on the tool surface. The mapping curve is a typical one that can be used to express the closeness between the tool surface and the surface to be machined. A novel tool path planning method is proposed for flank or plunge milling ruled surfaces based on the minimization of the one-sided Hausdorff distance （HD） from the mapping curve to the surface to be machined. It is a nonlinear optimization problem in best uniform approximation （BUA） or Chebyshev sense. A mathematical programming model for computing the minimum one-sided HD is proposed. The linearization method of the programming model is provided and the final optimal solutions are obtained by simplex method. The effectiveness of the proposed BUA method is verified by two numerical examples and compared with the least squares （LS） and double point offset （DPO） methods. The variation in tool orientation induced by the optimization of the tool positions is also evaluated.展开更多
文摘The proposed hybrid optimization algorithm integrates particle swarm optimizatio(PSO)with Ant Colony Optimization(ACO)to improve a number of pitfalls within PSO methods traditionally considered and/or applied to industrial robots.Particle Swarm Optimization may frequently suffer from local optima and inaccuracies in identifying the geometric parameters,which are necessary for applications requiring high-accuracy performances.The proposed approach integrates pheromone-based learning of ACO with the D-H method of developing an error model;hence,the global search effectiveness together with the convergence accuracy is further improved.Comparison studies of the hybrid PSO-ACO algorithm show higher precision and effectiveness in the optimization of geometric error parameters compared to the traditional methods.This is a remarkable reduction of localization errors,thus yielding accuracy and reliability in industrial robotic systems,as the results show.This approach improves performance in those applications that demand high geometric calibration by reducing the geometric error.The paper provides an overview of input for developing robotics and automation,giving importance to precision in industrial engineering.The proposed hybrid methodology is a good way to enhance the working accuracy and effectiveness of industrial robots and shall enable their wide application to complex tasks that require a high degree of accuracy.
基金Supported by Shanxi Provincial Natural Science Foundation(Grant No.2021JM010)The Youth Innovation Team of Shaanxi Universities.
文摘This study aimed to identify and compensate for the geometric errors of the double swiveling axes in a five-axis computer numerical control(CNC)machining center.Hence,a three-dimensional coordinate calculation algorithm for a measured point with additional rotational rigid body motion constraints is proposed.The motion constraints of the rotational rigid body were analyzed,and a mathematical model of the measured point algorithm in the swiveling axes was established.The Levenberg-Marquard method was used to solve the nonlinear superstatically determined equations.The spatial coordinate error was used to separate the spatial deviation of the measured point.An identification model of the position-independent and position-dependent geometric errors was established.The three-dimensional coordinate-solving algorithm of the measured point in the swiveling axis and geometric error identification method based on the Monte Carlo method were analyzed numerically.Geometric error measurement and cutting experiments were performed on a VMC25100U five-axis machining center,which integrated two swiveling axes.Geometric errors of the A-and B-axes were identified and measured experimentally.The angular positioning errors before and after compensation were measured using a laser interferometer,which verified the effectiveness of the proposed algorithm.A cutting experiment of a round table part was performed.The shape and position accuracy of the processed part before and after compensation were detected using a coordinate measuring machine.It verified that the geometric error of the swiveling axis was effectively compensated by the algorithm proposed herein.
基金supported by the Key R&D Program of Zhejiang Province(Nos.2023C01166 and 2024SJCZX0046)the Zhejiang Provincial Natural Science Foundation of China(Nos.LDT23E05013E05 and LD24E050009)the Natural Science Foundation of Ningbo(No.2021J150),China.
文摘Accuracy allocation is crucial in the accuracy design of machining tools.Current accuracy allocation methods primarily focus on positional deviation,with little consideration for tool direction deviation.To address this issue,we propose a geometric error cost sensitivity-based accuracy allocation method for five-axis machine tools.A geometric error model consisting of 4l error components is constructed based on homogeneous transformation matrices.Volumetric points with positional and tool direction deviations are randomly sampled to evaluate the accuracy of the machine tool.The sensitivity of each error component at these sampling points is analyzed using the Sobol method.To balance the needs of geometric precision and manufacturing cost,a geometric error cost sensitivity function is developed to estimate the required cost.By allocating error components affecting tool direction deviation first and the remaining components second,this allocation scheme ensures that both deviations meet the requirements.We also perform numerical simulation of a BC-type(B-axis and C-axis type)five-axis machine tool to validate the method.The results show that the new allocation scheme reduces the total geometric error cost by 27.8%compared to a uniform allocation scheme,and yields the same positional and tool direction machining accuracies.
