Rotary Axes Research Articles

Optimization of a Redundant Freedom Machining Toolpath for Scroll Profile Machining

The scroll disc is a critical functional component of the scroll compression mechanism, and its machining precision and quality directly impact the performance and longevity of the compressor. Current machining methods for scroll profiles face challenges in simultaneously achieving wide applicability, high precision, and high efficiency. This paper addresses issues related to unsmooth toolpaths of machine tool axes and high acceleration in the rotary axis during redundant degrees of freedom scroll profile machining. This paper proposes a toolpath optimization method for redundant axes, with optimization objectives focused on reducing the counts of directional changes in the linear axes and smoothing the trajectories of all axes. Experimental results demonstrate that the proposed method offers higher machining efficiency compared to traditional polar coordinate machining.

Simulation of Motion Nonlinear Error Compensation of CNC Machine Tools With Multi-Axis Linkage

In order to solve the problem of nonlinear error for a dual rotary table five-axis CNC machine tool due to the linkage of rotary and translational axes, the simulation of motion nonlinear error compensation for a multi-axis linkage CNC machine tool is proposed. The adjacent points in the tool position file are selected as the tool position points for building the model, and then the nonlinear error model resolved by the harmonic function is established according to the error distribution in the classical post-processing. The nonlinear error between the two tool position points is quickly predicted by the analytical expression of this model, and the real-time error compensation of the intermediate interpolation points is realized. Finally, MALTLAB simulation analysis is performed on the tool position file of an impeller part machining to verify the effectiveness of the proposed algorithm. The experimental results show that it can be seen from the distribution curve of the nonlinear error that it is about 10% after compensation as before compensation, thus verifying the effectiveness of the nonlinear error compensation mechanism. The correctness of the nonlinear error analysis and compensation method and the effectiveness of post-processing are verified.

A modified method for measuring geometric errors of rotary axes based on sensitivity analysis and error simulation

Complicated measurement for machine tools geometric errors limits the high-accuracy machining processes. This research is aimed at measuring and identifying geometric errors of rotary axes efficiently by designing and optimizing measurement method using double ballbar. First, the conical and tangential measurement patterns are designed to reduce the installation times of the double ballbar. Secondly, the effect of installation errors is reduced by analyzing the coefficient matrix to avoid error accumulation. Thirdly, measurement trajectories affected by position-independent geometric errors are simulated and eliminated. Finally, the error measurement and validation experiments were performed on a dual-turntable five-axis machine tool, and the machining precision was improved by 34.09%-48.89%. The results indicated that the scheme can effectively identify the geometric errors of rotary axes and has the advantages of high efficiency and accuracy.

Calibration of rotary axis angular positioning deviations in a six-axis robotic manipulator by using the R-Test

Prediction accuracy of the kinematic model plays a pivotal role in offline numerical compensation for three-dimensional (3D) positioning error of a six-axis robotic manipulator. In addition to the Denavit-Hartenberg (D-H) error that was typically discussed in the analogous research, this paper proposes a novel scheme to identify the bidirectional angular positioning deviations of all the rotary axes without using the commercial laser tracker. This proposed scheme employs the R-Test, which is significantly more cost-efficient than a laser tracker employed in many past works. Compared to the conventional D-H model, significantly improved prediction performance of the proposed model was experimentally investigated on three rectangular paths covering the entire workspace. Experimental results indicate that the proposed scheme reduces the residual error from 505.2 to 215.2 mm, compared to 118.8 mm with a laser tracker, while maintaining a significantly lower cost that is 1/100 of a commercial laser tracker. Uncertainty analysis also clarify that when only the D-H error parameters are identified, as in many conventional works, the angular positioning deviations can be a major uncertainty contributor to the identification of the D-H errors. The proposed scheme does not require the R-Test locations to be calibrated, and its influence on the uncertainty in the identified errors is assessed.

Research on positioning accuracy of the swivel head of milling and turning complex machining center

Abstract This article focuses on the swivel head of a milling-turning complex machining center and establishes a geometric error model between the rotary axes based on the multi-body system theory and the homogeneous coordinate transformation method. The double ball bar (DBB) is used to identify the geometric errors of the machine tool swivel head position-independent by measuring circular trajectories. The impact of PIGEs on the measurement trajectory is simulated. The swivel head is rotated at four angles (B0°, B45°, B90°, B-15°), and the laser tracker is used to analyze and study the linear axis straightness, perpendicularity, and the center coordinates and plane errors of the swivel head movement along the XZ plane. A swivel head rotation accuracy test fixture is designed to correct the positioning accuracy of a swivel head with a 45° inclination of the rotation axis. The research results show that the fluctuation of the center plane degree of freedom of the swivel head moving along the XZ plane is small, and the maximum value is 0.0086mm. Under the 45° angle posture of the swivel head, both the center coordinate error value and the plane error value are the largest. The simulation results of the swivel head position error are fairly consistent with the center coordinate error of the swivel head plane movement. A backward tilt displacement of 0.01mm~0.015mm of the machine column during assembly can reduce the influence of the weight of the swivel head on the perpendicularity and straightness of the vertical reciprocating motion, and adding auxiliary support near the base of the swivel head zero position can reduce machine straightness error.

Validating real time compensation: A thermal test piece for 5-axis machine tools to separate thermal errors in Z-direction

The accuracy of 5-axis machine tools is a key factor to manufacture multi-axes machined workpieces. However, thermal deformations of the machine structure often cause significant deviations at the tool centre point. To evaluate the impact of thermal errors on the accuracy of 5-axis machine tools under machining conditions, suitable thermal test pieces are required. Therefore, this paper introduces a 5-axis thermal test piece which is based on the thermal test piece for rotary axes being part of the standard ISO 10791-10:2022. The new thermal test piece identifies ten instead of five thermal errors during eight time steps. The additional features enable an error separation of the table-related thermal error and the thermal error pointing consistently in Z-direction. This error separation is especially important to analyse the accuracy of five-axis milling operations. In total, the developed 5-axis thermal test piece analyses five location, two length and three orientation errors without requiring a kinematic model of the machine tool. The conducted experiments comprise thermal load cases without and with metal working fluid and show a clear agreement between the thermal location errors and the dominant thermal orientation errors of the thermal test piece and an on-machine measurement cycle. On the other hand, the analysed thermal length errors of the thermal test piece indicate a clear effect of the thermal material expansion compared to the thermal positioning errors of the analysed machine tool. Furthermore, the analysed thermal load cases of the linear and rotary axes conducted without and with metal working fluid result in a different thermal behaviour of the machine tool depending on the use of metal working fluid. Finally, the developed 5-axis thermal test piece is used to evaluate a thermally compensated 5-axis machine tool under machining conditions for thermal load cases without and with metal working fluid. The self-learning thermal error compensation reduces the mean of the thermal location errors at the thermal test piece by up to 71%.

Hybrid Aerosol Jet Printing and Electrodeposition of Ferrite-Sandwiched Inductors

The additive manufacturing (AM) of inductors of suitable size to be integrated into packaged electronics is attractive to customize the device characteristics for the specific application. Magnetic ferrite cores are widely used in conventional inductors, however, wire wound inductors can be brittle, heavy, bulky. Planar spiral inductors in a sandwich configuration present a promising alternative. Aerosol jet printing, a direct write AM technology, can deposit metal inks at a resolution of < 10 µm. Metal nanoparticle inks have limited conductivity at < 40% bulk. Building a higher profile may result in loss of resolution. Electrodeposition offers the ability to plate thick layers of highly conductive metals, including copper and nickel which are normally hard to access as nanoparticle inks compatible with aerosol jetting. We have previously shown the construction of a multi-layer flyback transformer with this hybrid aerosol jet and electrodeposition method. [1]We present a three-layer planar inductor with the first layer being a 1.3mm stack of ferrite sheets (Fair-Rite) with a 9 mm x 9 mm footprint integrated onto a circuit board. The intermediate layer consists of a spiral inductor made by aerosol jet printing UTDots Ag40X silver nanoparticle ink as the seed layer. To achieve high accuracy, the inductor was printed with a rotary axis stage. Electrodeposition in an acidic CuSO4 plating bath on top of the Ag seed layer resulted in thicknesses of 50 µm. A submicron layer of Ni is added for oxidation protection by electrodeposition from a Ni-Sulfamate bath. Lastly, a top 1.3 mm ferrite stack, with laser cut holes, is added to provide pass throughs for wire bonding. Figure 1 shows a micrograph of an inductor as printed, after electrodeposition, and with the top ferrite layer. Electrical measurements including impedance characteristics will be presented.SNL is managed and operated by NTESS under DOE NNSA contract DE-NA0003525. The SAND No. is SAND2023-14571A.Figure 1. Construction of a ferrite-sandwiched inductor with (a) the aerosol jet printing of an Ag seed layer, (b) after electroplating of Cu and Ni.

Interference-enhanced micro-vision-based single-shot imaging of five degrees-of-freedom error motions for ultra-precision rotary axes

The measurement of five degrees-of-freedom (5-DOF) error motions, including radial, axial, and tilt motions, is crucial for ultra-precision rotary axes, which are key components of ultra-precision machine tools and instrumentation. In this study, we propose an interference-enhanced micro-vision technique to concurrently derive the 5-DOF error motions from a single-shot two-dimensional image, which was captured by a standard industrial camera equipped with an interference objective lens. By consolidating the essential features into a single optical path, the interference-enhanced micro-vision technique ingeniously merges machine micro-vision and modified white-light interference to detect in-plane and out-of-plane motions. Numerical simulations demonstrated, the basic principle for deriving the 5-DOF error motions, and the magnification of objective lens had inconsistent effects on the measurement accuracy for the radial and tilt motions, i.e. higher magnification led to higher radial accuracy but lower tilt accuracy. As practical application, the error motion detection capability was demonstrated by simultaneously measuring the 5-DOF synchronous and asynchronous error motions for a typical air bearing spindle at rotation speeds of 8.33, 108.33, and 308.33 rpm. The synchronous errors were nearly identical at various spindle speeds. However, because of system dynamics, increased vibrations were observed to be superimposed on the basic tilt error motions as the spindle speeds increased, which were verified by the vibration marks imprinted on the turned surfaces. For the 5-DOF motion measurements, the least-square fitting using large-volume edge and greyscale data of the captured image enabled super-high resolutions, despite using a camera with a relatively large pixel size and low bit depth. These results demonstrate that the proposed interference-enhanced micro-vision technique is a simple and effective tool for measuring spatial error motions in ultra-precision rotary axes.

Synchronous Measurement and Verification of Position-Independent Geometric Errors and Position-Dependent Geometric Errors of Rotary Axes on Five-Axis Machine Tools

Synchronous Measurement and Verification of Position-Independent Geometric Errors and Position-Dependent Geometric Errors of Rotary Axes on Five-Axis Machine Tools

Geometric error modeling and decoupling identification of rotary axis of five-axis machine tool based on spatial trajectory planning

This paper proposes a method for identification of geometric error and the improvement of measuring accuracy of rotary axes. The primary objective of this work concentrates on the decoupling identify of geometric errors of rotary axis, and the optimal selection of measurement parameters (velocity and measuring points), which can ensure measurement completeness and improve accuracy simultaneously. The proposed approach involves the construction of spatial trajectory driven four-axis motion synchronously. Subsequently, measurement parameters are optimal selected with identification matrix. In the next step, PDGEs are represented using NURBS rapidly solved. The investigations reveal that error decoupling can further enhance compensation accuracy. It was also shown that simply increasing the number of measurements does not improve identification accuracy. The result of experiment indicates that the average compensation rate of trajectory reaches 59.73 %. Therefore, the proposed method can be employed in the reliable calibration of geometric errors particular to five-axis machine tool.

A novel identification method for all geometric errors of rotary axis based on boundaryless constraint optimization method

For the redundancy in definition of position independent geometric errors(PIGEs) and position dependent geometric errors(PDGEs), it is difficult to identify all geometric errors of rotational axis simultaneously. A novel identification method using boundaryless constraint optimization method(BCOM) is established to improve PIGEs and PDGEs identification accuracy of rotary axis. For PIGEs, the two different dimension errors are identified separately based on least square method through appropriate measurement direction by double ball bar(DBB), and thus decrease condition number of identification matrix. For PDGEs, the B-spline curve is applied to fit the geometric errors and the objective function has been established. Several measurement paths are conducted and geometric errors are figured out by iterations of objective function. Furthermore, setup errors of DBB are investigated and discussed based on the sensitivity analysis. Finally, Simulations and experiments are conducted and their results demonstrate the effectiveness of the proposed method.

