﻿ 结合有限元仿真技术的船舶轴承承载仿真
 舰船科学技术  2024, Vol. 46 Issue (12): 73-76    DOI: 10.3404/j.issn.1672-7649.2024.12.013 PDF

1. 河北水利电力学院，河北 沧州 061001;
2. 河北省工业机械手控制与可靠性技术创新中心，河北 沧州 061001

Simulation of ship bearing load capacity based on finite element simulation technology
LIU Dong1,2, LIU Yu1,2, FU Yanhong1,2
1. Hebei University of Water Resources and Electric Engineering, Cangzhou 061001, China;
2. Hebei Industrial Manipulator Control and Reliability Technology Innovation Center, Cangzhou 061001, China
Abstract: This article studies finite element simulation technology, focuses on analyzing finite element calculation theory, and elaborates on the material model theory of ship bearings. At the same time, the stress-strain curve of the constitutive model of ship bearings is provided; A dynamic simulation analysis was conducted on ship bearings, and a suction device was used instead of a propeller during the simulation process. A calculation method for propeller torque excitation was provided, and the angular acceleration, angular velocity, and radial force of ship bearings were analyzed; Finally, finite element simulation was conducted on the bearing capacity of ship bearings, and simulation analysis was conducted on the amplitude, frequency, and force situation of ship bearings.
Key words: finite element analysis     ships     bearing
0 引　言

1 有限元仿真技术 1.1 有限元计算理论

 ${\boldsymbol{M}}{\ddot u_n} + K\left( {{u_n}} \right){u_n} = {R_n}。$ (1)

 ${u_{n + 1}} = {u_n} + \Delta {t_{n + 1}}{\dot u_n} + \frac{1}{2}\Delta t_{n + 1}^2{\ddot u_n}\text{，}$ (2)
 ${\dot u_{n + 1}} = {\dot u_n} + \frac{1}{2}\Delta {t_{n + 1}}\left( {{{\ddot u}_{n + 1}} + {{\ddot u}_n}} \right)\text{，}$ (3)
 $K_nu_n=\sum\limits_i\int_{V^{\left(l\right)}}B_n^{\mathrm{T}}S_n\mathrm{d}V。$ (4)

 $\left( {\frac{1}{{\Delta {t^2}}}M} \right){u_{n + 1}} = {R_n} - \sum\limits_i {F_n^i} - \frac{1}{{\Delta {t^2}}}\left( {{u_{n - 1}} - 2{u_n}} \right)\text{。}$ (5)

 $_0^tB_L^{\left(k\right)}=_0^tB_{L_00}^{\left(k\right)t}X^{\mathrm{T}}。$ (6)

 ${}^t{\hat F^{\left( m \right)}} = \int_{{0_V}} {{}_0^t} B_L^{{\mathrm{T}}_0^t}\tilde S{{\mathrm{d}}^0}V。$ (7)

 ${\hat X^m}\left( \zeta \right) = X_1^m + \left( {X_2^m - X_1^m} \right)\zeta 。$ (8)

 ${t_m} = \frac{1}{e}\hat X (\xi ) 。$ (9)

 $\mathop X\limits^ \wedge (\xi ) = X_2^m - X_1^m \text{，}$ (10)
 $e = \left\| {X_2^m - X_1^m} \right\|。$ (11)

 ${g_N} = \left[ {{X^s} - \left( {1 - \bar \zeta } \right)X_1^m - \bar \zeta X_2^m} \right]{n_m}。$ (12)

 $\bar \zeta = \frac{{\left( {{X^s} - X_1^m} \right){t_m}}}{e}。$ (13)

 ${t_N} = {a_N}{g_N}\text{，}$ (14)
 $t = {t_N}{N_m}\text{。}$ (15)
1.2 材料模型理论

 $S = \frac{{\partial U\left( F \right)}}{{\partial F}}。$ (16)

 $U = \sum\limits_{i + j}^N {{C_{ij}}{{\left( {{{\bar I}_1} - 3} \right)}^i}{{\left( {{{\bar I}_2} - 3} \right)}^j} + \sum\limits_{i = 1}^N {\frac{1}{{{D_i}}}{{\left( {{J_{el}} - 1} \right)}^{2i}}} } 。$ (17)

 $U' = \mu \left[ {\lambda _m^2\ln \left( \eta \right)\alpha \left( {\frac{{\bar I}}{2}} \right)} \right] + \frac{1}{D}\left[ {\frac{{J_{el}^2 - 1}}{2} - \ln {J_{el}}} \right]。$ (18)

 $\bar I = \left( {1 - \beta } \right){\bar I_1} + \beta {\bar I_2}\text{，}$ (19)
 $\eta = \sqrt {\frac{{\bar I - 3}}{{\lambda _m^2 - 3}}}。$ (20)

 $W\left( F \right) = \left( {1 - d} \right){W_0}F。$ (21)

 $d = \left\{ {\begin{array}{*{20}{l}} {d\left( x \right)}，{x > 0} ，\\ {d\left( {\max \left[ {x\left( s \right)} \right]} \right)}，{{\mathrm{others}}} 。\end{array}} \right.$ (22)

 $\kappa = 1 - \frac{1}{r}erf\left[ {\frac{1}{m}\left( {{W_m} - \bar W\left( {{\lambda _1},{\lambda _2}} \right)} \right)} \right]\text{。}$ (23)

 图 1 船舶轴承本构模型的应力应变曲线 Fig. 1 Stress-strain curve of ship bearing constitutive model
2 船舶轴承动力学仿真分析

 ${M_m} = \beta {M_e}\sin \left( {p\omega t + \varepsilon } \right)。$ (24)

 ${M_x} = {M_0} + \sum\limits_{k = 1}^\infty {{M_{k{Z_p}}}\sin \left( {k{Z_p}\omega t + {\varepsilon _{k{Z_p}}}} \right)}。$ (25)

 ${M_{{Z_p}}} = \beta {M_0}。$ (26)

 ${M_{v{z_p}}} = 9549.3\beta \frac{p}{{v{n_p}}}{\left( {\frac{{vn}}{{v{n_p}}}} \right)^2}\text{。}$ (27)

 图 2 船舶轴承的角加速度曲线 Fig. 2 Angular acceleration curve of ship bearings

 图 3 船舶轴承的角速度 Fig. 3 Angular velocity of ship bearings

 图 4 船舶中间轴承径向受力曲线 Fig. 4 Radial force curve of ship′s intermediate bearing
3 船舶轴承承载仿真分析

 图 5 船舶轴承振动幅值随频率变化曲线 Fig. 5 Frequency dependent curve of vibration amplitude of ship bearings

 图 6 不同轴承刚度下纵振频率的变化曲线 Fig. 6 The variation curve of longitudinal vibration frequency under different bearing stiffness
 $\omega = \frac{1}{{2{\text{π}}}}\sqrt {\frac{{{K_{th}}}}{m}}。$ (28)

 图 7 船舶轴承垂向承受的最大压力随转速的变化曲线 Fig. 7 The variation curve of the maximum vertical pressure borne by ship bearings with rotational speed

 图 8 船舶轴承受力随轴承弹性模量的变化曲线 Fig. 8 The variation curve of ship shaft bearing force with bearing elastic modulus
4 结　语

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