Cutter Contact Points Research Articles

A control algorithm for rapid movements near the radius compensation singularity in five-axis end milling

When the five-axis CNC system executes the 3D cutter radius compensation function, the angle between two adjacent radius compensation vectors might become very large and the linear axes would move too fast if the tool orientation vector is close to the surface normal. The reason that results in this phenomenon is analyzed based on building the transmission relationship between the cutter contact point and the cutter location point. By taking the square-end tool as an example, an optimization algorithm to control the undesired movements is advanced. For the singular area where sudden change exists, the number of interpolation cycles is determined by the cutter feedrate, the limit speeds of machine axes and the maximum allowable angle between radius compensation vectors of adjacent NC blocks. The radius compensation vector of each interpolation cycle is obtained by a kind of vector rotation method. By maintaining the perpendicularity between the radius compensation vector and the tool orientation vector, the rapid movements of the linear axes are eliminated. A trial-cut experiment is performed to verify the correctness and the effectiveness of the proposed algorithm.

Research on Cutter-Contact Point Data Calculation of Robotic Abrasive Belt Polishing for Gun-Receiver Surface

Coordinate transformation in robotic abrasive belt polishing system and the calculation method of robot working point by cutter-contact point data are analyzed in this paper. Calculation process of cutter-contact point data is given in this paper, the process mainly includes acquisition and discrete of polishing tool path and the associated vector calculation. Subsequently, detail of the process such as tool path pattern, row spacing, step distance and best contact conditions are analyzed and calculated. Finally, in visual studio environment, the cutter-contact point data of gun-receiver surface is generated by calling UG / Open API function.

Cutter location point calculation for five-axis surface machining with ellipse cutter

This paper presents an approach of the cutter location (CL) point calculation for five-axis surface machining with elliptic generatrix cutter. Firstly, based on the cutter contact (CC) point and its normal vector in workpiece coordinate system, the normal vector of the CC point in local coordinate system of the cutter is figured out according to the geometric relations between two coordinate systems. Secondly, the geometric properties of ellipse are analysed to obtain the local coordinate CC point with local coordinate normal vector. Thirdly, the position relation between the CC point and the ellipse centre in local coordinate system is determined. And this position relation is transformed into workpiece coordinate system according to the geometric relations between two coordinate systems. Then, the centre of the ellipse in workpiece coordinate system is calculated by the position relation and the CL point is figured out according to the ellipse centre. Finally, an example of CL point calculation with this method is carried out which proves that the method is effective.

Contour-parallel tool path generation for three-axis mesh surface machining based on one-step inverse forming

Recently, mesh surfaces have become the focus of considerable interest due to its simplicity for data exchange and geometric computation. However, for mesh surface machining, there are few tool path planning strategies but iso-planar method. In this article, a contour-parallel tool path method is presented for machining complicated mesh surfaces with holes or islands by introducing a so-called one-step inverse approach based on physical plastic deformation of metal materials. By rapidly simulating for the inverse forming process of sheet metal of auto-body panels, the machined surfaces are flattened into its initial flat blank on which the cutter contact points are calculated by iteratively offsetting the inner and outer contours of the blank. Then, using the mapping from the machined surfaces to the blank as a guide, the planar offset curves without self-intersection are inversely mapped onto the original mesh surfaces, forming the final contour-parallel tool paths. Benefiting the flattening method based on one-step inverse approach, the task of generating tool paths is reduced from a physical surface to a plane so that geometric computation of tool path generation is greatly simplified, especially for self-intersection elimination in offset curves. Moreover, a new data structure of offset curve is also introduced, which is used to effectively compute the self-intersections. The proposed method has been tested on several sample surfaces, and the experimental results show that the proposed method can deal with complicated mesh surfaces with holes or islands and is also more efficient compared with the traditional methods.

