Cutter Contact Points Research Articles

UG secondary development of path generation of straight profile toroidal worm finishing tool

Abstract Due to the complexity of the right and left tooth surfaces of the straight profile toroidal worm, it is difficult in 3D modeling and NC programming. Based on the equal residual height algorithm, this paper deduces the calculation formula of the cutter contact and cutter point of the tooth surface of the straight profile toroidal worm by using the round nose milling cutter, calculates the cutter point coordinates and rotation angles of each point of the tooth surface of the straight profile toroidal worm through the UG secondary development interface and Visual Studio software, and generates the numerical control code on this basis. The machining simulation and experiment show that the machining efficiency and error of the straight profile torus worm machined by the tool path prepared by the equal residual height method are better than that of the isoparametric method.

A novel tool path planning method for 5-axis single-point diamond turning

5-Axis single-point diamond turning adds two linked axes based on 3-axis single-point diamond turning, which can smoothly and continuously process complex surfaces. Compared to 3-axis turning, tool path planning for 5-axis single-point diamond turning is a complex decision-making process, which is a novel problem in the existing studies and a difficulty in multi-axis turning. In this study, a novel path planning method for 5-axis single-point diamond turning is proposed. Firstly, the mapping relation from scallop height to the distribution of cutter contact (CC) points is established in the non-uniform rational B-spline (NURBS) parameter space, thereby the planning of CC points is quickly achieved under fewer constraints. Furthermore, the local interference and global interference generation mechanism of 5-axis single-point diamond turning are revealed by geometrical analysis, combining diamond tool parameters and tool shank parameters. By transforming the motion of the cutter axis posture in 3D space into swings in two planes, the posture accessibility diagram of the cutter axis is efficiently constructed. Finally, the feasibility and effectiveness of the tool path planning method are verified by 5-axis single-point diamond turning experiment. And the contour accuracy is improved through the quadratic planning of the CC points (the contour accuracy after compensation is 3.2 μm compared to normal one 9.6 μm). This study extends the traditional 3-axis turning to 5-axis turning, providing a new perspective for the machining of complex surfaces.

An adaptive singularity avoidance method for five-axis toolpath generation with invariant cutter-contact points and bounded tool orientation variation based on the reduction of Jacobian condition number

To enhance the five-axis machine-tool performance, it is significant to avoid the singular configuration where the kinematic and dynamic performances degrade dramatically. Most existing methods aim at solving this issue by avoiding the singularity posture in the geometric manner. Different from them, this paper aims at avoiding the singular phenomenon by reducing the Jacobian-matrix condition number, and proposes an adaptive singularity avoidance toolpath generation method. This method adds a damping diagonal matrix into the computation of the pseudo-inverse Jacobian matrix to reduce its ill-condition extent during axial path generation, thus solving the singularity phenomenon. However, the adding of damping matrix gives arise to the toolpath error. To ensure the accuracy meanwhile, an adaptive law for determination of the damping matrix is presented to balance the singularity-avoiding effect and the path error, under the constraints of condition number and tool-orientation error-tolerance thresholds, as well as invariant cutter-contact points. Simulation and experimental tests verify that the proposed method can not only realize the singular avoidance without preliminary adjustment of the original toolpath, thus can be realized in real-time NC system, but also has better singular-avoiding performance and lower toolpath error when comparing with typical methods.

