Axial Error Motion Research Articles

A novel method for measuring radial and axial errors in a cylindrical coordinate system using a combined double ball bar

Multiaxis machine tools are widely used in manufacturing. The measurement of motion error is important to improve the machining accuracy of machine tools. A double ball bar (DBB), as a high-precision single-dimensional position reading device, is widely used to measure the motion error of the circular path of machine tools. However, the motion errors contain the cylindrical radial and axial errors with respect to the circular path plane. Therefore, the measurement results of the DBB are incomplete because they do not contain axial errors. To measure the motion error of the circular path accurately, completely and concisely, a novel measurement method based on the combined DBB (C-DBB) is proposed in this paper, which can directly measure the radius and axial motion error of the circular path in one measurement. First, the measuring principle of the C-DBB method is introduced, and the measurement model of the radius and axial motion error of the circular path is established. Then, a measuring device using the C-DBB method was designed based on the lever principle, and the error parameters of the designed device were analyzed. According to the error analysis results, the measurement results of the C-DBB method were compensated and corrected. Finally, the C-DBB method is used to measure the circular path on the vertical CNC milling machine, and the results are compared with the measurement results using the DBB method. It is shown that the proposed C-DBB method can obtain high-precision multidimensional motion error in a single measurement, and the designed measuring device based on the C-DBB method has high repeatability and good circular path measuring ability. The proposed method provides an effective method for machine tool multidimensional motion error measurement and compensation.

An optical method based auto-collimation for measuring five degrees of freedom error motions of rotary axis.

The paper presents an optical method based on auto-collimation to simultaneously measure five degrees of freedom error motions of the rotary axis. The proposed method consists of the collimated lasers, beam splitters, focusing lens, quadrant photodiode detectors, a high-precision steel ball, and a special mirror fixed to the rotary axis. The mathematical model is established byoptical ray tracing, and the corresponding optical path is also simulated by OpticStudio. Meanwhile, an adjusting mechanism for X-Y micro-displacement, based on the elastic deformation of the material, is designed to adjust the installation eccentricity error of the high-precision steel ball. The calibration results of the proposed system demonstrate that the displacement errors are ±0.25 µm within the measuring range of ±10 µm, and the tilt angle errors are ±0.6 arcsec within the measuring range of ±25 arcsec. Taking a direct drive (DD) motor as the test object, the radial error motions of the rotary axis range from -3.2 to 4.1 µm, the axial error motions range from -4.9 to 4.7 µm, and the tilt error motions around the X and Y axes range from -2.8 to 1.8 arcsec and -2.6 to 2.0 arcsec, respectively.

Simultaneous measurement of 5DOF spindle error motions in CNC machine tools.

We present a method for the simultaneous measurement of 5 degree-of-freedom (DOF) spindle error motions in computer numerical control (CNC) machine tools and develop a measurement system. The measurement system uses polarization-maintaining fiber coupled with a dual-frequency laser as the light source. The axial error motion of the spindle is measured by heterodyne interferometry, and other 4DOF error motions are obtained by collimation measurement. Based on the measurement system, a comprehensive measurement model of spindle error motion was established. The influence of system error on the measurement accuracy of the spindle tilt error motion and radial error motion was analyzed. According to the measurement model, a corresponding data-processing method is proposed, which removes some systematic errors. A series of experiments was conducted to verify the feasibility and effectiveness of the proposed measurement system and the corresponding measurement model.

Sparsity adaptive matching pursuit and spectrum line interpolation method for measuring radial and axial error motions of spindle rotation

This paper proposes a sparsity adaptive matching pursuit and spectrum line interpolation (SAMP-SLI) method for measuring the radial and axial error motions of spindle rotation of machine tool. The method measures the displacements from the outside surface of a custom-fabricated cylindrical precision artifact using capacitive displacement sensors. The measured error motions are reconstructed with sparse spectrum lines in the frequency domain by SAMP algorithm. The frequencies, amplitudes, and initial phases of these sparse spectrum lines are corrected using the spectrum line interpolation algorithm to reduce the effect of the spectral leakage and picket fence. Then, the relevant error motions of spindle rotation are separated from these corrected sparse spectra. A simulation is conducted to compare the calculation performance of the proposed method and the existing methods, the results of which shows that the proposed method has higher accuracy in decomposition of error motions. The method is then applied to the measurements of spindle of a numerical control (NC) vertical machining center. The measurement results of the proposed method are compared with that of the API spindle measurement system, which shows that the proposed method has obviously higher accuracy in spindle speed identification. Finally, the measurement uncertainty of the proposed method is analyzed.

