Rolling Bearing Calcula on

Rolling Bearing Calcula on Input data MESYS Rolling Bearing Calcula on 12-2017 - PiON Co., Seoul File name: D:/MESYS 12-2017/Applica on_examples/rbc/example-8point.xml Project name: 8 point ball bearing Descrip on: Date: 2018년 1월 22일월요일오전 11:13:13 Bearing Geometry Type of rolling bearing Four point ball bearing (axial) Bearing inner diameter d 500.000 mm Bearing outer diameter D 1030.0 mm Bearing width B 170.000 mm Number of rolling elements Z 14 Roller diameter Dw 135.000 mm Pitch diameter Dpw 765.000 mm Conformity inner race fi 0.53 Conformity outer race fe 0.53 Nominal contact angle α 45.000 Defini on of clearance User input as opera ng clearance Defini on of bearing tolerance Not considered Nominal axial clearance Pa 0.1000 mm Clearance genera on type axial direc on Configura on Number Posi on [mm] Axial offset [mm] Orienta on 1-85 0 le 2 85 0 le Loading Speed of inner ring ni 20.000 rpm inner ring rotates rela ve to load Speed of outer ring ne 0.0000 rpm outer ring is sta onary rela ve to load Axial force Fx 2000.0 kn Radial force Y Fy 0.0000 kn Radial force Z Fz 0.0000 kn 1/11

Moment Y My 0.0000 Nm Moment Z Mz 400000 Nm Reliability reliability 90.000 % Maximal permissible value for aiso aisomax 50 Temperature of inner ring T_i 20.000 C Temperature of outer ring T_e 20.000 C Material Surface hardness inner race HRC_i 58 Surface hardness outer race HRC_e 58 Ul mate strength of core inner race Rm_i 1200.0 MPa Ul mate strength of core outer race Rm_e 1200.0 MPa Material for inner ring Steel Material for outer ring Steel Material for rolling element Steel Lubrica on Lubricant ISO VG 100 mineral oil Kinema c viscosity at 40 C ν40 100.000 mm²/s Kinema c viscosity at 100 C ν100 11.000 mm²/s Oil density rhooil 880.000 kg/m³ Oil temperature ϑoil 70.000 C Oil does not contain effec ve EP addi ves Effec ve kinema c viscosity ν(ϑ) 27.094 mm²/s Effec ve oil density ρ(ϑ) 842.025 kg/m³ Lubricant cleanness Grease lubrica on, Normal cleanliness Results Centrifugal loads are considered Op on for gyroscopic moment Gyroscopic moment is not considered Bearing inner geometry Number of rolling elements Z 14 Roller diameter Dw 135.000 mm Pitch diameter Dpw 765.000 mm Conformity inner race fi 0.53 Conformity outer race fe 0.53 Nominal contact angle α 45.000 Distance between center of curvature inner and δcc 5.6776 mm outer ring Distance between center of curvature inner ring δcc_i 5.6776 mm Distance between center of curvature outer ring δcc_e 5.6776 mm Nominal diametral clearance Pd 0.0991 mm Nominal axial clearance Pa 0.1000 mm