Rotary Axes Research Articles

Aspek-Aspek Matematika pada Atribut yang Digunakan dalam Tradisi Temu Manten di Madiun

Ethnomathematics could be viewed as an effort to look back at how mathematics integrated in culture and life. Ethnomathematics appears to rectify the perception that mathematics has nothing to do with everyday life. This perception, directly or indirectly influences students’ understanding of mathematical concepts and alsi influences students’ interest in learning and developing these concepts. This study aims to examine the mathematical aspects contained in the attributes used in Temu Manten Tradition, especially the tradition carried out in Madiun City. In this article, the research is limited to only a few attributes used in Temu Manten. Ethnographic approach is used in this research. The results of subsequent research were processed qualitatively, so that it was concluded that the attributes used in this tradition, with deeper exploration could be associated with mathematical concepts, specifically on geometrical aspects such as plane, including transformation, perimeter or circumferences and area of the plane , solid geometry, congruency of triangles, rotating object, volumes of rotating objects, the rotary axis and the constant volume

An efficient method for measuring and identifying geometric and dynamic errors in dual five-axis machine tools

The dual five-axis machining machine is state-of-the-art equipment designed for producing thin-walled aerospace parts like skins and panels. It comprises two five-axis machine tools with mirrored synchronous motions: one bi-rotary machine for milling and the other machine for follow-up support. The high absolute accuracy of the five-axis machine tools themselves and the high synchronous motion accuracy between the two machines are both crucial to ensure machining accuracy. This paper proposes an efficient method to measure and identify geometric and dynamic errors of dual five-axis machine tools. Using the R-test combined with three measurement trajectories to measure the absolute motion error of two five-axis machine tools and the synchronous motion error between the two machines. The designed trajectories include the main rotary axis linkage conditions and can fully reflect the primary motion forms of the dual five-axis machine tool. The main position-independent geometric errors and rotational axis linkage dynamic errors are identified by converting quasi-static and dynamic measurement data from three different trajectories into a unified reference coordinate system. The entire process requires only one instrument installation, effectively avoiding time-consuming repetitive installations and calibration processes while reducing the impact of installation errors on results. The effectiveness of the proposed method for measuring and identifying the geometric and dynamic errors is analyzed combined with Monte Carlo simulation. Experiments were carried out on a dual five-axis mirror milling system (MMS) with a 5000 mm X-stroke. Both simulations and experiments confirmed that the proposed method is efficient in quickly identifying key error sources of the MMS.

Influence of rotary axis angular positioning error motions on robotic probing

The accuracy of touch-trigger probing by a six-axis robotic manipulator is determined by the accuracy of the robot forward kinematic model to estimate the stylus sphere position from angular positions of rotary axes. Many conventional studies have employed the Denavit–Hartenberg (DH) model, containing position and orientation errors of the rotary axis average lines as error sources. This paper proposes the application of a new kinematic model, containing the angular positioning deviations of all the rotary axes, to the robotic probing. The probing accuracy is experimentally investigated in profile probing of a straightedge over the robot's workspace.

Design and CFD simulation of guide vane for multistage Savonius wind turbine

This study proposes improving the performance of a fixed-axis multistage Savonius wind turbine by integrating a sixbladed guide vane. Guide vanes aim to direct the incoming wind towards the blades of the Savonius wind turbine so that it can increase the performance value of the turbine itself. There are two methods, the first method is computational fluid dynamics (CFD) simulation to evaluate the best performance guide vane angle variations. The second method is implementing real conditions using 3 m/s until 4.2 m/s wind speed. The implementation of the guide vane to the wind turbine will consider four (4) variants of angles (0°, 20°, 40°, and 60°). The purpose of testing with four kinds of guide vane angles is to find out which guide vane angle can provide the best results among other guide vane angles. This research proposed the initial design of the guide vane addition to the multistage Savonius wind turbine with a fixed rotary axis. From the CFD simulation, the implementation of a guide vane can improve the performance of the multistage Savonius wind turbine with a fixed rotary axis. On the other hand, for the proposed initial design in this research, the 20° angle of guide vane gives the best result compared to the 0°, 40°, 60°, and without guide vane.

R-test-based identification method for geometric errors of rotary axes in a five-axis machine tool with a rotary table and tilting head

This paper uses an R-test method to identify the 20 geometric errors of the two rotary axes in a five-axis machine tool with a tilting head and a rotary table. The Position-Independent Geometric Errors (PIGEs) result in deviations of the actual axis from the ideal axis, leading to the overall deviation of the set points on the circular trajectory. Therefore, the actual circular trajectory can be fitted by measuring the actual coordinates of the set points, and the actual axis can be further solved to establish the solution equation of PIGEs. Further, the volumetric error model for the set points is constructed, and the unknown motion matrices associated with the linear axes in the volumetric error model are adjusted, allowing for the determination of Position-Dependent Geometric Errors (PDGEs). This method can identify geometric errors of the two rotary axes by measuring six sets of circular trajectories under three setups.

