Rotary Axes Research Articles

An iterative contouring error compensation scheme for five-axis precision motion systems

Contouring error is one of the most important performance indexes for multi-axis motion systems, especially for five-axis ones. The contouring control performance of five-axis motion systems is difficult to improve mainly due to the following two factors. Firstly, the dynamic coupling between the translational and the rotary axes is strong. Secondly, the contouring error in five-axis systems includes tool tip error and tool orientation one, which are difficult to suppress simultaneously. In this paper, a novel contouring error iterative compensation scheme is proposed to realize the coordination control of spatial contouring error with multi-degree-of-freedom. Accurate contouring error estimation is firstly achieved through a numerical calculation method. And then the estimated contouring error is compensated to the reference trajectory by means of the proposed model-free compensation law. By iteratively implementing the above process, the convergence of which has been theoretically proved, the contouring performance can be further improved. A series of experiments have been conducted on a five-axis motion system. The experimental results consistently illustrate that, in comparison with existing contouring control methods, the proposed scheme can achieve excellent promotion of contouring accuracy, especially in extreme contours with large curvature and sharp corners.

Symmetry centering of artifacts on limited-range rotary carriages or joints

This note describes a symmetry-based technique to center a part or artifact having a complete, partial or intermittent fiducial surface having an axis-of- revolution onto the axis-of-rotation of a rotating joint, stage, or flexure which has limited rotational travel. It is shown that using limited rotations and by sensing in the X-direction, the Y misalignment can be independently determined and/or by sensing in the Y-direction the X misalignment can be independently determined. Further if measurements are balanced using an ±ε < 40° rotations then the sensed magnitude variation is approximately ε/30° times the offset in the orthogonal direction when the joint is balanced halfway between the ±ε excursions. This may also be of use when positioning hemispheres or artifacts on rotary tables with their axis of rotation perpendicular rather than parallel to the rotary table axis. This technique also allows for adjustments during the initial alignment when the error may be greater than the working range of a probe and thus preventing a full 180° reversal for centering determination. Although it is possible to get both eccentricity components using single direction measurement it is not recommended due to much higher sensor-noise-related uncertainty.

Improved Synchronous Motion of Linear and Rotary Axes While Avoiding Torque Saturation Under a Constant Feed Speed Vector at the Endmilling Point – Investigation of Motion Error Under Numerical Control Commanded Motion –

A five-axis machining center is known for its synchronous control capability, allowing complicated three-dimensional surfaces, such as propellers and hypoid gears, to be quickly created. Prior research has shown that it is necessary to improve not only the machined shape accuracy but also the machined surface roughness of free-form surfaces. Therefore, in this research, we aimed to maintain the feed speed vector at the endmilling point by controlling two linear axes and a rotary axis with a five-axis machining center to improve the machined surface quality. In previous research, we suggested reducing the shape error of machined workpieces (referred to as shape error in this research) by considering the differences in the servo characteristics of the three axes in the machining method. The shape error was significantly decreased by applying the proposed method, which uses a parameter (referred to as precedent control coefficient in this research) determined by calculation, rather than trial and error. Moreover, to maintain the feed speed vector at the endmilling point when machining complex shapes, a rapid velocity change in each axis is required, causing inaccuracy owing to torque saturation. The results of the experiments and simulations of previous research indicated that torque saturation can be evaluated via simulation. In this research, to reduce the shape error while avoiding torque saturation when movement has high angular velocity, we developed a theoretical method to obtain the most suitable precedent control coefficient of each axis by using a block diagram that considers torque saturation. Therefore, both shape error reduction and torque saturation avoidance can be realized by using the proposed method.

