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When planning tool orientations for 5-axis machining from the perspective of kinematics, existing works often tend to optimize the angular velocity or acceleration of the rotary axes rather than the angular jerk due to its calculation sensitivity to discretization variations, though the jerk is fundamentally tied to the tracking errors and residual vibrations of the actuators. In this paper, a study is reported on how to optimize the angular jerk of the rotary axes while comprehensively considering the kinematic constraints, thus achieving a jerk-optimal tool orientation along the tool path, with driving capacity of the rotary axes respected. In this method, the displacements of the rotary axes are continuously represented by two quintic B-spline curves, and then the angular velocity, acceleration, and jerk of the rotary axes, which are the derivatives of the displacements, can be succinctly represented as a B-spline curve. Taking advantage of the convex hull property of B-spline curve, the linear analytical representations of the kinematic constraints of the rotary axes can be successfully derived in form of control coefficient combinations. To prevent the machining interference at the same time, a greedy strategy that incorporates a process of alternately smoothing tool orientation and checking machining interference is employed. Then, the smooth displacement splines of the rotary axes can be obtained by solving a constructed quadratic programming (QP) model that minimizes the angular jerk along the tool path, while satisfying kinematic constraints and without machining interference. Moreover, to generate efficiently tool orientations for long tool paths, a piecewise planning strategy that optimizes the tool orientation from coarse to fine is developed. Finally, the conducted experiments validate the proposed method.

Gear drive is a common and efficient way to transfer power and motion. To ensure the machining accuracy of gears, the tooth flanks are formed by profile grinding technology in some cases. In the profile grinding process, the calculation of wheels using the information of gears named as the forward-calculation process and obtaining gears based on wheels (the backward-calculation process) traditionally adopt numerical ways. It is always time consuming and large code quantity. To conquer these drawbacks, this article presents an analytical method using the envelope theory to compute the contacting curves that are the basis of getting tooth flanks or wheels in the forward- or the backward-calculation process. For the forward-calculation process, the tooth flank is expressed in the form of an extended straight-line surface that can be taken as the generating line moving along the helix curve. The normal vector for an arbitrary point on the generating line is the same. By using this characteristic, the contacting curve can be explicitly gained as the function of only one parameter. Similarly, in the backward-calculation process, the formed wheel is expressed by a cross section rotating about its axis. For this type of surface, the guide curve is a circle, and the normal vectors of points on the guideline insect with the axis at the same point. Taking advantage of this principle, the contacting curve can be analytically expressed by only one unknown parameter. To verify the validity of the proposed method, some examples and comparative experiments are performed. The results show that the presented method is correct. When compared with the classical numerical way, the time span for the proposed method is 15 times less than that for the numerical way. When compared with the practical grinding wheel and the practical gear, the maximum errors are 0.18 mm and 0.0099 mm, respectively. The proposed method can be served as one of the universal ways to generate formed wheels or involute gears in the profile grinding process.

It is very prone to cause large-amplitude cutting vibrations, or even regenerative chatter, when milling thin-walled workpiece due to its low dynamic stiffness. The utilization of fixture support is one of the most effective measures to mitigate vibrations and improve stability limits, which has gained more and more attention. However, the dynamics model of the tool-workpiece-fixture system and the influence of fixture support force have not been fully developed. In this paper, a pneumatic fixture is designed and used to exert controllable support force on the thin-walled workpiece by precisely tunning the air pressure. The position-dependent modal parameters of the thin-walled workpiece under different fixture support forces are identified by combining experimental modal test and finite element analysis. The milling dynamics is then modeled into a delay differential equation with position-dependent coefficients. On this basis, the three-dimensional stability lobe diagrams (SLDs) are obtained in the parameter space of tool path, spindle speed, and axial depth of cut. Both stable and chatter cutting tests are performed to verify the predicted SLDs, and the cutting signals under different fixture support forces are compared in detail. Experimental results reveal that the proposed model can accurately predict the chatter stability of thin-walled workpiece with fixture support, and the stability limit can be successfully improved by tunning the support force. Some important conclusions on the influence of fixture support forces are also drawn based on detailed simulation and experimental analyses.

G01 blocks are the widespread format of toolpath in computer numerical controlled (CNC) machining. For achieving smooth motion and eliminating the geometrical discontinuity at the block transitions, various local corner smoothing methods have been developed. However, in these methods, the loss of featured information of parts is inevitable. Focused on this topic, this article proposes a new analytical G2 continuous corner smoothing method with G01 shape preserving for five-axis linear toolpath by locally inserting specially designed B-splines into the corners of consecutive segments. First, by analyzing the condition of G01 shape preserving, the configuration expression of control points for B-splines is yielded for passing through G01 point. On this basis, the tool tip position is smoothed by symmetrical B-splines with minimum curvature in the workpiece coordinate system (WCS). Then, another asymmetrical B-splines is used to smooth tool orientation in the machine coordinate system (MCS). After that, the satisfaction conditions of parametric synchronization between tool tip position and tool orientation are mathematically derived at junctions, while the corresponding maximum smoothing errors are also constrained in WCS. Compared with the existing methods, not only the tool tip points and orientation vectors specified in original G01 blocks are preserved but also the optimal control points considering the curvature of smooth splines can be obtained analytically. Finally, simulations and experiments are performed to validate the effectiveness of the developed method.

