Research Article
Three-Dimensional Modeling and Structured Vibration Modes of Two-Stage Helical Planetary Gears Used in Cranes
Table 2
Natural frequencies (Hz) and mode types for the example HPGs.
| | Multiplicity | | Mode type | | 3 | 4 | 5 | 6 | 7 | 8 | 9 |
| | 0 | 0 | 0 | 0 | 0 | 0 | 0 | Axial translational-rotational mode | | 496.02 | 509.75 | 517.49 | 521.95 | 524.43 | 525.61 | 525.91 | | 962.35 | 958.11 | 953.4 | 948.5 | 943.54 | 938.59 | 933.7 | | 1934.2 | 1871.8 | 1813.5 | 1758.6 | 1706.9 | 1658.6 | 1613.9 | | 2060.1 | 1994.5 | 1910.6 | 1840.5 | 1781.7 | 1731.4 | 1687.3 | | 2108.3 | 2068.5 | 2066.2 | 2065.2 | 2064.6 | 2064 | 2063.5 | | 3106.9 | 3106.6 | 3106.6 | 3106.5 | 3106.4 | 3106.3 | 3106.2 | | 3392 | 3393.6 | 3394.1 | 3394.3 | 3394.3 | 3394.3 | 3394.2 | | 4063.9 | 4111.3 | 4121.1 | 4124.6 | 4126.3 | 4127.4 | 4128 | | 4180.5 | 4238.7 | 4283.3 | 4312.6 | 4333.4 | 4349.2 | 4361.8 | | 4853.5 | 5138.5 | 5415.4 | 5664.8 | 5883.1 | 6063.3 | 6127.6 | | 6140.1 | 6140.8 | 6141.6 | 6142.8 | 6145.7 | 6159.9 | 6266.9 | | 6425 | 6425 | 6425 | 6425 | 6425 | 6425 | 6425 | | 7622 | 7811.8 | 8008.5 | 8213.8 | 8427.1 | 8646.2 | 8867.7 | | 8209.9 | 8748.5 | 9065.7 | 9130.9 | 9146.6 | 9153.9 | 9159.3 | | 8934.8 | 9159 | 9305.8 | 9497 | 9507.9 | 9513.7 | 9520.8 | | 9214.5 | 9345.8 | 9506 | 9583.4 | 9838.5 | 10086 | 10277 | | 9498.4 | 9501.9 | 9728.5 | 10203 | 10277 | 10277 | 10324 | | 10277 | 10277 | 10277 | 10280 | 10701 | 11186 | 11658 | | 25977 | 25981 | 25985 | 25990 | 25994 | 25999 | 26004 |
| | 1187.9 | 1179.4 | 1171 | 1162.6 | 1154.2 | 1146 | 1137.8 | Radical translational mode | | 1525.6 | 1566.3 | 1592.7 | 1609.1 | 1618.5 | 1622.9 | 1623.8 | | 1961.5 | 1954 | 1946.6 | 1939.4 | 1932.3 | 1925.4 | 1918.7 | | 2191.6 | 2214.6 | 2236.1 | 2255.3 | 2272 | 2286 | 2297.5 | | 3280.2 | 3280.8 | 3281.6 | 3282.4 | 3283.2 | 3284.1 | 3285 | | 4144.1 | 4126.6 | 4110.7 | 4097.4 | 4087.2 | 4079.6 | 4074.5 | | 4705.3 | 4754.8 | 4798.1 | 4831 | 4853.8 | 4868.7 | 4878.4 | | 5214.7 | 5217.2 | 5244.9 | 5294.1 | 5359.8 | 5437 | 5521 | | 5897.9 | 5898.1 | 5898.3 | 5898.6 | 5899 | 5899.5 | 5900.3 | | 6164.4 | 6168.1 | 6170.5 | 6172.3 | 6173.8 | 6175.2 | 6176.5 | | 6483.5 | 6489.4 | 6493 | 6495.4 | 6497.1 | 6498.5 | 6499.6 | | 7241.6 | 7283.9 | 7324.9 | 7365.2 | 7404.7 | 7443.3 | 7481 | | 7545.7 | 7798 | 7962.5 | 8036.5 | 8073.2 | 8098.7 | 8120.6 | | 8131.9 | 8186.1 | 8310.4 | 8510.9 | 8737.3 | 8965.9 | 9190.4 |
| | — | 4155.7 | 4155.7 | 4155.7 | 4155.7 | 4155.7 | 4155.7 | Planet mode | | 5897.3 | 5897.3 | 5897.3 | 5897.3 | 5897.3 | 5897.3 | | 7121.8 | 7121.8 | 7121.8 | 7121.8 | 7121.8 | 7121.8 | | 8074.7 | 8074.7 | 8074.7 | 8074.7 | 8074.7 | 8074.7 |
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