Five-axis Computer Numerical Control Research Articles

On the B-spline interpolated tool trajectories for five-axis sculptured surface machining

B-spline interpolation scheme is now available on modern five-axis Computer Numerical Control (CNC) machine tools. With this newly implemented interpolation scheme, a cutting tool can be directly commanded to trace B-spline trajectories, which approximate ideal 3D curved trajectories, in sculptured surface machining. The approximation of ideal tool trajectories by B-spline interpolated tool trajectories inevitably leads to machining errors, referred to as the geometry-based errors in the present work. It is essential to ensure synchronisation of the movements of the three translational and two rotational joints of a five-axis machine tool to reduce the geometry-based errors. This paper presents an effective method to achieve synchronisation of the machine joint movements. It first fits a 3D B-spline for the three translational joints and then uses a knot inheriting procedure to fit a 2D B-spline for the two rotational joints. Evaluation of the presented method was made through the machining of a typical bi-cubic Bezier surface on a five-axis machine tool capable of performing non-uniform B-spline interpolation. It was found that the resulting geometry-based errors, which were varying along the given isoparametric tool paths, were able to be maintained below 25m.

Determination of Geometry-Based Errors for Interpolated Tool Paths in Five-Axis Surface Machining

Five-axis computer numerical control (CNC) machining is characterized with a multitude of errors. Among them an important component comes from the computer-aided manufacturing software known as the geometry-based errors. A new and accurate method to determine these errors is presented in this paper as opposed to the conventional chordal deviation method. The present method allows establishing the exact linearly interpolated tool positions between two cutter contact points on a given tool path, based on the inverse kinematics analysis of the machine tool. A generic procedure has been developed to ensure wide applicability of the proposed method. Analytical derivation of the geometry-based errors provides insights regarding the origin of these errors and their affecting parameters. Due to the highly non-linear characteristics of the problem, analytical solutions can only be obtained for simple surface geometry. Numerical computation is able to determine the errors for general surface shapes but it would be difficult to uncover further insightful information from the calculated error values. Besides the local surface geometry, the configuration of the kinematic chain of the CNC machine has been found to be the primary factor controlling the resulting value and type of the geometry-based errors. Implementations with a typical complex free-form surface demonstrated that the conventional chordal deviation method was not reliable and could significantly underestimate the geometry-based errors.

Burn threshold of high-carbon steel in high-efficiency deep grinding

The burn-threshold of high-carbon steel (51CrV4) in the high-efficiency deep-grinding (HEDG) process is investigated. It is found that the burn threshold in HEDG is determined by the wheel-workpiece contact length, material removal rate and wheel speed. A theoretical expression for the burn threshold has been derived, which is based on the thermal modelling for deep grinding and takes account of the grinding parameters, wheel conditions, thermal properties of the workpiece and abrasive grain, and the heat convected away by the coolant and chips. The predicted upper and lower boundaries for occurrence of workpiece burn show good agreements with the experimental observations. It is shown that burn threshold in HEDG is related to the film boiling of process coolant and the critical heat flux increases as the specific material removal rate increases. The experiments were carried out on an Edgetek five-axis computer numerical control (CNC) grinding machine, which is capable of HEDG in a relatively wide range of process parameters.