基金supported by the National Natural Science Foundation of China(Nos.52005413,52022082)Natural Science Basic Research Plan in Shaanxi Province of China(No.2021JM-054)the Fundamental Research Funds for the Central Universities(No.D5000220135)。
文摘Geometric error,mainly due to imperfect geometry and dimensions of machine components,is one of the major error sources of machine tools.Considering that geometric error has significant effects on the machining quality of manufactured parts,it has been a popular topic for academic and industrial research for many years.A great deal of research work has been carried out since the 1970s for solving the problem and improving the machining accuracy.Researchers have studied how to measure,detect,model,identify,reduce,and compensate the geometric errors.This paper presents a thorough review of the latest research activities and gives an overview of the state of the art in understanding changes in machine tool performance due to geometric errors.Recent advances in measuring the geometrical errors of machine tools are summarized,and different kinds of error identification methods of translational axes and rotation axes are illustrated respectively.Besides,volumetric geometric error modeling,tracing,and compensation techniques for five-axis machine tools are emphatically introduced.Finally,research challenges in order to improve the volumetric accuracy of machine tools are also highlighted.
基金Supported by Natural Science Foundation of Shaanxi Province of China(Grant No.2021JM010)Suzhou Municipal Natural Science Foundation of China(Grant Nos.SYG202018,SYG202134).
文摘Laser tracers are a three-dimensional coordinate measurement system that are widely used in industrial measurement.We propose a geometric error identification method based on multi-station synchronization laser tracers to enable the rapid and high-precision measurement of geometric errors for gantry-type computer numerical control(CNC)machine tools.This method also improves on the existing measurement efficiency issues in the single-base station measurement method and multi-base station time-sharing measurement method.We consider a three-axis gantry-type CNC machine tool,and the geometric error mathematical model is derived and established based on the combination of screw theory and a topological analysis of the machine kinematic chain.The four-station laser tracers position and measurement points are realized based on the multi-point positioning principle.A self-calibration algorithm is proposed for the coordinate calibration process of a laser tracer using the Levenberg-Marquardt nonlinear least squares method,and the geometric error is solved using Taylor’s first-order linearization iteration.The experimental results show that the geometric error calculated based on this modeling method is comparable to the results from the Etalon laser tracer.For a volume of 800 mm×1000 mm×350 mm,the maximum differences of the linear,angular,and spatial position errors were 2.0μm,2.7μrad,and 12.0μm,respectively,which verifies the accuracy of the proposed algorithm.This research proposes a modeling method for the precise measurement of errors in machine tools,and the applied nature of this study also makes it relevant both to researchers and those in the industrial sector.
文摘A systematic geometric model has been presented for calibration of a newly designed 5-axis turbine blade grinding machine. This machine is designed to serve a specific purpose to attain high accuracy and high efficiency grinding of turbine blades by eliminating the hand grinding process. Although its topology is RPPPR （P： prismatic; R： rotary）, its design is quite distinct from the competitive machine tools. As error quantification is the only way to investigate, maintain and improve its accuracy, calibra- tion is recommended for its performance assessment and acceptance testing. Systematic geometric error modeling technique is implemented and 52 position dependent and position independent errors are identified while considering the machine as five rigid bodies by eliminating the set-up errors of workpiece and cutting tool. 39 of them are found to have influential errors and are accommodated for finding the resultant effect between the cutting tool and the workpiece in workspace volume. Rigid body kinematics techniques and homogenous transformation matrices are used for error synthesis.
