• Journal of the Korean Society for Precision Engineering
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• v.19 no.4
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• pp.124-131
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• 2002

In this paper, an extended volumetric error model considering backlash in a three-axis machine tool was proposed and utilized for calculating the volumetric error of the machine tool at any position in three-dimensional workspace. Backlashes are interrelated; i.e. the angular backlash affects the straightness errors which then affect talc calculated squareness errors. Therefore, a new concept was introduced to define the backlash of squareness errors to incorporate the backlash of squareness error into the volumetric error, and the characteristics of the backlash of squareness error were investigated. The effects of backlash errors were assessed, by experiments. for 21 geometric errors of a machine tool. The backlash error was shown to be one of the systematic errors of a machine tool. And a generalized volumetric error model formulator for three-axis machine tools was developed, which allowed us to formulate machine tool synthesis error models far all possible machine tool configurations only with machine tool topology information. Based on these volumetric error model and model formulator, a computer-aided volumetric error analysis system was developed for a three-axis machine tool in this paper. Then the volumetric error at an arbitrary position can be obtained, and displayed in a three-dimensional graphic form.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 2000.05a
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• pp.676-680
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• 2000

In this paper, an extended volumetric error model considering backlash in a three-axis machine tool was proposed and utilized for calculating the volumetric error of the machine tool at any position in three-dimensional workspace. Backlashes are interrelated; i.e. the angular backlash affects the straightness errors which then affect the calculated squareness errors. Therefore, a new concept was introduced to define the backlash of squareness errors to incorporate the backlash of squareness error into the volumetric error, and the characteristics of the backlash of squareness error were investigated. The effects of backlash errors were assessed, by experiments, fur 21 geometric errors of a machine tool. The backlash error was shown to be one of the systematic errors of a machine tool. Based on this volumetric error model, a computer-aided volumetric error analysis system was developed for a three-axis machine tool in this paper. Then the volumetric error at an arbitrary position can be obtained, and displayed in a three-dimensional graphic form.

• Proceedings of the KSME Conference
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• 2001.06b
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• pp.635-640
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• 2001

The small gear reductioner noise is caused by gear accuracy, assembling errors, and gear backlash. This main study is an investigation on noise quality of the small gear reductioner through the change of gear backlash. In this study included Gear design parameters related the small gear reductioner, the knowledge of rattle noise related gear backlash, and the experimentation results of the small reductioner noise through change of gear backlash. At last, this study propose the least method of the small gear reductioner noise that is caused by suitable existence of gear backlash.

• Journal of the Korean Society for Precision Engineering
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• v.20 no.12
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• pp.34-41
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• 2003

This paper suggests a methodology fur improving the machining accuracy by compensating for the machining errors based on on-machine measurement process. Probing errors and machine tool errors included in the measurement data were calibrated or compensated to obtain the actual machining errors. Machine tool errors were modeled in forward and backward directions according to the axis movement direction to consider the effects of backlash errors on the measurement data, and model parameters were determined by measuring a cube array artifact. A rectangular workpiece was machined and then measured with a touch probe as a verification experiment. Machining experiments showed that the machining errors were reduced to within the designated tolerance after compensating for the actual machining errors by modifying the original footpath for the next-step machining.

• Journal of the Korean Society for Precision Engineering
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• v.11 no.6
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• pp.117-126
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• 1994

This paper describes an application step of a $R^{-{\theta}}$ method which measures circular movements in machining centers. The detection of composite errors of circular movements and a high precision cutting method in machining centers were investigated by the analysis of data measured by $R^{\theta }$method which can detect the rotating angle and is applicable to variable measuring radius. When the error by squareness error and unbalance of position-loop-gain were mixed, the detection method of each error was proposed. Although the errors by squarenss error and backlash compensation were mixed, the errors by squareness error be detected. If the errors by unbalance of position-loop-gain and backlash compensation were mixed, the errors by unbalance of position-loop-gain could not detected. A high precision cutting mehod, which uses the NC program compensated by using feed-back data from error measured by the $R^{\theta }$method, was proposed.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 2002.10a
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• pp.650-653
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• 2002

