Thermal issues in machine tools

We give a deterministic algorithm for triangulating a simple polygon in linear time. The basic strategy is to build a coarse approximation of a triangulation in a bottom-up phase and then use the information computed along the way to refine the triangulation in a top-down phase. The main tools used are the polygon-cutting theorem, which provides us with a balancing scheme, and the planar separator theorem, whose role is essential in the discovery of new diagonals. Only elementary data structures are required by the algorithm. In particular, no dynamic search trees, of our algorithm.

Triangulating a simple polygon in linear time

Virtual machine tool

Research in automating the process level of machining operations has been conducted, in both academia and industry, over the past few decades. This work is motivated by a strong belief that research in this area will provide increased productivity, improved part quality, reduced costs, and relaxed machine design constraints. The basis for this belief is twofold. First, machining process automation can be applied to both large batch production environments and small batch jobs. Second, process automation can autonomously tune machine parameters (feed, speed, depth of cut, etc.) on-line and off-line to substantially increase the machine tool's performance in terms of part tolerances and surface finish, operation cycle time, etc. Process automation holds the promise of bridging the gap between product design and process planning, while reaching beyond the capability of a human operator. The success of manufacturing process automation hinges primarily on the effectiveness of the process monitoring and control systems. This paper discusses the evolution of machining process monitoring and control technologies and conducts an in-depth review of the state-of-the-art of these technologies over the past decade. The research in each area is highlighted with experimental and simulation examples. Open architecture software platforms that provide the means to implement process monitoring and control systems are also reviewed. The impact, industrial realization, and future trends of machining process monitoring and control technologies are also discussed.

Machining Process Monitoring and Control: The State-of-the-Art

Multisensor data fusion in dimensional metrology

Multi-axis tool paths are currently generated as a set of discrete data points consisting of a position vector, representing the tool tip, and an orientation unit vector, representing the tool axis. The CNC interpolator must convert these points into continuous machine tool axis motions. To achieve the highest quality parts, a constant feed and reduced angular acceleration must be maintained throughout the motion. This paper presents a new algorithm for off-line interpolation of the data points, followed by real-time axis command generation. The splines produced by the algorithm are C2 continuous, and independent of machine tool kinematics. Hence the motions produced will be the same on any five-axis machine tool, hexapod, or robotic arm. Three splines are computed: position, orientation, and reparameterization. The position spline is a near arc-length parameterized quintic polynomial spline. The paper introduces a near arc-length parameterized quintic spherical Bezier spline as the orientation spline. Coordinated motion is accomplished with an orientation reparameterization spline. The proposed algorithm is demonstrated using a practical example.

A constant feed and reduced angular acceleration interpolation algorithm for multi-axis machining

In this paper, kinematic modelling of a Coordinate Measuring Machine (CMM) is carried out and the methodology followed in modelling is explained in detail. The model is simplified by certain assumptions which may result in over-simplification of the model. Consequently, the model is investigated and enhanced by adding the relevant and suitable geometric error terms. Different approaches are employed to evaluate the model coefficients. In the first approach, a commercial ring gauge is measured in a structured lattice in the work volume of the CMM. Resulting errors in these measurements are used in conjunction with some statistical methods to arrive at sets of model coefficients values. The second approach is based on measurement of the individual 21 error terms in the CMM by means of laser interferometry. These measurements are used to evaluate another set of model coefficients. A compensation strategy is proposed and tested using the model and the sets of coefficients obtained. Volumetric Performance of the CMM is evaluated according to ASME standards, before and after compensation. Improvement in the CMM volumetric performance is demonstrated and compared.

Kinematic and geometric error compensation of a coordinate measuring machine

A generic solid modeller based milling process simulation system is developed for 3-axis milling of complex parts. Parts are described using a boundary representation solid model, and cutting edges are fitted with cubic Bezier curves. For every completed tool path (i.e., one NC block), the tool swept volume is generated and intersected with the part, yielding the corresponding removed material volume. The tool cutting edges are then intersected with that volume to produce the tool-part immersion geometry. The mechanistic milling process model produces an accurate simulation of cutting forces, torque and power. Modelling of tool and tool holder dynamics is included. The system is based on a generic procedure for extracting geometric data required to accurately simulate milling of complex parts. Any tool shape can be represented, and extension to 4- and 5-axis machining is straightforward. Related processes such as turning and drilling can be modelled in a similar way. The capability of the system is demonstrated experimentally for ball end milling.

Milling process simulation : A generic solid modeller based paradigm

This paper presents a dynamic force model and a stability analysis for ball end milling. The concept of the equivalent orthogonal cutting conditions, applied to modeling of the mechanics of ball end milling, is extended to include the dynamics of cutting forces. The tool is divided into very thin slices and the cutting force applied to each slice is calculated and summed for all the teeth engaged. To calculate the instantaneous chip thickness of each tooth slice, the method of regenerative chip load calculation which accounts for the effects of both the surface undulations and the instantaneous deflection is used. To include the effect of the interference of the flank face of the tool with the finished surface of the work, the plowing force is also considered in the developed model. Experimental cutting forces are obtained using a five-axis milling machine with a rotary dynamometer. The developed dynamic model is capable of generating force and torque patterns with very good agreement with the experimental data. Stability of the ball end milling in the semi-finishing operation of die cavities is also studied in this paper. The tangential and radial forces predicted by the method of equivalent orthogonal condition are fitted by the equations F t = K t ( Z ) bh av and F r = K r ( Z ) F t , where b is the depth of cut and h av is the average chip thickness along the cutting edge and Z is the tool axis coordinate. The polynomial functions K t ( Z ) and K r ( Z ) are the cutting force constants. The interdependency of the axial and radial depths of cut in ball end milling results in an iterative solution of the characteristic equation for the critical width of cut and spindle speed. In addition, due to different cutting characteristics of the cutting edge at different heights of the ball nose, stability lobes are represented by surfaces . Comparison of the time domain simulation for the shoulder removal process in die cavity machining with the analytical predictions shows that the proposed method is capable of accurate prediction of the stability lobes.

On the dynamics of ball end milling: modeling of cutting forces and stability analysis

Most existing machining simulation software is geometric in nature, and ignores the physical aspects of the process This paper reports research progress towards developing a comprehensive physical machining process simulation program based on a solid modelling kernel Both flat and ball end tools are modelled, and multi-axis motion is supported A Finite Element Analysis model is used to predict both tool and part deflection A special sweep representation is used for Boolean part model updating The system can be used for prediction as well as for intelligent factory floor control Several examples of completed work are included to illustrate developed techniques A discussion section presents computation time data, and outlines how parallel processing could be utilised

Integrated solid modeller based solutions for machining

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