scholarly journals 2D Dynamic Spindle Radial Error Motion Analysis Using Fourier Series in Polar Domain

2020 ◽  
Vol 19 (2) ◽  
pp. 151-159
Author(s):  
Kavitha Chellappan ◽  
Denis Sathiaseelan
Keyword(s):  
Fourier Series ◽  
Motion Analysis ◽  
Radial Error ◽  
Error Motion

Study on the influence of machine tool spindle radial error motion resulted from bearing outer ring tilting assembly

2018 ◽  
Vol 233 (9) ◽  
pp. 3246-3258 ◽  
Author(s):  
Xiaohu Li ◽  
Ke Yan ◽  
Yifa Lv ◽  
Bei Yan ◽  
Lei Dong ◽  
...  
Keyword(s):  
Rotation Speed ◽  
Total Error ◽  
Experimental System ◽  
Outer Ring ◽  
Operation Condition ◽  
Thermal Displacement ◽  
Radial Error ◽  
Spindle Rotation ◽  
Motion Characteristics ◽  
Error Motion

To reveal the spindle radial error motion characteristics in condition of bearing outer ring tilting assembly, mathematical method on spindle radial error motion were analyzed. Then, in real operation condition the natural frequency of the test rig was investigated. Experimental system and methods were designed to test axial thermal displacement, radial error motion and modal characteristic of spindle in condition of bearing outer ring tilting assembly. Results show that axial thermal extension and radial vertical rising of spindle front-end occurs during thermal displacement test. With the same outer spacer nonparallelism, the synchronous error motion and total error motion generally increase with spindle rotation speed, and reach a peak at certain rotation speed.

Analysis of error motions of axial locking-prevention hydrostatic spindle

2018 ◽  
Vol 233 (1) ◽  
pp. 3-17
Author(s):  
Penghai Zhang ◽  
Yaolong Chen
Keyword(s):  
Significant Influence ◽  
Harmonic Component ◽  
Necessary Condition ◽  
Third Harmonic ◽  
The Third ◽  
Fourth Harmonic ◽  
Radial Error ◽  
Tilt Error ◽  
Error Motion ◽  
Error Averaging

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.

Evaluation Method to Determine Radial Error of Spindle Units on Simulation Turntable

2011 ◽  
Vol 460-461 ◽  
pp. 311-316
Author(s):  
Zhi Yong Qu ◽  
Jun Wei Han
Keyword(s):  
Small Angle ◽  
Evaluation Method ◽  
Simulation System ◽  
Transformation Matrix ◽  
Hardware In The Loop ◽  
Error Sources ◽  
Know How ◽  
Form Errors ◽  
Radial Error ◽  
Error Motion

Many errors including radial error influence the accuracy of simulation turntable, which is a crucial equipment in hardware-in-the-loop simulation system. The aim of this paper is to propose a new method of radial error motion separation of rotating spindle on a simulation turntable. Based on transformation matrix and small angle approximation, gesture transformation matrix with various error items is achieved. As a result of this analysis, form errors of master ball are corrected and the eccentricity from the rotation error of a spindle is separated. This radial error analysis is carried out when this measurement result is applied to a simulation turntable. Furthermore, this study also permits the user to know how to minimize some error sources of the spindle system.

Measurement and Analysis of Radial Error Motion of a Miniature Ultra-High-Speed Spindle

2008 ◽  
Vol 381-382 ◽  
pp. 73-76
Author(s):  
Kengo Fujimaki ◽  
Kimiyuki Mitsui
Keyword(s):  
High Speed ◽  
Signal To Noise Ratio ◽  
High Signal ◽  
Signal To Noise ◽  
Measuring Device ◽  
Radial Error ◽  
Optical Measuring ◽  
Ultra High Speed ◽  
Measurement And Analysis ◽  
Error Motion

The optical measuring device developed in this study is based on laser autocollimation and can measure the radial error motions of a miniature ultra-high-speed spindle having a maximum rotational speed of 200 krpm. The maximum response frequency of this optical measuring device is over 500 kHz, while the frequency of the radial error motion at 200 krpm is 3.33 kHz for 1 undulation per revolution (upr), and 333 kHz for 100 upr. In addition, the optical measuring device is capable of a highly detailed analysis of the radial error motion of a miniature ultra-high-speed spindle since it has a high signal-to-noise ratio due to little susceptibility to electrical noises.