Diameter inner race di 627.628 mm Diameter outer race de 902.372 mm Radius inner race ri 71.550 mm Radius outer race re 71.550 mm Distance between rolling elements δre 35.229 mm Shoulder diameter inner ring dsi 724.500 mm Limit contact angle inner ring αlim_i 71.153 Shoulder diameter outer ring dse 805.500 mm Limit contact angle outer ring αlim_e 71.153 Extension contact ellipse inner ring dcimax 706.685 mm Extension contact ellipse outer ring dcemin 823.932 mm 2/11

Ellipse length ra o inner race elr_i 127.357 % Ellipse length ra o outer race elr_e 128.912 % Circumferen al ball advance Δb_circ 8.4146 mm Axial ball excursion Δb_ax 0.3908 mm Maximum spin to roll ra o maxspintoroll 0.990659 Forces and displacement Axial force Fx 2000.0 kn Radial force Y Fy 0.0000 kn Radial force Z Fz 0.0000 kn Displacement X ux 355.101 µm Displacement Y uy 319.133 µm Displacement Z uz -0.0000 µm Moment Y My 0.0000 Nm Moment Z Mz 400000 Nm Rota on around Y ry -0.0000 mrad Rota on around Z rz 1.0208 mrad Fric onal moment Mloss 4489.9 Nm Power loss Ploss 9404.7 W Maximal pressure inner race pmax_i 2431.2 MPa Maximal pressure outer race pmax_e 2193.0 MPa Maximal pressure pmax 2431.2 MPa Sta c safety factor SF 5.15586 Number Fx [kn] ux [mm] Fy [kn] uy [mm] Fz [kn] uz [mm] My [Nm] ry [mrad] Mz [Nm] rz [mrad] pmax [MPa] SF 1 1123.5 0.3551-310.668 0.2324-3.04774e-07 0.0000-0.00 0.00 226217.13 1.02 2431.17 5.16 2 876.496 0.3551 310.668 0.4059-2.82779e-07 0.0000-0.00 0.00 120969.33 1.02 2189.70 7.06 Life Load capacity factor bm 1.3 Dynamic load capacity Ca 1824.1 kn Sta c load capacity C0a 11110.2 kn Fa gue load limit Cua 182.985 kn Dynamic load capacity, system Casys 2963.3 kn Sta c load capacity, system C0asys 22220.4 kn Fa gue load limit, system Cuasys 365.971 kn Life modifica on factor for reliability a1 1 Viscosity ra o κ 0.200143 Contamina on factor ec 0.488132 Life modifica on factor aiso 0.145609 Reference load Pref 2.73095e+06 N Basic reference ra ng life L10r 1.27754 Basic reference ra ng life L10rh 1064.6 h Modified reference ra ng life Lnmr 0.186021 Modified reference ra ng life Lnmrh 155.017 h Life according ISO 281 Basic life L10 1.79193 Basic life L10h 1493.3 h Modified life Lnm 0.264659 Modified life Lnmh 220.549 h Sta c safety factor (ISO 76) S0 6.04458 Number κ ec aiso Pref [kn] L10r Lnmr L10rh [h] Lnmrh [h] L10h [h] Lnmh [h] S0 1 0.20 0.49 0.14 1474.22 1.89436 0.273596 1578.64 227.997 2155.84 315.503 6.04458 2 0.20 0.49 0.15 1231.61 3.24884 0.480226 2707.36 400.189 3995.47 601.108 6.983 3/11