A novel regional force control strategy based on seven-axis linkage grinding system to improve blade machining accuracy

The aero-engine blade has the characteristics of large curvature and uneven allowance distribution, which makes it difficult to ensure its machining accuracy during processing. The existing research mainly realizes the removal of blade allowance through constant contact force control strategy, which is difficult to achieve accurate removal of uneven allowance. This paper proposes a novel regional force control strategy based on seven-axis linkage grinding system. The ideal contact force is obtained according to the curvature and allowance distribution at each cutter-contact (CC) point, and the coefficient kp is calibrated by orthogonal grinding tests considering the initial rapid wear of the hollow ball abrasive belt. The ideal contact force is controlled by the regional force control strategy, which is composed of the regional division and the seventh axis controller. Considering the system response time and the distribution of the ideal contact force, the ideal contact force is divided into several regions through regional division algorithm, and then the actual contact force is controlled in real time during processing by the designed seventh axis controller to ensure the stability of the seventh axis. The force control accuracy with the seventh axis controller has increased by 63.7 % on the whole profile of the blade than that without the controller. The comparative robotic grinding experiment results show that the surface profile accuracy values at the four profile areas are improved by 57.6 %, 59.2 %, 70 % and 61.7 % than that with the passive compliance control (PCC) method, respectively.

Toolpath planning method with the constraint of cutting force fluctuation in slow tool servo turning for complex curved surface parts

Parts with the complex curved surface are commonly used in high-end equipment. The machining quality of the curved surface parts is important for the property of high-end equipment. With position control of the main spindle, i.e., the C axis, the slow tool servo (STS) turning is a very promising technique to effectively machine complex curved surface parts. However, the turning machining quality is restricted by the cutting force fluctuation in finishing turning. Hence, the STS turning toolpath generation approach with the constraint of the cutting force fluctuation is proposed in this study. As the cutting force is proportionate to the cutting area, the cutting area for turning complex curved surfaces is analyzed and calculated. Then the functional relation between the cutting force fluctuation and the feed rate is derived. Based on the geometrical characteristic of the first revolution of the toolpath, the feed rate is optimized with small cutting force fluctuation to derive the cutter contact points (CCPs) in the cylindrical coordinate system. From the validation experiment results, it can be seen that the cutting force fluctuation, the profile tolerance, and the surface roughness of parts are effectively reduced, and the surface roughness of the part machined with the proposed toolpath planning method is 17.625 nm. Thus, this study provides guidance for toolpath generation with the constraint of the fluctuation of the cutting force in STS turning for a complex curved surface.

Non-uniform machining allowance planning method of thin-walled parts based on the workpiece deformation constraint

In order to reduce the machining deformation of thin-walled parts during milling, a non-uniform allowance planning method for thin-walled parts based on the workpiece deformation constraint with the idea of adding materials in reverse material removal sequence is proposed in this paper. This method does not require accurate deformation prediction and extensive experiments compared to traditional error compensation methods. It strives to maximize the allowance to enhance the stiffness of the in-process workpiece. First, a cutting force threshold calculation method is proposed according to the finite element method. The cutting force threshold at different positions is calculated by obtaining the local stiffness characteristics at the cutter-contact point under the constraint of allowable deformation. And then, the maximum machining allowance at the cutter-contact point is calculated depending on the cutting force model. Considering that the stiffness of the workpiece is position-dependent and affected by material removal, the stiffness of the workpiece is updated by adding elements in the reverse cutting direction, and the finishing stock is obtained by surface fitting. Experimental results show that compared with the traditional uniform allowance method, the error of the proposed method is reduced by about 83%, which can effectively reduce the deformation and improve the machining accuracy.

A Novel Toolpath for Robotic Adaptive Grinding of Extremely Thin Blade Edge Based on Dwell Time Model

High precision and high efficiency in robotic grinding of aero-engine extremely thin blade edges is a challenging problem. In this article, a novel toolpath planning method is proposed based on the derived dwell time calculation model and the developed interpolation algorithm. The dwell time of each cutter contact point is solved based on the matrix method by consideration of the revised material removal model and machining allowance distribution. To optimize the previous interpolation algorithm based on geometric intersection, an arc length and Taylor binary expansion optimization are proposed to plan cutter contact points according to the dwell time and the curvature changes of blade edges. Subsequently, the tool orientation is corrected based on a double-vector controlling method to avoid the processing interference. Simulation results show that the proposed interpolation algorithm has improved the path coverage by 17.6%, and its computational efficiency is 34 times higher than that in previous algorithm. The comparative robotic grinding experiment results show that the proposed toolpath has improved the surface profile accuracy of blade edge to 0.042 mm, and its machining accuracy is 14.3–46.2% higher than that of other methods.