The iso-scallop method has been long adopted to achieve a shorter overall machining length. The efficiency and machining performance of this method are largely dominated by the initial tool path. The preferred direction field supplies the local best feed directions. Usually, the offset paths generated by the iso-scallop method largely deviate from the preferred directions, even though the initial path is strictly along the preferred directions. The matching degree of the offset paths and preferred direction field should be taken into consideration when selecting an initial tool path. This paper presents a novel initial path selection method for the iso-scallop method to make whole iso-scallop tool paths and the preferred direction field consistent as much as possible. A surface is re-parameterized to keep the conformality between the surface and parametric domain, which leads to the more regular offset paths on the new parametric domain. By fitting the vector field, streamlines are generated for representing the preferred feed direction on the parametric domain. The offset similarity metric defined by the initial path and streamlines is constructed to measure the matching degree between offset paths and preferred feed directions. Then the feasible path with the best offset similarity for the streamlines will be selected as the initial tool path. In our case study, feed directions with the maximum strip width are chosen. The test results have shown that the tool paths generated by the proposed method achieved a better matching for the selected feed directions and a shorter overall length compared with some existing tool path generation methods.

In this paper, a new generalized parametric interpolation method is proposed for optimized five-axis machining with the consideration of both the machine contour errors and the feedrate fluctuation elimination. An analytic processing is presented for linearization of contour errors with respect to feedrate limit. For machine configuration, explicit analytical modeling of the contour error and the tracking error with respect to feedrate is presented; thus, the error constraint problem is nicely converted to a kinematic constraint problem. On this basis, an accurate feedrate upper limit with confined contour errors is further determined by using a shifted Frenet frame with linear computational complexity. With the consideration of both the motion smoothness and machining efficiency, a time-based optimization algorithm is proposed for time-optimal feedrate scheduling. For eliminating the feedrate fluctuation, a new real-time interpolation algorithm is developed for free derivation between the path parameter and the arc length for smoothed five-axis tool path generation. Laboratory testing experiments were conducted for validation and were presented in the paper. And the experimental results indicate that the proposed feedrate interpolation method is capable of confining both the tool tip contour error and tool orientation contour error simultaneously, as well as maintaining a satisfactory interpolation performance in both computation efficiency and accuracy. The presented methods can be used for five-axis machining and the feedrate optimization of complex part machining.

Regenerative chatter is a pivotal obstacle for achieving required machining quality and efficiency in turning operations, especially when turning of low-stiffness parts. Accurate prediction of chatter stability prior to actual machining is of great significance for the judgment on feasibility and the optimization selection of cutting parameters that are free of chatter. To this end, this paper presents a comprehensive study which allows accurately predicting the chatter stability in turning of low-stiffness parts made of pure iron. The dynamic model for a double-flexible turning system with the regenerative effect is established in orthogonal directions on the basis of a nonlinear turning force model with accurately calibrated nonlinear force coefficients. In the nonlinear turning force model, both shearing and edge effects are considered, in which shearing force components are formulated as the exponential functions of the instantaneous uncut chip thickness to reflect the size effect. In addition, the geometric feature of the tool nose radius is also taken into account by precisely discretizing the instantaneous uncut chip area. The chatter stability of the resulting system is further predicted by an extended second-order semi-discretization method (2nd SDM). To verify the proposed method, a series of cutting tests are conducted on a CNC lathe, and experimental results indicate that proposed method can achieve an accurate prediction of chatter stability in turning of low-stiffness pure iron parts.

The onset of chatter is extremely disadvantageous to machining process, which will induce poor surface quality, low processing efficiency and severe tool wear, especially in the milling of weakly rigid thin-walled workpieces, so it should be detected as early as possible to avoid further damage. To handle this issue, a multi-synchrosqueezing transform (MSST) based early chatter detection method as well as a novel feature selection algorithm is proposed in this paper to monitor the occurrence of chatter in thin-walled parts machining. MSST is firstly conducted on the sampled vibration signal to generate a time–frequency (TF) representation. The periodic components associated with spindle rotation are removed from the TF matrix and the chatter-related signal is recovered by multi-ridge detection. Then, features in time and frequency domains are extracted from the reconstructed chatter signal. A feature selection algorithm combining multi-feature distance evaluation technique (MFDET) and distance correlation analysis is subsequently presented to determine the optimal feature subset. Compared with other chatter indicators given in existing works, the selected compact feature set is more discriminative and has low redundancy. Furthermore, random forest (RF) is utilized to intelligently diagnose the machining stability. Several experiments under constant and variable conditions are performed to evaluate the performance of the proposed method in terms of early chatter detection. The experimental results demonstrate that the presented chatter monitoring method is highly efficient and robust, which can recognize the chatter onset timely and accurately for thin-walled parts milling under different machining conditions.

In order to meet the growing industrial demand of high quality and high efficiency machining, long cutters with larger axial depth of cut are extensively implemented in peripheral milling of deep pockets, grooves, and thin-wall parts. However, due to their high flexibilities, chatter easily occurs during the machining process. It has been demonstrated that milling cutters with variable pitch and/or variable helix angles can mitigate the chatter, which are gaining increasingly important applications. Although this kind of cutters have been studied in some detail in previous research, few studies have focused on the interaction dynamics complicated by actual cutter runout in long tool-part contact zone. This paper systematically studies the dynamics and stability of variable-pitch/helix milling system with long end cutters. The cutters are divided into a series of axial disks, and each axial disk includes several cutting elements which are equal to the number of teeth. Variations of pitch and helix angles, cutter run-outs including radial offset and axial tilt, and mode shapes with the cross terms in the orthogonal direction, are assigned to these cutting elements. The system, involving multiple regenerative delays as well as the axially varying dynamics, is formulated as a matrix form of time-periodic delay differential equation with multi-modal dynamic parameters. An updated cross-axis and cross-point modal testing method is then proposed to obtain the dynamic parameters, which can effectively avoid multiple hits when impacting the cutter with hammer. The stability lobes are predicted in state space by developing an improved semi-discretization method, by which the pitch variations and actual runout effects on stability are investigated. It is shown that the stability lobes differ significantly when the combined effects of cross-axis and cross-point FRFs and actual cutter runout are considered. A series of cutting experiments is conducted to demonstrate the proposed model and method. Results show that these lobes well agree with the experimental results.