基金Supported by National Natural Science Foundation of China (Grant No.51975369)National Key Science and Technology Research Program of China (Grant No.2019ZX04027001)。
文摘Assembly geometric error as a part of the machine tool system errors has a significant influence on the machining accuracy of the multi-axis machine tool.And it cannot be eliminated due to the error propagation of components in the assembly process,which is generally non-uniformly distributed in the whole working space.A comprehensive expression model for assembly geometric error is greatly helpful for machining quality control of machine tools to meet the demand for machining accuracy in practice.However,the expression ranges based on the standard quasistatic expression model for assembly geometric errors are far less than those needed in the whole working space of the multi-axis machine tool.To address this issue,a modeling methodology based on the Jacobian-Torsor model is proposed to describe the spatially distributed geometric errors.Firstly,an improved kinematic Jacobian-Torsor model is developed to describe the relative movements such as translation and rotation motion between assembly bodies,respectively.Furthermore,based on the proposed kinematic Jacobian-Torsor model,a spatial expression of geometric errors for the multi-axis machine tool is given.And simulation and experimental verification are taken with the investigation of the spatial distribution of geometric errors on five four-axis machine tools.The results validate the effectiveness of the proposed kinematic Jacobian-Torsor model in dealing with the spatial expression of assembly geometric errors.
基金Projects(2012ZX04010-011,2009ZX02037-02) supported by the Key National Science and Technology Project of China
文摘In order to improve the process precision of an XY laser annealing table, a geometric error modeling, and an identification and compensation method were proposed. Based on multi-body system theory, a geometric error model for the laser annealing table was established. It supports the identification of 7 geometric errors affecting the annealing accuracy. An original identification method was presented to recognize these geometric errors. Positioning errors of 5 lines in the workspace were measured by a laser interferometer, and the 7 geometric errors were identified by the proposed algorithm. Finally, a software-based error compensation method was adopted, and a compensation mechanism was developed in a postprocessor based on LabVIEW. The identified geometric errors can be compensated by converting ideal NC codes to actual NC codes. A validation experiment has been conducted on the laser annealing table, and the results indicate that positioning errors of two validation lines decreased from ±37 μm and ±33 μm to ±5 μm and ±4.5 μm, respectively. The geometric error modeling, identification and compensation method presented in this work can be straightforwardly extended to any configurations of 2-dimensional worktable.
基金This project is supported by National Advanced ResearchFoundation (No.PD521910) and National Natural ScienceFoundation of Ch
文摘The methods of identifying geometric error parameters for NC machine tools are introduced. According to analyzing and comparing the different methods, a new method-displacement method with 9 lines is developed based on the theories of the movement errors of multibody system (MBS). A lot of experiments are also made to obtain 21 terms geometric error parameters by using the error identification software based on the new method.
基金Project(RTI04-01-03) supported by the Regional Technology Innovation Program of the Ministry of Knowledge Economy (MKE),Korea
文摘A finite element model was established for analyzing the geometric errors in turning operations and a two-step analyzing process was proposed. In the first analyzing step, the cutting force and the cutting heat for the cutting conditions were obtained using the AdvantEdge. Also, the deformation of a workpiece was estimated in the second step using the ANSYS. The deformation was analyzed for a 150 mm-long workpiece at three different measuring points, such as 10, 70 and 130 mm from a reference point, and the amounts of the deformation were compared through experiments. /n the results of the comparison and analysis, the values obtained from these comparison and analysis represent similar tendencies. Also, it is verified that their geometric errors increase with the increase in temperature. In addition, regarding the factors that affect the deformation of a workpiecc, it can be seen that the geometric error in the lathe is about 15%, the error caused by the cutting force is about 10%, and the deformation caused by the heat is about 75%.
文摘Rotary tables are equipments in precision machinery applied in five-axis Machine Tools and CMM （Coordinate Measuring Machines）, offering rotational （C-axis） and tilting motion （A-axis）, allowing the obtaining of several configurations for manufacturing or inspection of parts with complex geometries. The demand for high accuracy, high efficiency and fewer errors in the positioning of the part in precision machines increases every day, thus ensuring their high confidence and the use of aerostatic bearings enable constructive innovations to the equipment. In this context, this work presents the mechanical design, the development and error analysis of a prototype of an aerostatic rotary table. This study emphasizes the analysis of a prototype that uses the air as a working principle for reducing friction between moving parts, increasing the mechanical efficiency, and its influence of motion error is also discussed based on the experimental results. For the geometrical errors analysis, experimental tests were realized in laboratory using a DBB （Double Ballbar）. The tests are performed with only one axis moving, observing the behavior of the system for different feedrate at the C-axis.
基金Supported by the National Natural Science Foundation of China(Grant Nos.52375448,52275440).