Wear parameters Fric onal moment Mloss 4489.9 Nm Power loss Ploss 9404.7 W Wear parameter PVmax PVmax 119.295 MPa m/s Wear parameter PVavg_max PVavg_max 53.980 MPa m/s Total thermal resistance R 0.1038 K/W Number Mloss [Nm] Ploss Ploss_i Ploss_e PVmax [MPa m/s] PVavg_max [MPa m/s] QV R [K/W] 1 1249.34 2617.13 1364.72 1252.41 65.1553 30.6935 26171.3 0.223135 2 3240.56 6787.57 3735.63 3051.94 119.295 53.9802 67875.7 0.194087 Subsurface stresses Maximal shear stress for inner race τmax_i 773.498 MPa Depth for maximal shear stress inner race h(τmax_i) 1.8999 mm Shear yield stress for core inner race τyield_i 510.000 MPa Shear fa gue limit for core inner race τa_i 306.000 MPa Shear stress at core inner race τ_i 306.000 MPa Maximal shear stress for outer race τmax_e 700.984 MPa Depth for maximal shear stress outer race h(τmax_e) 2.1285 mm Shear yield stress for core outer race τyield_e 510.000 MPa Shear fa gue limit for core outer race τa_e 306.000 MPa Shear stress at core outer race τ_e 306.000 MPa Required hardness depth inner race hdmin_i 8.9174 mm Required hardness depth outer race hdmin_e 8.9318 mm Damage Frequencies Speed of inner ring ni 0.33 1/s (20rpm) Speed of outer ring ne 0.00 1/s (0rpm) Rota on speed of cage fc 0.15 1/s (9rpm) Damage frequency for inner race fip 2.62 1/s (157rpm) Damage frequency for outer race fep -2.04 1/s (-123rpm) Damage frequency for rolling element frp -1.86 1/s (-112rpm) Bearing s ffness matrix ux [µm] uy [µm] uz [µm] ry [mrad] rz [mrad] Fx [N] 13539.891-2796.502 0.001-0.111-222150.564 Fy [N] -2796.805 7098.055 0.000 0.113-1161231.673 Fz [N] -0.001 0.000 5542.901 1724210.203-0.113 My [Nm] -0.000 0.000 1725.117 940699.333-0.043 Mz [Nm] -218.707-1163.427-0.000-0.043 1170117.864 4/11

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Result table for bearing 1 9/11

Ball ψ [ ] αi_l [ ] αe_l [ ] Qi_l [N] Qe_l [N] pi_l [MPa] pe_l [MPa] αi_r [ ] αe_r [ ] Qi_r [N] Qe_r [N] pi_r [MPa] pe_r [MPa] elr_i elr_e 1 0.00 43.42 43.74 36974.2 65007.6 1348.78 1451.04 43.78 43.50 64948.4 36928.3 1626.76 1201.50 1.97 2.00 2 25.71 43.73 43.66 42252.8 39881.1 1409.65 1232.87 43.69 43.80 39825.4 42230.2 1382.17 1256.76 2.20 2.23 3 51.43 44.61 43.44 59010.9 0 1574.15 0.00 43.45 44.61 0 59013.2 0.00 1406.03 1.97 2.00 4 77.14 45.82 43.11 88531.1 0 1799.61 0.00 43.09 45.82 0 88533.4 0.00 1611.27 1.72 1.75 5 102.86 47.15 42.72 129054 0 2037.40 0.00 42.67 47.15 0 129056 0.00 1829.09 1.52 1.54 6 128.57 48.33 42.36 172994 0 2243.37 0.00 42.27 48.33 0 172997 0.00 2018.93 1.38 1.40 7 154.29 49.14 42.10 207743 0 2382.24 0.00 41.98 49.14 0 207745 0.00 2147.54 1.30 1.32 8 180.00 49.42 42.00 221033 0 2431.17 