Optogenetics is emerging as an ideal method for controlling cellular activity. It overcomes some notable shortcomings of conventional methods in the elucidation of neural circuits, promotion of neuroregeneration, prevention of cell death and treatment of neurological disorders, although it is not without its own limitations. In this review, we narratively review the latest research on the improvement and existing challenges of optogenetics, with a particular focus on the field of brain injury, aiming at advancing optogenetics in the study of brain injury and collating the issues that remain. Finally, we review the most current examples of research, applying photostimulation in clinical treatment, and we explore the future prospects of these technologies.

Surface profile is one of the foremost aspects to evaluate milling performance. Its generation mechanism is affected by a variety of factors such as tool geometry, runout values, and process parameters and thus still deserves further investigation. This paper aims to propose a unified method to study the surface generation mechanism and to predict the machining quality for variable pitch tools considering runout. First, a Floquet theory based algorithm is extended to analyze the machining stability and output the dynamic responses of the machining system. The resultant trajectories of cutting edges are obtained by kinematic synthesis of system vibrations, tool rotations, and machining feed. Next, both the surface location error (SLE) and the surface roughness are simultaneously extracted from the edge trajectories. A series of cutting tests are performed to validate the prediction results. Some new characteristics of the machined surface profile in terms of form errors and teeth marks are discovered and theoretically explained. Finally, the joint influences of tool geometry, runout values, and process parameters on the surface generation mechanism and quality are analyzed in detail with the proposed method.

Reduction of contour error is crucial for multi-axis computer numerical control (CNC) machining to produce products with required geometric and dimensional accuracy. Although various contour error pre-compensation methods have been developed, few studies are dedicated to five-axis machines when compared with three-axis ones. In this paper, a new contour error pre-compensation method that integrates analytical prediction of contour error, optimal path-reshaping model, and decoupling solution algorithm is proposed for five-axis machining. First, by analyzing the dynamic responses of servo drive to the typical step and ramp signals, linear expression of servo tracking error with respect to the sequence of discrete axis positions is yielded for the prediction of contour error ahead of servo loops. Then, using the Taylor-series expansion and the pseudo-inverse matrix of the Jacobian function, a least-square optimization-based path-reshaping model that implies the satisfaction condition of zero contour error is analytically built. Thus, the complicated nonlinear contour error pre-compensation problem is converted into a simple quadratic programming problem. Concerning the effects of tool orientation reshaping on tool-tip contouring accuracy, a simple yet effective synchronous compensation strategy is subsequently proposed, through which both tool tip and tool orientation contour errors are reduced to near-zero without any iteration. To address the neighbor-dependence of the contour error compensation in adjacent cutter locations, a progressive solution algorithm with linear computational complexity is also briefly presented. Both numerical simulations and laboratorial experiments are conducted to validate the effectiveness of the proposed method.

The feedrate scheduling of parametric interpolator is one of the most important factors for a high-performance CNC machining, since it directly concerns the machining efficiency, machining accuracy, and cutting stability. In this paper, an adaptive feedrate scheduling method with limited contour error and axis jerks is proposed for free-form contour machining based on a strategy of moving knot sequence. The analytical relations between dynamic contour error and feedrate are first derived explicitly, and then the formula of maximum feedrate limit under confined contour error and axis jerks is yielded using a numerical decoupling scheme. Consequently, the maximum feedrate limit satisfying the above constraints is obtained for each predefined parametric segment of the tool path. Further, a bidirectional scanning algorithm is employed to globally adjust the local minimum feedrate values of all feedrate segments. On the basis of feedrate segments with local minimum value and maximum recommendation value, an exact knot sequence configuration method for the B-spline curve, which is used to express the initial feedrate profile, is proposed. Finally, a simple feedrate relaxation algorithm is performed to generate the final feedrate profile with entirely limited contour and axis jerks by utilizing a strategy of moving knot sequence. The proposed feedrate scheduling method is validated by several typical experimental tests, and the results demonstrate the effectiveness and reliability of the proposed method.

This paper presents a new Planar Least-Squares Projection (PLSP) method to accurately construct the layered contours directly from the point cloud for additive manufacturing. With the rapid development of 3D measuring technology, the dense and accurate point cloud, which can represent more accurate geometry information of a physical object than before, has been readily available. Additive manufacturing based directly on such point cloud is considered to be a promising alternative for fabricating the complex parts, but it requires the research on effective processing methods of the point set surface. In this paper, the presented PLSP method addresses this technical challenge for additive manufacturing. Mathematical modeling and processing of point cloud are presented to identify projections and construct accurate layered contours by considering both the least-square projection errors and projection distance selection criteria from measured point cloud. Technique of assigning new set of weights on measure scattered point cloud is discussed to achieve accurate layered contour development. The presented PLSP method with the new weight function and the consideration of point cloud deviation distances in sliced contour development is able to avoid the occurrence of the wrong projection that many other current methods suffer from. Technique of integrating the presented PLSP with the boundary point sequence curve (PSC) method is also discussed in this paper to eliminate contour development errors by considering the similarity in shape and closeness in distance for the ideal layered contours. Since this presented method does not involve the non- linear optimization, it is mathematically robust, and it can ensure the constructed layered contours lie accurately on the underlying nominal surface, and also has the ability of recognizing and processing the multi-contours on a common slicing plane. Both computational and experimental results based on the presented method are presented for validation.