文摘The CNC machine tool is the fundamental equipment of the manufacturing industry,particularly in sectors where achieving high levels of accuracy is crucial.Geometric accuracy design is an important step in machine tool design and plays an essential role in determining the machining accuracy of the workpiece.Researchers have extensively studied methods to model,extract,optimize,and measure the geometric errors that affect the geometric accuracy of machine tools.This paper provides a comprehensive review of the state-of-the-art approaches and an overview of the latest research progress associated with geometric accuracy design in CNC machine tools.This paper explores the interrelated aspects of CNC machine tool accuracy design:modeling,analysis and optimization.Accuracy analysis,which includes geometric error modeling and sensitivity analysis,determines a machine tool’s output accuracy through its volumetric error model,given the known accuracy of its individual components.Conversely,accuracy allocation designs the accuracy of the machine tool components according to given output accuracy requirements to achieve optimization between the objectives of manufacturing cost,quality,reliability,and environmental impact.In addition to discussing design factors and evaluation methods,this paper outlines methods for verifying the accuracy of design results,aiming to provide a practical basis for ensuring that the designed accuracy is achieved.Finally,the challenges and future research directions in geometric accuracy design are highlighted.
文摘A new instrument for checking the quality of elevator guide rails is introduced.With this instrument,the general geometric errors such as straightness,flatness,squareness,twist,thickness and height can be measured automatically,simultaneously in a short time with high accuracy.It is very useful for elevator guide rail factories to improve their work efficiency and the quality of their products.
基金supported by the National Natural Science Foundation of China (Grant No. 51075054)the National Basic Research Program of China ("973" Program) (Grant Nos. 2005CB726100 and 2011CB706800)the Fundamental Research Funds for the Central Universities (Grant No. DUT10ZD205)
文摘The cutter runout effect has significant influence on the shape of cutter swept surface and the machining surface quality. Hence,it is necessary to integrate the cutter runout effect in cutter swept surface modeling,geometric error prediction and tool path optimization for five-axis flank machining. In this paper,an envelope surface model considering cutter runout effect is first established,and geometric errors induced by runout effect are derived based on the relative motion analysis between the cutter and part in machining. In the model,the cutter runout is defined by four parameters,including inclination angle,location angle,offset value and the length of cutter axis. Then the runout parameters are integrated into the rotation surface of each cutting edge that is used to form the final cutter envelope surface for the five-axis machining process. Thus,the final resulting geometric errors of the machined surface induced by cutter runout can be obtained through computing the deviations from the nominal cutter swept surface. To reduce these errors,an iterative least square method is used to optimize the tool paths for five-axis flank machining. Finally,a validation example is given for a specific ruled surface. Results show the effectiveness and feasibility of the analytical model of geometric errors induced by cutter runout,and also show that the geometric errors can be reduced significantly using the proposed tool path planning method.
基金supported partially by the National Natural Science Foundation of China under Grant Nos.10871195 and 60821002/F02National Center for Mathematics and Interdisciplinary Sciences of Chinese Academy of Sciences
文摘This paper considers geometric error control in the parabola-blending linear interpolation method(Zhang,et al.,2011).Classical model of chord error by approximation with contact circle on the parabolas leads to incorrect result.By computing the geometric error directly without accumulating the approximation error and chord error,the authors realize correct geometric error control by establishing inequality constraints on the accelerations of the motion.
基金supported by the National Research Foundation and the Ministry of Education, Science and Engineering of Korea through the National Creative Re-search Initiative Program (R16-2007-030-01001-0)
文摘We propose a novel spatial phase-shifting interferometry that exploits a genetic algorithm to compensate for geometric errors. Spatial phase-shifting interferometry is more suitable for measuring objects with properties that change rapidly in time than the temporal phase-shifting interferometry. However, it is more susceptible to the geometric errors since the positions at which interferograms are collected are different. In this letter, we propose a spatial phase-shifting interferometry with separate paths for object and reference waves. Also, the object wave estimate is parameterized in terms of geometric errors, and the error is compensated by using a genetic algorithm.