Self-optimizing thermal error compensation models with adaptive inputs using Group-LASSO for ARX-models

Thermal errors have a significant impact on the machining accuracy of five-axis machine tools. The thermal adaptive learning control (TALC), which combines adaptable data-based models and on-machine measurements, realizes a precise and robust long-term reduction of thermal errors of machine tools. To further improve the precision and the robustness of data-based models for thermal error compensation, this publication introduces a new method to realize adaptive model inputs. This method combines the Group-LASSO (least absolute shrinkage and selection operator) for autoregressive models with exogenous inputs (ARX) and the particle swarm optimization to realize a simultaneous estimation of the optimal inputs, the model structure, and the model parameters. Additionally, the self-optimization ability of thermal error compensation models, based on the TALC, is increased by introducing error-specific action control limits to define the frequency of model updates. The newly developed methods are applied to compensate the thermal errors of a swiveling and a rotary axis of a five-axis machine tool during a long-term test series of 350 h. Randomly generated speed profiles of the linear and rotary axes as well as the spindle and changing ambient conditions ensure a high variety of thermal load cases within in the analyzed long-term test series. The results show that the prediction accuracy measured as peak-to-peak values and the robustness of the thermal error compensation models are improved by up to 36% and 58% respectively when adaptive instead of static model inputs are used. Furthermore, the compensation results of the new method outperform the previously used sequential input selection method regarding prediction accuracy and repeatability. The average peak-to-peak value of the compensated translational thermal errors is reduced by 23% and the repeatability of the corresponding compensation results is increased by 57%. Consequently, the consideration of the resulting model structure during the selection of the optimal model inputs significantly enhances the performance of the resulting data-based thermal error compensation models.

Deep learning LSTM for predicting thermally induced geometric errors using rotary axes’ powers as input parameters

Temperature changes within a machine tool, which are partly due to internal heat sources related to the power consumption at the machine drives, result in thermally induced geometric errors of the machine. Predicting the thermally affected machine geometry facilitates the prediction of volumetric errors throughout the 5-axis machine volume. Measuring power instead of temperature is easier to implement in practice but causes drift issues. Stacked Long Short Term Memory (LSTM) with two hidden LSTM layers is applied to determine the relationship between powers and the thermal variation of geometric error parameters by remembering previous states and learning complex non-linear relationships through optimized generalized parameters of the predicting model. Optimizers Adam, RMSprop, and SGD based on exponential moving average of first order and second order moments of gradients are combined with Stacked LSTM for faster learning convergence to an optimal solution. Validation trials with various B- and C-axis motion sequences demonstrate a capability of predicting multi time steps ahead over a 40 hours period without re-measuring the geometric error parameters of the model. Stacked LSTM with the Adam optimizer has the best capability by predicting up to 93% of the main geometric error compared to the other optimizers.

Equivalent geometric errors of rotary axes and novel algorithm for geometric errors compensation in a nonorthogonal five-axis machine tool

The indirect identification of the geometric errors (GEs) in the rotary axis of a machine tool yields six equivalent GEs (EGEs) that are position-dependent; through an analytical proof, this study demonstrates that these errors also represent four position-independent GEs of the axis. Moreover, a novel algorithm using ball bar measurements to calculate the EGEs of a nutating rotary B-axis and a rotary C-axis is presented herein. This paper also presents a new analytical solution for the actual inverse kinematics of a nonorthogonal five-axis machine tool; this solution is used for GE compensation. The presented algorithms are implemented in a self-developed software that alters the nominal numerical control code in order to eliminate GEs. The compensation accuracy and efficiency are tested using a simulation system. The results demonstrate that the proposed compensation algorithm eliminates all identified GEs. Lastly, a cutting test executed on a machine confirms that the proposed algorithms considerably improve machining accuracy.

A self-calibration scheme to monitor long-term changes in linear and rotary axis geometric errors

A calibration scheme of position and orientation errors of rotary axis average lines based on touch-trigger probing is widely available on many commercial five-axis machine tools. Such a measurement is influenced by error motions of both linear and rotary axes. This paper proposes a novel scheme to separately identify linear and rotary axis geometric errors by using a touch-trigger probe and an uncalibrated test piece. Whereas the proposed scheme is based on well-developed self-calibration schemes for the circularity measurement, an original contribution is that it is applied to separate linear and rotary axis geometric errors. Two case studies are presented. First, the proposed tests are performed on the same five-axis machine tool for half a year to observe a long-term change in linear and rotary axis geometric errors. The second case study investigates the influence of room temperature change on linear axis and rotary axis error motions.

