Cutter Contact Path Research Articles

Posture Optimization in Robotic Flat-End Milling Based on Sequential Quadratic Programming

AbstractRobotic flat-end milling of complex surfaces offers advantages such as high flexibility and high machining efficiency. In the process of planning the toolpath based on the cutter contact path, the robot functional redundancy and the tool orientation need to be solved carefully. This paper presents a posture optimization method for robotic flat-end milling. Taking the weighted sum of the machining width and the toolpath smoothness performance criterion as the objective function, an optimization model considering the joint limits and gouging avoidance is established. An efficient algorithm based on sequential quadratic programming is proposed to solve this nonconvex problem. During the execution of the algorithm, the machining width is efficiently calculated by an iterative method based on conformal geometric algebra, while its derivatives are approximated analytically. Simulations and experiments demonstrate that the presented technique can resolve the tool axis direction and the robot redundancy effectively to increase the machining width and improve the toolpath smoothness, thus reducing the time for machining and improving the surface quality.

Tool Path Generation Algorithm Based on Rough Machining of Jade Carving Surface

To improve the quality of tool paths in surface machining, different machining requirements are considered in the tool path generation algorithm. In the traditional tool path generation algorithm, due to the lack of a unified mathematical calculation framework, these requirements often need to be considered separately, but they often compete with each other, so that different requirements cannot be satisfied at the same time and the tool path cannot achieve the optimal. To resolve this issue, an extensive tool path generation algorithm framework for arbitrary surfaces was proposed. The proposed algorithm transforms the tool path calculation framework into a constrained functional optimization problem by establishing an optimization function based on the potential energy field and an inequality function based on the gradient field in the machining area. By establishing finite element approximation, the functional optimization problem is transformed into a numerical optimization problem, which reduces the difficulty of solving. According to the machining requirements of die surface such as tool path smoothness, line width constraint and cutting direction constraints were transformed into the constraints of potential energy field isopotential line, and the method of generating reciprocating cutter path and cutter contact path isosection cutter path was proposed by optimizing the method. It is evident from the simulation and machining experiments results that continuous and smooth tool paths can be generated by using this algorithm, and machining quality and machining efficiency can be improved. By adding different machining requirements into the framework, a tool path with different optimization objectives can be generated.

Modelling of Energy Consumption for Milling of Circular Geometry

Machine tools are dominant end users of electrical energy in manufacturing, and responsible for high carbon emissions. There is hardly any research work on the energy modelling for curved surface milling. The present study aims to develop energy consumption model for milling of circular geometries as a part of process planning for machining operations to reduce cost, improve energy efficiency and general productivity. The circular geometry may have concave or convex shape which leads to change in magnitude of curvature. Therefore, the magnitude and distribution of cutting forces and concerned cutting powers are quite different in both these machining situations. This necessitates the need to investigate this aspect comprehensively. A process geometry model is developed based on process geometry variables of feed per tooth along cutter contact path, entry and exit angles of tooth, engagement angle, undeformed chip thickness, etc. Next, the process geometry variables in conjunction with mechanistic cutting constants are used to develop a force model for estimating the feed force and normal force components. Lastly, a power consumption model is developed based on the instantaneous force component and velocity of milling cutter to estimate both the instantaneous and average power consumed during the milling process. Machining experiments are performed to conform the validity of the proposed model by comparing the measured power to their predicted counterpart. The developed model can be used for estimating the power consumption for milling of circular geometries reliably and efficiently without conducting the costly experiments. In addition to this, the proposed model extends the existing model by considering the effect of workpiece curvature and aims at providing a useful aid for prediction of power consumption in peripheral milling of circular surfaces. Therefore, an attempt has been made to provide a basic platform for in-depth comprehension and characterization of energy consumption. The proposed model has many applications particularly in die-mold manufacturing and aircraft industry and it can be extended to curved geometries having variable curvatures.