A study of interferential tool position correcting algorithms in 3D impeller variable-axis rough plunge milling

Plunge milling has significantly improved the rough machining efficiency of 3D impeller channels. However, in conventional plunge milling cutter position planning, interferences occurring at the end of every cutter position due to the sudden increase of radial depth is inevitable. This can seriously compromise the service life of the machine tool and cutter, and also reduce the efficiency at the interferential phase. This study optimised the tool path cutter axis vector of conventional rough machining of 3D impeller variable-axis plunge milling, thus making the angle between the normal vector of workpiece surfaces at the cutter contact point, and the cutter-axis vector of the adjacent tool position, gradually increase from the outlet to inlet on a very small scale. Based on this, an iterative algorithm for the tool centre position and cutter safety height was obtained, thus making the hub allowance of the optimised tool path for plunge milling as small as possible without affecting subsequent machining by avoiding the interferential phenomenon. Finally, the proposed method was verified by relevant numerical examples.

An Energy Efficiency Tool Path Optimization Method Using a Discrete Energy Consumption Path Model

As the energy cost accounts for about one-third of the total manufacturing cost, there is great significance in evaluating and managing energy consumption in manufacturing processes. The energy consumption during multi-axis end milling, which represents a large part of the industrial energy costs, is usually extraordinarily large, especially for complex free-form surfaces requiring multi-finish-machining. To obtain the most efficient tool path, the tool orientation is adjusted to obtain the largest cutting stripe width at each cutter contact point. However, the use of excessive driving energy consumption and cutting energy to obtain the largest cutting stripe width may reduce the energy efficiency of the tool path. To solve this problem, the geometry features of the tool path are analyzed firstly, and the global energy consumption analysis, which includes a cutting energy analysis and driving energy analysis, is conducted. The discrete energy consumption path model is constructed to find the most energy-efficient tool orientation sequence for a tool path. Finally, contrast experiments are carried out to validate the proposed method.

Machining-path mapping from free-state to clamped-state for thin-walled parts

Thin-walled parts with curved surface are widely used in industrial applications and the high-quality machining is still a major problem because of the low stiffness. By using the machining-path obtained from the design model of thin-walled parts with curved surface, the machining accuracy requirement may easily not be met due to the springback of clamping deformation when the machining process is finished. It is a novel idea that when the machining-path mapping from free-state to clamped-state is realized based on the clamping deformation, the final machining-path of thin-walled parts can be re-designed to directly ensure the machining accuracy requirement after the fixture is released. Based on the concomitant thought of curved surface and the elastic deformation theory of thin shell in this study, the mathematical model for the machining-path mapping from free-state to clamped-state is established for the thin-walled parts with curved surface. Then, the corresponding relationship of cutter contact (CC) points is calculated by grid mapping. Finally, the machining-path for the thin-walled parts with curved surface is re-designed under the clamped-state. Taking a thin-walled cylinder workpiece as an example, the experiment results show that the proposed method can achieve the avoiding purpose for the machining error caused by clamping deformation. These research achievements are of vital importance for realizing high-quality machining of the thin-walled parts with curved surface.