The vector field based tool path method can conveniently generate the desired tool paths according to the preferred feed directions which reflect the machining intent of the designers at CC (cutter contact) points, thus recently, it has become the focus of interests. But, the current methods are still limited to the single surface machining. When machining the compound surface patch by patch, it has to plan additional tool path to machine the blending areas of the adjacent patches, and more importantly, the solutions of the key issue, i.e. tool path construction over the vector field, are still heuristic due to the high computational complexity. To solve the problems, this paper develops a unified method of generating tool paths based on multiple vector fields for CNC machining of the compound NURBS surfaces. In this method, the preferred feed directions on the surfaces are mapped into the corresponding parameter domains, and for the vector field on each parameter domain, a stream function which is a polynomial with B-spline basis is reconstructed to represent the vector field and is used to produce the streamlines along these preferred feed directions. A novel algorithm is subsequently proposed to blend the vector fields in the adjacent parameter domains with G 1 continuity. Meanwhile, to guarantee the tool path, obtained by reversely mapping the streamline onto the surface, be smooth, continuous and no unappealing visual artifact left at the blending area of two adjacent patches, the condition maintaining G 1 continuity of the vector fields between the adjacent patches is also given, avoiding planning additional tool paths to machine the blending areas. Further, to make our method be implemented easily in CAD/CAM systems, a specific implementation process is also briefly presented. Finally, three examples are given to demonstrate the validity of the proposed method.

Linear segments are widely used to describe the tool path in five-axis NC machining. However, the geometrical discontinuity of adjacent segments will inevitably result in the feedrate fluctuation and excessive acceleration, thus deteriorating the machining accuracy and machining quality. In this paper, a new circumscribed corner rounding method for a five-axis linear tool path is proposed based on double cubic B-splines. Compared with commonly used inscribed corner rounding method, the transition curves generated by the circumscribed method have smaller curvatures, which is benefit of improving the feedrate of the corner regions of the tool path. A configuration of control points for the circumscribed corner transition spline is first given, and double cubic B-splines are subsequently employed to smooth the trajectories of the tool tip point and the second point on the tool axis according to the maximum approximation error. Then, based on the parametric synchronization between the bottom and top B-splines, the first and second geometrical derivative continuous conditions of the tool orientation are derived at the junctions between the remaining linear tool path and the transition curves. The proposed corner rounding method is capable of achieving tool orientation continuous change without any iteration, which can be used in a high-efficiency way. Simulations are performed to show the feasibility and efficiency of the proposed method.

The parts, in automotive, aerospace, die/mold industry, which have extremely high demands on the quality and integrity of the surface, are usually milled by CNC machine tools. In order to obtain the desirable surface quality, it is an effective way to choose the appropriate cutting parameters before machining by simulating the surface topography formed in the milling process. To do so, this paper develops a model based on the swept surface of the cutting edge and N-buffer model for predicting the surface topography and studies the effect of various cutting parameters. In this developed model, the mathematical equation of the cutting edge is first given, and then based on the relative motion between the cutter and the workpiece, the swept surface of the cutting edge along the tool path is accurately analyzed and modeled from the perspective of kinematics, which is used to describe realistically the cutting interaction between the cutter and the workpiece. Subsequently, the milling process is simulated by an improved N-buffer model by means of the proposed accurate interpolation method for calculating the cusp height. This procedure presents the advantage of not requiring any numerical iteration or approximation to gain the cusp height of any point on workpiece. On basis of the model, the effect of the cutting parameters such as spindle speed, feedrate, inclination angle, path interval, and cutter runout is investigated. Finally, the real machining experiments are performed and compared with the predicted results. The simulated surface topography shows a good agreement with the experimental one. This demonstrates that the developed model can predict accurately the surface topography and also provide the great potential for the surface quality control and the cutting parameter selection in actual production.

In advanced manufacturing, tool point frequency response function (FRF) is the most extensive requirement in avoiding the unstable condition of a machine tool, especially in generating a stability lobe diagram which is widely used in predicting the milling stability for chatter avoidance. However, compared with the analytical method that uses a Euler-Bernoulli beam model for calculating the tool point FRF, the analysis based on a Timoshenko beam model mathematically or analytically is seldom provided. Experimental validation is also not sufficient. In this paper, an approach of tool point frequency response prediction based on Timoshenko beam model is presented, using receptance coupling substructure analysis. This approach employs the combination of experimental result and numerical beam analysis. The proposed receptance calculate theory allows to better estimate the matrix of receptance related to rotation. Based on this theory, an unknown tool point FRF can be predicted by an already known tool point FRF. In the meantime, no additional experiment is required after a single experiment to compute tool holder frequency response. Prediction method has been verified by experiments. The results show the effectiveness and reliability of the proposed method in tool point frequency prediction and effective manufacturing.

Due to the high computational accuracy and good applicability with a low complexity of algorithm, semi-discretization method has a significant application for predicting milling stability, but to some extent it has some limitations in computational efficiency. Based on the Newton interpolation polynomial and an improved precise time-integration (PTI) algorithm, a second-order semi-discretization method for efficiently and accurately predicting the stability of the milling process is proposed. In the method, the milling dynamic system considering the regenerative effect is first approximated by a time-periodic delayed-differential equation (DDE) and then reformulated in state-space form. After discretizing the time period into a finite number of time intervals, the equation is integrated on each discrete time interval. In order to improve the approximation accuracy of the time-delay item, a second-order Newton interpolation polynomial is utilized instead of a linear function used in the original first-order semi-discretization method (SDM). Next, with a rapid matrix computation technique, an improved precise time-integration algorithm is employed to calculate the resulting exponential matrices efficiently. Finally, transition matrix of the system is constructed over the discretization period and the milling stability boundary is determined by Floquet theory. Compared with the typical discretization methods, the proposed method indicates a faster convergence rate. Further, two benchmark examples are given to validate the effectiveness of the proposed method from the aspects of computational efficiency and accuracy.