Calibration of link errors in rotary axes of five-axis machine tools using a six-dimensional motion measuring device

In this study, the position-independent geometric errors (PIGEs) of five-axis machine tools are identified and calibrated using a Stewart–Gough platform (SGP) based Motion Measuring Device (MMD). As the MMD of micrometer-level accuracy is cable of six-dimensional pose measurements, a closed kinematic chain is established by installing the upper and lower plate of the MMD to the spindle and rotary worktable of the machine tool, respectively. Particularly, the sensor-mounting misalignments, which are inevitable but mostly ignored in the previous PIGE identification methods, are formulated and identified together with the PIGEs. Thus, the sensor-mounting misalignments will not affect the accuracy of PIGE calibration. The proposed method is verified by simulation and experimental results. The synchronous motion test (SMT) demonstrates that the five-axis machine tool owns a high accuracy of 5 micrometers in the tested motion range after PIGE calibration.

New machining test for identifying geometric and thermal errors of rotary axes for five-axis machine tools

This paper presents a new machining test for identifying the geometric and thermal errors of rotary axes for a five-axis machine tool. A disc-shaped test piece containing 12 rectangular grooves is designed and processed. A coordinate-measuring machine is used to measure the rectangular grooves to identify four position-independent geometric errors (PIGEs) and six position-dependent geometric errors (PDGEs) of the rotary axis. On-machine measurements are performed under heating and cooling conditions to identify the six thermal errors. The identification principle and analytical solution of each geometric and thermal error are provided, and an uncertainty analysis is performed. Compared with two classical machining tests, the results of the proposed method are in good agreement; the agreement degrees of the PIGE, PDGE, and thermal error are 90.9%, 91.3%, and 85.1%, respectively. The identification principle and analytical solution of each error are simple and not affected by linear axes, thereby improving accuracy.

A Novel Sampling-Based Optimal Motion Planning Algorithm for Energy-Efficient Robotic Pick and Place

Energy usage in robotic applications is rapidly increasing as industrial robot installations grow. This research introduces a novel approach, using the rapidly exploring random tree (RRT)-based scheme for optimizing the robot’s motion planning and minimizing energy consumption. Sampling-based algorithms for path planning, such as RRT and its many other variants, are widely used in robotic motion planning due to their efficiency in solving complex high-dimensional problems efficiently. However, standard versions of these algorithms cannot guarantee that the generated trajectories are always optimum and mostly ignore the energy consumption in robotic applications. This paper proposes an energy-efficient industrial robotics motion planning approach using the novel flight cost-based RRT (FC-RRT*) algorithm in pick-and-place operation to generate nodes in a predetermined direction and then calculate energy consumption using the circle point method. After optimizing the motion trajectory, power consumption is computed for the rotary axes of a six degree of freedom (6DOF) serial type of industrial robot using the work–energy hypothesis for the rotational motion of a rigid body. The results are compared to the traditional RRT and RRT* (RRT-star) algorithm as well as the kinematic solutions. The experimental results of axis indexing tests indicate that by employing the sampling-based FC-RRT* algorithm, the robot joints consume less energy (1.6% to 16.5% less) compared to both the kinematic solution and the conventional RRT* algorithm.

Sensitivity analysis of inverse multilateration based on tracking interferometer measurement for a bi-rotary head five-axis machine tool

This paper proposes a novel inverse multilateration that improves the accuracy by sensitivity analysis and calibration of rotary axes’ position-independent geometric errors. In recent years, the tracking interferometer measurement with inverse multilateration has been widely adopted in the assessment and compensation of the five-axis machine tool. It uses the bi-rotary head as the steering mechanism to reduce cost, which also introduces errors from rotary axes. In this paper, a sensitivity analysis for position-independent geometric errors of rotary axes is proposed to reveal the error propagation mechanism and identify the main error sources. An optimization for the number and distribution of measured points is investigated based on the result of sensitivity analysis. Monte Carlo simulations and experiments are carried out on a bi-rotary head five-axis machine tool to verify the proposed method. The results show that the accuracy and efficiency of inverse multilateration measurement have been significantly improved.