Development of a Forecasting Compensatory Control System for Cylindrical Grinding

1987 ◽  
Vol 109 (4) ◽  
pp. 385-391 ◽  
Author(s):  
K. H. Kim ◽  
K. F. Eman ◽  
S. M. Wu
Keyword(s):  
Control System ◽  
Substantial Improvement ◽  
Error Source ◽  
Mechanical Motion ◽  
Cylindrical Grinding ◽  
Radial Error ◽  
Electric Drive System ◽  
Compensatory Control ◽  
Grinding Operations ◽  
Error Motion

A forecasting compensatory control (FCC) system was developed to improve workpiece roundness in cylindrical grinding operations. The spindle radial error motion (SREM) at the grinding position, identified as the dominant error source was modeled by an autoregressive model and compensated for by a forecasting algorithm. A digital method for measuring SREM at the grinding position which incorporates master roundness compensation was proposed and a piezo-electric drive system for the generation of the compensatory mechanical motion was developed. The implementation of the proposed method resulted in a substantial improvement of workpiece roundness.

Error motion analysis and design of a synthetic probe of thread functional diameter based on the compliant mechanism

2018 ◽  
Vol 29 (12) ◽  
pp. 125010
Author(s):  
Zurong Qiu ◽  
Chenglin Wang ◽  
Zhikun Su ◽  
Jie Xue ◽  
Xinghua Li ◽  
...  
Keyword(s):  
Motion Analysis ◽  
Compliant Mechanism ◽  
Analysis And Design ◽  
Synthetic Probe ◽  
Error Motion

Radial Error Motion Measurement of Ultraprecision Axes of Rotation With Nanometer Level Precision

2017 ◽  
Vol 139 (7) ◽  
Author(s):  
Qiang Shu ◽  
Mingzhi Zhu ◽  
XingBao Liu ◽  
Heng Cheng
Keyword(s):  
Spherical Surface ◽  
Eccentric Rotation ◽  
Nonlinearity Error ◽  
Motion Measurement ◽  
Error Separation ◽  
Radial Error ◽  
Lateral Offset ◽  
Error Motion ◽  
Measurement Efficiency ◽  
Aerostatic Spindle

Error motion of an ultraprecision axis of rotation has great influences on form error of machined parts. This paper gives a complete error analysis for the measurement procedure including nonlinearity error of capacitive displacement probes, misalignment error of the probes, eccentric error of artifact balls, environmental error, and error caused by different error separation methods. Nonlinearity of the capacitive displacement probe targeting a spherical surface is investigated through experiments. It is found that the additional probe output caused by lateral offset of the probe relative to the artifact ball greatly affects the measurement accuracy. Furthermore, it is shown that error motions in radial and axial directions together with eccentric rotation of the artifact lead to lateral offset. A novel measurement setup which integrates an encoder and an adjustable artifact is designed to ensure measurement repeatability by a zero index signal from the encoder. Moreover, based on the measurement setup, once roundness of the artifact is calibrated, roundness of the artifact can be accurately compensated when radial error motion is measured, and this method improves measurement efficiency while approaches accuracy comparable to that of error separation methods implemented alone. Donaldson reversal and three-probe error separation methods were implemented, and the maximum difference of the results of the two methods is below 14 nm. Procedure of uncertainty estimation of radial error motion is given in detail by analytical analysis and Monte Carlo simulation. The combined uncertainty of radial error motion measurement of an aerostatic spindle with Donaldson reversal and three-probe methods is 14.8 nm and 13.9 nm (coverage k = 2), respectively.

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