Research of the Tool Orientation Optimization with Kinematical Constraints

Drastic change of the tool axis vector for five-axis CNC machining due to avoid global interference, proposed gentle forward, over-backward correction method to optimize the tool axis vector. Established a machine tool axis of rotation angular velocity constraints, and feed coordinate system, through the feed coordinate system adjust the inclination angle and swing angle of the existing tool axis vector to make the tool axis vector change between each adjacent cutter contact points satisfy the machine axis of rotation kinematics constraints and to ensure the continuity of feed rate during processing. Algorithm simulation examples show that the proposed method is reasonably practicable, make the tool axis vector changes fairing to ensure the smooth and efficient processing.

Collisionless tool orientation smoothing above blade stream surface using NURBS envelope

In five-axis machining, tool orientation above a blade stream surface may lead to tool collision and a decrease in workpiece rigidity. Hence, collisionless tool orientation smoothing (TOS) becomes an important issue. On the basis of a constant scallop height tool path, the triangular facets in the faces, vertices format are constructed from cutter contact (CC) using the Voronoi incremental algorithm. The cutter location (CL) points candidate set is represented by an oblique elliptic cone whose vertex lies at CC using NURBS envelope. Whether the CL point is above its CC is judged by the dot product between the normal vector and the point on triangulation nearest to the CL point. The curvatures at CC are obtained by fitting a moving least square (MLS) quadratic patch to the local neighborhood of a vertex and calculating eigenvectors and eigenvalues of the Hessian matrix. Triangular surface elastic energy is employed as the weight in selection from the NURBS envelope. The collision is judged by NURBS surface intersection. TOS can then be expressed by selecting a CL point for each CC point and converted into a numerical control (NC) code automatically according to the postprocessor type of the machine center. The proposed method is verified by finishing of a cryogenic turboexpander impeller of air separation equipment.

Tool Path Planning of NC Machining for Surface Similarto Revolution Body

Aiming at NC machining for surface similar to revolution body with high feed rate, a tool path planning method with toroid cutter under helix driving mode is proposed. Firstly, a helical line is constructed as the guide curve of the surface. Secondly, the initial cutter contact(CC) point corresponding with the subsquent guide point is estimated based on the tangential direction of the CC point locus known on the surface, and the center of the toroid cutter at the initial CC point is calculated. Thirdly, the distances between the initial cutter center and the objective cutter location(CL) point corresponding with the subsqent guide point in circumferential direction and axial direction are computed. Then the direction and step for searching the objective CC point are figured out with the quasi similarity relation between adjacent CL points and adjacent CC points. Finally the objective CC point and CL point are searched with an iterative process. Also the error calculation method is proposed based on analyzing the curvature of the surface and the cutter at CC point. The algorithm is used in tool path planning of shoe last 5-axis NC machining. The result shows that the algorithm works with a high searching efficiency and it has value of both theory and application. The shoe last 5-axis NC machining experiment is also carried out, which verifies the effectiveness of the algorithm.

A Method to Calculate Tool Accessible Domain Based on the Point Model for the Multi-Axis CNC Machining

This paper puts forward a kind of method which can calculate tool accessible domain for tool axis optimization in the complex curved surface multi-axis machining. At first , the point model has been construced on the base of constrained surface.The second, based on any possible direction of tool axis vector of a given cutting contact point, the distance between a point and a line is used to decide whether occurs collision and interfence. The third, two angles related with cutter-axes vector is definied. The regulation of tool accessible domain can be implemented by getting the boundary of the discrete points in the coordinate planes. Finally, a tool has been developed to calculate tool accessible domain, and an example is given to verify the effectiveness of the method.

Non-redundant tool trajectory generation for surface finish machining based on geodesic curvature matching

The increasing complexity of surface has put forward higher demands for CNC machining trajectory generation. The constant scallop height method has the disadvantage of point redundancy during trajectory discretization. Therefore, a non-redundant tool trajectory generation method for surface finish machining is put forward. The cutting row spacing is determined by the geodesic curvature according to scallop height and the convexity or concavity of the local surfaces. The adjacent cutter contact (CC) points with constant scallop height are expressed point by point from the present CC point. The redundant points are removed by maximizing each cutting step length through making the chord error equal to the machining allowable error. The dual NURBS ruled surface is constructed to realize smooth transition of the tool trajectories and tool axis vector. The prototype system taking ACIS R13 and HOOPS V11.0 as modeling kernel has been developed to verify the proposed method. The experiment results proved that the proposed method can realize non-redundant tool trajectory considering tool interference during surface finish machining.

