A New Dynamics Analysis Model for Five-Axis Machining of Curved Surface Based on Dimension Reduction and Mapping

The equipment used in various fields contains an increasing number of parts with curved surfaces of increasing size.Five-axis computer numerical control(CNC)milling is the main parts machining method,while dynamics analysis has always been a research hotspot.The cutting conditions determined by the cutter axis,tool path,and workpiece geometry are complex and changeable,which has made dynamics research a major challenge.For this reason,this paper introduces the innovative idea of applying dimension reduction and mapping to the five-axis machining of curved surfaces,and proposes an efficient dynamics analysis model.To simplify the research object,the cutter position points along the tool path were discretized into inclined plane five-axis machining.The cutter dip angle and feed deflection angle were used to define the spatial position relationship in five-axis machining.These were then taken as the new base variables to construct an abstract two-dimensional space and establish the mapping relationship between the cutter position point and space point sets to further simplify the dimensions of the research object.Based on the in-cut cutting edge solved by the space limitation method,the dynamics of the inclined plane five-axis machining unit were studied,and the results were uniformly stored in the abstract space to produce a database.Finally,the prediction of the milling force and vibration state along the tool path became a data extraction process that significantly improved efficiency.Two experiments were also conducted which proved the accuracy and efficiency of the proposed dynamics analysis model.This study has great potential for the online synchronization of intelligent machining of large surfaces.

Tool wear condition monitoring method of five-axis machining center based on PSO-CNN

The effective monitoring of tool wear status in the milling process of a five-axis machining center is important for improving product quality and efficiency,so this paper proposes a CNN convolutional neural network model based on the optimization of PSO algorithm to monitor the tool wear status.Firstly,the cutting vibration signals and spindle current signals during the milling process of the five-axis machining center are collected using sensor technology,and the features related to the tool wear status are extracted in the time domain,frequency domain and time-frequency domain to form a feature sample matrix;secondly,the tool wear values corresponding to the above features are measured using an electron microscope and classified into three types:slight wear,normal wear and sharp wear to construct a target Finally,the tool wear sample data set is constructed by using multi-source information fusion technology and input to PSO-CNN model to complete the prediction of tool wear status.The results show that the proposed method can effectively predict the tool wear state with an accuracy of 98.27%;and compared with BP model,CNN model and SVM model,the accuracy indexes are improved by 9.48%,3.44%and 1.72%respectively,which indicates that the PSO-CNN model proposed in this paper has obvious advantages in the field of tool wear state identification.

Fault monitoring and diagnosis of motorized spindle in five-axis Machining Center based on CNN-SVM-PSO

A spindle fault diagnosis method based on CNN-SVM optimized by particle swarm algorithm(PSO)is proposed to address the problems of high failure rate of electric spindles of high precision CNC machine tools,while manual fault diagnosis is a tedious task and low efficiency.The model uses a convolutional neural network(CNN)model as a deep feature miner and a support vector machine(SVM)as a fault state classifier.Taking the electric spindle of a five-axis machining centre as the experimental research object,the model classifies and predicts four labelled states:normal state of the electric spindle,loose state of the rotating shaft and coupling,eccentric state of the motor air gap and damaged state of the bearing and rolling body,while introducing a particle swarm algorithm(PSO)is introduced to optimize the hyperparameters in the model to improve the prediction effect.The results show that the proposed hybrid PSO-CNN-SVM model is able to monitor and diagnose the electric spindle failure of a 5-axis machining centre with an accuracy of 99.33%.In comparison with the BP model,SVM model,CNN model and CNN-SVM model,the accuracy of the model increased by 10%,6%,4%and 2%respectively,which shows that the fault diagnosis model proposed in the paper can monitor the operation status of the electric spindle more effectively and diagnose the type of electric spindle fault,so as to improve the maintenance strategy.