A novel selected force controlling method for improving robotic grinding accuracy of complex curved blade

Nonlinear time-varying contact state is a crucial factor to prevent the traditional robotic belt grinding method from precision machining of blade. In this case, a novel selected force controlling method (SFC) with consideration of regional division (RD) based on machining allowance is proposed for improving robotic grinding accuracy of complex curved blade, on basis of the self-developed adaptive impedance controller. Ideal normal grinding force at each cutter-contact (CC) point is calculated by principal curvature radius and regional allowance of blade surface. Then, the CC points with similar ideal normal grinding force are divided into one region along grinding path based on the force threshold. Furthermore, an adaptive impedance controller with neural network online compensation algorithm (AICNN) is developed, and the verification test results of grinding four profile areas of intake side, exhaust side, convex and concave, indicate that the force control accuracy with AICNN has increased by 80.33%, 50.58%, 82.65% and 69.01% than that without the controller, respectively. Based on this, the grinding experiment of typical turbine blade is conducted with SFC, and the surface profile accuracy values at the four profile areas have evidently improved by 48.79%, 35.67%, 59.54%, and 66.90% than that with conventional grinding (CG), respectively.

A normal section plane method for profile error analysis of five-axis machine tools based on the ideal tool flank milling surface

The existing studies on profile error analysis and machining accuracy measurement do not consider the impact of the theoretical errors on the machine tool accuracy measurement. Therefore, this study proposes an estimation method of the surface profile error based on the normal section plane, using the theoretical flank milled surface for comparison. This effectively improves the accuracy of profile error estimation. The theoretical flank milled surface is the surface machined by flank milling under ideal conditions. Hence, compared to the traditional analysis method based on the designed three-dimensional model of S-shaped test pieces, the calculated profile error of this method does not include theoretical errors, thereby eliminating the impact of theoretical errors on machine tool accuracy measurement and evaluation. First, an improved method for continuous parameterized dual spline interpolation was proposed. It simplifies the solution of the singular problem of the coefficient matrix of the spline basis function and obtains a continuous ideal machining tool axis trajectory surface with complete geometric characteristics. Next, a method for constructing the theoretical flank milled surface machined with a cylindrical milling tool using equidistant mapping characteristics was proposed; then, the differential transformation relationship at the cutting contact point of the curved surface under the influence of tool path errors was established. Furthermore, the normal section plane method based on the differentiation of the cutting contact point was proposed. The problem of solving the distance from a point to a surface is converted to the problem of solving the distance from a point to a curve in the normal section plane. This improves the accuracy of profile error estimation. The effectiveness of the method was verified by comparing the analysis results of the profile errors of a typical cylindrical surface with the point to surface and the point to curve methods.

A trajectory planning method on error compensation of residual height for aero-engine blades of robotic belt grinding

While the traditional trajectory planning methods are used in robotic belt grinding of blades with an uneven machining allowance distribution, it is hard to obtain the preferable profile accuracy and surface quality to meet the high-performance requirements of aero-engine. To solve this problem, a novel trajectory planning method is proposed in this paper by considering the developed interpolation algorithm and the machining allowance threshold. The residual height error obtained from grinding experiments of titanium alloy sample was compensated to modify the calculation model of row spacing, and a new geometric algorithm was presented to dynamically calculate the cutter contact points based on this revised calculation model and the dichotomy method. Subsequently, the off-line machining program is generated based on a double-vector controlling method to obtain an optimal contact posture. On this basis, three sets of robotic grinding tests of titanium alloy blades were conducted to investigate the advantages of the proposed method. The comparative experimental results revealed that the presented algorithm had improved the surface profile accuracy of blade by 34.2% and 55.1%, respectively. Moreover, the average machined surface roughness was achieved to 0.3 µm and the machining efficiency was obviously promoted. It is concluded that this research work is beneficial to comprehensively improve the machined quality of blades in robotic belt grinding.

Tool Orientation Optimization and Path Planning for 5-Axis Machining

Tool path generation is a fundamental problem in 5-axis CNC machining, which consists of tool orientation planning and cutter-contact (CC) point planning. The planning strategy highly depends on the type of tool cutters. For ball-end cutters, the tool orientation and CC point location can be planned separately; while for flat end cutters, the two are highly dependent on each other. This paper generates a smooth tool path of workpiece surfaces for flat end mills from two stages: Computing smooth tool orientations on the surface without gouging and collisions and then designing the CC point path. By solving the tool posture optimization problem the authors achieve both the path smoothness and the machining efficiency. Experimental results are provided to show the effectiveness of the method.

