저작자표시 - 비영리 - 변경금지 2.0 대한민국 이용자는아래의조건을따르는경우에한하여자유롭게 이저작물을복제, 배포, 전송, 전시, 공연및방송할수있습니다. 다음과같은조건을따라야합니다 : 저작자표시. 귀하는원저작자를표시하여야합니다. 비영리. 귀하는이저작물을영리목적으로이용할수없습니다. 변경금지. 귀하는이저작물을개작, 변형또는가공할수없습니다. 귀하는, 이저작물의재이용이나배포의경우, 이저작물에적용된이용허락조건을명확하게나타내어야합니다. 저작권자로부터별도의허가를받으면이러한조건들은적용되지않습니다. 저작권법에따른이용자의권리는위의내용에의하여영향을받지않습니다. 이것은이용허락규약 (Legal Code) 을이해하기쉽게요약한것입니다. Disclaimer

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Figure 1 Schematic views of a gas foil journal bearing [6] Figure 2 Parameters of a bump foil. F: Applied static load, H B : Bump height, t T : Top foil thickness, t b : Bump foil thickness, t S : Shim foil thickness, L B : Bump length, P: Bump pitch, C: Clearance. Figure 3 Schematic view of test bearing depicting fixed end locations Figure 4 Static load test rig for bump foil journal bearings Figure 5 Typical hysteresis loop for mechanical damping [18] Figure 6 Bearing displacement versus static load for test bearing Figure 7 Bearing displacement versus static load excluding soft region Figure 8 Static load versus bearing displacement and structural stiffness versus bearing displacement for push load Figure 9 Static load versus bearing displacement and structural stiffness versus bearing displacement for pull load Figure 10 Structural stiffness versus bearing displacement for push and pull loads - x -

Figure 11 Structural stiffness versus static load for (a) push and (b) pull loads Figure 12 Structural stiffness and bearing displacement for three independent measurements for push and pull loads Figure 13 Bearing displacement versus static load with local hysteresis loops Figure 14 Measured local hysteresis. Figure highlights one of local hysteresis loops with dissipated energy and local stiffnesses Figure 15 Structural stiffness and loss factor versus bearing displacement for local hysteresis loops Figure 16 Bearing displacement versus static load for preloads of 4 and 64 N Figure 17 Structural stiffness versus bearing displacement for preloads of 4 and 64 N Figure 18 Loss factor versus bearing displacement for preloads of 4 and 64 N Figure 19 Loss factor versus damping parameters for preload of 4 N - xi -

Figure 20 Loss factor versus damping parameters for preload of 64 N Figure 21 Comparison of hysteresis loops for one top foil (Top 1) and two top foils (Top 2) Figure 22 Structural stiffness versus bearing displacement for push load condition. One top foil (Top 1) and two top foils (Top 2). Figure 23 Structural stiffness versus bearing displacement for pull load condition. One top foil (Top 1) and two top foils (Top 2). Figure 24 Comparison of hysteresis loops of bearing without and with viscoelastic tape Figure 25 Structural stiffness versus bearing displacement for push load condition Figure 26 Structural stiffness versus bearing displacement for pull load condition Figure 27 Comparison of prediction and test result: Static load versus bearing displacement. Test data taken from push load condition Figure 28 Comparison of prediction and test result: Structural stiffness versus bearing displacement. Test data taken from push load - xii -

condition Figure 29 Schematics of test setup Figure 30 Schematics of bump sliding and deflection under push and pull loads Figure 31 Bump displacement versus static load for flat and arch type bump foils Figure 32 Structural stiffness versus static load for flat and arch type bump foils Figure 33 Bump displacement versus static load for bump foil with fixed end Figure 34 (a) Curve-fitted curve with push load and (b) Structural stiffness versus static load for push and pull loads with fixed end Figure 35 Bump displacement versus static load for bump foil without fixed end (free-free end condition) Figure 36 (a) Curve-fitted curve with push load and (b) Structural stiffness versus static load for push and pull loads with free end (free-free end condition) - xiii -