Geometric error calibration and analysis of rotary axes on a five-axis dispensing machine

Geometric rotary axis errors are one of the main factors affecting the dispensing positioning accuracy of five-axis vision dispensing machines. Hence, the accurate detection and compensation of these error terms is an important and challenging problem. In this study, a decoupling identification method for both position-dependent geometric errors and position-independent geometric errors of a rotary dispensing table is proposed based on vision measurement technology. According to this strategy, the screw theory and exponential product formula are used to establish a kinematic model of the end-effector, followed by the definition of the mapping relationship between position-independent geometric errors and axis posture. Then, to separate the coupling error terms of the rotating axes, a step-by-step identification strategy is proposed based on the least squares method. Furthermore, a coordinate search-based error compensation algorithm is developed, which avoids the inverse singular value problem and is insensitive to the error model. Finally, the effectiveness of the proposed identification algorithm and compensation algorithm is experimentally validated.

Accurate X-ray diffraction data required for proper evaluation of bond valence sums and global instability indexes: redetermination of the crystal structures of diamond-like Cu2CdSiS4 and Cu2HgSnS4 as a case study.

Our calculations of the global instability index (G) values for some diamond-like materials with the general formula I2-II-IV-VI4 have indicated that the structures may be unstable or incorrectly determined. To compute the G value of a given compound, the bond valence sums (BVSs) must first be calculated using a crystal structure. Two examples of compounds with high G values, based on data from the literature, are the wurtz-stannite-type dicopper cadmium silicon tetrasulfide (Cu2CdSiS4) and the stannite-type dicopper mercury tin tetrasulfide (Cu2HgSnS4), which were first reported in 1967 and 1965, respectively. In the present study, Cu2CdSiS4 and Cu2HgSnS4 were prepared by solid-state synthesis at 1000 and 900 °C, respectively. The phase purity was assessed by powder X-ray diffraction. Optical diffuse reflectance UV/Vis/NIR spectroscopy was used to estimate the optical bandgaps of 2.52 and 0.83 eV for Cu2CdSiS4 and Cu2HgSnS4, respectively. The structures were solved and refined using single-crystal X-ray diffraction data. The structure type of Cu2CdSiS4 was confirmed, where Cd2+, Si4+ and two of the three crystallographically unique S2- ions lie on a mirror plane. The structure type of Cu2HgSnS4 was also verified, where all ions lie on special positions. The S2- ion resides on a mirror plane, the Cu+ ion is situated on a fourfold rotary inversion axis and both the Hg2+ and the Sn4+ ions are located on the intersection of a fourfold rotary inversion axis, a mirror plane and a twofold rotation axis. Using the crystal structures solved and refined here, the G values were reassessed and found to be in the range that indicates reasonable strain for a stable crystal structure. This work, together with some examples gathered from the literature, shows that accurate data collected on modern instrumentation should be used to reliably calculate BVSs and G values.

Improved Method for Synchronous Accuracy of Linear and Rotary Axes under a Constant Feed Speed Vector at the End Milling Point while Avoiding Torque Saturation

Improved Method for Synchronous Accuracy of Linear and Rotary Axes under a Constant Feed Speed Vector at the End Milling Point while Avoiding Torque Saturation

Simultaneous identification for geometric error of dual rotary axes in five-axis machine tools

For the rotary axes, the position-dependent geometric errors (PDGEs) and position-independent geometric errors (PIGEs) affect their rotational accuracy concurrently. Therefore, aiming at analyzing this coupling effect of geometric errors, a novel method is presented to identify the PDGEs and PIGEs of dual rotary axes simultaneously. The identification model is established based on the geometric error model and actual distances between the two retroreflectors, by which all geometric errors of two rotary axes can be obtained simultaneously. The identification results are validated by predicting volumetric errors, in which the deviations between the predicted and measured VEs are within 21.7 μm in three directions. Moreover, the root mean square error between the predicted and measured volumetric errors is 6.8 μm, which indicates that the proposed method can effectively accomplish the simultaneous identification of geometric errors. This identification method facilitates the further study of the coupling effect of PDGEs and PIGEs.

Method and system for simultaneously measuring six degrees of freedom motion errors of a rotary axis based on a semiconductor laser.

