Accurate tool position for five-axis ruled surface machining by swept envelope approach

This paper presents a swept envelope approach to determining tool position for five-axis ruled surface machining. The initial tool position is traditionally located to contact with two directrices of a ruled surface. The swept profile of the tool is then determined based on the tool motion. By comparing the swept profile with the ruled surface, the tool position is corrected to avoid machining errors. The cutter's swept envelope is further constructed by integrating the intermediate swept profiles, and applied to NC simulation and verification. This paper presents the explicit solution for the swept profile of a taper-end cutter in five-axis ruled surface machining. The relation of the ruled surface geometry, the tool motion and the machining errors is developed. Therefore, the error sources can be detected early and prevented during tool path planning. The explicit swept envelope indicates that the machined surface is not a ruled surface in five-axis ruled surface machining. Manufacturing industries should take extra care in high precision ruled surface machining. Computer illustrations and example demonstrations are shown in this paper. The results reveal that the developed method can accurately position tool location and reduce machining errors for five-axis ruled surface machining.     

Machine models and tool motions for simulating five-axis machining

This paper presents a method of determining the tool motion of a five-axis machine. The method is motivated by the imprint point method, where points on the machined surface are computed based on the tool position and tool motion. While simple linear motion can be used as a coarse approximation to this motion, this paper looks at more accurate models of tool motion based on machine kinematics that can be generalized and applied to any CNC machine with one tool head. A kinematic chain is created by decomposing the linear motion of a machine’s translational and rotational axes into parameterized affine transformations, and a hierarchical model of the machine combines the transformations to provide an accurate model of machine motion.     

The sweep plane algorithm for global collision detection with workpiece geometry update for five-axis NC machining

A new algorithm based on the sweep plane approach for global collision detection for five-axis NC machining is presented. This algorithm takes into account not only collisions between the tool and workpiece, but also collisions between the other parts of the CNC machine, especially the change of the workpiece geometry is included in the detection process. The workpiece and machine bodies are firstly approximated by an octree of bounding spheres. Collision detection is conducted between these spheres. If there is any interference between these bounding spheres, their subspheres are further tested. The subdivision process is recursively performed until the resolution reaches the desired precision level. If there is no interference between the spheres, there is no need to subdivide any more. When the interference is detected between the spheres in the last octree level, the slices within these colliding spheres are further checked by using the sweep plane algorithm to determine whether the enclosed objects really collide with each other. In the sweep plane algorithm, most of the slices of the moving bodies stay parallel and their collisions are detected by checking the interference between these parallel slices using 2D polygon clipping. Whereas, if the slices are not parallel to the reference slicing direction (due to the rotary axes), the interference detection is conducted by examining overlaps of the projections of these slices on the three perpendicular planes XY,YZ, and ZX. The accuracy of the algorithm can be adjusted by changing the distance between the sweep planes. The algorithm can be applied to any five-axis CNC machines.     

Inverse kinematics for optimal tool orientation control in 5-axis CNC machining

The problem of determining the inputs to the rotary axes of a 5-axis CNC machine is addressed, such that relative variations of orientation between the tool axis and surface normal are minimized subject to the constraint of maintaining a constant cutting speed with a ball-end tool. In the context of an orientable-spindle machine, the results of a prior study are directly applicable to the solution of this inverse-kinematics problem. However, since they are expressed in terms of the integral of the geodesic curvature, a discrete time-step solution is proposed that yields accurate rotary-axis increments at high sampling frequencies. For an orientable-table machine, a closed-form solution that specifies the rotary-axis positions as functions of the surface normal variation along the toolpath is possible. In this context, however, the feasibility of a solution is dependent upon the surface normal along the toolpath satisfying certain orientational constraints. These inverse-kinematics solutions facilitate accurate and efficient 5-axis machining of free-form surfaces without “unnecessary” actuation of the machine rotary axes.     

Estimation of tool orientation contour errors for five-axismachining

Recently, there has been a growth of interest in high-precision machining in multi-axis feed drive systems, which are subject to problems such as friction, cutting force and incompatibility of individual driving axis dynamics. Tracking errors in an individual driving axis during five-axis machining result in tool tip contour error and tool orientation contour error. Based on the conventional definition of the tool orientation contour error, that is, it is the deviation in the normal direction from the desired orientation in spherical coordinates, even if the tool tip and tool orientation contour errors are very small, a mismatch between the tool tip position and tool orientation causes an overcut or undercut when these errors are treated independently. To address this problem of mismatch, this paper presents a new definition of the actual tool orientation contour error. This definition considers synchronization between the tool tip and tool orientation contour errors. In addition, we propose an estimation model for the tool orientation contour error. Experimental results demonstrate that the proposed model provides a better indication of the actual tool orientation contour error than the conventional definition.     