Continuity control method of cutter posture vector for efficient five-axis machining

During five-axis machining of impeller, the excessive local interference avoidance leads to inconsistency of cutter posture, low quality of machined surface and increase of processing time. Therefore, in order to improve the efficiency of five-axis machining of impellers, it is necessary to minimize the cutter posture changes and create a continuous tool path while avoiding interference. By using an MC-space algorithm for interference avoidance, an MB-spline algorithm for continuous control was intended to create a five-axis machining tool path with excellent surface quality and economic feasibility. A five-axis cutting experiment was performed to verify the effectiveness of the continuity control. The result shows that the surface shape with continuous method is greatly improved, and the surface roughness is generally favorable. Consequently, the effectiveness of the suggested method is verified by identifying the improvement of efficiency of five-axis machining of an impeller in aspects of surface quality and machining time.

PLANNING METHOD OF TOOL ORIENTATION IN FIVE-AXIS NC MACHINING

The planning method of tool orientation in the five-axis NC machining is studied. The problem of the existing method is analyzed and a new method for generating the global smoothing tool orientation is proposed by introducing the key frame idea in the animation-making. According to the feature of the part, several key tool orientations are set without interference between the tool and the part. Then, these key tool orientations are inter- polated by the spline function. By mapping the surface parameter to the spline parameter, the spline function value is obtained and taken as the tool orientation when generating the CL file. The machining result shows that the proposed method realizes the global smoothing of the tool orientation and the continuity of the rotational speed and the rotational acceleration. It also avoids the shake of the machine tool and improves the machining quality.

Jerk-limited feedrate scheduling and optimization for five-axis machining using new piecewise linear programming approach

In this paper, a new computation method and an optimization algorithm are presented for feedrate scheduling of five-axis machining in compliance with both machine drive limits and process limits. Five-axis machine tool with its ability of controlling tool orientation to follow the sculptured surface contour has been widely used in modern manufacturing industry. Feedrate scheduling serving as a kernel of CNC control system plays a critical role to ensure the required machining accuracy and reliability for five-axis machining. Due to the nonlinear coupling effects of all involved drive axes and the saturation limit of servo motors, the feedrate scheduling for multi-axis machining has long been recognized and remains as a critical challenge for achieving five-axis machine tools’ full capacity and advantage. To solve the nonlinearity nature of the five-axis feedrate scheduling problems, a relaxation mathematical process is presented for relaxing both the drive motors’ physical limitations and the kinematic constraints of five-axis tool motions. Based on the primary optimization variable of feedrate, the presented method analytically linearizes the machining-related constraints, in terms of the machines’ axis velocities, axis accelerations and axis jerks. The nonlinear multi-constrained feedrate scheduling problem is transformed into a manageable linear programming problem. An optimization algorithm is presented to find the optimal feedrate scheduling solution for the five-axis machining problems. Both computer implementation and laboratorial experiment testing by actual machine cutting were conducted and presented in this paper. The experiment results demonstrate that the proposed method can effectively generate efficient feedrate scheduling for five-axis machining with constraints of the machine tool physical constraints and limits. Compared with other existing numerical methods, the proposed method is able to find an accurate analytical solution for the nonlinear constrained five-axis feedrate scheduling problems without compromising the efficiency of the machining processes.

Efficiently constructing collision-free regions of tool orientations for holder in five-axis machining of blisk

Blisks with the integral structure are key parts used in new jet engines to promote the performance of aircrafts,which also increases the complexity of tool orientation planning in the five-axis machining.It is an essential task to find the collision-free tool orientation when the tool holder is pushed deep into the channel of blisk to increase rigidity and reduce vibration.Since the radius of the holder varies with the height,the line-visibility is no longer applicable when constructing collision-free regions of tool orientation.In this paper,a method of constructing collisionfree regions without interference checking is proposed.The work of finding collision-free regions resorts to solving the local contact curves on the checking surfaces of blisk.And it further transforms into searching the locally tangent points(named critical points)between the holder and surface.Then a tracking-based algorithm is proposed to search the sample critical points on these local contact curves.And the corresponding critical vectors are also calculated synchronously.Besides,the safety allowance,discrete precision and acceptable deviation are introduced in the algorithm to ensure accuracy by controlling the angle between two adjacent critical vectors properly.After that,the searched critical vectors are mapped orderly to two-dimensional space and the collisionfree regions are constructed.This method is finally verified and compared with a referenced method.The results show that the proposed method can efficiently construct collision-free regions for holder under the given accuracy.