Inverse kinematics for a novel hybrid parallel–serial five-axis machine tool

A unique successful postprocessor for a hybrid parallel-serial machine tool is developed.Smart machining must be accomplished without forcing the tool to make sharp turns when HSM controls detect a turn approaching.NC codes are recalculated to form a new path for the pivot that can avoid the discretization near the singularity points in this study.The novelty of the paper is successfully to propose a new hybrid parallel-serial five-axis machining model.The manufacturers that are interested in integrating the inverse kinematics into the design process of their hybrid product. Instead of obsessively emphasizing to interpolate more points from the linearization algorithm, the NC codes are recalculated to form a new path for the pivot that can avoid the discretization near the singularity points in this study. In previous studies, orientable-spindle machines were directly used to generate smooth tool paths traversing singular positions through inverse kinematics. In many characteristics and practices, PKMs (parallel kinematic machines) and serial machines are the opposites of each other. Fully PKMs have relatively very limited working-space, especially in terms of orientation characteristics. Fully serial machines have a problem of error accumulation. This paper presents a modular method to construct a postprocessor system for a novel hybrid parallel-serial five-axis machine tool. A hybrid parallel-serial mathematical model is introduced to analyze a structural configuration. The configuration decomposition of machine tools is used to create the kernel of the postprocessor. The proposed modified DenavitHartenberg notation is used in the coordinate conversion procedure, and then an algorithm is used for developing the inverse kinematics of five-axis machines. The feasibility of solutions depends on the surface normal along the tool path satisfying certain orientation constraints. The proposed algorithm can be easily adapted to convert between cutter contact path and cutter location code and implemented on computer-aided design and computer-aided manufacturing systems. Examples with end-milling and side-milling tools are demonstrated and real cutting parts are implemented for verifying the algorithm.

Tool Path Calculation Based on the Actual Tool Profile

Due to tool wear and making errors, calculating the tool path based on the tool theory model has a great deal of influence on the accuracy of surface finishing machining. In order to solve the above problem, a photogrammetry method is used to extract the rotary cutter profile, and then the tool surface is get by letting the fitting profile curve revolves about the cutter axis, finally the cutter contact path is obtained based on the minimal orientation-distance algorithm. Experiments prove the cutter contact path is just on the theory surface of the workpiece. Therefore the accuracy of surface finishing machining will be greatly improved by the method.

Tool path generation for triangular meshes using least-squares conformal map

Tool path generation is an interesting and challenging task in free-form surface machining. Iso-planar tool path generation is one of the common approaches to dealing with this task. However, it suffers from an inherent drawback that intersecting intervals of the iso-planar method are limited to surface geometric features. This results in poor machining efficiency in flat regions due to redundant machining paths. For this problem, a new tool path generation method for triangular meshes is proposed based on the least-squares conformal map (LSCM). After LSCM parameterisation with minimal stretching energy, the triangular meshes are unfolded on a plane, where the principal component analysis (PCA) technique is employed to determine a suitable drive line for calculating cutter contact paths by the iso-planar strategy. Therefore, the tool paths are generated in a plane and the unevenness of the traditional iso-planar method is improved. The feasibility and effectiveness of the developed method is demonstrated through a test experiment.

Combined reparameterization-based spiral toolpath generation for five-axis sculptured surface machining

Reparameterization-based toolpath generation methods are usually adopted for machining triangular meshes, trimmed surfaces and compound surfaces. The quality of the reparameterization has an important effect on that of the surface. In this paper, a combined reparameterization procedure is introduced to generate an optimal mapping between the designed surface and a specified planar circular region with relatively less distortion both in length and in angle. Then, for five-axis sculptured surface machining the mathematical model of spiral guide path with maximum path interval is constructed in the circular region. Cutter contact paths are obtained by inversely mapping the guide path onto the designed surface. Under constraints of gouging and collision, continuous and optimal cutter orientations are subsequently calculated. Finally, the results of simulation and experiment of the machining process are given to illustrate the feasibility and applicability of the proposed method.

