In order to explore the influence of manufacturing errors on the performance of air bearings, a rotor-bearing model with inner race surface waviness and rotor tilt motion is proposed. First, a theoretical solution to Reynolds equation is derived by considering tilt motion with a 4-degree-of-freedom system, which includes two tilt and two translational degrees of freedom. The results are then compared and validated against highly cited literature. Next, three different surface waviness on bearing inner race—sine wave, triangular wave, and square wave—are modeled, with two possible wave propagation directions: axial and circumferential. The impact of these waviness patterns is analyzed to determine the bearing performance parameters. The study systematically discusses the variations in circumferential and axial friction coefficients with respect to the changes in waviness. Finally, the results show that sinusoidal waviness and triangular waviness show similar regularities, that is, they show inhibition in axial direction and positive effect in circumferential direction at even wavelength. Square waviness exhibits excellent performance both axially and circumferentially, in detail, to reduce the friction coefficient, select the axial square waviness (A = 4 <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11071_2025_11135_Article_IEq1.gif" Format="GIF" Height="12" Rendition="HTML" Resolution="72" Type="Linedraw" Width="15" /> </InlineMediaObject> <EquationSource Format="TEX">$\mu $</EquationSource> <EquationSource Format="MATHML"><math> <mi>μ</mi> </math></EquationSource> </InlineEquation>m, <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11071_2025_11135_Article_IEq2.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="61" /> </InlineMediaObject> <EquationSource Format="TEX">$\lambda =L/3$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>λ</mi> <mo>=</mo> <mi>L</mi> <mo stretchy="false">/</mo> <mn>3</mn> </mrow> </math></EquationSource> </InlineEquation>); to increase the load capacity and the stiffness coefficient, select the circumferential square waviness (A = 4 <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11071_2025_11135_Article_IEq1.gif" Format="GIF" Height="12" Rendition="HTML" Resolution="72" Type="Linedraw" Width="15" /> </InlineMediaObject> <EquationSource Format="TEX">$\mu $</EquationSource> <EquationSource Format="MATHML"><math> <mi>μ</mi> </math></EquationSource> </InlineEquation>m, <InlineEquation ID="IEq4"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11071_2025_11135_Article_IEq4.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="74" /> </InlineMediaObject> <EquationSource Format="TEX">$\lambda =\pi D/3$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>λ</mi> <mo>=</mo> <mi>π</mi> <mi>D</mi> <mo stretchy="false">/</mo> <mn>3</mn> </mrow> </math></EquationSource> </InlineEquation>). When the optimum square wave circumferential waviness parameter ((A = 4 <InlineEquation ID="IEq5"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11071_2025_11135_Article_IEq1.gif" Format="GIF" Height="12" Rendition="HTML" Resolution="72" Type="Linedraw" Width="15" /> </InlineMediaObject> <EquationSource Format="TEX">$\mu $</EquationSource> <EquationSource Format="MATHML"><math> <mi>μ</mi> </math></EquationSource> </InlineEquation>m, <InlineEquation ID="IEq6"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11071_2025_11135_Article_IEq4.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="74" /> </InlineMediaObject> <EquationSource Format="TEX">$\lambda =\pi D/3$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>λ</mi> <mo>=</mo> <mi>π</mi> <mi>D</mi> <mo stretchy="false">/</mo> <mn>3</mn> </mrow> </math></EquationSource> </InlineEquation>)) is introduced into a specific aerostatic spindle, it is found that the vibration response of the spindle end is reduced by 23.89%.

Effect of various surface waviness and rotor tilt motion on the performance of air radial bearing

期刊论文
发表日期：

2025年4月12日

查看全文

Jianghai Shi,
Xin Feng,
Hongrui Cao

摘要

In order to explore the influence of manufacturing errors on the performance of air bearings, a rotor-bearing model with inner race surface waviness and rotor tilt motion is proposed. First, a theoretical solution to Reynolds equation is derived by considering tilt motion with a 4-degree-of-freedom system, which includes two tilt and two translational degrees of freedom. The results are then compared and validated against highly cited literature. Next, three different surface waviness on bearing inner race—sine wave, triangular wave, and square wave—are modeled, with two possible wave propagation directions: axial and circumferential. The impact of these waviness patterns is analyzed to determine the bearing performance parameters. The study systematically discusses the variations in circumferential and axial friction coefficients with respect to the changes in waviness. Finally, the results show that sinusoidal waviness and triangular waviness show similar regularities, that is, they show inhibition in axial direction and positive effect in circumferential direction at even wavelength. Square waviness exhibits excellent performance both axially and circumferentially, in detail, to reduce the friction coefficient, select the axial square waviness (A = 4 $\mu $ $μ$ m, $\lambda =L/3$ $λ = L / 3$ ); to increase the load capacity and the stiffness coefficient, select the circumferential square waviness (A = 4 $\mu $ $μ$ m, $\lambda =\pi D/3$ $λ = π D / 3$ ). When the optimum square wave circumferential waviness parameter ((A = 4 $\mu $ $μ$ m, $\lambda =\pi D/3$ $λ = π D / 3$ )) is introduced into a specific aerostatic spindle, it is found that the vibration response of the spindle end is reduced by 23.89%.