Prediction and compensation of motion accuracy in a linear motion bearing table

Khim, Gyungho; Park, Chun Hong; Shamoto, Eiji; Kim, Seung-Woo

doi:10.1016/j.precisioneng.2010.12.006

Cited by 44 publications

(26 citation statements)

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“…The transfer function is introduced to calculate the reaction forces of the bearing [5, 7, 8]. This is defined as the ratio of the amplitude of f e ( ω ) to that of e ( ω ) at a spatial frequency ω (where ω = 2 π / λ ).…”

Section: Modeling Motion Error With 5 Dofsmentioning

confidence: 99%

“…The difference in the distance between the centers of curvature A b and A r may then be regarded as the elastic deformation of the ball, ξ ijk , which can be expressed as follows [7, 11]:

\begin{matrix} ξ_{i j k} (x) = \bar{A_{b}^{'} A_{r}^{'}} - \bar{A_{b} A_{r}} = \sqrt{V_{y, i j k} {(|, x)}^{normal2} + V_{z, i j k} {(|, x)}^{normal2}} - l_{0} + χ_{p}, \\ l_{0} = 2 R - D_{a}, \\ V_{y, i j k} (x) = l_{0} \cos β - {(- 1)}^{j} ε_{y, i j k} (x) + {(- 1)}^{j} e_{y, i} (x), \\ V_{z, i j k} (x) = l_{0} \sin β - {(- 1)}^{k} ε_{z, i j k} (x) + {(- 1)}^{k} e_{z, i} (x), \end{matrix}

where χ p is the preload on the ball and R is the radius of curvature of the rail and the bearing block grooves.…”

Section: Modeling Motion Error With 5 Dofsmentioning

confidence: 99%

“…By applying the Hertz contact equation [7, 11, 12], the force P ijk that acts on each ball can be obtained; that is,

\begin{matrix} P_{i j k} (x) = C \sqrt{D_{a}} {(ξ_{i j k} (x))}^{3 / 2}, \end{matrix}

where C is a constant that depends on the ratio of the radius of curvature of the groove to the diameter of the ball.…”

Section: Modeling Motion Error With 5 Dofsmentioning

confidence: 99%

“…The vertical transfer function was calculated by summing the vertical components of the reaction forces, P ijk , at the spatial frequency ω of the rail-form error with a unit magnitude, assuming that the bearing block moves with no motion errors. A detailed explanation of this can be found in [7, 8]. …”

Section: Modeling Motion Error With 5 Dofsmentioning

confidence: 99%

“…The transfer function method has been used to calculate motion errors in two degrees of freedom (DOFs) using a hydrostatic feed table, with a reverse technique to determine the rail-form errors from the measured motion errors [5, 6]. A similar approach has been followed to describe motion error in a linear motion bearing table, and the motion error was reduced to less than a micrometer by correcting for the rail-form error [7]. We have previously extended the transfer function method to analyze motion errors in five DOFs [8].…”

Section: Introductionmentioning

confidence: 99%

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A Method of Calculating Motion Error in a Linear Motion Bearing Stage

Khim

Park

2015

The Scientific World Journal

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We report a method of calculating the motion error of a linear motion bearing stage. The transfer function method, which exploits reaction forces of individual bearings, is effective for estimating motion errors; however, it requires the rail-form errors. This is not suitable for a linear motion bearing stage because obtaining the rail-form errors is not straightforward. In the method described here, we use the straightness errors of a bearing block to calculate the reaction forces on the bearing block. The reaction forces were compared with those of the transfer function method. Parallelism errors between two rails were considered, and the motion errors of the linear motion bearing stage were measured and compared with the results of the calculations, revealing good agreement.

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Section: Modeling Motion Error With 5 Dofsmentioning

confidence: 99%

“…The difference in the distance between the centers of curvature A b and A r may then be regarded as the elastic deformation of the ball, ξ ijk , which can be expressed as follows [7, 11]: