Qingzhen Bi

A GPU-based algorithm for generating collision-free and orientation-smooth five-axis finishing tool paths of a ball-end cutter

A graphics process unit (GPU) based approach that generates collision-free and orientation-smooth tool paths for five-axis NC finishing machining of complicated shapes is presented. A new GPU-based method is proposed to compute accessibility cones of cutter location (CL) points for a ball-end cutter and tool orientations are then optimised in the accessibility cones. Three steps in the approach are GPU-based accessibility computation, feasibility map and orientation optimisation. Unlike the existing visibility concept, the diameters of both tools and tool-holders are taken into consideration and the actual accessibility cone is computed directly and efficiently based on occlusion query functionality of the graphics hardware. Next, a feasibility map is used to select feasible orientations due to the limits of collision avoidance and the machine tool. Finally, tool orientations are globally optimised to generate an orientation-smooth tool path. The proposed algorithms allow an acceptable computing time and hardware requirement to generate collision-free and orientation-smooth tool paths for complicated shapes. Examples show the efficiency of computing accessibility cones. The finishing tool paths for machining an impeller are generated as examples and cutting experiments confirm the validity of the proposed approach.

A practical continuous-curvature bézier transition algorithm for high-speed machining of linear tool path

A continuous-curvature smoothing algorithm is developed to approximate the linear tool path for high speed machining. The new tool path composed of cubic Bezier curves and lines, which is everywhere G2 continuous, is obtained to replace the conventional linear tool path. Both the tangency and curvature discontinuities at the segment junctions of the linear tool path are avoided. The feed motion will be more stable since the discontinuities are the most important source of feed fluctuation. The algorithm is based upon the transition cubic Bezier curve that has closed-form expression. The approximation error at the segment junction can be accurately guaranteed. The maximal curvature in the transition curve, which is critical for velocity planning, is analytically computed and optimized. The curvature radii of all transition Bezier curves are also globally optimized to pursue the high feed speed by a linear programm model. Therefore, the algorithm is easy to implement and can be integrated into a post-process system.

An algorithm to generate compact dual NURBS tool path with equal distance for 5-Axis NC machining

A new algorithm is proposed to generate compact dual NURBS tool paths with equal distance (DNTPED) for 5-axis NC machining. The DNTPED has significant advantages over conventional linear tool path in the NC machining of free-form surface since it reduces the tangency discontinuities along the tool path. The discontinuities, the inherent character of the linear interpolation, are the important sources of practical feed-speed fluctuation of the machine tool. The new algorithm is proposed to generate DNTPED based on the theories of rational motion. Here the rational rigid movement of a cutter is represented by a B-spline curve in dual quaternion space. DNTPED is obtained directly from the B-spline dual quaternion curve with the help of the blossom form of the B-spline curve. Comparing with the existing method, the DNTPED consists of less data and each NURBS can be treated as one curve, not as a collection of bezier segments.

Generating collision-free tool orientations for 5-axis NC machining with a short ball-end cutter

A novel tool orientation optimisation algorithm is proposed for 5-axis NC machining with a short ball-end cutter. It can generate collision-free and smooth tool orientations along with a safe and shortest tool length (SSTL). The use of shorter cutters without collision is a key advantage of 5-axis machining because the magnitude of tool deflection and the stability of cutting process are greatly affected by the slenderness ratio of the cutter. Existing methods can calculate the SSTL in the NC simulation process. However, the SSTL is essentially determined by the tool orientations and should be considered in the process of tool path generation. To overcome this limitation, a new tool orientation optimisation algorithm is proposed. The SSTL is determined by optimising the tool orientations under the constraints of global collision avoidance and tool orientation smoothness. The algorithm first computes the global accessibility cone and the SSTL along each accessible tool orientation. Then the tool orientations are optimised based on the discrete dynamic programming with the SSTL along the whole tool path being the optimisation objective. Finally, the tool path is generated by globally smoothing the tool orientations. Computational examples and cutting experiment are given to illustrate the validity and efficiency of the proposed algorithm.

Five-axis flank milling of impellers: Optimal geometry of a conical tool considering stiffness and geometric constraints

Based on the Rayleigh–Ritz method, this article proposes an indicator to quantify the stiffness of a conical cutter for flank milling of impellers. Its validity is verified by the finite element analysis. A mathematical model is then developed to optimize the geometry of the conical cutter. The objective is to improve the stiffness of the cutter. Three kinds of geometric constraints are considered. First, the ball end of the cutter should be tangential to the hub surface. Second, the cutter should be interference-free with the adjacent blade. Finally, the machining error should satisfy the precision requirements. All these geometric constraints are characterized by the signed point-to-surface distance function. Based on the differential property of the distance function, a sequential linear programming method is applied to obtain the optimal geometry of the cutter along with the tool path. Simulation results confirm the effectiveness of the proposed model and algorithm.