Novel kinematic model of a SCARA-type robot with bi-directional angular positioning deviation of rotary axes

Novel kinematic model of a SCARA-type robot with bi-directional angular positioning deviation of rotary axes

Alignment method for rotary stage axis and optical axis in the polar coordinate direct laser writing system

As a crucial part of a high-speed polar coordinate laser writing system, the alignment of the rotatory stage axis and the writing laser optical axis has been a key point that influences the accuracy of the whole system and the fabrication patterns. An alignment method of the rotatory stage axis and the writing laser optical axis is proposed. An alignment system is established and the imaging subsystem is calibrated by a high precision calibration object. A circle center lookup algorithm is applied to find the axis of the rotary stage. The accuracy of the alignment could reach 400 nm. The results of the alignment indicate that the proposed alignment method is a good method for the alignment of the rotary stage axis and the writing laser optical axis. The proposed alignment is useful in the fields of high-resolution maskless laser lithography in polar coordinates.

Traceable determination of non-static XCT machine geometry: New developments and case studies

It is fundamental to determine the machine geometry accurately for dimensional X-ray computed tomography (XCT) measurements. When performing high-accuracy scans, compensation of a non-static geometry, e.g. due to rotary axis errors or drift, might become necessary. Here we provide an overview of methods to determine and account for such deviations on a per projection basis. They include characterisation of stage error motions, in situ geometry measurements, numerical simulations, and reconstruction-based optimization relying on image quality metrics and will be discussed in terms of their metrological performance. Since a radiographic calibration is always required to provide an initial absolute geometry, this method will be presented as well. The improvements of the XCT geometry correction methods are presented by means of case studies. The methods can be applied individually or in combination and are intended to provide a toolbox for XCT geometry compensation.

Five-Axis Trajectory Generation Considering Synchronization and Nonlinear Interpolation Errors

Abstract This paper presents a novel real-time interpolation technique for five-axis machine tools to attain higher speed and accuracy. To realize computationally efficient real-time interpolation of 6-DOF tool motion, a joint workpiece–machine coordinate system interpolation scheme is proposed. Cartesian motion of the tool center point (TCP) is interpolated in the workpiece coordinate system (WCS), whereas tool orientation is interpolated in the machine coordinate system (MCS) based on the finite impulse response filtering. Such an approach provides several advantages: (i) it eliminates the need for complex real-time spherical interpolation techniques, (ii) facilitates efficient use of slower rotary drive kinematics to compensate for the dynamic mismatch between Cartesian and rotary axes and achieve higher tool acceleration, and (iii) mitigates feed fluctuations while interpolating near kinematic singularities. To take advantage of such benefits and realize accurate joint WCS–MCS interpolation scheme, tool orientation interpolation errors are analyzed. A novel approach is developed to adaptively discretize long linear tool moves and confine interpolation errors within user set tolerances. Synchronization errors between TCP and tool orientation are also characterized, and peak synchronization error level is determined to guide the interpolation parameter selection. Finally, blending errors during non-stop continuous interpolation of linear toolpaths are modeled and confined. Advantages of the proposed interpolation scheme are demonstrated through simulation studies and validated experimentally. Overall, proposed technique can improve cycle times up to 10% while providing smooth and accurate non-stop real-time interpolation of tool motion in five-axis machining.