The rotary axis is the basis of rotational motion. The motion errors of a rotary axis have an extremely important impact on the accuracy of precision machining measuring equipment such as CNC machines, robot manipulators, and laser trackers. It is a difficult problem to realise the fast and precision simultaneous measurement of multi-degree-of-freedom motion errors of a rotary axis. Therefore, a novel method for the simultaneous measurement of six-degree-of-freedom motion errors of a rotary axis by a single-mode fiber coupled semiconductor laser is proposed in this paper. The corresponding system is developed, which has the advantages of high measurement efficiency, simple structure and low cost. A phase-solving method taking the advantages of both the eight-subdivision and the Cordic algorithm is proposed to solve the phase of interference signal, cannot only realize the high-resolution solving of the current signal phase but also quickly obtain high-precision interferometric results. A series of experiments were carried out on the developed system. An experimental system was built and a series of experiments were performed. The experimental results show that the standard deviation of stability for 1 hour of the six-degree-of-freedom measurement is 0.03 µm, 0.02 µm, 0.03 µm, 0.10 ' ' , 0.05 ' ' and 0.03 ' ' , respectively. The repeatability deviation of measuring a rotary axis is ±0.16 µm, ± 0.29 µm, ± 0.25 µm, ± 0.65 ' ' , ± 0.62 ' ' and ±13.42 ' ' , respectively. The maximum deviation of comparison with standard instruments is 0.46 µm, 1.00 µm, 0.49 µm, 1.06 ' ' , 1.53 ' ' and 0.74 ' ' , respectively. It provides a low-cost and high-precision measurement method for simultaneous measurement of six-degree-of-freedom motion errors of rotary axis of precision machining and measuring equipment.

A C3 continuous double circumscribed corner rounding method for five-axis linear tool path with improved kinematics performance

Abstract Corner rounding methods have been widely developed to pursue the smooth motions of machine tools. However, most corner rounding methods, which adopt the double inscribed transitions, still remain an inherent issue of retaining large curvatures of transition curves. Even for those double circumscribed transitions-based methods with relatively small curvatures, they also constrain excessively the transition lengths and are limited to a low-order continuity, deteriorating the feedrate and jerk of machine tools. For addressing these problems, a C3 continuous double circumscribed corner rounding (DCCR) method is proposed for five-axis linear tool path. In this method, the C3 continuous double circumscribed B-splines are specially designed to round the corners of tool position and tool orientation, whose transition lengths are analytically determined by jointly constraining the approximation errors, overlaps elimination, and parameter synchronization. Moreover, the excessive constrains of transition lengths imposed by traditional methods are alleviated by fully considering the effects of overlaps and parameter synchronization, and the jerk of rotary axes is also limited with a high-order continuity. Compared to the existing double inscribed corner rounding (DICR) and DCCR methods, experiment results demonstrate that our method can improve further the feedrate while limiting the jerk of machine tools.

Non-redundant identification of geometric errors in multilateration of rotary axis

The multilateration measurement acquires sufficient data for the identification of the position-independent geometric errors (PIGEs) and position-dependent geometric errors (PDGEs) of the rotary axis. However, because of redundancy in the used intermediate parameters, existing identification methods suffer from a loss of accuracy and precision caused by the relatively lower stability to the influences of random errors. Meanwhile, this may result in a more complicated process if additional constraints are added to reinforce stability. This paper proposes a non-redundant method for identifying both the PIGEs and PDGEs of the rotary axis. Firstly, the identification model, in which the rotating component pose errors are fully and non-redundantly described by the twists, is established to identify the pose errors caused by geometric errors. Then, by deriving the relationship between the pose error twists and the PIGE & PDGE parameters, the sequential decoupling algorithm applying the least squares condition, together with identification models, for both the PIGEs and PDGEs is developed. Comparative simulations and experiments are carried out. With no redundancy, the proposed method exhibits smaller discrepancies between the identified and preset test lengths in the cone path test simulation, yielding an average improvement of 15.73% and 56.97% in two identification modes, respectively. Furthermore, the method demonstrates smaller discrepancies between the predicted and measured test data in the cross-validation experiment with an average improvement of 80.21% and 86.87% in the two modes, respectively. These results jointly verify the improvement in accuracy for identifying the PIGE and PDGE parameters. In addition, an overall reduction of the PIGE and PDGE uncertainties is observed in the Monte-Carlo simulations, which verifies the precision improvement.

Virtual-Axis Injection Based Online Parameter Identification of PMSM Considering Cross Coupling and Saturation Effects

Existing online parameter identification methods of permanent magnet synchronous motors (PMSMs) are generally based on the voltage equations, the precision of which is affected by the cross coupling and magnetic saturation effects. In order to deal with this issue, a virtual-rotary-axis high-frequency signal injection (VHFSI) based online parameter identification method is proposed in this paper, where the cross coupling and magnetic saturation effects on the traditional d-q axis model are analyzed. On this basis, an optimized voltage model under the composite magnetic field rotary axis is introduced. In the proposed method, the cross-coupling angle and the d-q axis inductances can be identified by injecting the high-frequency signal into the constructed virtual rotary axis. In addition, the complex Simpson integral algorithm is adopted to obtain the information of the incremental and apparent inductances. Finally, the permanent magnet flux linkage can be estimated based on the composite magnetic field rotary axis voltage equations. The effectiveness and feasibility of the proposed method are verified by the experiments on a 2.2-kW PMSM drive.