Simultaneous Measurement Method and Error Analysis of Six Degrees of Freedom Motion Errors of a Rotary Axis Based on Polyhedral Prism

A novel method is proposed for measuring the six degrees-of-freedom (DOF) geometric motion errors of a rotary axis based on a polyhedral prism. An error-sensitive unit which consists of a polyhedral prism and a planar reflector, is designed to carry out measurement of all six DOF errors, including the angular positioning error, the tilt motion error around the Y axis, the tilt motion error around the X axis, the radial motion error along the X and Y axes, and the axial motion error along the Z axis. The mathematical error model, including the six DOF geometric motion errors of the rotary axis, the installation errors between the polyhedral prism and the rotary axis, the manufacturing errors of the polyhedral prism, and the position errors of the sensors, are established. The effectiveness of the proposed method and the compensation model was simulated and experimentally verified.

Measurement of five-degrees-of-freedom spindle error motion using multi probe error separation

Herein, a precision measurement method is proposed to evaluate the radial, axial, and tilt error motions of rotating devices such as precision spindles. To improve the accuracy of the estimated multiple-degree-of-freedom error motion components, form error signals in the runout signals are separated and precompensated for before the calculation of the five-degrees-of-freedom error motion components. Fourier model-based multi probe error separation (MPES) techniques, which can prevent the occurrence of harmonic distortions, are applied to separate the form error signals. A three-probe method is applied to layers on the side surface of the cylindrical artifact, and a modified two-probe method is developed and applied to the upper surface. The radial, tilt, and axial error motions are calculated using the runout signals that do not contain the separated form error signals. The measurement system uses eight capacitive probes to detect the runout signals of the cylindrical artifact mounted at the center of the rotating device. To compare the proposed method with the five-probe-based conventional measuring method, an evaluation test simulation is conducted repeatedly five times. Results indicate that the proposed MPES method calculated the uncertainty using the deviation between the computed results from the existing and novel methods; additionally, the input signal in terms of the radial, tilt (layers 1 and 2), and axial error motions are [Formula: see text], [Formula: see text], [Formula: see text], and [Formula: see text], respectively. It is confirmed that the undesirable effects of the form error signals are successfully removed and that the accuracies of the measured spindle error motion components improve.

Effect of design parameters and operational conditions on the motion accuracy of hydrostatic thrust bearing

In this study, the effect of design parameters and operational conditions on motion accuracy of the closed configuration hydrostatic thrust bearing was researched. Key design parameters include land width, nominal oil film thickness, and perpendicularity error between mandrel and thrust plates. Oil supply pressure, external load, and rotation load are the considered operational conditions. Predictions of the induced effect are made by introducing oil film clearance function, governing equations, flow rate continuity equations, and dynamic equations of mandrel to model axial rotation error and angular motion error. The results show that the axial rotation accuracy increased, as land width (larger than 8 mm), nominal oil film thickness, and oil supply pressure increased, but there was little impact on angular motion error. The axial rotation error and angular motion error increased with the increase in the external load and rotation speed. Confirmation of the perpendicularity error has been achieved, in this study, by conducting experiments, using ultra-precision measuring machine. In addition, axial rotation error was tested on a hydrostatic rotary table and compared with the simulation results to check the validity of the proposed method. The results provide useful design guidelines and operation advice for hydrostatic thrust bearing in high-precision machine tools.

Detecting 6 DoF geometrical errors of rotary tables

An error separation method called three-rosette method allows all errors in rotary tables integrated into coordinate measuring machines (CMMs) to be determined by means of an uncalibrated circular ball plate. The calibration procedure takes advantage of the fact that error contributions can be separated and eliminated by means of multiple measurements of each ball center in well-defined measurement positions. The skilled evaluation of these results allows all six degrees of freedom (DoF) of a rotary table to be detected: the angular positioning error motion, the axial error motion and two error components for describing both the tilt error motion and the radial error motion. The method is of practical and economic relevance, as ball plates can be manufactured at low cost and require no further calibration. A detailed measurement and evaluation strategy as well as example results are presented.