0.00 41.88 49.42 0 221035 0.00 2192.98 1.27 1.29 9 205.71 49.14 42.10 207743 0 2382.24 0.00 41.98 49.14 0 207745 0.00 2147.54 1.30 1.32 10 231.43 48.33 42.36 172994 0 2243.37 0.00 42.27 48.33 0 172997 0.00 2018.93 1.38 1.40 11 257.14 47.15 42.72 129054 0 2037.40 0.00 42.67 47.15 0 129056 0.00 1829.09 1.52 1.54 12 282.86 45.82 43.11 88531.1 0 1799.61 0.00 43.09 45.82 0 88533.4 0.00 1611.27 1.72 1.75 13 308.57 44.61 43.44 59010.9 0 1574.15 0.00 43.45 44.61 0 59013.2 0.00 1406.03 1.97 2.00 14 334.29 43.73 43.66 42252.8 39881.1 1409.65 1232.87 43.69 43.80 39825.4 42230.2 1382.17 1256.76 2.20 2.23 ψ : Posi on of ball αi : Contact angle inner race αe : Contact angle outer race Qi : Force at inner race Qe : Force at outer race pi : Maximal pressure inner race pe : Maximal pressure outer race elr_i : Ellipse length ra o inner race elr_e : Ellipse length ra o outer race Ball _i_l _e_l i_l e_l QV_i_l QV_e_l PVmax _i_l [MPa m /s] PVmax _e_l [MPa m /s] _i_r _e_r i_r e_r QV_i_r QV_e_r PVmax PVmax _i_r _e_r [MPa m [MPa m /s] /s] 1 6.4 4.9 6.6 5.2 877.6 1397.4 46.7 43.1 6.3 4.9 6.7 5.1 1838.2 674.2 65.2 32.5 2 6.4 4.9 6.7 5.1 1044.2 738.4 49.2 32.1 6.4 4.9 6.7 5.1 967.5 796.9 47.9 33.3 3 0.5 0.0 6.7 0.0 136.9 0.0 8.3 0.0 0.0 0.9 0.0 5.2 0.0 235.4 0.0 9.6 4 0.6 0.0 6.7 0.0 270.0 0.0 12.4 0.0 0.0 0.9 0.0 5.2 0.0 385.4 0.0 12.5 5 0.7 0.0 6.6 0.0 504.9 0.0 18.1 0.0 0.0 0.8 0.0 5.2 0.0 603.5 0.0 16.2 6 0.8 0.0 6.6 0.0 820.0 0.0 24.1 0.0 0.0 0.8 0.0 5.2 0.0 850.5 0.0 19.8 7 0.8 0.0 6.6 0.0 1108.6 0.0 28.8 0.0 0.0 0.8 0.0 5.3 0.0 1051.4 0.0 22.5 8 0.8 0.0 6.6 0.0 1227.2 0.0 30.6 0.0 0.0 0.8 0.0 5.3 0.0 1129.5 0.0 23.5 9 0.8 0.0 6.6 0.0 1108.6 0.0 28.8 0.0 0.0 0.8 0.0 5.3 0.0 1051.4 0.0 22.5 10 0.8 0.0 6.6 0.0 820.0 0.0 24.1 0.0 0.0 0.8 0.0 5.2 0.0 850.5 0.0 19.8 11 0.7 0.0 6.6 0.0 504.9 0.0 18.1 0.0 0.0 0.8 0.0 5.2 0.0 603.5 0.0 16.2 12 0.6 0.0 6.7 0.0 270.0 0.0 12.4 0.0 0.0 0.9 0.0 5.2 0.0 385.4 0.0 12.5 13 0.5 0.0 6.7 0.0 136.9 0.0 8.3 0.0 0.0 0.9 0.0 5.2 0.0 235.4 0.0 9.6 14 6.4 4.9 6.7 5.1 1044.2 738.4 49.2 32.1 6.4 4.9 6.7 5.1 967.5 796.9 47.9 33.3 Result table for bearing 2 Ball ψ [ ] αi_l [ ] αe_l [ ] Qi_l [N] Qe_l [N] pi_l [MPa] pe_l [MPa] αi_r [ ] αe_r [ ] Qi_r [N] Qe_r [N] pi_r [MPa] pe_r [MPa] elr_i elr_e 1 0.00 42.59 42.93 119316 158192 1994.94 1950.41 42.95 42.69 157969 119246 2189.70 1774.71 1.62 1.65 2 25.71 42.97 42.93 116856 113682 1980.31 1747.01 42.94 43.06 113496 116818 1961.22 1763.13 1.74 1.76 3 51.43 44.06 42.93 111554 19592.1 1947.57 972.20 42.92 44.11 19501.2 111552 1090.34 1737.74 1.71 1.74 4 77.14 45.63 42.92 107844 0 1922.37 0.00 42.90 