Spindle Thermal Error Optimization Modeling of a Five-axis Machine Tool

Aiming at the problem of low machining accu- racy and uncontrollable thermal errors of NC machine tools, spindle thermal error measurement, modeling and compensation of a two turntable five-axis machine tool are researched. Measurement experiment of heat sources and thermal errors are carried out, and GRA（grey relational analysis） method is introduced into the selection of tem- perature variables used for thermal error modeling. In order to analyze the influence of different heat sources on spindle thermal errors, an ANN （artificial neural network） model is presented, and ABC（artificial bee colony） algorithm is introduced to train the link weights of ANN, a new ABC- NN（Artificial bee colony-based neural network） modeling method is proposed and used in the prediction of spindle thermal errors. In order to test the prediction performance of ABC-NN model, an experiment system is developed, the prediction results of LSR （least squares regression）, ANN and ABC-NN are compared with the measurement results of spindle thermal errors. Experiment results show that the prediction accuracy of ABC-NN model is higher than LSR and ANN, and the residual error is smaller than 3 pm, the new modeling method is feasible. The proposed research provides instruction to compensate thermal errors and improve machining accuracy of NC machine tools.

Identification of Kinematic Errors of Five-axis Machine Tool Trunnion Axis from Finished Test Piece

Compared with the traditional non-cutting measurement,machining tests can more accurately reflect the kinematic errors of five-axis machine tools in the actual machining process for the users.However,measurement and calculation of the machining tests in the literature are quite difficult and time-consuming.A new method of the machining tests for the trunnion axis of five-axis machine tool is proposed.Firstly,a simple mathematical model of the cradle-type five-axis machine tool was established by optimizing the coordinate system settings based on robot kinematics.Then,the machining tests based on error-sensitive directions were proposed to identify the kinematic errors of the trunnion axis of cradle-type five-axis machine tool.By adopting the error-sensitive vectors in the matrix calculation,the functional relationship equations between the machining errors of the test piece in the error-sensitive directions and the kinematic errors of C-axis and A-axis of five-axis machine tool rotary table was established based on the model of the kinematic errors.According to our previous work,the kinematic errors of C-axis can be treated as the known quantities,and the kinematic errors of A-axis can be obtained from the equations.This method was tested in Mikron UCP600 vertical machining center.The machining errors in the error-sensitive directions can be obtained by CMM inspection from the finished test piece to identify the kinematic errors of five-axis machine tool trunnion axis.Experimental results demonstrated that the proposed method can reduce the complexity,cost,and the time consumed substantially,and has a wider applicability.This paper proposes a new method of the machining tests for the trunnion axis of five-axis machine tool.

High accuracy NURBS interpolation for five-axis machine of table-rotating/spindle-tilting type

In this paper, the definition of NURBS curve and a speed-controlled interpolation in which the feed rate is automatically adjusted in order to meet the specified chord error limit were discussed. Besides those, a definition of linear interpolation error of post-processed data was proposed, which should be paid more attention to because it will not only reduce quality of the surface but also may cause interference and other unexpected trouble. In order to control the error, a robust algorithm was proposed, which successfully met a desired error limit through interpolating some essential CL data. The excellence of the proposed algorithm, in terms of its reliability and self-adaptiveness, has been proved by simulation results.

Rotary axis calculation for five-axis FDM printer using a point-fitting optimization method

This paper presents an optimization method to compute the rotary axes of a 5-axis FDM printer whose A-and C-axes have large deviations relative to the x-and z-directions.The optimization model is designed according to the kinematic model in which a point rotates around a spatial line in the machine coordinate system of the printer.The model considers the A-and C-axes as two spatial lines.It is a two-object optimization model including two aspects.One is that the sum of deviations between the measured and computed points should be small;the other is that the deviations should be uniformly distributed for every measured point.A comparison of the new optimization method with conventional error-compensation methods reveals that the former has higher location accuracy.Using the optimized AC axes,5-axis 3D printing paths are planned for some complex workpieces.Data analysis and printing samples show that the optimized AC axes satisfy 5-axes FDM printing requirements for nozzles with a diameter of 1.0 mm.