Improving Machined Accuracy Under a Constant Feed Speed Vector at the End-Milling Point by Estimating Machining Force in Tool Approach

A five-axis machining center (5MC) is capable of synchronous control, which makes it a feasible tool for quickly and accurately machining complicated three-dimensional surfaces, such as propellers and hypoid gears. Recently, the necessity of improving both the machined shape accuracy and the machined surface roughness of free-form surfaces is growing. Therefore, in our previous study, we aimed to maintain the feed speed vector at the end-milling point by controlling two linear axes and a rotary axis of the 5MC to improve the quality of the machined surface. Additionally, we developed a method for maintaining the feed speed vector at the end-milling point by controlling the three axes of the 5MC to reduce the shape error of the machined workpieces (referred to as the shape error herein), considering the approach path of the tool determined via calculation. However, a high machining force at the start of the workpiece cutting was observed and the factor contributing to this phenomenon was not determined, although this phenomenon leads to a shape error to a certain degree according to the machining condition. In this study, the main objective is to suggest a method to reduce the machining force at the start of the workpiece cutting and shape error. Hence, we develop a theoretical method to estimate the machining force by using an instantaneous cutting force model, which considers the synchronized motion of two linear axes and a rotary axis of the 5MC. Subsequently, we determine the most suitable approach path of the tool considering the prediction of the machining force. The results of this study indicate that the machining force can be estimated by applying an instantaneous cutting force using the feed per tooth and machining angle, and that both a high machining force at the start of the workpiece cutting and shape error reduction can be realized by using the proposed approach path of the tool.

A new machining test to identify position-independent geometric errors of rotary axes for five-axis machine tools

A new machining test to identify position-independent geometric errors of rotary axes for five-axis machine tools

Laser differential confocal axicon surface profile measurement method

Aiming to address the challenging problem of high-precision axicon profile measurement, a laser differential confocal axicon profile normal tracking (LDCNT) measurement method with high spatial resolution and anti-tilt capability is proposed in this paper. This method utilizes the principle of normal direction adaptive tracking for axicon profile measurements. It employs the Phase-Sensitive Detector (PSD) image plane spot position to calculate the normal angle and a high-precision rotary axis to drive the sensor normal to the measured surface to achieve the normal direction adaptive tracking measurement of the axicon profile and reduce the difficulty of pose adjustment of the measured axicon. Using the laser differential confocal focusing principle, the differential confocal signal is normalized to improve the axial resolution and avoid the Abbe error generated by the local inclination of the surface, thus realizing high-resolution and anti-tilt measurement of the axicon profile. Through the reference frame error decoupling axicon profile measurement and evaluation technique, spatial error compensation, three-dimensional profile reconstruction, and evaluation of the measurement data are performed to reduce the systematic measurement error and realize high-precision measurement and reconstruction of the axicon profile. Finally, the feasibility of the method is verified by measuring the profile of a standard cylinder and axicon at different axicon angles. The experimental analyses show that this method provides a new method for high-precision measurement of the axicon profile with Peak-to-Valley (PV) repeatability better than 40 nm (3σ) and Root-Mean-Square (RMS) repeatability better than 15 nm (3σ).

Geometric Error Measurement of Rotary Axes on Five-Axis Machine Tools: A Review

Geometric Error Measurement of Rotary Axes on Five-Axis Machine Tools: A Review

Nondimensional analysis and experimental assessment of the PII1/2DD1/2 position control of a rotary axis

Fractional Order controllers, based on derivatives and integrals of non-integer order, represent a propitious and promising research area since they can improve the performance of mechatronic systems compared to traditional Integer Order PID controllers without requiring hardware upgrades, but only using their higher tuning flexibility. Nevertheless, Fractional Order controllers are still rarely applied in real automation tasks, since their tuning is more complex and in general requires a model-based optimization for full exploitation of their capabilities. Recently, the PII1/2DD1/2 controller has been proposed, extending the classical PID by introducing a half-integral and a half-derivative term. A Bode plot-based tuning method has been presented for this controller, deriving the PII1/2DD1/2 parameters from a given set of PID gains. This method enables a significant reduction in tracking error for position control of a mechatronic axis without the need for complex model-based optimizations. In this paper, the previous results of this PII1/2DD1/2 tuning methodology have been generalized by employing a nondimensional approach. This approach highlights the conditions under which the benefits of this Fractional Order controller over the PID are most significant. The findings have been validated through experimental tests on a rotary axis, confirming the correctness and usefulness of the method.