Generating direct diamond shaping tool paths using special-purpose computer-aided-machining post-processor

ABSTRACT Ultra-precision direct diamond shaping (DDS) is an attractive method for manufacturing highly accurate and complex features. DDS employs 4 of the 5-axes in an Ultra-Precision Machine (UPM) with a conventional diamond tool to machine features on a workpiece mounted on a rotary axis. It has been proven to be effective and flexible in manufacturing intricate features, from microfluidics to Fresnel lenses. However, a significant technical hurdle in the practical implementation of DDS is the complexity of its non-conventional tool path generation. Current practices in generating DDS tool paths rely on programming and significant mathematical manipulation. This is not only time consuming but also requires the user to overcome a steep learning curve. Moreover, conventional Computer-Aided Machining (CAM) software does not support DDS tool paths, but instead supports tool path generation for common machining processes like milling and turning. This paper discusses the use of a special-purpose post processor to bridge the compatibility gap between CAM and DDS tool path generation. The mathematics and logic of converting CAM milling tool paths to DDS would be discussed. Finally, the post processor was experimentally verified using a case study.

Groove shape change by WEDM with 2-axis rotary axis Spiral groove machining

Spiral groove shape machining is possible by wire electric discharge machining with the addition of a rotary axis. Furthermore, by adding a two-axis rotary axis that can rotate and tilt, we have performed spiral groove machining that changes the groove width. The combination of the rotation direction and the tilt direction determines whether the groove width becomes narrower or wider. The previous report was a process in which the groove width was widened by forward rotation and downward tilt. At that time, we compared and examined the machining accuracy of the NC program generation method. In this report, machining was performed with the remaining three types of combinations of rotation and tilt, and the shape accuracy was compared along with the difference in NC program. In all the results, it was found that the groove width tends to be widened on the entrance side of the groove machining, and the groove width becomes closer to the design shape as the machining progresses.

Optimization method for complex surface partitioning and cutting parameters in 5-axis machining

For complex surfaces with variable geometric features and high processing requirements, the current stage still uses more conservative machining cutting parameters to generate five-axis machining tool positions, which inevitably leads to some parts not to obtain the best cutting state, and the generated machining tool positions are poorly adapted, so it will produce a great processing deformation error seriously affects the surface quality. In addition, conservative cutting parameters applied to different geometric features of the surface area is very likely to induce dramatic changes in the machining process cutting forces and machine motion parameters, resulting in uneven distribution of machining errors and local super poor, seriously affecting the quality of machining. In five-axis machining, due to the introduction of two rotary axes, the tool vector can be rotated arbitrarily in the spatial domain. When machining complex surfaces, the distance between the tool center coordinates and the oscillation center or rotation center of the five-axis machine will change with the curvature of the surface. surface quality. Therefore, the optimization of tool cutting parameters in 5-axis simultaneous machining is a technical bottleneck that needs to be solved urgently.

Study on the influence of the actual industrial constrains during WEDM roughing of Fir Trees on Inconel® 718 disks

The manufacture of Fir Trees on aeronautical discs is an operation with high requirements in terms of accuracy and surface integrity. In recent years, Wire EDM has become a real alternative thanks to the last developments on generator technology with minimum thermal damage and the better understanding of EDM effects on the part surface. However, to achieve a competitive production, the cutting speed needs to be increased in industrial conditions. This work focuses on the WEDM rough of Fir Trees. In this stage, a high removal rate (MRR) is prioritized over quality concerns because the final surface integrity and accuracy is achieved by the finishing passes. In most of the cases, the geometry of the discs imposes the part to be allocated on a two-axis rotary table, relative far from the nozzles and then machine table. This is a non-optimal position because the WEDM process is developed in bad flushing conditions and the wire guides are also far from the cut zone. The MRR is the main parameter affected but additionally, other secondary effects like the process of wear in the current feeders can influence the overall performance. To study these effects, it was proposed to analyse the discharge process under different industrial conditions for the rough cut of Inconel 718 parts. Discharge current and voltage were acquired and post-processed using advanced algorithmics in order to extract the most significant characteristics of the process. Results show how the energy input decreases when cutting height increases, a rotary axis is included or depending of the current feeder wear. The effects on part accuracy and surface integrity were also analysed.