A Generic Kinematic Model for Three Main Types of Five-axis Machine Tools

Material removal is one of the most used processes in manufacturing. Five-axis CNC machines are believed to be the best tools in sculptured surface machining. In this study, a generic and unified kinematic model was developed as a viable alternative to the particular solutions that are only applicable to individual machine configurations. This versatile model is then used to verify the feasibility of the two rotational joints within the kinematic chain of three main types of a five-axis machine-tool. This versatile model is very useful applied to the design of five-axis machine tools.

Tool Positioning Algorithm Based on Smooth Tool Paths for 5-axis Machining of Sculptured Surfaces

The current research of the 5-axis tool positioning algorithm mainly focuses on searching the local optimal tool position without gouging and interference at a cutter contact（CC） point,while not considering the smoothness and continuity of a whole tool path.When the surface curvature varies significantly,a local abrupt change of tool paths will happen.The abrupt change has a great influence on surface machining quality.In order to keep generated tool paths smooth and continuous,a five-axis tool positioning algorithm based on smooth tool paths is presented.Firstly,the inclination angle,the tilt angle and offset distance of the tool at a CC point are used as design variables,and the machining strip width is used as an objective function,an optimization model of a local tool positioning algorithm is thus established.Then,a vector equation of tool path is derived by using the above optimization model.By analyzing the equation,the main factors affecting the tool path quality are obtained.Finally,a new tool position optimization model is established,and the detailed process of tool position optimization is also given.An experiment is conducted to machine an aircraft turbine blade by using the proposed algorithm on a 5-axis blade grinding machine,and the machined blade surface is measured with a coordinate measuring machine（CMM）.Experimental and measured results show that the proposed algorithm can ensure tool paths are smooth and continuous,improve the tool path quality,avoid the local abrupt change of tool paths,and enhance machining quality and machining efficiency of sculptured surfaces.

Development of Virtual Simulation System for Remote Collaborative Surface Machining

Most researches about virtual machine tool are emphasized on simulations of machine motion and machining process for single machine. In this paper,a virtual simulation system for remote collaborative surface machining is developed. The motion command of machine tool is generated by an interpolator,which can derive synchronized motion commands according to feedrate. Thus,the system can estimate the machining time. For universal assembly of five-axis virtual machine tool,it is based on the D-H notation representation and machining constraints consideration. The remote collaborative virtual manufacturing system based on the CORBA technology is proposed in this paper. It demonstrated that the developed virtual machine tool can be used to verify and simulate the machining process for the collaboration of the surface design and manufacturing team.

Analytical modeling of geometric errors induced by cutter runout and tool path optimization for five-axis flank machining

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.

VARIABLE FEEDRATE INTERPOLATION OF NURBS TOOLPATH WITH GEOMETRIC AND KINEMATICAL CONSTRAINTS FOR FIVE-AXIS CNC MACHINING

Variable feedrate interpolation algorithms for five-axis parametric toolpath are very promising but still rather limited currently.In this paper,an off-line feedrate scheduling method of dual NURBS curve is presented with geometric and kinematical constraints.For a given dual parametric curve,the feedrates of sampling points are first scheduled sequent with confined feedrate of cutter tip and machine pivot,chord error,normal acceleration and angular feedrate.Then,the feedrate profiles of angular feed acceleration sensitive regions of the path are adjusted using a bi-directional scanning algorithm.After that,a linear programming method is used to adjust the feedrate profiles of linear feed acceleration sensitive regions and control the linear feed acceleration of both cutter tip and machine pivot within preset values.Further,a NURBS curve is used to fit the feedrates of sampling points.Finally,illustrative examples are carried out to validate the feasibility of the proposed feedrate scheduling method.The results show that the proposed method has the ability of effectively controlling the angular feed characters of cutter axis as well as the chord error and linear feed characters of cutter tip and machine pivot,and it has potential to be used in high accuracy and high quality five-axis machining.

