舰船科学技术  2017, Vol. 39 Issue (2): 97-102 PDF

Influence of misalignment angle error on the load-bearing properties of shafting bearing
ZHANG Xin-bao, GU Xing-chen
School of Mechanical Science and Engineering, Huazhong University of Science and Technology, Wuhan 430074, China
Abstract: In this paper, the calculation model of the Misalignment angle error of the radial sliding bearing was established. The expression of liquid film thickness in the integrated error included the inclination angle and the offset angle of the shaft neck and the inner hole of the bearing was also derived. The influences of the angle of inclination and the angle of offset on the liquid film pressure distribution, bearing capacity and the additional moment of the bearing were analyzed. The results show that the inclination angle and the offset angle error between the inner hole and the shaft neck, even if the values are below the national standard 3.5×10-4 rad, will still have a significant impact on the load-bearing properties of the bearing. With the increase of the angle error, the minimum film thickness is reduced, the bearing capacity of the bearing is more uneven, the additional moment of the bearing is greatly increased, and effect of shafting alignment is also affected. And it is suggested that the process method of installing the bearing by conforming to the curve axis of the shaft axis to ensure the good lubrication effect and the mechanical properties of the bearing should be considered.
Key words: marine shafting     radial sliding bearing     misalignment angle error     load-bearing properties

1 Reynolds 方程的求解原理

 $\frac{\partial }{{\partial \varphi }}\left( {{H^3}\frac{{\partial P}}{{\partial \varphi }}} \right) + {\left( {\frac{d}{L}} \right)^2}\frac{\partial }{{\partial \lambda }}\left( {{H^3}\frac{{\partial P}}{{\partial \lambda }}} \right) = \frac{{\partial H}}{{\partial \varphi }}\text{。}$ (1)

 $F = \sqrt {{F_x}^2 + {F_y}^2} \approx {F_y}\text{，}$ (11)

 $\left\{ \begin{array}{l} f(\varepsilon ) = \left| {\frac{{W - {F_y}}}{W}} \right| < ERR\text{，}\\ g(\theta ) = \left| {\frac{{{F_x}}}{{{F_y}}}} \right| < ERR\text{。} \end{array} \right.$ (12)

3.2 轴承处的附加力矩

 $\left\{ {\begin{array}{*{20}{l}} \begin{array}{l} \!\!\!\!\!\!\!\!\!\!{M_x} = {\rm{ - }}\int_{ - 1}^1 {\int_0^{2 } {{P_{ij}}\cos (\theta + \varphi )} } \lambda {\rm d}\varphi {\rm d}\lambda \approx \\[5pt] \!\!\!\!{\rm{ - }}\sum\limits_{i = 1}^{m + 1} {\sum\limits_{j = 1}^{n + 1} {{P_{ij}}\cos(\theta \!+\! {\varphi _i})\left[ { \!-\! 1 \!+\! \Delta \lambda \cdot (j \!-\! 1)} \right]} } \Delta \varphi \Delta \lambda \text{，} \end{array}\\[15pt] \begin{array}{l} \!\!\!\!\!\!\!\!\!\!{M_y} = {\rm{ - }}\int_{ - 1}^1 {\int_0^{2 } {{P_{ij}}{\rm sin}(\theta + \varphi )\lambda } } {\rm d}\varphi {\rm d}\lambda \approx \\[5pt] \!\!\!\!{\rm{ - }}\sum\limits_{i = 1}^{m + 1} {\sum\limits_{j = 1}^{n + 1} {{P_{ij}}\sin(\theta \!+\! {\varphi _i})} } \left[ { - 1 \!+\! \Delta \lambda \cdot (j \!-\! 1)} \right]\Delta \varphi \Delta \lambda \text{。} \end{array} \end{array}} \right.$ (13)

 $\left\{ \begin{array}{l} M = \sqrt {{M_x}^2 + {M_y}^2} \text{，}\\ {\varphi _M} = {\rm{arctan}}\frac{{{M_x}}}{{{M_y}}}\text{。} \end{array} \right.$ (14)
3.3 轴承处运转摩擦力的计算

 $F = \int_{ - L/2}^{L/2} {\int_0^x {{\tau _x}{|_{y = h}}{\rm d}A} }\text{，}$ (15)

 ${F_1} \!\!=\!\! \int_{ - L/2}^{L/2} {\int_0^{{x_1}} {{\tau _x}{\rm d}x{\rm d}z} } \!\!=\!\! \int_{ - L/2}^{L/2} {\int_0^{{x_1}} {\left( {\frac{h}{2}\frac{{\partial p}}{{\partial x}} \!\!+\!\! \frac{{\eta U}}{h}} \right){\rm d}x{\rm d}z} }\text{，}$ (16)