Pre-compensation of contour errors is an effective method for predicting and compensating contour errors to position command; however, some challenges remain, such as modeling and precise control strategies specifically for contour errors. This paper presents an improved method for pre-compensation of contour error through a novel adaptive cross-coupled prediction compensation controller (ACPCC), in order to enhance robustness and the capacity to resist disturbance. Its central structure is constituted by a fuzzy PID controller, in which the bottom width of membership functions is optimized by improved particle swarm optimization. Estimation of tracking error and contour error is based on the servo system parameters and error-modeling, respectively, and contour error is regulated by the ACPCC and decoupled to each axis to modify reference commands ahead of sending them to the machine tool. Simulations and experiments are performed on a three-axis machine tool to validate effectiveness. The results demonstrate that the proposed method can significantly reduce tracking error and contour error compared with other control schemes.

Smooth continuous spiral tool paths are preferable for computer numerical control (CNC) machining due to their good kinematic and dynamic characteristics. This paper presents a new method to generate spiral tool paths for the direct three-axis CNC machining of the measured cloud of point. In the proposed method, inspired by the Archimedean spiral passing through the radial lines in a circle, 3D radial curves on the cloud of point are introduced, and how to construct the radial curves on the complex cloud of point is discussed in detail and then a practical and effective radial curve construction method of integrating boundary extraction, region triangulation, mesh mapping, and point projection is proposed. On the basis of the radial curves, the spiral tool path can be generated nicely by interpolating the radial curves using a spiral curve. Besides, the method of identifying and eliminating the overcuts and undercuts in the spiral tool path resulting from the interpolation error is also presented for good surface quality. Finally, several examples are given to validate the proposed method and to show its potential in practical applications when quality parametric models and mesh models are not available.

When a cutter traverses a region local to the singularity in 5-axis machining, the stability of machine tool motion may be violated and inevitably lead to a reduction in machining quality and accuracy. In this paper, the underlying cause of the singular machine behaviors is first investigated by differentiating tool path motions, on the basis of the tool path motion expressions in part and machine coordinate systems. A further investigation indicates abrupt kinematic changes to be inevitable when the rotary axes approach a singularity. To eliminate such possible singular risks in 5-axis machining, a local tool path modification method is proposed by adjusting the two rotary axes out of a singular configuration. The critical kinematics smoothing and the consequent gouging concerns resulting from reorientation are comprehensively incorporated in the process of singularity avoidance, by means of a novel tool orientation optimization model. Specifically, the algorithm starts with the determination of an appropriate adjustment range in a simple yet effective manner, and then the primary rotary axis is adjusted in a constrained region away from zero, so as to avoid singularity. After that, the second rotary axis is accordingly adjusted, with no gouging requirements being violated. In this way, singularity problems in 5-axis machining are solved, and both the machine axes kinematics and surface gouging errors are under control. Machining simulation and laboratory experiments were conducted to validate the effectiveness of the proposed method.

For 5-axis ball-end machining, it is desired to maintain the expected cutting performance of tool orientation when adjusting tool orientation for improving the motions of rotary axes of 5-axis machine. For this purpose, a cutting performance maintained (CPM) method is proposed to adjust the tool orientations, the objective of which is to minimize the sum of the absolute deviations between the initial and adjusted coordinates of the rotary axes while improving the kinematics performance of the rotary axes and ensuring no machining interferences. In order to speed up the solving of the optimization objective, the analytical linear representations for the drive limits of rotary axes and especially irregular geometry feasible domains (GFDs) of tool orientations are first discussed in detail. The nonlinearity of the objective function is then eliminated by introducing two new auxiliary variables for further simplifying the computation of optimal tool orientation. After rewriting the drive limits and GFD constraints with the two auxiliary variables, the linear objective function can be efficiently solved by the simple linear programming method. The tool orientations adjusted by the proposed CPM method can not only improve the interference-free motions of the rotary axes, but also can maintain the expected cutting performance. Finally, the computer simulation and real milling were conducted to validate the proposed method.

NC machining of a nonzero genus triangular mesh surface is being more widely confronted than before in the manufacturing field. At present, due to the complexity of geometry computation related to tool path generation, only one path pattern of iso-planar type is adopted in real machining of such surface. To improve significantly 5-axis machining of the nonzero genus mesh surface, it is necessary to develop a more efficient and robust tool path generation method. In this paper, a new method of generating spiral or contour-parallel tool path is proposed, which is inspired by the cylindrical helix or circle which are a set of parallel lines on the rectangular region obtained by unwrapping the cylinder. According to this idea, the effective data structure and algorithm are first designed to transform a nonzero genus surface into a genus-0 surface such that the conformal map method can be used to build the bidirectional mapping between the genus-0 surface and the rectangular region. In this rectangular region, the issues of spiral or contour-parallel tool path generation fall into the category of simple straight path planning. Accordingly, the formula for calculating the parameter increment for the guide line is derived by the difference scheme on the mesh surface and an accuracy improvement method is proposed based on the edge curve interpolation for determining the cutter contact (CC) point. These guarantee that the generated tool path can meet nicely the machining requirement. To improve further the kinematic and dynamic performance of 5-axis machine tool, a method for optimizing tool orientation is also preliminarily investigated. Finally, the experiments are performed to demonstrate the proposed method and show that it can generate nicely the spiral tool path or contour-parallel tool path on the nonzero genus mesh surface and also can guarantee the smooth change of tool orientation. A new method of generating spiral or contour-parallel tool paths on the nonzero genus mesh surface is proposed.The analytical formulas of computing CC points and parameter increment for path interval are derived.A simple and efficient method of optimizing tool orientation is also preliminarily investigated.