Cutter size optimisation and interference-free tool path generation for five-axis flank milling of centrifugal impellers

Strategies for cutter size optimisation and interference-free tool path generation are proposed for five-axis flank milling of centrifugal impellers. To increase the material removal rate and provide a stronger tool shank during flank milling, the cutter size is first maximised under a set of geometric constraints. The tool path is then globally optimised in accordance with the minimum zone criterion for the determined optimal cutter size. Aside from the local interference of the cutter with the design surface, the global interferences with the hub surface and the adjacent blade surface are also considered in the optimisation models. Interference is indicated by the signed distance from the sampled point on the blade surface to the tool envelope surface. This distance is calculated without constructing the envelope surface. On the basis of the differential property of the distance function, we choose a sequential linear programming method in implementing the optimisations. This approach applies to generic rotary cutters, such as cylindrical and conical tools. Simulations are conducted to obtain the optimal cutter size and generate an interference-free tool path for a practical impeller. Simultaneously, a software module that can generate tool envelope surfaces and verify geometric errors is used to validate the proposed method.

Dual-Bézier path smoothing and interpolation for five-axis linear tool path in workpiece coordinate system

The tool path composed of consecutive short linear segments (G01 blocks) is still the widespread tool path representation form in five-axis machining. The inherent shortcoming of linear tool path is first-order discontinuity at the corner, which is the bottleneck to achieve high-speed and high-accuracy machining. In this article, a dual-Bézier path smoothing algorithm for five-axis linear tool path in workpiece coordinate system is proposed. There are three steps involved in our method. First, the corner error distribution model is introduced to assign the given tolerance to the smoothing approximation error constraint and the chord error constraint to ensure the interpolation trajectory error within the given tolerance. Second, segment junctions of the linear tool path in workpiece coordinate system are smoothed by double G2 continuous cubic Bézier curves. One cubic Bézier curve is used to round the corner of the tool tip point path, and the other Bézier curve is used to round the corner of the tool axis point path. This algorithm takes the conditions of approximation error constraint, the parameterized synchronization constraint, and continuous curvature constraint into consideration. Hence, the tangency and curvature continuities are both guaranteed in the new path. Third, an adaptive feedrate scheduling method is introduced to interpolate the new path. Simulation and experiment are performed to verify the effectiveness of the proposed method in five-axis tool path smoothing, speed smoothing, and trajectory accuracy controlling.

Real-Time Normal Measurement and Error Compensation of Curved Aircraft Surface Based on On-line Thickness Measurement

Large aerospace thin-walled workpieces easily give rise to random deformation in clamping and machining processes, in which the real-time monitoring of wall thickness needs a high-quality normal technology. A high-precision on-line surface normal measurement and a real-time compensation strategy are developed in this paper. Firstly, the deviation between the actual normal vector and the spindle direction of curved workpiece surface is calculated from the data measured by four eddy current displacement sensors which are installed at the front end of the spindle; then, the deviation is converted into the compensation of each axis via homogeneous coordinate transformation and post-processing of tools. Meanwhile online compensation results get finished on the move. A simulated and experimental platform is established on an A-C five-axis machine tool in order to measure deviations of sensors at each point position and record the result of compensation. The application of this method in practical engineering can greatly improve the efficiency of measurement and control.

Design Method and Performance Effects of Curvature-Smooth Centrifugal Compressor Blades

Blade curvature has an important effect on the pressure distribution over the blade surface as well as the quality of airfoil machining, but curvature smoothing method in design environments is little studied. A new geometry generator is developed for the design of curvature-smooth airfoils. The sections of an airfoil can be initially designed by a conventional method, and each of the sections is then regenerated by fitting a fifth order B-spline curve. The first order differential of the curvature with respect to arc length of the blade surface is used as a curvature smoothness measure. The distance between discrete points and the curve, and the integral of the square of the first derivative along the streamwise section curve are simultaneously minimized in the fitting process. The design of a transonic centrifugal compressor for turbocharger application is presented to study the effects of the curvature-smooth blade on centrifugal compressor performance. A numerical study was carried out and the results are discussed.© 2015 ASME

Five-Axis Flank Milling for Design and Manufacture of Turbocharger Compressor Impeller

Modern turbocharging has imposed multiply stringent requirements on turbocharger compressor impellers. They must be highly efficient and quiet in operation, have longevity in service, be cheaply made and be quick to market. The traditionally cast compressor impellers are struggling to meet these demands. The turbocharger compressor impellers machined from solid have many advantages in geometric accuracy, material property and design-to-production time compared with their cast counterpart. However, the benefits of machined impeller had been hindered by high manufacturing cost. The high cost comes mainly from long machining time with traditional five-axis point milling. Compared with the point milling, five-axis flank milling has much higher material removal rate, and this significantly reduces machining cost and makes machining from solid competitive. Turbocharger industry uses to design their impellers for casting or five-axis point-milling, and the impeller blade surfaces are usually freeform surfaces. Current CAM (Computer Aided Manufacture) software has provided flank milling function for smooth straight-line-surfaces (SLS), but they cannot handle the freeform surfaces. The conversion from arbitrary surface to SLS becomes necessary. The conversion method has been developed, but few of them concern the important manufacturing constraints such as the smoothness of cutter movement and the developability of the SLS. Furthermore, the conversion may be used in the manufacturing process only, and the effect of the deviation between the original freeform surface and the SLS may be ignored. In this paper, we put forward a new approach. First a flank milling conversion method is described. It takes into account of important manufacturing constraints when converting an arbitrary surface into a SLS. The method is fast and produces good approximation. Next we describe how the method can be integrated into daily impeller design suite to make impeller design and subsequent manufacturing more effective. The approach is illustrated and verified by the design and machining experiment of a turbocharger impeller.Copyright