Floor, wall and ceiling approach for ball-end tool pocket machining

This paper presents a floor-wall and ceiling (FWC) approach to determining the tool axes for five-axis pocket machining. The FWC method generates tool axes by simply linking the corresponding points between tool location paths on floor and tool axial paths on ceiling. The geometry of the floor, wall, and ceiling of a pocket are first discussed. The construction and manipulations of the tool location paths and the tool axial paths are then addressed. The relationship between the tool axis variation and the manipulations is analyzed such that the generated tool axes are guaranteed to be smooth, optimized, and collision-free. By using the FWC method, the complexity of determining the tool axes can be significantly reduced. Computer illustrations and example demonstrations are shown in this paper. The results reveal that the FWC method can generate much higher quality tool axes than the traditional methods.     

The Domain of Admissible Orientation concept: A new method for five-axis tool path optimisation

This work deals with the optimisation of tool paths in five-axis machining. The objective is to improve the kinematic behaviour of machine tools during milling. The orientation of the tool axis at each point of a tool path is optimised while ensuring quality constraints. These are modelled using the Domain of Admissible Orientation (DAO) concept expressed in the P-System and transformed into the M-System. This article aims at defining the DAO and presents an example of optimisation using this concept. This optimisation is a minimisation of the movement generated by each rotation axis and is applied to two test parts.     

Automatic generation of gouge-free and angular-velocity-compliant five-axis toolpath

Existing works in automatic generation of interference-free five-axis surface machining toolpaths bear a serious drawback — in order to avoid the obstacles, the tool is often required to make drastic change in its orientation between neighboring contact points. Such a quick change in the tool’s orientation can never be made possible in reality due to the stringent physical limit on the speed and acceleration of the rotary motions of the machine tool. The usual ad hoc solution to this problem is to smooth the toolpath in the configuration space, which, however, is prone to special situations of failure and is not able to guarantee the absolute compliance with the given angular velocity limit. In this paper we present an approach to this problem by directly involving the angular velocity limit in the search process. The presented algorithm will automatically generate a five-axis toolpath that not only is interference-free but also guarantees the angular-velocity compliance. Delicate computation and manipulation of visibility maps and their derivative data ensure that the proposed algorithm is computationally feasible with acceptable computing time and memory requirement. Test examples are given to demonstrate the promising use of the proposed solution.     

Smooth tool path generation for 5-axis machining of triangular mesh surface with nonzero genus

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.     

Optimal and collision free tool posture in five-axis machining through the tight integration of tool path generation and machine simulation

The generation of collision free NC-programs for multi-axis milling operations is a critical task, which leads to multi-axis milling machines being exploited below their full capacities. Today, CAM systems, generating the tool path, do not take the multi-axis machine movements into account. They generate a multi-axis tool path, described by a sequence of tool postures (tool tip+tool orientation), which is then converted by a NC-postprocessor to a machine specific NC-program. As the postprocessing is normally done in batch mode, the NC-programmer does not know how the machine will move and the chance for having collisions between (moving) machine components is often very high. The execution of a machine test run or the application of a machine simulation system (NC-simulation) is the only solution to inform the NC-programmer about possible machine collisions during operation.This paper describes a multi-axis tool path generation algorithm where the tool orientation is optimised to avoid machine collisions and at the same time to maximise the material removal rate along the tool track. To perform efficient collision avoidance, the tool path generation module (traditional CAM), the postprocessing (axes transformation) and machine simulation has been integrated into one system. Cutting tests have been carried out to define the allowable tool orientation changes for optimisation and collision avoidance without disturbing the surface quality.The developed multi-axis tool path generation algorithm is applicable for the machining of several part surfaces within one operation. This, together with tool path generation functionality to adapt the tool orientation for both, maximal material removal and avoidance of collisions between (moving) machine components, are the innovative aspects of the presented research work.     

Continuity-preserving tool path generation for minimizing machining errors in five-axis CNC flank milling of ruled surfaces

Five-axis CNC flank machining has been commonly used in the industry for shaping complex geometries. Geometrical errors typically occur in five-axis flank finishing of non-developable surfaces using a cylindrical cutter. Most existing tool path planning methods adjust discrete cutter locations to reduce these errors. An excessive change in the cutter center or axis between consecutive cutter locations may deteriorate the machined surface quality. This study developed a tool path generation method for minimizing geometrical errors on finished surfaces while preserving high-order continuity in the cutter motion. A tool path is described using the moving trajectory of the cutter center and changes in two rotational angles in compact curve representations. An optimization scheme is proposed to search for optimal curve control points and the resulting tool path. A curve subdivision mechanism progressively increases the control points during the search process. Simulation results confirm that the proposed method not only enhances the computational efficiency of tool path generation but also improves the machined surface finish. This study provides a computational approach for precision tool path planning in five-axis CNC flank finishing of ruled surfaces.     

CA摆头五轴机床校验与优化

在充分分析摆头类五轴机床结构特性以及机床运动学误差的基础上,针对机床两旋转轴的旋转中心位置及其方向偏离本来的位置和方向,及主轴旋转中心位置存在偏离的情况,建立了一种CA摆头五轴机床运动学模型.结合特定机床运动及运动学相关理论,提出了一种CA摆头误差校验及自动测量和补偿优化算法,并开发了一种CA摆头五轴机床运动学误差测量系统,根据测量值对机床进行优化,实现并验证了算法的正确性.     