 $\begin{split} \\[-12pt] & {F_1} = \displaystyle\int_{ - L/2}^{L/2} {\int_0^{{x_1}} {\left( {\frac{h}{2}\frac{{\partial p}}{{\partial x}} + \frac{{\eta U}}{h}} \right){\rm d}x{\rm d}z} } =\frac{{3\eta UrL}}{{2c}}\\ & \ \displaystyle\int_{ - 1}^1 {\int_0^{{\varphi _1}} {\left( {H\displaystyle\frac{{\partial p}}{{\partial \varphi }}} \right){\rm{d}}\varphi {\rm{d}}\lambda } } + \displaystyle\frac{{\eta UrL}}{{2c}}\int_{ - 1}^1 {\int_0^{{\varphi _1}} {\displaystyle\frac{1}{H}{\rm{d}}\varphi {\rm{d}}\lambda } } = \\ & \ {\rm{ }}\displaystyle\frac{{\eta UrL}}{{2c}}\int_{ - 1}^1 {\int_0^{{\varphi _1}} {\left( {3H\frac{{\partial p}}{{\partial \varphi }} + \frac{1}{H}} \right){\rm d}\varphi {\rm d}\lambda } } \text{，} \end{split}$ (17)

 $\overline {{F_1}} = \frac{{{F_1}}}{{\frac{{\eta UrL}}{{2c}}}}{\rm{ = }}\int_{ - 1}^1 {\int_0^{{\varphi _1}} {\left( {3H\frac{{\partial p}}{{\partial \varphi }} + \frac{1}{H}} \right)d\varphi d\lambda } }\text{。}$ (18)

 $\begin{split} \\[-12pt] \overline {{F_1}} {\rm{ = }}\int_{ - 1}^1 {\int_0^{{\varphi _1}} {\left( {3H \displaystyle\frac{{\partial p}}{{\partial \varphi }} + \frac{1}{H}} \right){\rm d}\varphi {\rm d}\lambda } } \approx \\ \quad \quad \sum\limits_{i = 1}^{{m_\varphi }} {\sum\limits_{j = 1}^{n + 1} {\left( {3{H_i}_j \displaystyle\frac{{{p_{i + 1,j}} - {p_i}_j}}{{\Delta \varphi }} + \frac{1}{{{H_{ij}}}}} \right)} } \Delta \varphi \Delta \lambda \text{。} \end{split}$ (19)

 ${F_2} = \int_{ - L/2}^{L/2} {\int_{{x_1}}^{2 r} {\frac{{\eta U}}{h} \cdot \frac{{{h_1}}}{h}{\rm d}x{\rm d}z} } \text{，}$ (20)

 $\begin{split} \\[-12pt] {F_2} = & \int_{ - L/2}^{L/2} {\int_{{x_1}}^{2 r} {\displaystyle\frac{{\eta U}}{h} \cdot \frac{{{h_1}}}{h}{\rm d}x{\rm d}z} } =\\ & {\rm{ }}\int_{ - 1}^1 {\int_{{\varphi _1}}^{2 } {\displaystyle\frac{{\eta U}}{{Hc}} \cdot \frac{{{H_1}c}}{{Hc}} \cdot \frac{L}{2} \cdot r{\rm d}\varphi {\rm d}\lambda } } =\\ & {\rm{ }}\displaystyle\frac{{\eta ULr}}{{2c}}\int_{ - 1}^1 {\int_{{\varphi _1}}^{2 } {\frac{{{H_1}}}{{{H^2}}}{\rm d}\varphi {\rm d}\lambda } } \text{。} \end{split}$ (21)

 $\overline {{F_2}} {\rm{ = }}\frac{{{F_2}}}{{\displaystyle\frac{{\eta ULr}}{{2c}}}} = \int_{ - 1}^1 {\int_{{\varphi _1}}^{2 } {\frac{{{H_1}}}{{{H^2}}}{\rm d}\varphi {\rm d}\lambda } }\text{，}$ (22)

 $\overline {{F_2}} {\rm{ = }}\int_{ - 1}^1 {\int_{{\varphi _1}}^{2 } {\frac{{{H_1}}}{{{H^2}}}{\rm d}\varphi {\rm d}\lambda } } {\rm{ = }}\sum\limits_{i = {m_\varphi }}^{m + 1} {\sum\limits_{j = 1}^{n + 1} {\frac{{{H_{1(i,j)}}}}{{H_{i,j}^{^2}}}} } \Delta \varphi \Delta \lambda \text{，}$ (23)

 $\overline F = \overline {{F_1}} + \overline {{F_2}} \text{。}$
4 算例分析

 图 3 夹角误差影响下的无量纲液膜压力的等值线图 Fig. 3 The contour map of the dimensionless film pressure under the influence of angle error

 图 4 夹角误差对轴承承载性能的影响 Fig. 4 Influence of angle error on bearing bearing performance

 图 5 不对中夹角误差引起的附加力矩 Fig. 5 The additional torque caused by misalignment angle error

 图 6 轴承不对中夹角误差对轴颈无量纲摩擦阻力的影响 Fig. 6 Effect of misalignment angle error on dimensionless frictional resistance of bearing
5 结语

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