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1-4 of 4
Clint R. Carter
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Journal Articles
Article Type: Research Papers
J. Eng. Gas Turbines Power. August 2011, 133(8): 082503.
Published Online: April 6, 2011
Abstract
Rotordynamic data are presented for a rocker-pivot tilting pad bearing in load-on-pad (LOP) configuration for (345–3101 kPa) unit loads and speeds from 4000 rpm to 13,000 rpm. The bearing was directly lubricated through a leading edge groove with five pads, 0.282 preload, 60% offset, 57.87 deg pad arc angle, 101.587 mm (3.9995 in.) rotor diameter, 0.1575 mm (0.0062 in.) diametral clearance, and 60.325 mm (2.375 in.) pad length. Measured results were reported for this bearing by Carter and Childs (2008, “Measurements Versus Predictions for the Rotordynamic Characteristics of a 5-Pad, Rocker-Pivot, Tilting-Pad Bearing in Load Between Pad Configuration,” ASME Paper No. GT2008-50069) in the load-between-pad (LBP) configuration. Results for the LOP are compared with predictions from a bulk-flow Navier–Stokes model (as utilized by San Andres (1991, “Effect of Eccentricity on the Force Response of a Hybrid Bearing,” STLE Tribol. Trans., 34, pp. 537–544) ) and to the prior LBP results. Frequency effects on the dynamic-stiffness coefficients were investigated by applying dynamic-force excitation over a range of excitation frequencies. Generally, the direct real parts of the dynamic-stiffness coefficients could be modeled as quadratic functions of the excitation frequency, and accounted for by adding a mass matrix to the conventional [ K ] [ C ] model to produce a frequency-independent [ K ] [ C ] [ M ] model. Measured added-mass terms in the loaded direction approached 60 kg. The static load direction in the tests was y . The direct stiffness coefficients K y y and K x x depend strongly on the applied unit load, more so than speed. They generally increased linearly with load, shifting to a quadratic dependence at higher unit loads. At lower unit loads, K y y and K x x increase monotonically with running speed. The experimental results were compared with predictions from a bulk-flow computational fluid dynamics analysis. Stiffness orthotropy was apparent in test results, significantly more than predicted, and it became more pronounced at the heavier unit loads. Measured K y y values were consistently higher than predicted, and measured K x x values were lower. Comparing the LOP results to prior measured LBP results for the same bearing, at higher loads, K y y is significantly larger for the LOP configuration than LBP. Measured values for K x x are about the same for LOP and LBP. At low unit loads, stiffness orthotropy defined as K y y / K x x is the same for LOP and LBP, progressively increasing with increasing unit loads. At the highest unit load, K y y / K x x = 2.1 for LOP and 1.7 for LBP. Measured direct damping coefficients C x x and C y y were insensitive to changes in either load or speed, in contrast to predictions of marked C y y sensitivity for changes in the load. Only at the highest test speed of 13,000 rpm were the direct damping coefficients adequately predicted. No frequency dependency was observed for the direct damping coefficients.
Proceedings Papers
Proc. ASME. GT2009, Volume 6: Structures and Dynamics, Parts A and B, 867-880, June 8–12, 2009
Paper No: GT2009-59696
Abstract
Rotordynamic data are presented for a rocker-pivot tilting-pad bearing in load-on-pad (LOP) configuration for (345–3101 kPa) unit loads and speeds from 4k to 13k rpm. The bearing was direct lubricated through a leading-edge groove with 5 pads, .282 preload, 60% offset, 57.87° pad arc angle, 101.587 mm (3.9995 in) rotor diameter, 0.1575 mm (.0062 in) diametral clearance, and 60.325 mm (2.375 in) pad length. Measured results were reported for this bearing by Carter and Childs in 2008 in the load-between-pad (LBP) configuration. Results for the LOP are compared to predictions from a bulk-flow Navier-Stokes model (as utilized by San Andres in 1991) and to the prior LBP results. Frequency effects on the dynamic-stiffness coefficients were investigated by applying dynamic-force excitation over a range of excitation frequencies. Generally, the direct real parts of the dynamic-stiffness coefficients could be modeled as quadratic functions of the excitation frequency and accounted for by adding a mass matrix to the conventional [K][C] model to produce a frequency-independent [K][C][M] model. Measured added mass terms in the loaded direction approached 60 kg. The static load direction in the tests was y . The direct-stiffness coefficients K yy and K xx depend strongly on the applied unit load, more so than speed. They generally increased linearly with load, shifting to a quadratic dependence at higher unit loads. At lower unit loads, K yy and K xx increase monotonically with running speed. The experimental results were compared to predictions from a bulk-flow CFD analysis. Stiffness orthotropy was apparent in test results, significantly more than predicted, and it became more pronounced at the heavier unit loads. Measured K yy values were consistently higher than predicted, and measured K xx values were lower. Comparing the LOP results to prior measured LBP results for the same bearing, at higher loads, K yy is significantly larger for the LOP configuration than LBP. Measured values for K xx are about the same for LOP and LBP. At low unit loads, stiffness orthotropy defined as K yy / K xx is the same for LOP and LBP, progressively increasing with increasing unit loads. At the highest unit load, K yy / K xx = 2.1 for LOP and 1.7 for LBP. Measured direct damping coefficients C xx and C yy were insensitive to changes in either load or speed in contrast to predictions of marked C yy sensitivity for changes in the load. Only at the highest test speed of 13 krpm were the direct damping coefficients adequately predicted. No frequency dependency was observed for the direct damping coefficients.