Spiral cutting operation strategy for machining of sculptured surfaces by conformal map approach

Although compound surfaces and polyhedral models are widely used in manufacturing industry, the tool path planning strategies are very limited for such surfaces in five-axis machining and high speed machining. In this paper, a novel conformal map based and planar spiral guided spiral tool path generation method is described for NC machining of complex surfaces. The method uses conformal map to establish a relationship between 3D physical surface and planar circular region. This enables NC operation to be performed as if the surface is plat. Then through inversely mapping a planar spiral defined by a mathematical function into 3D physical space, the spiral cutter contact paths are derived without inheriting any corners on the boundary in the subsequent interior paths. The main advantage of the proposed method is that a smoother, longer and boundary conformed spiral topography tool path is developed. Therefore, the machined surface can be cut continuously with minimum tool retractions during the cutting operations. And it allows both compound surfaces and triangular surfaces can be machined at high speed. Finally, experimental results are given to testify the proposed approach.

Design and implementation of a real-time NURBS surface interpolator

In recent years, various parametric curve interpolators have been proposed for high-speed and high-accuracy machining. However, these methods are based on a constant cutter location (CL) velocity. Hence, the cutter contact (CC) velocity along the surface tends to vary, resulting in a nonuniform machining performance. Furthermore, machining complex surfaces requires the provision of a large number of tool paths and therefore the associated NC data files are generally very large. To overcome these limitations, the current study presents a novel real-time NURBS surface interpolator which ensures a constant CC velocity along the CC paths and its intervals. A PC-based real-time motion control network utilizing SSCNET is developed to achieve the goal of multi-axis synchronous motion. In this study, both the NURBS surface interpolator algorithms and the SSCNET communication protocols are realized by Embedded XP with the RTX real-time kernel. The experimental results confirm that the proposed real-time NURBS surface interpolator is capable of achieving a satisfactory performance.

Modelling of tooth trajectory and process geometry in peripheral milling of curved surfaces

The paper presents modelling of tooth trajectory and process geometry in peripheral milling of curved surfaces. The paper differs from previous work in this area, in two respects. Firstly it deals with milling of variable curvature geometries unlike zero and constant curvature geometries dealt in the past. Secondly true tooth trajectories are considered for modelling process geometry in milling of curved surfaces instead of simpler circular tooth trajectories. Mathematical expressions for, feed per tooth along cutter contact path, entry and exits angles of tooth, undeformed chip thickness and surface error are derived and effect of workpiece curvature on these variables is studied. As cutting forces depend on these process variables, physical experiments were also performed to study the effect of workpiece curvature on cutting forces. Process simulation experiments carried out show the need for modelling true tooth trajectories instead of circular tooth trajectories particularly for curved geometries. Results also show that using simpler constant curvature models to variable curvature geometries for the purpose of estimation of process geometry variables could be erroneous.

A real-time NURBS surface interpolator for precision three-axis CNC machining

Due to the fact that the cutting occurs around the cutter contact (CC) point, the efficiency and quality of CNC machining can be improved significantly if the CC velocity along the surface is kept costant. Conventional approaches to machining mainly maintain a constant cutter location (CL) velocity, so that the CC velocity along the surface is often not constant and usually results in non-uniform machining and unsatisfactory quality. To overcome this difficulty, this paper presents a novel NURBS surface interpolator that is capable of real-time generation of CL motion command for ball-end milling of NURBS surfaces and maintaining a constant CC velocity along the CC path and its intervals. For performance evaluation, a three-axis servomechanism driven by three servomotors is controlled to track segments represented by NURBS surfaces. Experimental results verify the effectiveness of the proposed method.