Toolpath Regeneration in Subregional Contour-Parallel Processing Based on Isoscallop Method

Advanced manufacturing technologies have made great progress in the fields of aerospace, resources, and power, and the complex curved surface parts with local rapidly varied geometric feature are increasingly and widely used. On account of the complex geometric feature for this kind of parts, global processing technology cannot meet the requirements of high quality and high-efficiency processing, and the subregional processing method is used. However, the existing methods usually lead to bad machining quality at the boundary and are also prone to form obvious machined trace at the center of machining region in subregional processing. Hence, in this article, a subregional toolpath regeneration method for contour-parallel processing based on the isoscallop method is proposed. First, the initial toolpath generation is finished, which can ensure machining quality at the boundary. Then, establishing the arc length error calculation model for the innermost loop of toolpaths, the arc length error is averaged in the side-step direction and the feeding direction by modifying the cutter contact points. Finally, the toolpath regeneration is realized, which can reduce machined trace at the center of machining region. Experimental results show that with the proposed method, the profile arithmetic average error and the maximum of profile deviation decrease by 32.03% and 53.38%, respectively, at the innermost loop of toolpaths compared with the results of the conventional isoscallop method. For that, the proposed method can improve the machining quality effectively for complex curved surface in subregional contour-parallel processing.

Influence mechanism of machining angles on force induced error and their selection in five axis bullnose end milling

In the machining of complicated surfaces, the cutters with large length/diameter ratios are used widely and the deformation of the machining system is one of the principal error sources. During the process planning stage, the cutting direction angle, the cutter lead and tilt angles are usually optimized to minimize the force induced error. It may lead to a low machining efficiency for bullnose end mills, as the material removal rates are different largely for different machining angles. In this paper, the influence mechanism of the machining angles on the force induced error is studied based on the models of the instantaneous cutting force when the cutter flute traveling through the cutting contact point and the stiffness of the machining system. In order to evaluate the machining angles, the force induced error/efficiency indicator (FEI) is defined as the division of the force induced error and the equal volume sphere of the removed material. FEI is dimensionless, with the lower FEI, the lower force induced error and the higher machining efficiency. For optimal selection of the machining angles, the critical FEI is calculated with the constraint of force induced error and the desired material removal rate, and the critical FEI separate the set of the machining angles into two subsets. After the feed rate scheduling process, the machining angles in the optimal subset would have higher machining accuracy and efficiency, while the machining angles in the other subset have lower machining accuracy and efficiency. Through the machining experiment of five axis machining and freeform surface machining, the effectiveness and superiority of the proposed FEI method is verified with a bullnose end mill, which can improve the machining efficiency with the constraint of force induced error.

Global tool axis vector optimization based on the minimum angular acceleration of rotary axes

The parts with complex surface are widespread application for industrial manufacturing field, and 5-axis machining with ball-end cutter is a common measure for surface machining. In order to achieve high-quality surface machining, it is especially important to optimize the pose of the tool and the workpiece. The local tool axis vector optimization can effectively reduce the machining error of the complex surface parts with abrupt curvature. However, when tool axis vectors optimizing interval is overmuch, the local tool axis vector optimization is time-consuming and ineffective. To solve this defect, aiming at the minimum angular acceleration, a global tool axis vector control method is proposed in this research. Firstly, the feasible spaces of the tool axis vectors at the CC (cutter contact) points are obtained. Then, the toolpath is divided by the property of concavity or convexity for the toolpath curve, and the key tool axis vectors on the toolpath curve are determined. Finally, tool axis vectors are adjusted based on the minimum rotary axes’ angular acceleration in each interval, and the tool axis vectors at the joint position of the adjacent segments are adjusted to smooth tool axis vectors for the entire toolpath. Through the simulation and experiment on the test part, the validity of the method is proved, and the global optimization method can effectively decrease the machining errors and promote the machining quality of the complex surface.