Proceedings Papers
Proc. ASME. GT2008, Volume 5: Structures and Dynamics, Parts A and B, 891-901, June 9–13, 2008
Paper No: GT2008-50069
Abstract
Rotordynamic data are presented for a rocker-pivot tilting-pad bearing in a load-between-pad (LBP) configuration for unit loads over the range [345, 3101 kPa] and speeds over the range [4k to 13k rpm]. The bearing was direct lubricated through a leading-edge groove with the following specifications: 5 pads, .282 preload, 60% offset, 57.87° pad arc angle, 101.587 mm (3.9995 in) rotor diameter, .1575 mm (.0062 in) diametral clearance, 60.325 mm (2.375 in) pad length. Dynamic tests were performed over a range of frequencies to investigate frequency effects on the dynamic-stiffness coefficients. Under most test conditions, the direct real parts of the dynamic stiffnesses could be approximated as quadratic functions of the excitation frequency and accounted for with the addition of an added mass matrix to the conventional [K][C] matrix model to produce a frequency-independent [K][C][M] model. Measured added mass terms in the loaded direction approached 60 kg. At low speeds, “hardening” direct dynamic stiffness coefficients that increased with increasing frequency were obtained that produced negative added-mass terms. No frequency dependency was obtained for the direct damping coefficients. The dynamic experimental results were compared to predictions from a bulk-flow CFD analysis. The static load direction in the tests was y . The direct stiffness coefficients K xx and K yy were slightly over predicted. Measured direct damping coefficients C xx and C yy were insensitive to changes in either load or speed in contrast to predictions of marked C yy sensitivity for changes in the load. Only at the highest test speed of 13000 rpm were the direct damping coefficients adequately predicted. Measurable cross-coupled stiffness coefficients were obtained for the bearings with K xy and K yx being approximately equal in magnitude but opposite in sign — clearly destabilizing. However, the whirl frequency ratio was found to be zero at all test conditions indicating infinite stability for the bearing.
Journal Articles
Article Type: Research Papers
J. Eng. Gas Turbines Power. January 2009, 131(1): 012507.
Published Online: October 13, 2008
Abstract
Rotordynamic data are presented for a rocker-pivot tilting-pad bearing in the load-between-pad configuration for unit loads over the range 345 – 3101 kPa and speeds over the range 4000 – 13,000 rpm . The bearing was directly lubricated through a leading-edge groove with the following specifications: Five pads, 0.282 preload, 60% offset, 57.87 deg pad arc angle, 101.587 mm ( 3.9995 in. ) rotor diameter, 0.1575 mm ( 0.0062 in. ) diametral clearance, and 60.325 mm ( 2.375 in. ) pad length. Dynamic tests were performed over a range of frequencies to investigate frequency effects on the dynamic stiffness coefficients. Under most test conditions, the direct real parts of the dynamic stiffnesses could be approximated as quadratic functions of the excitation frequency and accounted for with the addition of an added-mass matrix to the conventional [ K ] [ C ] matrix model to produce a frequency-independent [ K ] [ C ] [ M ] model. Measured added-mass terms in the loaded direction approached 60 kg . At low speeds, “hardening” direct dynamic stiffness coefficients that increased with increasing frequency were obtained, which produced negative added-mass terms. No frequency dependency was obtained for the direct damping coefficients. The dynamic experimental results were compared to predictions from a bulk-flow computational fluid dynamics analysis. The static load direction in the tests was y . The direct stiffness coefficients K x x and K y y were slightly overpredicted. Measured direct damping coefficients C x x and C y y were insensitive to changes in either the load or speed in contrast to predictions of marked C y y sensitivity for changes in the load. Only at the highest test speed of 13,000 rpm were the direct damping coefficients adequately predicted. Measurable cross-coupled stiffness coefficients were obtained for the bearings with K x y and K y x being approximately equal in magnitude but opposite in sign—clearly destabilizing. However, the whirl frequency ratio was found to be zero at all test conditions indicating infinite stability for the bearing.