A local toolpath smoothing method for a five-axis hybrid machining robot

Smooth transitions between two adjacent five-axis toolpaths can reduce feedrate fluctuation,improving machining quality and efficiency.Hybrid robots’flexibility to adjust the orientation is advantageous in five-axis machining,but their kinematic issues raise challenges for toolpath smoothing.This paper proposes a G3continuous toolpath smoothing method for a hybrid robot.B-splines in the machine coordinate system(MCS)are inserted at corners to synchronize five-axis transitions.The transition errors of the tool position and orientation paths are estimated with the golden section method.These approximation errors are constrained by adaptively modifying the B-splines,i.e.,adding anchor points and optimizing the control points.A bisection search method is proposed for these geometric modifications,guaranteeing the user-defined error tolerance limit.Compared to the method based on the workpiece coordinate system(WCS),the proposed framework generates a smoother trajectory under the same error tolerance limit.Simulations and experiments are provided to validate the effectiveness.

Tool Orientation Optimization Based on Spatial Tractrix Method for Five-Axis CNC Machining with Ball End Cutters

When milling part surfaces with a ball-end tool in 5-axis CNC machining,maintaining a constant cutting speed by keeping a fixed inclination angle between the tool axis and surface normal is crucial to ensure safe operation and achieve high quality of the machined surface.Under this constraint,the variation of tool orientation is expected to be“smoothest possible”to reduce the angular speed of the rotary axes for the efficient and robust machining.To address this issue,the spatial tractrix which is the extension of classic tractrix is presented to establish the geometry model of the tool orientation kinematics in the part coordinate system.The proposed model describes the relations between the tilt angle and the variation of ball-end tool orientation.Two spatial tractrix-based methods,synchronizing tractrix-based method and equilibrating tractrix-based method,are developed to minimize the variation of tool orientation by controlling the variation of tilt angle.These methods are used to plan the tool orientation on a part surface modeled by a bicubic spline surface.The performance evaluation carried by intense simulations demonstrates the equilibrating tractrix-based method provide the best results in most cases compared with the existing differential geometry-based methods such as the tractrix-based method and parallel transport method.The synchronizing tractrix-based method works well in some special cases.

Wholly smoothing cutter orientations for five-axis NC machining based on cutter contact point mesh

Cutting forces with respect to different cutter orientations are analyzed for five-axis NC machining of a ball-end cutter.A measure is then defined to quantify the effects of cutter orientation variation.According to the measure,a novel model and algorithm are proposed to wholly optimize cutter orientations based on a cutter contact(CC) point mesh.The method has two advantages.One is that the cutter orientation smoothnesses along the feed direction and pick-feed direction are both wholly optimized.The other is that only the accessibility cones of mesh points are required to compute and the computation efficiency is improved.These advantages are shown by simulating the machining efficiency,the stability of feed velocities and the smoothness of cutting force.A computational example and a cutting experiment are finally given to illustrate the validity of the proposed method.

Third-order point contact approach for five-axis sculptured surface machining using non-ball-end tools (Ⅰ): Third-order approximation of tool envelope surface

In this paper, the geometric properties of a pair of line contact surfaces are investigated. Then, based on the observation that the cutter envelope surface contacts with the cutter surface and design surface along the characteristic curve and cutter contact (CC) path, respectively, a mathematical model describing the third-order approximation of the cutter envelope surface according to just one given cutter location (CL) is developed. It is shown that at the CC point both the normal curvature of the normal section of the cutter envelope surface and its derivative with respect to the arc length of the normal section can be determined by those of the cutter surface and design surface. This model characterizes the intrinsic relationship among the cutter surface, cutter envelope surface and design surface in the neighborhood of the CC point, and yields the mathematical foundation for optimally approximating the cutter envelope surface to the design surface by adjusting the cutter location.