A novel geometric error identification and prediction approach

This paper proposed an integrated geometric error identification and prediction method to solve the uncertainty problem of the PDGEs of rotary axis. First, based on homogeneous transform matrix (HTM) and multi-body system (MBS) theory, The transfer matrix only considering the C-axes rotated is derived to the position error model. Then a geometric errors identification of rotary axis is introduced by measuring the error increment in three directions. Meanwhile the geometric errors of C-axis are described as truncated Fourier polynomials caused by fitting discrete values. Thus, The geometric error identification is converted into the function coefficient. Finally, the proposed new prediction and identification model of PDGEs in the global frame are verified through simulation and experiments with double ball-bar tests.

Signal processing method for measuring the radial motion error of rotary axis by interferometry

Signal processing method for measuring the radial motion error of rotary axis by interferometry

A novel error mapping of bi-directional angular positioning deviation of rotary axes in a SCARA-type robot by “open-loop” tracking interferometer measurement

To further extend the application of an industrial robot to e.g. the machining, it is crucial to ensure its three-dimensional (3D) positioning accuracy over its entire workspace. Numerous past works presented numerical compensation based on the robot kinematic model containing position and orientation errors of rotary axes average lines, widely known as Denavit-Hartenberg (D-H) parameters. This paper presents two novel contributions. First, this paper proposes a kinematic model with the angular positioning deviation “error map” of each rotary axis, which is given as a function of command angular positions. Furthermore, to model the backlash influence, it is modelled dependent also on the direction of rotation. The second contribution is on the proposal of the “open-loop” tracking interferometer measurement to indirectly identify the angular positioning deviation of each rotary axis. It measures the distance from the retroreflector, fixed on the table, to the robot's end effector at many points over the entire workspace by using a laser interferometer attached to the robot's end effector. The identified kinematic model's accuracy is experimentally investigated, and is compared to the conventional D-H model.

Simultaneous calibration of probe parameters and location errors of rotary axes on multi-axis CNC machines by using a sphere

On-machine measurement (OMM) systems with touch-triggered probes are efficacious in productivity improvement. Machine motion errors impose major limitations on their accuracy for any OMM systems, especially when rotary axes motions are involved. This research proposes a precise measurement method to address this problem by simultaneously identifying the probe parameters and the location errors of rotary axes, using a touch-triggered probe to sample a sphere. This method is suitable for both periodic machine checks and OMM system recalibrations. The method formulates a mathematical model based on machine kinematics to represent errors between the theoretical probed data and the actual recorded data, minimizing which can solve for necessary parameters. Two proposed probing patterns simplify the solution to the model. Experiment results demonstrate that the method is effective and accurate. Monte Carlo simulations were carried out to prove the robustness of the method.

Volume decomposition for multi-axis support-free and gouging-free printing based on ellipsoidal slicing

Continuous multi-axis printing has drawn more and more attention owing to its unique advantages of eliminating the need of support (at least in theory) when printing complex models with overhang features and significantly reducing the stair-step effect of the conventional three-axis printing. For continuous multi-axis printing, the printing layers are typically not planar but curved, so to capitalize the extra DOFs provided by the rotary axes of the printer. When a printing layer is concave (i.e., its curvature vector points inward at the printing point), the potential nozzle-layer local gouging becomes a serious concern, which is especially problematic for metal printing wherein the size of the nozzle head is usually large. Unfortunately, this convexity issue has received little attention in the existing curved slicing algorithms, making them prone to the local gouging quandary. In this paper, we propose a novel curved layer decomposition algorithm based on the use of (only the positive sides of) ellipsoidal surfaces. To facilitate the generation of ellipsoidal printing layers for an arbitrary freeform solid model with a complex topology (e.g., having a non-zero genus number), the powerful algebraic technique of skeletonization is employed by our algorithm to first decompose the model into a suitable set of sub-entities, for each of which a series of ellipsoidal printing layers are then generated, wherein the parameters of ellipsoidal layers are adaptively adjusted to satisfy the necessary constraints such as support-free and other requirements. Preliminary experiments in both computer simulation and physical printing of the proposed algorithm are conducted, and the results give a positive validation on the effectiveness and feasibility of the proposed methodology.