A machining test to identify rotary axis geometric errors on a five-axis machine tool with a swiveling rotary table for turning operations

Lately, a cylindrical workpiece of relatively large diameter is often machined by turning operations by a swiveling rotary table in a five-axis machining center. This paper presents a machining test containing features finished by a turning operation by a swiveling rotary table. Unlike conventional machining tests for turning operations described in ISO 13041-6:2009, the present machining test can identify a complete set of position and orientation errors of the axis average line of rotary axes from the geometry of the finished test piece. The radial and axial error motions of the rotary table can be also observed when the swiveling axis is positioned horizontal (A=0∘) and vertical (A=−90∘). Experimental demonstration is presented. The rotary axis geometric errors identified from the finished test piece's geometry are compared with those estimated by a conventional error calibration test using a touch-triggered probe and a precision sphere. The uncertainty analysis for the present machining test is also presented.

Error-compensation model for simultaneous measurement of five degrees of freedom motion errors of a rotary axis

This paper introduces an error-compensation model for our measurement method to measure five motion errors of a rotary axis based on fibre laser collimation. The error-compensation model is established in a matrix form using the homogeneous coordinate transformation theory. The influences of the installation errors, error crosstalk, and manufacturing errors are analysed. The model is verified by both ZEMAX simulation and measurement experiments. The repeatability values of the radial and axial motion errors are significantly suppressed by more than 50% after compensation. The repeatability experiments of five degrees of freedom motion errors and the comparison experiments of two degrees of freedom motion errors of an indexing table were performed by our measuring device and a standard instrument. The results show that the repeatability values of the angular positioning error εz and tilt motion error around the Y axis εy are 1.2″ and 4.4″, and the comparison deviations of the two motion errors are 4.0″ and 4.4″, respectively. The repeatability values of the radial and axial motion errors, δy and δz, are 1.3 and 0.6 µm, respectively. The repeatability value of the tilt motion error around the X axis εx is 3.8″.

Analysis of error motions of axial locking-prevention hydrostatic spindle

Hydrostatic spindles are widely used in precision optical grinder and lathe. Their high precision comes from the error averaging effect of oil film. The purpose of this paper is to give the quantitative analysis of the error averaging effect for a newly developed axial locking-prevention hydrostatic spindle. An approximate error motion model of the hydrostatic spindle is established to analyze the internal relationship between the geometric errors of the shaft and the error motions of the spindle including radial, tilt and axial error motions. The theoretical analysis shows that, the roundness errors of the two journals have a major impact on error motions while the coaxiality errors of two journals, the perpendicularity errors of front thrust plate and the coaxiality errors of the land of back thrust bearing, have no significant influences on error motions. The elliptical component of roundness errors of the two journals has significant influence on the axial error motion but no influence on the pure radial and tilt error motions, resulting into the fourth harmonic component of axial error motion. The trilobal component of roundness errors of the two journals has significant influence on the pure radial and tilt error motions but no influence on the axial error motion, resulting in the third harmonic component of pure radial and tilt error motions. The changes of recess pressures are not necessary condition for the error motions. Additionally, the experiment analysis shows that, the third harmonic component is the main part of the measured radial error motion and the third, fourth harmonic components are the main parts of the measured face error motion, which can be reasonably explained by the theory. The model proposed in this paper can be used to guide the precision design and optimization of hydrostatic spindle.

Research on Measurement Accuracy of Laser Tracking System Based on Spherical Mirror with Rotation Errors of Gimbal Mount Axes

Abstract This paper presents a novel experimental approach for confirming that spherical mirror of a laser tracking system can reduce the influences of rotation errors of gimbal mount axes on the measurement accuracy. By simplifying the optical system model of laser tracking system based on spherical mirror, we can easily extract the laser ranging measurement error caused by rotation errors of gimbal mount axes with the positions of spherical mirror, biconvex lens, cat’s eye reflector, and measuring beam. The motions of polarization beam splitter and biconvex lens along the optical axis and vertical direction of optical axis are driven by error motions of gimbal mount axes. In order to simplify the experimental process, the motion of biconvex lens is substituted by the motion of spherical mirror according to the principle of relative motion. The laser ranging measurement error caused by the rotation errors of gimbal mount axes could be recorded in the readings of laser interferometer. The experimental results showed that the laser ranging measurement error caused by rotation errors was less than 0.1 μm if radial error motion and axial error motion were within ±10 μm. The experimental method simplified the experimental procedure and the spherical mirror could reduce the influences of rotation errors of gimbal mount axes on the measurement accuracy of the laser tracking system.