Reduction of contour error plays an important role in improving the machining accuracy. However, as an important means, the feedrate planning mainly focuses on confining the chord error and drive constraints in CNC machining, without taking into account the contour error. To ensure the contour machining accuracy for a given parameter curve and simultaneously release the computational burden in real-time interpolation, this paper proposes an new off-line feedrate planning method constrained by the contour error, axis accelerations, and jerks, as well as the chord error. First, a contour error model is built based on a high-order transfer function, from which the feedrate can be scheduled in the contour error violated zones of tool path. Then, the initial feedrate profile is constructed with confined contour error and chord error using a method based on the direct deformation of target curve. In order to further guarantee the drive performances, an iterative proportional adjustment algorithm is used to update the positions of feedrate sampled from the axis accelerations/jerks violated zones of the path curve, and in each adjustment, a curve evolution strategy is utilized to deform the target feedrate profile to the updated positions without using the re-interpolation of entire feedrate profile. Only through several rounds of iterative operation, the final feedrate profile will be achieved without violated constraints. Finally, simulations are performed on two NURBS curves to validate the proposed method. The results demonstrate the effectiveness and feasibility of the proposed method.

The surface integrity of a titanium workpiece is closely related to its surface quality and performance. In order to improve the surface integrity, low plasticity burnishing is adopted. In this study, the effects of burnishing pressure (5–20 Mpa), speed (50–600 mm/min) and feed rate (0.05–0.5 mm) on the surface integrity are studied by single factor experiments. Four aspects of the surface integrity are investigated, namely surface roughness, surface microhardness, surface residual stresses, and surface topography. The results show that increasing the burnishing pressure or number of passes can improve the surface microhardness and the residual stress. However, increasing the burnishing pressure or number of passes contributes to reducing the surface roughness. Increasing the feed rate also leads to an increase in the surface roughness. Decreasing the burnishing speed is beneficial for increasing the surface residual stress. The analysis results of power spectral density profiles reveal that the burnishing pressure and feed rate are the dominant factors on the surface topography of the burnished workpieces. The surface residual stress changes from −67.7 Mpa to −400.5 Mpa after the burnishing process. The surface roughness reaches the minimum value of 0.057 μm at the feed rate of 0.05 mm. There is nearly a 36 % increase in the surface microhardness as compared to that of the unburnished workpiece. It shows that low plasticity burnishing can efficiently improve the surface integrity of a titanium workpiece.

Rolling burnishing is an effective method to improve the surface integrity of the machined part. It not only increases the hardness of the machined surface but also reduces the surface roughness. In this paper, experimental studies are performed to investigate the influence of roller burnishing parameters (i.e., spindle speed, burnishing depth, and burnishing feed) on the surface roughness and microhardness of TA2 alloy. The aim is to model the relations between some relevant process parameters and the surface performances of surface roughness and microhardness after roller burnishing, which can give an optimum combination of process parameters to produce desired surface roughness and microhardness. To achieve this goal, by utilizing response surface methodology and Box-Behnken experimental design techniques, workable empirical models are developed to predict surface roughness and microhardness. Analysis of variance is applied to investigate the relationship between process parameters and the output responses. The validation tests are performed to evaluate the effectiveness of the model and the response surface optimization techniques. The results indicate that the prediction values of surface roughness and microhardness have good agreement with the experimental ones. Among the process parameters, the spindle speed and burnishing depth are the significant parameters for reducing the surface roughness and raising the surface microhardness. Meanwhile, the experimental results also indicate that the roller burnishing process can obviously enhance the surface performances, which can lead to the reduction of surface roughness by 63 % and the increase of microhardness by 28 % compared to pre-machined surfaces.

Stability analysis is essential for milling operations to enable high machining productivities without sacrificing surface quality and introducing significant surface errors. Its exact implementation depends on the dynamics modeling with reliable requirement of system’s dynamic parameters. However, existing modal testing strategies neglect the cross-axis mode coupling effect along the multi-point-contact zone between the tool and workpiece. This leads to some losses of accuracy for the dynamic parameters and further makes the dynamic model fail to reflect the real tool-workpiece interaction mechanism. Aiming at improving the model accuracy, a novel modal testing strategy is proposed, which takes both the cross-axis and cross-point mode coupling effects into account in identifying the dynamic parameters. Meanwhile, new parameter identification technique is theoretically given when processing measured direct, cross-axis and cross-point frequency response functions. And matrix assembly technique is also presented for matching the identified dynamic parameters to the system dynamic equation. On the other hand, instead of single-point-contact dynamics assumed at the tool tip, a dynamic model with multi-point-contact dynamics is developed for a common multi-delay milling system, where run-out effect is included for calculating multiple regenerative dynamic cutting forces. The resulting multi-delay system dynamic equation is then solved by an improved semi-discretization method. To validate the developed model with the dynamic parameters obtained by the proposed modal testing strategy, down and up milling experiments are carried out, and two cutters with different diameter are employed in the experiments. The results show that the proposed approach significantly improves the stability prediction accuracy of a milling system especially involving a big axial depth of cut.

This paper presents a new vector-field-based streamline smoothing method in the parametric space and a tool orientation optimization technique for five-axis machining of complex compound surfaces with torus-end cutters. Iso-planar tool path is widely used in the machining of various types of surfaces, especially for the compound surface with multiple patches, but the operations of intersecting the compound surface with a series of planes have depended considerably on the complicated optimization methods. Instead of intersecting the surface directly with planes, a novel and effective tool path smoothing method is presented, based on the iso-planar feed vector fields, for five-axis milling of a compound surface with torus-end cutters. The iso-planar feed vector field in the parametric domain is first constructed in the form of stream function that is used to generate the candidate streamlines for tool path generation. Then, a G1 blending algorithm is proposed to blend the vector fields within the adjacent parametric domains to ensure smooth transition of cross-border streamlines. Based on the smoothened streamlines in the parametric domains, pathlines along with their correspondent side sizes are selected as desirable tool paths. Concerning a high performance machining, detailed computational techniques to determine the tool axis orientation are also presented to ensure, at each cutter contact (CC) point, the torus-end cutter touches the part surface closely without gouging. Both the computational results and machined examples are demonstrated for verification and validation of the proposed methods.