基金Projects(51575010,51575009)supported by the National Natural Science Foundations of ChinaProject(Z1511000003150138)supported by Beijing Nova Program,China
文摘In heavy duty machine tools, hydrostatic turntable is often used as a means for providing rotational motion and supporting workpiece, so the accuracy of turntable is crucial for part machining. In order to analyze the influence of load-indcued errors on machining accuracy, an identification model of load-induced errors based on the deformation caused by applied load of hydrostatic turntable of computerized numerical control(CNC) gantry milling heavy machine is proposed. Based on multi-body system theory and screw theory, the space machining accuracy model of heavy duty machine tool is established with consideration of identified load-induced errors. And then, the influence of load-induced errors on space machining accuracy and the roundness error of a milled hole is analyzed. The analysis results show that load-induced errors have a big influence on the roundness error of machined hole, especially when the center of the milled hole is far from that of hydrostatic turntable.
基金Supported by the National Natural Science Foundation of China(Grant Nos.U21A20122,51975523 and 51905481)the Natural Science Foundation of Zhejiang Province(Grant No.LY22E050012)the Students in Zhejiang Province Science and technology Innovation Plan(Grant No.2020R403054).
文摘In order to improve the low output accuracy caused by the elastic deformations of the branch chains,a finite element-based dynamic accuracy analysis method for parallel mechanisms is proposed in this paper.First,taking a 5-prismatic-spherical-spherical(PSS)/universal-prismatic-universal(UPU)parallel mechanism as an example,the error model is established by a closed vector chain method,while its influence on the dynamic accuracy of the parallel mechanism is analyzed through numerical simulation.According to the structural and error characteristics of the parallel mechanism,a vector calibration algorithm is proposed to reduce the position and pose errors along the whole motion trajectory.Then,considering the elastic deformation of the rod,the rigid-flexible coupling dynamic equations of each component are established by combining the finite element method with the Lagrange method.The elastodynamic model of the whole machine is obtained based on the constraint condition of each moving part,and the correctness of the model is verified by simulation.Moreover,the effect of component flexibility on the dimensionless root mean square error of the displacement,velocity and acceleration of the moving platform is investigated by using a Newmark method,and the mapping relationship of these dimensionless root mean square errors to dynamic accuracy is further studied.The research work provides a theoretical basis for the design of the parameter size of the prototype.
基金support from the National Natural Science Foundation of China(51575028)National Natural Science Foundation of China(51605258)the Fundamental Research Funds for the Central Universities of China(YWF-18-BJ-J-75)。
文摘The unsatisfied surface quality seriously impedes the wide application of incremental sheet forming(ISF)in industrial field.As a novel approach,the interpolator method is a promising strategy to enhance the surface quality in ISF.However,the mechanism for the improvement of surface quality and the influence of interpolator properties on surface roughness are not well understood.In this paper,the influences of process variables(i.e.tool diameter,step size and thickness of interpolators)on the forming process(e.g.surface roughness,forming force and geometric error)are investigated through a systematic experimental approach of central composite design(CCD)in two-point incremental sheet forming(TPIF).It is obtained that the increase in thickness of interpolators decreases the surface roughness in direction vertical to the tool path while increases the surface roughness in direction horizontal to the tool path.Nevertheless,the combined influence between thickness of interpolators and process parameters(tool diameter and step size)is limited.Meanwhile,the placement of interpolator has little influence on the effective forming force of blank.In addition,the geometric error enlarges with the increase of step size and thickness of interpolator while decreases firstly and then increase with an increase in tool diameter.Finally,the influencing mechanism of the interpolator method on surface quality can be attributed to the decrease of thecontact pressure due to the increase of contact area with the unchanged contact force.Meanwhile,the interpolator method eliminates the sliding friction on the surface of blank due to the stable relative position between the blank and the interpolator.
基金supported by the National Natural Science Foundation of China (51175065)
文摘Motivated by the definition of the machining errors induced by tool path planning methods, a mapping curve of the tool axis of a cylindrical cutter is constructed on the tool surface. The mapping curve is a typical one that can be used to express the closeness between the tool surface and the surface to be machined. A novel tool path planning method is proposed for flank or plunge milling ruled surfaces based on the minimization of the one-sided Hausdorff distance （HD） from the mapping curve to the surface to be machined. It is a nonlinear optimization problem in best uniform approximation （BUA） or Chebyshev sense. A mathematical programming model for computing the minimum one-sided HD is proposed. The linearization method of the programming model is provided and the final optimal solutions are obtained by simplex method. The effectiveness of the proposed BUA method is verified by two numerical examples and compared with the least squares （LS） and double point offset （DPO） methods. The variation in tool orientation induced by the optimization of the tool positions is also evaluated.