45.63 0 107846 0.00 1720.53 1.65 1.68 5 102.86 47.34 42.92 109024 0 1925.58 0.00 42.86 47.34 0 109026 0.00 1729.40 1.57 1.60 6 128.57 48.89 42.91 114901 0 1956.06 0.00 42.83 48.88 0 114904 0.00 1762.41 1.49 1.51 7 154.29 49.95 42.91 121752 0 1991.66 0.00 42.81 49.95 0 121754 0.00 1798.55 1.42 1.44 8 180.00 50.33 42.91 124772 0 2007.09 0.00 42.80 50.33 0 124774 0.00 1813.95 1.40 1.42 9 205.71 49.95 42.91 121752 0 1991.66 0.00 42.81 49.95 0 121754 0.00 1798.55 1.42 1.44 10 231.43 48.89 42.91 114901 0 1956.06 0.00 42.83 48.88 0 114904 0.00 1762.41 1.49 1.51 10/11

Ball ψ [ ] αi_l [ ] αe_l [ ] Qi_l [N] Qe_l [N] pi_l [MPa] pe_l [MPa] αi_r [ ] αe_r [ ] Qi_r [N] Qe_r [N] pi_r [MPa] pe_r [MPa] elr_i elr_e 11 257.14 47.34 42.92 109024 0 1925.58 0.00 42.86 47.34 0 109026 0.00 1729.40 1.57 1.60 12 282.86 45.63 42.92 107844 0 1922.37 0.00 42.90 45.63 0 107846 0.00 1720.53 1.65 1.68 13 308.57 44.06 42.93 111554 19592.1 1947.57 972.20 42.92 44.11 19501.2 111552 1090.34 1737.74 1.71 1.74 14 334.29 42.97 42.93 116856 113682 1980.31 1747.01 42.94 43.06 113496 116818 1961.22 1763.13 1.74 1.76 ψ : Posi on of ball αi : Contact angle inner race αe : Contact angle outer race Qi : Force at inner race Qe : Force at outer race pi : Maximal pressure inner race pe : Maximal pressure outer race elr_i : Ellipse length ra o inner race elr_e : Ellipse length ra o outer race Ball _i_l _e_l i_l e_l QV_i_l QV_e_l PVmax _i_l [MPa m /s] PVmax _e_l [MPa m /s] _i_r _e_r i_r e_r QV_i_r QV_e_r PVmax PVmax _i_r _e_r [MPa m [MPa m /s] /s] 1 6.2 4.7 6.6 5.1 4060.5 4420.3 101.8 78.6 6.1 4.8 6.7 5.1 5841.3 3100.1 119.3 69.4 2 6.2 4.8 6.7 5.1 3948.2 2895.1 98.3 64.9 6.2 4.8 6.6 5.1 3807.9 3001.2 97.2 66.1 3 6.2 4.9 6.7 5.0 3683.6 353.7 90.6 28.4 6.4 4.7 6.5 5.2 419.6 2778.3 38.0 59.2 4 0.7 0.0 6.7 0.0 375.0 0.0 15.1 0.0 0.0 0.8 0.0 5.2 0.0 475.4 0.0 14.0 5 0.7 0.0 6.6 0.0 381.4 0.0 15.2 0.0 0.0 0.9 0.0 5.2 0.0 506.1 0.0 14.7 6 0.7 0.0 6.6 0.0 415.8 0.0 16.0 0.0 0.0 0.9 0.0 5.2 0.0 559.3 0.0 15.7 7 0.7 0.0 6.6 0.0 457.5 0.0 16.9 0.0 0.0 0.9 0.0 5.3 0.0 612.7 0.0 16.6 8 0.7 0.0 6.6 0.0 476.4 0.0 17.3 0.0 0.0 0.9 0.0 5.3 0.0 635.5 0.0 16.9 9 0.7 0.0 6.6 0.0 457.5 0.0 16.9 0.0 0.0 0.9 0.0 5.3 0.0 612.7 0.0 16.6 10 0.7 0.0 6.6 0.0 415.8 0.0 16.0 0.0 0.0 0.9 0.0 5.2 0.0 559.3 0.0 15.7 11 0.7 0.0 6.6 0.0 381.4 0.0 15.2 0.0 0.0 0.9 0.0 5.2 0.0 506.1 0.0 14.7 12 0.7 0.0 6.7 0.0 375.0 0.0 15.1 0.0 0.0 0.8 0.0 5.2 0.0 475.4 0.0 14.0 13 6.2 4.9 6.7 5.0 3683.6 353.7 90.6 28.4 6.4 4.7 6.5 5.2 419.6 2778.3 38.0 59.2 14 6.2 4.8 6.7 5.1 3948.2 2895.1 98.3 64.9 6.2 4.8 6.6 5.1 3807.9 3001.2 97.2 66.1 11/11