Comparing the kinematic efficiency of five-axis machine tool configurations through nonlinearity errors

Five-axis CNC machines represent a particular class of machine tools characterized by superior versatility. Little attempts were made in the past to compare directly their performances through a common indicator. In this sense, the present study proposes nonlinearity error as a valuable method to quantify the kinematic efficiency of a particular five-axis configuration. Nonlinearity error is defined as the maximum deviation of the cutter-location point from the reference plane generated by the initial and final orientations of the tool during linearly interpolated motions of the cutter along the intended tool path. The proposed concept has demonstrated that nonlinearity error occurs approximately around the middle of the linearly interpolated interval and therefore has validated the current post-processing practice of halfway cutter-location point insertion. The employment of nonlinearity error in the evaluation of the kinematic efficiency of vertical spindle-rotating five-axis machine tools revealed that for an identical machining task, configurations involving the vertical rotational axis tend to move more than those involving only horizontal rotational axes.     

Rough and finish tool-path generation for NC machining of freeform surfaces based on a multiresolution method

Progressive fitting and multiresolution tool path generating techniques are proposed in this paper, by which multi-level (LOD) models fitting for different subsets of sampled points are obtained, and then multiresolution rough-cut and finish-cut tool paths are generated based on the LOD models. The advantages of the proposed method are: (1) the user need not care for data reduction in CAD modeling; (2) final result is obtained by interpolating two lower-level reconstructed surfces, and each lower multiresolution CAD representation can be used to generate rough-cut tool paths; (3) different manufacturing requirements utilize different level models to generate tool paths; (4) selective refinement can be applied by interpolating selceted areas at different levels of details. The key avantage of the prograssive fitting algorithm is that it can use different level surfaces to generate adaptive rough-cut and finishi-cut tool path curves directly. Therefore, based on the proposed techniques, tool path length is reduced. Sharp concers are smothed out and large tools can be selected for rough machining. The efficiency of this algorithm has been demonstrated, and it results in a 20% reduction in machining time.     

A tool path generation method for freeform surface machining by introducing the tensor property of machining strip width

Due to the complexity of geometry, the feed direction with maximal machining strip width usually varies among different regions over a freeform surface or a shell of surfaces. However, in most traditional tool path generation methods, the surface is treated as one machining region thus only local optimisation might be achieved. This paper presents a new region-based tool path generation method. To achieve the full effect of the optimal feed direction, a surface is divided into several sub-surface regions before tool path computation. Different from the scalar field representation of the machining strip width, a rank-two tensor field is derived to evaluate the machining strip width using ball end mill. The continuous tensor field is able to represent the machining strip widths in all feed directions at each cutter contact point, except at the boundaries between sub-regions. Critical points where the tensor field is discontinuous are defined and classified. By applying critical points in the freeform surface as the start for constructing inside boundaries, the surface could be accurately divided to such that each region contain continuous distribution of feed directions with maximal machining strip width. As a result, tool paths are generated in each sub-surface separately to achieve better machining efficiency. The proposed method was tested using two freeform surfaces and the comparison to several leading existing tool path generation methods is also provided.     

A numerical tool to simulate the kinematics of the ingress movement in variably-dimensioned vehicles for elderly and/or persons with prosthesis

This paper presents a method for simulating the kinematics of the vehicle ingress movement of elderly people and/or people with prostheses (represented by a humanoid mannequin with a head, trunk, pelvis and lower limbs) in variably-dimensioned vehicles, starting from real experimental data. To solve this “complex” problem, we propose a three-stage method. The first stage concerns the construction of an “exploitable” movement database, containing movements resulting from the numerical processing of the ingress movements measured in experiments carried out on two vehicles with 2 distinct geometries. The second stage, consisting of 4 phases, analyzes and automatically identifies the ingress movement strategies. By the end of this stage, 2 ingress strategies and 6 sub strategies were identified. The third stage is the simulation. It uses the results from stages 1 and 2 to simulate the ingress movement of a subject in the database, adopting a given sub-strategy for a vehicle with a different geometry. The simulation of the ingress movement of the same subject but for another vehicle is formulated as an inverse kinematics problem, which is solved by constrained nonlinear programming.Simulations involving elderly people and/or people with prostheses made it possible to validate the proposed method for the two ingress strategies. Despite the differences with the measured movements, the simulated movements conform to the sub-strategies adopted by the subjects during the experiments. Furthermore, the simulations made it possible to partially explain the shifts in strategy of some subjects when they changed vehicles during the experiments. Finally, simulations on fictitious vehicles highlighted some of the limitations of our simulation tool. This study opens several perspectives for future research. For example, we could improve the simulation tool by considering the subjects' intra-individual differences.Relevance to industryThis study can aid ergonomists and car manufacturers to simulate the ingress movement in variably-dimensioned vehicles for elderly and/or prosthesis having persons. The results of the simulations can be used in the products' (Vehicles) evaluation and adaptation processes. The developed methodology can be extended to the simulation of other movements as it can be integrated into digital human models (DHMs) software.