Real-Time Generation of Cutter Location Curves for Pen-Cutting of Sculptured Surface

An algorithm is proposed on the real-time generation of cutter location curves for pen-cutting of sculptured surface. First of all, the parameter of driving curves can be calculated based on Taylor series expansion according the kinematics and geometric relation between cutter contact loci and driving curves. Cutter contact points on the surface can be achieved. Then cubic B-spline curves are used to fit the ideal cutter location curves. Examples and analysis results have indicated that the algorithm can realize the regeneration of tool path, simplifying the NC programming and improving the precision of sculptured surface machining.

Tool Path Generation for Clean-up Machining of Impeller by Point-searching Based Method

Machining quality of clean-up region has a strong influence on the performances of the impeller. In order to plan clean-up tool paths rapidly and obtain good finish surface quality, an efficient and robust tool path generation method is presented, which employs an approach based on point-searching. The clean-up machining mentioned in this paper is pencil-cut and multilayer fillet-cut for a free-form model with a ball-end cutter. For pencil-cut, the cutter center position can be determined via judging whether it satisfies the distance requirement. After the searching direction and the tracing direction have been determined, by employing the point-searching algorithm with the idea of dichotomy, all the cutter contact (CC) points and cutter location (CL) points can be found and the clean-up boundaries can also be defined rapidly. Then the tool path is generated. Based on the main concept of pencil-cut, a multilayer fillet-cut method is proposed, which utilizes a ball-end cutter with its radius less than the design radius of clean-up region. Using a sequence of intermediate virtual cutters to divide the clean-up region into several layers and given a cusp-height tolerance for the final layer, then the tool paths for all layers are calculated. Finally, computer implementation is also presented in this paper, and the result shows that the proposed method is feasible.

The Error Estimation for 5-Axis Spindle-Rotating CNC Machine Tool

5-axis CNC machine is be the best tools in sculptured surfaces machining. Current CAM algorithms for 5-axis machining only consider the surfaces' geometric information when generating cutter contact points (CC points). Hence, the step length, which is the distance between two CC points, is determined only by the surface parameters for current CAM system. Because of the cutting tool can rotate, the actual cut trajectory is no longer a straight line between two consecutive CC points for 5-axis machining. Thus the cut error and the maximum step length should depend on the structural of 5-axis CNC machines tool and the surface's geometry. This paper proposed a new algorithm to estimate the maximum step length based on the cut error of 5-axis machining, and the result shows that this estimation algorithm provides better than traditional algorithms.

Kinematics constrained five-axis tool path planning for high material removal rate

Traditional five-axis tool path planning methods mostly focus on differential geometric characteristics between the cutter and the workpiece surface to increase the material removal rate (i.e., by minimizing path length, improving curvature matching, maximizing local cutting width, etc.). However, material removal rate is not only related to geometric conditions such as the local cutting width, but also constrained by feeding speed as well as the motion capacity of the five-axis machine. This research integrates machine tool kinematics and cutter-workpiece contact kinematics to present a general kinematical model for five-axis machining process. Major steps of the proposed method include: (1) to establish the forward kinematical relationship between the motion of the machine tool axes and the cutter contact point; (2) to establish a tool path optimization model for high material removal rate based on both differential geometrical property and the contact kinematics between the cutter and workpiece; (3) to convert cutter orientation and cutting direction optimization problem into a concave quadratic planning (QP) model. Tool path will finally be generated from the underlying optimal cutting direction field. Through solving the time-optimal trajectory generation problem and machining experiment, we demonstrate the validity and effectiveness of the proposed method.