Toolpath topology design based on vector field of tool feeding direction in sub-regional processing for complex curved surface

Conventional global processing technology with uniform processing parameters for complex curved surface parts easily tends to uneven error distribution and local out-of-tolerance, and the sub-regional processing method is proposed. However, existing criterions for surface segmentation are merely based on the geometric feature, lacking comprehensive consideration of feeding direction and feeding motion stability during processing, which induces local out-of-tolerance and obvious cutting vibration. A toolpath topology design method in sub-regional processing based on the vector field of tool feeding direction is proposed. By calculating optimal feeding direction at each cutting contact point through a bi-objective optimization model, the space vector field is built by the optimal feeding direction. Then, the primary surface segmentation is achieved based on the divergence and the rotation of the projected vector field, and after fitting of the streamline by feeding vectors, the surface subdivision is finished by judging the abrupt change of kinematics parameters when the axes of machine tool feed along streamlines. Finally, two frequently-used toolpath modes are designed in sub-regions based on the shape feature of sub-regional streamline and the sub-regional toolpath topology is generated. The comparison experiments show that surface roughness and profile error of the machining region decrease by 22.52 % and 40.21 % compared with conventional global processing, which proves that the proposed method can reduce machining error and improve processing quality effectively. The research provides important guidance for toolpath generation of the complex curved surface parts in engineering practice.

Study on tool orientation feasible region with constraint of non-linear error for high-precision five-axis machining

Five-axis machine is one of the most versatile machine tools in complex surface machining while the machining interference occurs easily. To avoid the adverse consequences caused by interference, interference detection, and feasible region, solution are proposed. However, with the required processing accuracy of the complex surface parts increasing, the common feasible region solution is generally difficult to achieve. The error caused by the tool orientation variation along the tool path, just the non-linear error, may exceed the specified tolerance. Considering that both the interference problem and the non-linear problem could be solved by modifying the tool orientation, this study proposes a feasible region solution for tool orientation with the constraint of non-linear error, which can avoid tool interference and achieve high geometric accuracy for tool path planning in the extreme high-precision machining. The detection region that corresponds to the tool orientation at cutter contact (CC) point is calculated to avoid the collision firstly, and the feasible region of tool orientation for a certain CC point is established. After building the tool path equations between two adjacent CC points, the relationship between the movement angles of rotation axis and the machining error is built. By considering the non-linear error of the different rotatory axes respectively, the calculation formula for the movement angle variation of the rotation axis is deduced. Finally, according to the single point non-interference feasible region of the tool angle, the non-interference feasible region for the extreme high-precision processing is constructed with the constraint of non-linear error. A comparative experiment is carried out to verify the proposed feasible region construction method. The experimental results show that with the proposed method, the profile arithmetic average error and the maximum of profile deviation are 53 μm and 71 μm, respectively, which decrease by 30.13% and 32.31% compared with the conventional non-interference feasible region. The achievements have good applicability and are significant for the improvement of processing quality, which provide guidance for the extreme high-precision machining of complex surface parts.

Interactive system to control the kinematic error of a five-axis milling machine

The kinematic error (KE) of a five-axis milling machine is an important measure of the accuracy. The proposed software allows to interactively position the cutter contact (CC) points to reduce the KE. The system helps to optimize the tool path by a trial and error approach and provides a learning experience for the users of five-axis machines. The code works with the STL and OFF files as well as with parametric surfaces. The Interactive system (IS) was offered to unexperienced users as a game with a goal to reduce visible kinematic errors while keeping the number of available CC points. The users were able to achieve a decrease of of the maximum KE by 91.73% and of the average KE by 43.70%. The program has been verified with a post processor from HAAS VF-2TR machining center (Trunnion VMCs).