An omnidirectional spatial monocular visual localization and tracking method for indoor unmanned aerial vehicles based on the two-axis rotary table

Aiming at the complexity and poor adaptability of the calibration process in the traditional unmanned aerial vehicles (UAV) indoor visual positioning, this paper proposes an omnidirectional spatial tracking and localization method for indoor UAV based on the two-axis rotary table. Firstly, the position of the UAV fuselage feature points in the camera coordinate system of the turntable camera is computed by the Pespective-n-Point algorithm utilizing known position information of a plurality of feature points with pixel coordinate information in the corresponding image. Pixel coordinate information is extracted by obtaining UAV body-specific feature points from rotary table camera shots. Then, UAV localization in omnidirectional space can be obtained by using the calibrated rotary axis parameters of the rotary table and the rotation angle of the rotary table and substituting them into Rodriguez’s formula to unify the UAV position information acquired by the rotary table camera at different positions into a unified coordinate system. Finally, the angle at which the rotary table should rotate is calculated from the obtained UAV pose and the spatial position of the camera optical center and the rotary axis of the rotary table. The calculated angle is fed back to the turntable as feedback information. The rotary table receiving the feedback information is rotated to a position where the UAV is located at the center of the camera image. Thereby the tracking and localization of the UAV is realized. The experimental results show that the spatial range of localization is greatly expanded with the localization accuracy reaching the level of binocular visual localization. The omnidirectional spatial tracking and localization of indoor UAV can be conveniently realized by this method.

Block processing time-based programming for high-speed, high-precision 5-axis machining

For high-speed and high-precision machining with orthogonal 3-axis minute line segment commands, a program should be generated by appropriately reducing the chord error (tolerance) or the block length (line segment length) based on the computer numerical control (CNC) block processing time Tb. The block processing time Tb is the duration from when the CNC decodes one block command in a program until when it controls the motors, depending on the processing power of the CNC. Accordingly, even in simultaneous 5-axis machining, it is necessary to research whether programs generated based on Tb can achieve high-speed and high-precision machining. Therefore, this study aims to realize simultaneous 5-axis machining at higher speed and precision using CNC programs with minute line segment commands based on Tb. In addition, we propose a more general identification method compared with that used in previous studies to identify Tb. Simultaneous 5-axis programs include two cases of control, namely, tool center point (TCP) control and Non-TCP control, and Tb was identified for both controls. For the machining method, using the block length based on Tb, we generated programs to machine the upper flat surface of a workpiece using simultaneous 5-axis machining while rotating the two rotary axes using a ball-end mill. We machined the workpiece and evaluated the machining speed and precision of the machined surface. We showed that simultaneous 5-axis machining with higher speed and precision can be achieved using programs based on Tb. In addition, we analyzed and considered the reasons for the higher-speed and higher-precision machining.

Geometric error compensation method using the Laser R-test

Traditional methods for measuring geometric errors in machine tools, including interferometry and Double Ball Bar (DBB), are known to be expensive and time-intensive. Consequently, a non-contact calibration system called the “Laser R-test” has been developed. This innovative system is designed to measure both position-independent geometric errors (PIGEs) and position-dependent geometric errors (PDGEs) efficiently. Since its development in 2000, this tool has been instrumental in analyzing eccentricity errors, angular position errors, and simultaneous trajectory errors. Through extensive research, it has been determined that the total error in a five-axis machine tool can be controlled to below 40 µm after compensating for eccentricity parameters and angular position errors. However, reducing this error to below ± 10 µm is challenging, primarily due to wobble errors in the orientation of the rotary axis without compensating. In this study, a new methodology based on Laser R-test and Rodrigues’ rotation formula has been developed to establish a PIGE model of rotary axis. Based on the methodology, the 8 PIGEs can be analyzed by measuring 5 coordinate positions. The compensation of 8 PIGEs in the rotary axis is completed within 30 min using the inspection path. Compatibility with ISO-10791–6 standards for BK1, BK2, and BK4 path tests is confirmed, validating the compensation effects. A precision of below ± 10 µm is achieved, with inspection time reduced by over 50%. This system can complete multiple errors by simply using the different paths. This greatly reduces the setup time for future users, enhancing its commercial applicability.

Adaptive Identification of the Position-independent Geometric Errors for the Rotary Axis of Five-axis Machine Tools to Directly Improve Workpiece Geometric Errors

Adaptive Identification of the Position-independent Geometric Errors for the Rotary Axis of Five-axis Machine Tools to Directly Improve Workpiece Geometric Errors