Figure 37 Comparison of hysteresis loops of fixed and free bump foils Figure 38 Structural stiffness versus bump displacement and static load in fixed and free bump foils Figure 39 Schematics of bump deflection versus static load dificting different loading condition due to inaccurately fabricated bump foil Figure 40 Comparison of hysteresis loops of fixed and free bump foils. Data taken from condition for cases 3 and 4 Figure 41 Structural stiffness versus static load. Data taken from condition for cases 3 and 4 Figure 42 Bump deflection versus static load for one layer bump foil. Measurements with three bump foils with identical geometry Figure 43 Structural stiffness versus static load for one layer bump foil Figure 44 Bump displacement versus static load for three-layer bump foils Figure 45 Structural stiffness versus static load for three-layer bump foils Figure 46 Bump displacement versus static load for bump foil in series with aluminum plate and another bump foil - xiv -

Figure 47 Structural stiffness versus static load for bump foil in series with aluminum plate and another bump foil Figure 48 Bump deflection versus static load for bump foil in series with shim foil and another bump foil Figure 49 Structural stiffness versus static load for bump foil in series with shim foil and another bump foil Figure 50 Bump deflection versus static load for cases 1, 3, 6, 7, and 8 Figure 51 structural stiffness versus static load for cases 1, 3, 6, 7, and 8 Figure 52 Schematic view of overlapped bump foils Figure 53 Static load versus bump deflection Figure 54 Static load versus structural stiffness Figure 55 Local hysteresis loops with preload of 50 N and 100 N for one layer bump foil Figure 56 Local hysteresis loops with preload of 50 N and 100 N for two-layer bump foils - xv -

Figure 57 Local hysteresis loops with preload of 50 N for one layer bump foil Figure 58 Local hysteresis loops with preload of 100 N for one layer bump foil Figure 59 Local hysteresis loops with preload of 50 N for two-layer bump foils Figure 60 Local hysteresis loops with preload of 100 N for two-layer bump foils Figure 61 Structural stiffness versus bump deflection. Preload of 50 N and 100 N for one layer and two-layer bumps Figure 62 Loss factor versus bump deflection. Preload of 50 N and 100 N for one layer and tow-layer bump foils Figure 63 Instruments for calibration of load cell Figure 64 Test setup for calibration of displacement sensor Figure 65 Output voltage of eddy current sensor versus displacement for sensitivity of the sensor - xvi -

Figure 66 Output voltage of eddy current sensor versus applied static load to shaft Figure 67 Local hysteresis loop with applied static load 4 N Figure 68 Local hysteresis loop with applied static load 24 N. Figure 69 Comparison of stiffness estimated by curve fit, average of each points and representative slope Figure 70 Comparison of loss factor estimated by average of each points and representative slope Figure 71 Static load versus bearing displacement for estimation of structural stiffness Figure 72 Static load versus bearing displacement for estimation of loss factor Figure 73 Local hysteresis loop for estimation of loss factor Figure 74 Bump foil parameters Figure 75 Coordinate system in the foil bearing for prediction of bearing stiffness [22] - xvii -

Figure 76 Static load versus bearing displacement. Comparison to data in Reference [4] Figure 77 Structural stiffness versus bearing displacement. Comparison to data in Reference [4] - xviii -

Table 1 Geometry of test bump foil journal bearing Table 2 Loss factors and damping parameters for local hysteresis loops Table 3 Dissipated energy, stiffness, and loss factor with preload of 4 N for bump deflection of 10 μm, 20 μm, 40 μm, and 60 μm Table 4 Dissipated energy, stiffness, and loss factor with preload of 64 N for bump deflections of 7 μm, 13 μm, 18 μm, and 24 μm Table 5 Dissipated energy, stiffness, and loss factor of one layer bump with preload of 50 N for bump deflection of 6 μm, 12 μm, 18 μm, and 24 μm Table 6 Dissipated energy, stiffness, and loss factor of one layer bump with preload of 100 N for bump deflection of 6 μm, 12 μm, 18 μm, and 24 μm Table 7 Dissipated energy, stiffness, and loss factor of two-layer bump foils with preload of 50 N for bump deflection of 6 μm, 12 μm, 18 μm, and 24 μm - xix -