In this paper, a methodology to assess machine tool errors quickly is suggested using a touch probe and a cube array artifact. Parameterized error models derived are expressed of model coefficient vectors and backlash errors to be determined. To determine the unknown model coefficient vectors, a cube array artifact is proposed. Considering CMM measurement data of cube vertex coordinates. error vectors for all axes ate obtained and used to complete the error model. Some simulation results show that the suggested error model can follow the true values within 10$\mu\textrm{m}$. To verify the error model, a circular part with two concentric circles is measured and simulated. The results show that the differences between CMM and OMM radius errors are smaller than 15$\mu\textrm{m}$.

• Proceedings of the KIEE Conference
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• 2001.07d
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• pp.2390-2392
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• 2001

The small gear head noise is caused by gear accuracy, assembling errors, and gear backlash. This main study is an investigation on noise quality of the small gear head through the change of gear backlash. In this study included gear design parameters related the small gear head, the knowledge of rattle noise related gear backlash, and the experimentation results of the small head noise through change of gear backlash. At last, this study propose the least method of the small gear head noise that is caused by suitable existence of gear backlash.

• Journal of the Korean Society for Precision Engineering
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• v.10 no.2
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• pp.54-65
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• 1993

The paper describes and alternative method based on a new idea to measure the circular movement of machining centers. ISO has employed three testing methods for the acceptance tests of machine tools; the first is a rotating one-dimensional probe method, the second is a two-dimensional probe and a master circular ring, and the third is a kinematic ball bar. The last two methods were proposed and introduced by W. Knapp and J. B. Bryan, respectively. The newly developed method is superior to above two methods; the rotating angle can be detected and the rotating radius is variable. Circular movement errors of machining centers were investigated by the analysis of data measured by R- .THETA. method. Followint observations are obtained 1) The errors which depend on positions, i.e., periodical errors by the pitch of ball screws, errors by compensation of backlash and errors by perpendicularity of X and Y-axis, were analyzed. 2) The errors which depend on NC control system, i.e., errors by the unbalance of position-loop-gaians, errors by velocity-loop-gains and errors by feed speeds, were quantiatively analyzed. 3) The method of extracting error information, which uses moving technique of averaging angle and fourier's analysis data mesured by the R- .THETA. method, was proposed.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.20 no.7
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• pp.677-684
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• 2010

Backlashes of gears provide gears for good lubrication and for removal of the interference between teeth by the wear and manufacturing errors. The backlash is the strong nonlinear factor to gears. This study deals with nonlinear modeling of helical gears with backlash. Excitation of helical gears comes from torque variation, the tooth surface error, and the periodical change of mesh stiffness. To study the effect of torque fluctuation, equation of motion for the single degree of freedom torsional model of helical gears with the periodical change of mesh stiffness and the backlash was derived. The Newmark beta method and the Newton-Raphson method were used to obtain the nonlinear behaviors of mesh forces of helical gears. All excitation frequencies initially caused the tooth separation and single-sided impacts of the gear pair and eventually led to the normal tooth contact. However, some special excitation frequencies caused the single-sided impacts in the entire time as well as the initial time. Damping increase reduced the duration of single-sided impacts, and the backlash increase caused those in the entire time domain.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 2002.05a
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• pp.632-635
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• 2002

In this paper, a general procedure to determine machine tool errors from the on-machine measurement (OMM) data is described. First, a parameterized error model of a machine tool is illustrated by approximating error components as linear function of axis positions, and a modified error model is proposed which includes backlash effects. To determine the unknown model coefficient vectors of the forward and backward error model, an artifact with 8 cutes is made and calibrated on CMM. Then, lower-left and upper-right cube corners are measured with a touch-trigger probe mounted on the machine tool spindle. Measured error data are used to determine the coefficient vectors. The positioning errors in the XY plane at the fixed z position are simulated for the forward and backward error model.