An analytical method for obtaining cutter workpiece engagement during a semi-finish in five-axis milling

In five-axis milling, determining the continuously changing Cutter Workpiece Engagement (CWE) remains a challenge. Solid models and discrete models are the most common methods used to predict the engagement region. However, both methods suffer from long computation times. This paper presents an analytical method to define the CWE for toroidal and flat-end cutters during semi-finish milling of sculptured parts. The staircase workpiece model that resulted from rough milling was used to verify the method. The length of each cut at every engagement angle can be determined by finding two points: the lower engagement (LE) point and the upper engagement (UE) point. An extension of the method used to calculate the grazing point in swept envelope development was utilized to define the LE-point. The test showed that the existence of an inclination angle significantly affected the location of the LE-point.For the UE-point, it was first assumed that the workpiece surface was flat. A recalculation of the CWE was then performed to obtain a more accurate engagement profile with the actual surface. A technique called the Toroidal-boundary method was employed to obtain the UE-point when it was located on the toroidal side of the cutting tool. Alternatively, a method called the Cylindrical-boundary method was used to calculate the UE-point for a flat-end cutter on the cylindrical side of the toroidal cutter. The proposed model was successfully used to generate CWE data for two model parts with different surface profiles. The accuracy was verified twice: first, by comparing the coordinates of the UE-points with respect to the workpiece surface and second, by using Siemens-NX. The results proved that the proposed method was accurate. Moreover, because this method is analytical, it is more efficient in terms of computation time compared with discrete models.     

Wholly smoothing cutter orientations for five-axis NC machining based on cutter contact point mesh

Cutting forces with respect to different cutter orientations are analyzed for five-axis NC machining of a ball-end cutter.A measure is then defined to quantify the effects of cutter orientation variation.According to the measure,a novel model and algorithm are proposed to wholly optimize cutter orientations based on a cutter contact(CC) point mesh.The method has two advantages.One is that the cutter orientation smoothnesses along the feed direction and pick-feed direction are both wholly optimized.The other...     

Arc–surface intersection method to calculate cutter–workpiece engagements for generic cutter in five-axis milling

Calculating cutter–workpiece engagements (CWEs) is essential to the physical simulation of milling process that starts with the prediction of cutting forces. As for five-axis milling of free form surfaces, the calculation of CWEs remains a challenge due to the complicated and varying engagement geometries that occur between the cutter and the in-process workpiece. In this paper, a new arc–surface intersection method (ASIM) is proposed to obtain CWEs for generic cutter in five-axis milling. The cutter rotary surface is first represented by the family of section circles which are generated by slicing the cutter with planes perpendicular to the tool axis. Based on the envelope condition, two grazing points on each section circle are analytically derived, which divide the circle into two arcs. The feasible contact arc (FCA) is then extracted to intersect with workpiece surfaces. Using arc/surface intersection and distance fields based approach, the boundary of the closed CWEs is accurately and efficiently calculated. Compared with the solid modeler based method and the discrete method, the ASIM has higher computational efficiency and accuracy. Moreover, an analytical solution for calculating CWEs can be obtained with this method in five-axis milling of the workpiece merely comprising of flat and quadric surfaces. Finally, two case tests are implemented to confirm the validity of the ASIM and comparisons have been made with a Vericut based system which utilizes the Z-buffer method. The results indicate that the ASIM is computationally efficient, accurate and robust.     

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.     

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.     

The Jacobian condition number as a dexterity index in 6R machining robots

The use of robots for machining operations is growing because of their flexibility to perform a broad spectrum of tasks at a lower cost when compared with machine tools. In this paper the Jacobian condition number is used as a performance index intended to make a better use of revolute-jointed six-degree-of-freedom serial robots in five-axis machining. This index is of the kinetostatic type, low-frequency dynamic effects not being relevant to this study. Indeed, dynamic effects can be neglected because, during machining, the robot is not working at high speed, the spindle motion affecting only the structural, high-frequency modes of the system. The condition number is known to be a measure of Jacobian invertibility; it is used here as an index to improve joint-rate distribution. A low condition number is shown to translate into a smoother joint-rate time history.     

The influence of different electronic maps and displays on performance and operator state in a geographic orientation task

Mobile electronic displays for geographic orientation and navigation are used increasingly in various civil and military domains. But it is still unclear which displays and kinds of map presentation suit best for specific purposes. In the present experiment, a head-mounted display (HMD) and a display from a personal digital assistant (PDA) were compared in a simulated geographic orientation task in an urban environment. Furthermore, the effect of three kinds of map presentation (egocentric, geocentric and geocentric with colour cues) was analysed. The simulated orientation task was projected on a screen and participants controlled their locomotion within the urban area by means of a joystick. Task completion time, peripheral attention, workload, fatigue and simulator sickness were registered as dependent variables. In comparison to the geocentric map the egocentric map showed a significant shorter task completion time and the geocentric map with colour cues a significant higher peripheral attention. Task completion time of the HMD and the PDA did not differ significantly. However, peripheral attention and most indices of workload, fatigue and simulator sickness were significantly better for the PDA. Therefore, the results recommend to apply PDAs and egocentric maps for comparable orientation tasks.