This paper presents a new spiral smoothing method to generate smooth curved tool paths directly on mesh surfaces. Spiral tool paths are preferable for computer numerical control (CNC) milling, especially for high-speed machining. At present, most spiral tool path generation methods aim mainly for pocketing, and a few methods for machining complex surface also suffer from some inherent problems, such as selection of projecting direction, preprocessing of complex offset contours, easily affected by the mesh or mesh deformation. To address the limitations, a new spiral tool path method is proposed, in which the radial curves play a key role as the guiding curves for spiral tool path generation. The radial curve is defined as one on the mesh surface that connects smoothly one point on the mesh surface and its boundary. To reduce the complexity of constructing the radial curves directly on the mesh surface, the mesh surface is first mapped onto a circular region. In this region, the radial lines, starting from the center, are planned and then mapped inversely onto the mesh surface, thereby forming the desired radial curves. By traversing these radial curves using the proposed linear interpolation method, a polyline spiral is generated, and then, the unfavorable overcuts and undercuts are identified and eliminated by supplementing additional spiral points. Spline-based technique of rounding the corners is also discussed to smooth the polyline spiral, thereby obtaining a smooth continuous spiral tool path. This method is able to not only greatly simplify the construction of radial curves and spiral tool path but also to have the ability of processing and smoothing complex surfaces. Experimental results are presented to validate the proposed method.

Chatter is a very detrimental phenomenon occurring in milling process especially in thin-wall milling, which has been a limitation to achieve high productivity and good surface quality. The prediction of milling stability for chatter avoidance plays a key role in high performance milling. However, compared with the case of milling a part with a flexible cutter, the stability analysis and experimental validation for thin-wall milling are seldom provided. In this paper, an approach to obtaining the 3D stability lobe in thin-wall milling is proposed considering both the helix angle effect of cutter and the dynamic behavior of thin-walled part. A systematic cutting force model, which is capable of incorporating the helix angle effect and run-out effect of cutter, is first built. After the effective stiffness of the thin-walled part along the entire tool position is acquired by combining FEM with an impact experiment, the model of dynamic milling system with respect to the mode shape of thin-walled part is then developed. Based on the model, an extended high-order time domain method is subsequently utilized to generate the 3D stability lobe diagram considering helix angle effect. Finally, the proposed method is validated by the results of dedicated experiments.

Geometrically, a tool path can be generated by successively offsetting its adjacent path on the surface with a given path interval, which preferably starts from one of the surface boundaries or a primary curve. The key issues involved in offset path planning are the generation of raw offset paths and the elimination of the self-intersection of raw offset paths. Most researches available in this area are focused on how to generate the raw offset paths, however, the latter, especially how to eliminate the self-intersection of the offset paths on mesh surfaces, has not been sufficiently addressed. In this paper, a mapping-based approach to eliminating the self-intersection of offset paths is proposed for the CNC machining of mesh surfaces. The method first flattens the mesh surface onto a predefined plane by using a mesh mapping technique, and then taking the mapping as a guide, the offset paths are also naturally mapped onto the plane, from which those invalid self-intersection loops can be effectively identified and eliminated. To handle the issue of self-intersection for all types of offset path, a notion of local loop is introduced to detect and eliminate the invalid self-intersection loops. After that the planar paths are inversely mapped into the physical space and the final tool paths used for the machining of mesh surface are obtained. Meanwhile, in order to improve the kinematic and dynamic performance of the machine tool when machining along the generated offset paths, a method for rounding the sharp corners of tool paths, which result from the process of eliminating the self-intersection of raw offset paths, is also preliminarily investigated. Finally, the proposed method is validated by the results of simulations and machining experiments. A method of eliminating self-intersection of offset paths on mesh surfaces is proposed.The new orientation rule based on the local loop is developed and discussed in detail.The method of rounding the sharp corner is preliminarily investigated.Simulation and real machining are performed.

During automatic polishing process, path trajectory is an important factor affecting the quality of machining. In this paper, a path generation algorithm based on adaptive Hilbert curves which can cover the curved surface evenly is proposed. The generated path not only makes the coverage density adjustable but also is able to pass through the points on the curved surface in more directions which is helpful to get a finished part without stripes. Using the proposed algorithm, the uniform distributed grid points are obtained in the parameter domain and then these node points with adjustable density can be calculated accordingly. Thus, according to the construction rule of adaptive Hilbert curve, the objective toolpaths are subsequently obtained. After that, by means of a mapping strategy, the path trajectory can be obtained on the physical space. To verify the proposed algorithm, uniform polishing paths with variable density are planned on two typical curved surfaces. The result of the machining experiment shows that the curved mirror-like surface can be achieved, and it also indicates the applicability of the proposed method.

Polishing is usually indispensable process when better surface roughness is required for the parts such as injection mold. However, polishing process is often performed by manual operations. In this paper, an automatic polishing method for the metal parts with curved surfaces is proposed based on a machining centre. In order to realize the control of contact force, the relationship between the displacement of polishing disk and the force impacted on the polished part is first established. Then, within the contact zone between the polishing disk and the polished part, a pressure distribution model is derived for planar and curved surface polishing according to the specific process parameters. On this basis, the model of removal depth distribution along the vertical direction of feed is built for each polishing pass, and thus a suitable stepover size is further obtained so as to reduce the fluctuations of remove depth to most extent. Finally, an effective planning algorithm of cutter location data in polishing is proposed for a given CNC machine tools, and validation experiments are performed on planar and curved parts. The results show that the proposed automatic polishing scheme is able of achieving a mirror effect surface and keep a good global uniformity, at the same time it improves the polishing efficiency and realizes the integration with milling process.