Relationship between geometric errors of thrust plates and error motions of hydrostatic thrust bearings under quasi-static condition

A new model using approximate formulas is established to predict the error motions of hydrostatic thrust bearings. Three different types of geometric errors of thrust plates are listed in this paper including tilt errors, saddle shaped errors and petal shaped errors. The influences of them on lateral tilt error motion, longitudinal tilt error motion and axial error motion are discussed. Definitions of averaging coefficients are made based on the approximate formulas. It is found that the time-varying tilt errors are the main reason for the error motions of hydrostatic thrust bearings. The thrust bearings with six pairs of recesses have priority over the thrust bearings with four and three pairs of recesses in the view of rotation accuracy. Experiments are done using a hydrostatic rotary table with an outer diameter of 2m. It is found that the second harmonic errors are the main component of the radial run-out and the results agree well with the results calculated from the approximate formulas.

Averaging Effect on Pitch Errors in Hydrostatic Lead Screws With Continuous Helical Recesses

The motion errors of hydrostatic lead screws can be smaller than the pitch errors due to the averaging effect of oil films, which is the so-called averaging effect on the pitch errors (AEPE). This paper investigates the factors influencing AEPE under low speeds and a constant external load. An equivalent model of hydrostatic lead screws with continuous helical recesses is established, and the axial motion errors of the nut are obtained by combining the dichotomy and finite difference methods. The results show that (a) the motion errors caused by the pitch errors of the lead screw have additivity, and the pitch errors of the nut have little influence on the motion errors, (b) when the lead screw only has cumulative pitch errors, the motion errors are equal to the average value of the cumulative pitch errors located on the two flank surfaces of the lead screw, and (c) when the lead screw only has periodic pitch errors, the number of nut threads with helical recesses n and the period of the pitch errors of the lead screw T are the main influencing factors on AEPE.

Miniature silicon Michelson interferometer characterization for dimensional metrology

Dimensional metrology applications require performing measurements of profile and form/shape of parts at a nanometer-level of accuracy. Therefore, the metrological characteristics of a miniature optical micro-probe based on a Michelson interferometer are evaluated. The optical micro-probe is designed to perform dimensional measurements with a target uncertainty in the order of few nanometers. Two micro-probe designs having reflection-transmission ratios of 75–25% and 25–75%, are characterized. Two optical setups have been implemented as well: firstly, using a single laser diode with a 1550.3nm wavelength and secondly using a tunable laser source in the C-L bands. The characterization of the two micro-probes is performed using a new ultra-precise test bench, with respect to both dissociated metrology structure and Abbe principles. The experiments allow the evaluation of the error sources such as: stability, axial motion errors (residual errors), material dependence, tilt angle and roughness of the tested object. The experimental results revealed that dimensional measurements could be achieved with nanometer-scale errors, ranging from 2nm to 15nm, depending on the probe design and the reflectance of the device under test.

An AFM-based methodology for measuring axial and radial error motions of spindles

This paper presents a novel atomic force microscopy (AFM)-based methodology for measurement of axial and radial error motions of a high precision spindle. Based on a modified commercial AFM system, the AFM tip is employed as a cutting tool by which nano-grooves are scratched on a flat surface with the rotation of the spindle. By extracting the radial motion data of the spindle from the scratched nano-grooves, the radial error motion of the spindle can be calculated after subtracting the tilting errors from the original measurement data. Through recording the variation of the PZT displacement in the Z direction in AFM tapping mode during the spindle rotation, the axial error motion of the spindle can be obtained. Moreover the effects of the nano-scratching parameters on the scratched grooves, the tilting error removal method for both conditions and the method of data extraction from the scratched groove depth are studied in detail. The axial error motion of 124 nm and the radial error motion of 279 nm of a commercial high precision air bearing spindle are achieved by this novel method, which are comparable with the values provided by the manufacturer, verifying this method. This approach does not need an expensive standard part as in most conventional measurement approaches. Moreover, the axial and radial error motions of the spindle can both be obtained, indicating that this is a potential means of measuring the error motions of the high precision moving parts of ultra-precision machine tools in the future.