Table 8 Dissipated energy, stiffness, and loss factor of two-layer bump foils with preload of 100 N for bump deflection of 6 μm, 12 μm, 18 μm, and 24 μm Table 9 Measurement results of voltage Table 10 Specifications of equipment - xx -

μ μ μ - xxi -

μ ζ δ μ - xxii -

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Figure 1 Schematic view of gas foil journal bearing [6] - 2 -

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T T - 9 -

Figure 2 Parameters of bump foil. F: applied static load, H B : bump height, t T : top foil thickness, t b : bump foil thickness, t S : shim foil thickness, L B : bump length, P: bump pitch, C: clearance. Figure 3 Schematic view of test bearing depicting fixed end locations - 10 -

Parameter Symbol Normalize to shaft diameter Bearing sleeve outer diameter D 0 Bearing sleeve inner diameter D I Shim foil thickness t s Top foil thickness t T Bump foil thickness Bump pitch P Bump length L B Bump height H B Clearance C Shaft diameter D - 11 -

Figure 4 Static load test rig for bump foil journal bearings - 12 -

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Δ Figure 5 Typical hysteresis loop for mechanical damping [18] max - 14 -

max max max - 15 -

μ - 16 -

Figure 6 Bearing displacement versus static load for test bearing Figure 7 Bearing displacement versus static load excluding soft region - 17 -

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(a) Static load versus bearing displacement (b) Structural stiffness versus bearing displacement Figure 8 Static load versus bearing displacement and structural stiffness versus bearing displacement for push load - 19 -

(a) Static load versus bearing displacement (b) Structural stiffness versus bearing displacement Figure 9 Static load versus bearing displacement and structural stiffness versus bearing displacement for pull load - 20 -

Figure 10 Structural stiffness versus bearing displacement for push and pull loads - 21 -

(a) Structural stiffness versus static load for push load (b) Structural stiffness versus static load for pull load Figure 11 Structural stiffness versus static load for (a) push and (b) pull loads - 22 -

(a) Structural stiffness versus bearing displacement for push load (b) Structural stiffness versus bearing displacement for pull load Figure 12 Structural stiffness and bearing displacement for three independent measurements for push and pull loads - 23 -

μ μ Δ μ - 24 -

Figure 13 Bearing displacement versus static load with local hysteresis loops Figure 14 Measured local hysteresis. Figure highlights one of local hysteresis loops with dissipated energy and local stiffnesses - 25 -

Table 2 Loss factors and damping parameters for local hysteresis loops μ Δ - 26 -

(a) Structural stiffness versus bearing displacement (b) Loss factor versus bearing displacement Figure 15 Structural stiffness and loss factor versus bearing displacement for local hysteresis loops - 27 -

μ μ μ μ μ μ μ μ μ μ - 28 -

(a) Bearing displacement versus static load for preload of 4 N (b) Bearing displacement versus static load for preload of 64 N Figure 16 Bearing displacement versus static load for preloads of 4 and 64 N - 29 -

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Figure 17 Structural stiffness versus bearing displacement for preloads of 4 and 64 N Figure 18 Loss factor versus bearing displacement for preloads of 4 and 64 N - 31 -

(a) Loss factor versus logarithmic decrement (b) Loss factor versus equivalent viscous damping ratio Figure 19 Loss factor versus damping parameters for preload of 4 N - 32 -

(c) Loss factor versus equivalent viscous damping coefficient Figure 19 Continued - 33 -

(a) Loss factor versus logarithmic decrement (b) Loss factor versus equivalent viscous damping ratio Figure 20 Loss factor versus damping parameters for preload of 64 N - 34 -