Analisis Peningkatan Kinerja dan Umur Pahat Karbida Pada Proses Pembubutan Baja Aisi 1045 dengan Menggunakan Coating Tialn

Lathe is a machine tool that is used to cut the object being rotated. Lathe itself is a workpiece cutting process in which the incision is made by rotating the workpiece and then being applied to the tool which is moved translationally with the rotary axis of the workpiece. In this study the method used was an experimental research method consisting of TiAlN coating to turning process. The results showed that the cutting speed is inversely proportional to the life of the tool, where the higher the cutting speed, the shorter the life of the tool. The higher the cutting speed, the lower the surface roughness value. TiAlN coating has a significant effect on the surface quality of the workpiece and the life of the tool, where the TiAlN coating has a lower surface roughness value than the tool without coating at the same cutting speed.

Five-Axis Trochoidal Sweep Scanning Path Planning for Free-Form Surface Inspection

Freeform surface inspection is a vital process in manufacturing, and the newly emerged five-axis continuous sweep scanning technology is one of the most efficient and accurate means for free-form surface inspection. The key in employing the five-axis inspection technology is to plan an effective and efficient sweep scanning path respecting both the inspection surface and the properties of the inspection device. Current sweep scanning paths suffer from the oscillating pattern that forces the high-speed stylus of the five-axis inspection device to swing back and forth frequently, which imposes excessive kinematic loading on the probe head, and in turn, undermines the inspection stability and efficiency. In this paper, we present a new trochoidal sweep scanning path for freeform surface inspection. The proposed method is novel in that the generated inspection path is a smooth trochoidal-shaped curve on the surface without causing any oscillation during a sweep scanning process. The kinematic performance of the probe head is significantly improved, which enables much better inspection stability and efficiency. Both computer simulation and physical inspection experiments of the proposed method have been conducted, whose results convincingly validate the feasibility and superiority of the proposed trochoidal sweep scanning path over the traditional oscillating sweep scanning path in terms of inspection stability and efficiency. Note to Practitioners—This work is motivated by the high requirements on the stability and efficiency of the newly emerged five-axis sweep scanning technology for freeform surface inspection. A novel trochoidal sweep scanning path is generated to make the original heavy-loaded rotary axes of the five-axis inspection machine move smoothly without needing frequent acceleration and deceleration as suffered from a traditional five-axis oscillating sweep scanning path. The kinematic loads of the five-axis inspection device are significantly reduced based on the proposed sweep scanning path; thus, the inspection machine could afford a higher sweep velocity of inspection, and the inspection stability and efficiency could be improved considerably as well. Compared with a traditional oscillating sweep scanning path, in our tests, the proposed method can improve the inspection efficiency by more than 20%, while the maximal kinematic loads (e.g., the velocity and jerk of the C-axis) can be reduced by 55%-85%. With superior inspection efficiency and stability, the proposed trochoidal sweep scanning path can be utilized for accurate and efficient inspection of large freeform surfaces like those in the aerospace and automotive industries.

Geometric error measurement uncertainty analysis of rotary axis based on Monte Carlo method

Ballbar is widely used for geometric error measurement of the rotary axis, and the uncertainty analysis is of great significance to ensure the reliability of error identification. This study analyzes the measurement uncertainty based on the Monte Carlo method. First, this study clarifies the uncertainty mechanisms caused by tool setting error, translational axis motion error, and ballbar installation error, and proposes a measurement model comprehensively considering the uncertainty sources. In this study, the same ballbar measurement experiments were carried out 10 times in three measurement modes, and the standard deviation of the ballbar length change under different rotation angles was analyzed to ensure that the uncertainty of the geometric error can be effectively analyzed. Furthermore, the uncertainty of each error at different angles of the rotary axis is evaluated based on the measurement model. The results show that the translational axis motion error and tool setting error are important sources of uncertainty. The measurement uncertainty of the angle positioning error is the largest in A- and C-axis, and its standard uncertainty reaches 9.38″ and 2.81″. After optimizing the sine and cosine terms in the identification model, the standard uncertainties of the angular positioning errors are reduced to 6.43″ and 2.26″, and also the estimated errors are close to the actual values, which verifies the validity of the uncertainty analysis method.