Theoretical and experimental analysis of the effect of error motions on surface generation in fast tool servo machining

Abstract The fast tool servo (FTS) machining process provides an indispensable solution for machining optical microstructures with sub-micrometer form accuracy and a nanometric surface finish without the need for any subsequent post processing. The error motions in the FTS machining play an important role in the material removal process and surface generation. However, these issues have received relatively little attention. This paper presents a theoretical and experimental analysis of the effect of error motions on surface generation in FTS machining. This is accomplished by the establishment of a model-based simulation system for FTS machining, which is composed of a surface generation model, a tool path generator, and an error model. The major components of the error model include the stroke error of the FTS, the error motion of the machine slide in the feed direction, and the axial motion error of the main spindle. The form error due to the stroke error can be extracted empirically by regional analysis, the slide motion error and the axial motion error of the spindle are obtained by a kinematic model and the analysis of the profile in the circumferential direction in single point diamond turning (SPDT) of a flat surface, respectively. After incorporating the error model in the surface generation model, the model-based simulation system is capable of predicting the surface generation in FTS machining. A series of cutting tests were conducted. The predicted results were compared with the measured results, and hence the performance of the model-based simulation system was verified. The proposed research is helpful for the analysis and diagnosis of motion errors on the surface generation in the FTS machining process, and throws some light on the corresponding compensation and optimization solutions to improve the machining quality.

Phase Algorithms for Reducing Axial Motion and Linearity Error in Indirect Time of Flight Cameras

Indirect time of flight cameras are increasingly being used in a variety of applications to provide real-time full field of view range measurements. Current generation cameras suffer from systematic linearity errors due to the influence of harmonics in the system and motion errors due to the requirement of taking multiple measurements. This paper demonstrates that replacing the standard phase detection algorithm with the windowed discrete Fourier transform can improve the root mean square (RMS) axial motion error with distance from 0.044±0.002 m to 0.009±0.004 m and the range from 0.112±0.007 m to 0.03±0.01 m for an object with a velocity of 2 m/s using a measurement time of 125 ms. This algorithm also improves the linearity of the camera by removing systematic errors due to harmonics, decreasing the RMS linearity error from 0.018±0.002 m to 0.003±0.001 m. This paper establishes the robustness of the windowed discrete Fourier transform, demonstrating that it effectively eliminates axial motion error over a variety of velocities and modulation frequencies. The potential for tailoring phase detection algorithms to specific applications is also demonstrated.

Research on the Online Test of the Fly Cutting Machine Tool Spindle

The online test system of the vertical spindle motion error of the ultra-precision fly cutting machine tool was established. And then using the online test system established to test and analyze the state of the rotary motion of the spindle under the idling condition. The axial synchronous motion error value of the spindle under 390rpm is about 61 nm, and the asynchronous error motion is about 33nm. The radial error motion value is about 91nm, and the asynchronous error is about 35nm. Through the test, we found that the axial and radial spindle error motion accuracy under idling speed can been improved with the spindle speed increases.

Analysis of error motions of ultra-high-speed (UHS) micromachining spindles

This paper presents an experimental approach to analyze radial and axial error motions of miniature ultra-high-speed (UHS) spindles. The present work focuses on identifying the sources of error motions and quantifying them, specifically for the UHS spindles with hybrid ceramic bearings. Since effective application of micromachining processes, which commonly utilize miniature UHS spindles, require a high level of dimensional accuracy, form accuracy, and surface finish, the (unwanted) motions of the UHS spindles (and the associated tool-tip runout) must be well-understood. In this work, a laser Doppler vibrometer (LDV)-based measurement technique is used to measure radial and axial motions of the spindle from a sphere-on-stem precision artifact. The influence of temperature fluctuations, dynamically-induced effects, contact-bearing defects, and tool-attachment errors are analyzed. The spindle speeds are varied from 40krpm to 160krpm, and the over-hang lengths of 15mm and 7.5mm are considered. The variations arising from tool attachment to the collet are also studied. It is seen that (1) the thermal state of the spindle exhibits a cyclic behavior that results in significant changes to the spindle motions, (2) spindle speed and over-hang length significantly affect the spindle motions, and (3) the variations arising from the tool attachment to the collet can be described using a normal distribution, and may cause more than ±50% amplitude variations to the spindle motions.