(c) Loss factor versus equivalent viscous damping coefficient Figure 20 Continued Table 3 Dissipated energy, stiffness, and loss factor with preload of 4 N for bump deflection of 10 μm, 20 μm, 40 μm, and 60 μm μ Δ - 35 -

Table 4 Dissipated energy, stiffness, and loss factor with preload of 64 N for bump deflections of 7 μm, 13 μm, 18 μm, and 24 μm μ Δ - 36 -

Figure 21 Comparison of hysteresis loops for one top foil (Top 1) and two top foils (Top 2) - 37 -

Figure 22 Structural stiffness versus bearing displacement for push load condition. One top foil (Top 1) and two top foils (Top 2). Figure 23 Structural stiffness versus bearing displacement for pull load condition. One top foil (Top 1) and two top foils (Top 2). - 38 -

μ Figure 24 Comparison of hysteresis loops of bearing without and with viscoelastic tape - 39 -

Figure 25 Structural stiffness versus bearing displacement for push load condition Figure 26 Structural stiffness versus bearing displacement for pull load condition - 40 -

Figure 27 Comparison of prediction and test result: Static load versus bearing displacement. Test data taken from push load condition - 41 -

Figure 28 Comparison of prediction and test result: Structural stiffness versus bearing displacement. Test data taken from push load condition - 42 -

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Figure 29 Schematics of test setup Figure 30 Schematics of bump sliding and deflection under push and pull loads - 44 -

범프포일단품실험을위한측정장비는 2.3.1절에서언급한동일한장비를사용하였다. 범프포일의변형량을측정하기위해범프포일위에올려진평평한판에와전류타입의변위센서를사용하였다. 하중이가해질때판의기울어짐을고려하기위해동일한두개의변위센서를사용하였으며, 이들의평균값을사용하여범프포일의변형량을측정하였다. 로드셀및변위센서를보정하는방법또한 2.3.1절에언급한방법과동일하다. - 45 -

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Figure 31 Bump displacement versus static load for flat and arch type bump foils Figure 32 Structural stiffness versus static load for flat and arch type bump foils - 47 -

Figure 33 Bump displacement versus static load for bump foil with fixed end - 48 -

(a) Curve-fitting of static load-bump displacement data above ~90 N for bump foil with fixed end under push load (b) Structural stiffness versus static load for push and pull load for bump foil with fixed end Figure 34 (a) Curve-fitted curve with push load and (b) Structural stiffness versus static load for push and pull loads with fixed end - 49 -

Figure 35 Bump displacement versus static load for bump foil without fixed end (free-free end condition) - 50 -

(a) Curve-fitting of static load-bump displacement data above ~60 N for bump foil with free end under push load (b) Structural stiffness versus static load for push and pull load for bump foil with free end Figure 36 (a) Curve-fitted curve with push load and (b) Structural stiffness versus static load for push and pull loads with free end (free-free end condition) - 51 -

Figure 37 Comparison of hysteresis loops of fixed and free bump foils - 52 -

(a) Comparison of structural stiffness versus bump displacement of Case 1 and Case 2 for push load (b) Comparison of structural stiffness versus static load of Case 1 and Case 2 for push load Figure 38 Structural stiffness versus bump displacement and static load in fixed and free bump foils - 53 -

Figure 39 Schematics of bump deflection versus static load dificting different loading condition due to inaccurately fabricated bump foil - 54 -

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Figure 40 Comparison of hysteresis loops of fixed and free bump foils. Data taken from condition for cases 3 and 4 Figure 41 Structural stiffness versus static load. Data taken from condition for cases 3 and 4-56 -

Figure 42 Bump deflection versus static load for one layer bump foil. Measurements with three bump foils with identical geometry - 57 -

Figure 43 Structural stiffness versus static load for one layer bump foil - 58 -

Figure 44 Bump displacement versus static load for three-layer bump foils Figure 45 Structural stiffness versus static load for three-layer bump foils - 59 -