New criteria for tool orientation determination in five-axis sculptured surface machining

The problem of optimal tool orientation determination in five-axis flat-end milling of sculptured surfaces is examined in this paper. The optimal tool orientation avoids local and global gouging of the tool and maximises a specific criterion related to machining efficiency. Two new criteria are introduced in this paper to quantify the tool orientation quality at a cutter contact point: infinitesimal machining volume (IMV) and infinitesimal machining area (IMA). The IMV criterion is used to maximise the material removal at the cutter contact point. The IMA criterion attempts to identify tool orientations that would lead to minimised overall tool path length. Using one of these criteria, an optimisation problem can be formulated to determine the optimal tool orientation among feasible gouge-free orientations. It is shown that the commonly adopted criterion of machining strip width in the determination of the optimal tool orientation cannot contribute towards maximising the material removal and does not really result in minimum overall tool path length. Results from various case studies have indicated that the newly introduced criteria can be used to generate optimal tool orientations that significantly increase machining efficiency.

Improving the dynamics of five-axis machining through optimization of workpiece setup and tool orientations

Existing works in optimization of five-axis machining mainly focus on the machining efficiency and precision, while the dynamic performance of the machine tools has not been fully addressed, especially in high-speed machining, in which the rotary actuators have limited dynamic ability. In this paper, a study is reported on how to generate a tool path so that the maximal angular accelerations of the rotary axes of the five-axis machine can be reduced. Two independent methods are proposed for this task: (1) by optimizing the setup of the workpiece on the machine’s table, and (2) by finding better tilt and yaw angles for the tool orientations. In this paper, the setup parameters of the workpiece are incorporated into the inverse kinematic equations, and angular acceleration functions are established according to the numerical solutions of those equations. While varying the tool orientations unquestionably would affect the surface quality of the machining, we introduce the so called Domain of Geometric Constraints that will restrict the allowable tilt and yaw angle of the tool at the cutter contact points on the part surface, so to ensure the satisfaction of the requirement of both local-gouging-free and cusp-height. For the first method–finding the optimal workpiece setup–a heuristic-based approach, i.e., the Genetic Algorithm (GA), is adopted, whereas for the second method–the constrained optimization of tool orientations–we present an elaborate algorithm based on the results from the analysis conducted by the authors. At the end of the paper, computer simulation experiments are reported that demonstrate the effectiveness of our proposed methods and algorithms.

Minimization of the kinematics error for five-axis machining

Kinematics of a particular five-axis milling machine can drastically change the machining accuracy. Therefore, the reduction of the kinematics error is an important problem associated with the tool path planning. Our new optimization method employs a closed form of the kinematics error represented as a function of the positions of the cutter contact points. The closed form is derived from the inverse kinematics associated with a particular five-axis machine and obtained through automatic symbolic calculations. The second component of the algorithm is the optimal setup of the part surface on the mounting table employed in an iterative loop with the generation of the cutter contact points. For a prescribed tolerance the proposed optimization allows for substantial reduction in the number of required cutter contact points. The reduction can be significant and may amount to long hours of machining if the machining time at the programmed feed is less than the sampling time of the controller. In turn, when the number of cutter location points is fixed, the error can be substantially reduced. However, this refers to commanded error wherein the dynamics of machine tool are not taken into account. We present an analysis, systematic numerical experiments and results of real cutting (ball nose and flat-end cutters) as an evidence of the efficiency and the accuracy increase produced by the proposed method. We also evaluate the relative contributions of the setup and the point optimization. The method is shown to work with advanced tool path generation techniques proposed earlier such as the adaptive space filling curves. The numerical and machining experiments demonstrate that the proposed procedure outperforms tool paths based on the equi-arclength principle and paths generated by MasterCam 9.