A good adaptive feedrate will be helpful for improving machining accuracy and efficiency, as well as avoiding the excess of the machine’s physical capabilities and feed fluctuations during machining. Therefore, it is highly desirable to consider the constraints of geometric error, cutting performance, and drive constraints in the feedrate scheduling of the parametric curve interpolator for five-axis computer numerical control machining. In this paper, a novel multiconstraints feedrate scheduling method is proposed for the parametric curve interpolator in five-axis machining. In the method, the feed optimization model is first built with the constraints of geometric error, the maximum feedrate and acceleration of cutter tip, and the maximum feedrate and acceleration of five-drive axes. Then, the relations between each constraint and the cutter tip feedrate are derived by means of near arc length parameterization. After that, a linear programming algorithm is applied to obtain the optimal feed profile on the sampling positions of the given tool path. Finally, illustrated examples are given to validate the feasibility and applicability of the proposed feedrate scheduling method. The comparison results show that the proposed method has an ability of the simultaneous guarantees of geometric accuracy, cutting performance, and drive characters of machine tools.

Non-uniform rational b-spline (NURBS) tool path is becoming more and more important due to the increasing requirement for machining geometrically complex parts. However, NURBS interpolators, particularly related to five-axis machining, are quite limited and still keep challenging. In this paper, an adaptive feedrate scheduling method of dual NURBS curve interpolator with geometric and kinematic constraints is proposed for precision five-axis machining. A surface expressed by dual NURBS curves, which can continuously and accurately describe cutter tip position and cutter axis orientation, is first used to define five-axis tool path. For the given machine configuration, the calculation formulas of angular feedrate and geometric error aroused by interpolation are given, and then, the adaptive feedrate along the tool path is scheduled with confined nonlinear geometric error and angular feedrate. Combined with the analytical relations of feed acceleration with respect to the arc length parameter and feedrate, the feed profiles of linear and angular feed acceleration sensitive regions are readjusted with corresponding formulas and bi-directional scan algorithm, respectively. Simulations are performed to validate the feasibility of the proposed feed scheduling method of dual NURBS curve interpolator. It shows that the proposed method is able to ensure the geometric accuracy and good machining performances in five-axis machining especially in flank machining.

Cutter orientation modification with kinematic constraints is very necessary and effective for five-axis machining especially machining at high speed. It is very helpful for achieving a smooth cutter motion and keeping the process steady. Therefore, a cutter orientation adjustment method is proposed to obtain an optimized tool path which makes best use of the kinematic characteristics of angular feed for five-axis machining. For the given five-axis cutter location path and the feed profile of cutter tip point both expressed by b-spline formats with the same parameterization, the analytic relations of angular feed, angular feed acceleration, and jerk with respect to the geometric and tangential feed parameters of the cutter tip trajectory are first derived. Then, the conditional inequalities of these kinematic constraints used for orientation adjustment are built. Subsequently, the determination method of feasible cutter orientation and detailed algorithm of orientation adjustment are given. Finally, illustrated examples are conducted to validate the proposed orientation adjustment method. The results show that the developed method is effective and can be applied to optimize geometrically complex five-axis tool path by taking the angular feed, angular feed acceleration, and jerk into account.

Almost 80 % of the milling operations to produce mechanical parts are produced by NC pocket milling, especially in aerospace and automobile industry. At present, for 2.5D pocket machining, direction-parallel and contour-parallel machining strategies have gained nearly universal acceptance. However, in such tool path, abrupt change of path direction, frequent acceleration and deceleration, and sharp velocity discontinuous are found to significantly limit the machining efficiency of pockets. To address these problems, this paper introduces a method for generating a spiral tool path that maintains a steady-state cutting process by as smoothly as possible curvature evolution of the tool path for pocket machining. First, the machined region of a layer of a pocket is mapped onto a circular domain by means of mesh mapping, which reduces the task of tool path generation from the geometrically complex pocket region to a topologically simple disk. On this disk, a guide spiral is constructed according to a mathematical function constrained by the calculated path interval map. Using the mapping from the pocket to the disk as a guide, the guide spiral is inversely mapped into the interior of the pocket and then a smooth low-curvature spiral path is derived. The generated tool paths are guaranteed to not inherit any corners in the subsequent interior tool paths and allows cutting of the pocket without tool retractions during the cutting operations. Finally, the proposed method is implemented and tested on several typical sample pockets to demonstrate its validity and significance.

Polyhedral surfaces are used as representation model for CAM and process planning purposes because of its simplicity for data exchange and geometric computation. However, there are few tool path planning strategies for such surfaces but isoplanar method. This paper presents a contour offset approach to tool path generation for three-axis ball-end milling of polyhedral surfaces, based on a novel method for offsetting curves on polyhedral surfaces. One of its salient features is to reduce the task of removing complex interfering of offsets from 3D physical surfaces to 2D plane by flattening mesh surfaces and avoid costly 3D Boolean set operations and relatively expensive distance calculation. Moreover, in practical implement, the procedures of calculating offset points and removing interfering loops are merged and carried out simultaneously results in an efficient tool path generation method. Empirical examples illustrate the feasibility of the proposed method.

The parametric surfaces of some manufactured parts are often subjected to the Boolean operation of other objects; generating suitable NC tool paths from such trimmed surface remains a challenge. This paper presents a new planar development-based method to generate contour-parallel offset paths of trimmed surfaces. To avoid direct frequent identifications and removals of interferences of offset curves on 3D-trimmed surface possibly with multiple holes or restricted regions, the original surface is flattened in the plane domain using a two-stage approach which consists of conformal mapping with free boundary and further nonlinear accuracy improvement. Then, sequent offsets of the boundary curves of the planar region are generated, and the global interferences are detected and removed using an efficient and robust divide-and-conquer strategy. Based on a tree data structure, a tool-path linking algorithm is also given with less or no tool retractions, and subsequently, the resulting planar paths are inversely mapped to the physical space. Illustrated examples have been conducted to testify the affectivity and the applicability of the proposed contour-parallel offset machining method.

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