Figure 46 Bump displacement versus static load for bump foil in series with aluminum plate and another bump foil - 60 -

Figure 47 Structural stiffness versus static load for bump foil in series with aluminum plate and another bump foil - 61 -

Figure 48 Bump deflection versus static load for bump foil in series with shim foil and another bump foil - 62 -

Figure 49 Structural stiffness versus static load for bump foil in series with shim foil and another bump foil - 63 -

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Figure 50 Bump deflection versus static load for cases 1, 3, 6, 7, and 8 Figure 51 structural stiffness versus static load for cases 1, 3, 6, 7, and 8-65 -

Figure 52 Schematic view of overlapped bump foils - 66 -

Figure 53 Static load versus bump deflection Figure 54 Static load versus structural stiffness - 67 -

Figure 55 Local hysteresis loops with preload of 50 N and 100 N for one layer bump foil - 68 -

Figure 56 Local hysteresis loops with preload of 50 N and 100 N for two-layer bump foils μ μ μ μ - 69 -

Figure 57 Local hysteresis loops with preload of 50 N for one layer bump foil Figure 58 Local hysteresis loops with preload of 100 N for one layer bump foil - 70 -

Table 5 Dissipated energy, stiffness, and loss factor of one layer bump with preload of 50 N for bump deflection of 6 μm, 12 μm, 18 μm, and 24 μm μ Δ Table 6 Dissipated energy, stiffness, and loss factor of one layer bump with preload of 100 N for bump deflection of 6 μm, 12 μm, 18 μm, and 24 μm μ Δ μ μ μ μ - 71 -

Figure 59 Local hysteresis loops with preload of 50 N for two-layer bump foils - 72 -

Figure 60 Local hysteresis loops with preload of 100 N for two-layer bump foils Table 7 Dissipated energy, stiffness, and loss factor of two-layer bump foils with preload of 50 N for bump deflection of 6 μm, 12 μm, 18 μm, and 24 μm μ Δ - 73 -

Table 8 Dissipated energy, stiffness, and loss factor of two-layer bump foils with preload of 100 N for bump deflection of 6 μm, 12 μm, 18 μm, and 24 μm μ Δ - 74 -

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Figure 61 Structural stiffness versus bump deflection. Preload of 50 N and 100 N for one layer and two-layer bumps Figure 62 Loss factor versus bump deflection. Preload of 50 N and 100 N for one layer and tow-layer bump foils - 76 -

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부록 1.1 로드셀, 인디케이터보정 Figure 63 Instruments for calibration of load cell - 86 -

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1.2 변위센서보정 Figure 64 Test setup for calibration of displacement sensor - 90 -

Figure 65 Output voltage of eddy current sensor versus displacement for sensitivity of the sensor Table 9 Measurement results of voltage - 91 -

Figure 66 Output voltage of eddy current sensor versus applied static load to shaft - 92 -

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Figure 67 Local hysteresis loop with applied static load 4 N Figure 68 Local hysteresis loop with applied static load 24 N. - 94 -

Figure 69 Comparison of stiffness estimated by curve fit, average of each points and representative slope Figure 70 Comparison of loss factor estimated by average of each points and representative slope - 95 -

μ μ - 96 -

Figure 71 Static load versus bearing displacement for estimation of structural stiffness - 97 -

Figure 72 Static load versus bearing displacement for estimation of loss factor - 98 -

Figure 73 Local hysteresis loop for estimation of loss factor Δ - 99 -

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sin α α α α μ Figure 74 Bump foil parameters ζ η - 102 -

ζ ζ cos sin ζ ζ - 103 -

ζ ζ cos sin β cos sin - 104 -

Figure 76 Static load versus bearing displacement. Comparison to data in Reference [4] Figure 77 Structural stiffness versus bearing displacement. Comparison to data in Reference [4] - 105 -

μ - 106 -

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Table 10 Specifications of equipment Ω - 112 -

Table 10 Continued - 113 -

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