Geometrical Error Analysis and Control for 5-axis Machining of Large sculptured surfaces

One of the important tasks in five-axis machining of large sculptured surfaces is to control and reduce the machined errors. This paper presents the methods to control geometrical errors based on the establishment of the link between geometrical errors and the parameters of tool path planning. Nonlinear errors, which are the majority of geometrical errors during five-axis machining, are is strictly analysed and formulated. An adaptive step length method is proposed to control effectively the cutter contact path error. The measures to reduce the scallop error in machining of the large sculptured surfaces are discussed also. With the combination of this research with CAM software, both large Kaplan and Francis hydroturbine blades have been successfully machined. It shows that the machined errors can be controlled effectively and the machining efficiency can be improved in the machining of the large sculptured surfaces by the proposed methods.

볼엔드 밀링에서의 일정 절삭력을 위한 NURBS 곡면 인터폴레이터

This study presents a new type of CNC interpolator that is capable of generating cutter paths for ball-end milling of NURBS surfaces. The proposed surface interpolator comprises real-time algorithms for cutter contact (CC) path scheduling and CC path interpolator. Especially in this study, a new interpolator module to regulate cutting forces is developed. This propose algorithm utilizes variable-feedrate commands along the CC path according to the curvature of machined surfaces during the interpolation process. Additionally, it proposes an OpenGL graphic library for computer graphics and animation of interpolated tool-position display. The proposed interpolator is evaluated and compared with the existing method based on constant feedrates through computer simulations.

Guide surface based tool path generation in 3-axis milling: an extension of the guide plane method

Proposed in this paper is a new tool path generation method of 3-axis milling by using the guide surface, which is constructed with the machining region to be cut on the part surface. The guide surface, as an extension of the guide plane, globally takes the shape characteristic of the machining region into consideration well, and plays a key role as a domain space for planning the guide paths. Therefore, the proposed method can handle the region consisting of several trimmed surfaces just like the guide plane method. The final tool paths are calculated from the cutter contact-paths obtained by projecting the guide tool paths onto the machining region. Unevenly spaced tool paths, the major drawback of using conventional methods, can be also overcome by employing one of the projecting directions proposed. Tool path generation, an example of clean-up machining, is described for explaining the proposed method in detail. Some illustrative examples show the possibility that the method can be applied to the various 3-axis milling operations including high-speed machining.

CNC machine tool surface interpolator for ball-end milling of free-form surfaces

This paper presents a new type of CNC machine tool interpolator that is capable of generating the cutter path for ball-end milling of a free-form surface. The surface interpolator comprises on-line algorithms for cutter-contact (CC) path scheduling, CC path interpolation, and tool offsetting. The interpolator algorithms for iso-parametric, iso-scallop and iso-planar machining methods are developed, respectively. The proposed surface interpolator method gains the advantages for minimizing the data loaded to the CNC machine tool and maintaining the desired feedrate and position accuracy along the CC path.

Real-time generation and control of cutter path for 5-axis CNC machining

This paper presents a new approach to real-time generation and control of the cutter path for 5-axis machining applications. The cutter path generation method comprises real-time algorithms for cutter-contact path interpolation, cutter offsetting, and coordinate conversion. In addition, a global feedback loop is closed by the CNC interpolator so as to augment the controlled accuracy in practical cutter path generation. An error compensation algorithm and a feedrate adaptation algorithm for the control loop are developed, respectively.

A CAD/CAM system from 3D coordinate measuring data

SUMMARY A CAD/CAM system with some new numerical methods is presented in this paper. This system mainly consists of two stages. In stage 1, the least squares method is applied to fit a best form of parametric surface to a set of data points obtained from a 3D coordinate measuring machine, with the errors caused by the probe compensated. In stage 2, from the best form of parametric surface obtained in stage 1, a new efficient method—adaptive path planning—which has better performance than the old parametric method is developed to generate the cutter path. By application of adaptive path planning, machining time can be reduced. By transforming the cutter contact path to the cutter location path, the curvature method for detecting gouging is presented by which a tool path with gouging avoidance can be generated.