The Variable Cross-Section Helix Turning Trajectory Algorithm Used on the Middle-Convex and Varying Ellipse Piston Skirt

In order to turning the skirt of middle-convex and varying ellipse piston, this paper proposes a Variable Cross-section Helix Turning Trajectory (VCHTT) algorithm. it divide the turning trajectory of the piston skirt into transversal and helix, then obtain the coordinates of ellipse transversal cutter-contact points on the basis of centric polar radius arc interpolation (CPRAI) algorithm, and uses line surface intersection method to obtain the coordinates of helix cutter-contact points on the middle-convex and varying ellipse piston skirt. At last，merge two coordinates matrices to obtain the final coordinate surface of cutter-contact points of turning tool. With comparison, it finds that the VCHTT algorithm improves the interpolation accuracy by 0.04um than other methods.

Machining Accuracy Analysis and Error Compensation Approach with the Effects of Cutting Tool Tip’s Radius in NC Lathe Machining Process

With the wide use of NC, higher accuracy in machining is increasingly required for premium mechanical components. However, machining accuracy is affected by many factors, especially by the way of the tool positioning and the geometry of the tool nose. This paper, based on the actual NC lathe tool and turning, generalized and abstracted the machining process by establishing the imaginary tool nose and the tool tip’s arc centre as the cutter-contact point, and analyzed systematically the influence of the factors, including the way of the tool positioning, the nose, and the tool tip’s arc radius, on the machining accuracy when machining transverse, cylindrical-surface, circular cone, quarter-circular and some surfaces can be expressed by formula etc.. Derived the error calculating formulas for turning in different surfaces. Put forward two error compensation methods, direct calculating method and enveloping method of error compensation. Experiments were carried out and results have shown that the two error compensation methods can considerably reduce the machining error in NC turning operations.

Adaptive tool-path generation on point-sampled surfaces

► Tool path generating algorithm on point cloud is proposed via direct projection. ► A reference surface is constructed to plan the points to be projected. ► Curve fitting on projecting points is used to rearrange cutter location points. ► It is a rapid, practical method and inexpensive in calculation. In this paper, we present a new approach to generate tool paths for machining point sampled surfaces using a direct projection algorithm, which is based on generating tool paths along planar intersection curves. In our implementation, a guide surface, with simple geometry like planes or cylinder surfaces, is first created according to the bound volume of the point cloud and initial tool paths are planned on it in terms of the motion pattern of the cutters. For each point of the initial tool paths, then, the corresponding cutter contact point (CC) of the point set surface is located by projecting the point onto the point cloud using the direct projection algorithm. In order to obtain adaptive cutter location points (CL), a least squares-based curve fitting method is applied to approximate the CC points using piecewise cubic Bezier, and a numerical method derived to estimate the length of the curve is used to adjust the position of the points along the curve, and make them evenly spaced on the curve with equal arc lengths. In addition, considering that offset curves or surfaces are necessary for locating CL points in many applications, such as machining using ball end milling cutter, torus ended milling cutters, an offset strategy for cubic Bezier curves is also studied. By testing the proposed method on several point clouds, it has been demonstrated to be promising.

Free-Form Surface Five-Axis Machining Tool Path and Tool Posture Simultaneous Multi-Objective Optimization Theory Research

In view of all sorts of questions existing in CNC machining, such as machining vibration, so proposed a new simultaneous multi-objective optimization algorithm on free-form surface five-axis machining tool path and tool posture based on constant scallop height. In the algorithm, we first complete the surface fitting on the base of feature points obtained. Secondly calculate principal curvatures of the surface, select tools, and at the same time generate tool axis vector in the current cutter-contact point tool axis. Once again get the maximum spacing and surface curvature in accordance with the tool effective cutting radius, discrete into cutter-contact point, and calculate the cutting depth to adjust the machine feed rate. And finally connect adjacent curve path using the diagonal to achieve a continuous cutting scallop height tool path. This algorithm can achieve the goals such as the same precision, improving processing efficiency, reducing the number of tool cutting in and out, reducing cutting vibration and tool wear and so on. That is the algorithm can achieve simultaneous multi-objective optimization of the free-form surface NC machining finally.