升船机螺母柱传力系统内力解析及案例分析

doi:10.11988/ckyyb.20240434

摘要/Abstract

摘要：

全平衡齿轮齿条爬升式垂直升船机螺母柱传力系统,具有边界条件非线性和材料应力-应变关系非线性的特点,易导致有限元结构计算繁琐且不收敛。基于螺母柱传力系统的结构组成、物理特性和受力条件,建立螺母柱和调整梁内力分析的半无限长双弹性耦合地基梁模型,提出螺母柱传力系统轴向力传递的分布函数假定,推导了螺母柱和调整梁的挠度、内力和强度的计算公式,并成功应用于三峡升船机螺母柱传力系统的结构内力与应力计算,揭示了基于轴向界面分布力假定螺母柱和调整梁的结构内力、最大正应力及剪应力的分布规律。研究成果对传力系统初始设计阶段的快捷计算具有重要指导意义。

关键词: 升船机, 螺母柱传力系统, 双弹性耦合地基梁模型, 轴向界面分布力, 内力

Abstract:

[Objective] This study aims to establish an efficient and reliable mechanical model to accurately evaluate internal forces and stresses within the force transmission system of fully balanced rack-and-pinion vertical shiplifts, providing reliable theoretical foundations for engineering design, structural optimization, and safety assessment. [Methods] Based on a comprehensive analysis of the structural configuration, material properties, and loading conditions of the nut-column force transmission system, a novel semi-infinite double elastic coupling foundation beam model is proposed. In this approach, the nut column and adjustment beam were modeled as interacting elastic bodies while incorporating their mutual deformation and force transmission mechanisms. To describe axial load transmission at the interface with complex contact mechanics, exponential distribution functions were introduced. The model integrated elastic foundation beam theory with fundamental mechanics of materials, enabling the derivation of closed-form expressions for deflection, internal forces (bending moments and shear forces), and stresses (normal and shear) in both the nut column and adjustment beam. These expressions accurately characterized the distinct mechanical behavior of the force transmission system under different loading scenarios. [Results] Theoretical predictions were validated through physical model testing, yielding several key findings. (1) Model validation: At x=L=4 950 mm, both deflections and internal forces of the nut column and adjustment beam approached zero, demonstrating the validity of the semi-infinite beam assumption. This simplified boundary condition treatment and provided a novel analytical approach for similar structural systems. (2) Parameter sensitivity insights: By comparing results under two interface constraint assumptions with α=π and α=2π, the model revealed the significant impact of α on structural response. While the α=2π assumption yielded more conservative results, α=π aligned better with experimental data. (3) New understanding of stress distribution: Contrary to conventional assumptions, the maximum bending moment in the nut column occurred not at the end but near it, indicating that the traditional use of end-moment M0 as the design load was inadequate. Moreover, except for axial force, all other internal forces in the adjustment beam exceeded those in the nut column, providing critical insights for structural optimization. (4) Stress comparison: Calculated stress values, though slightly exceeding experimental results, remained within allowable stress limits, demonstrating the rationality of the current design. The results obtained with α=π exhibited better agreement with experimental data, further confirming the model’s reliability. [Conclusion] The nut column force transmission system of the Three Gorges Ship Lift is structurally robust. The proposed semi-infinite elastic foundation beam model proves effective and applicable for similar designs. Incorporating the Pasternak elastic foundation beam model in future studies can further enhance analytical accuracy, providing a promising direction for both theoretical advancements and engineering applications.

Key words: shiplift, nut column force transmission system, double elastic coupling foundation beam model, axial interfacial distribution force, internal force

中图分类号:

TV34金属结构

王蒂, 廖乐康, 金辽. 升船机螺母柱传力系统内力解析及案例分析[J]. raybet体育在线院报, 2025, 42(8): 144-152.

WANG Di, LIAO Le-kang, JIN Liao. Analysis and Case Study of Internal Forces in Nut Column Transmission System of Shiplifts[J]. Journal of Changjiang River Scientific Research Institute, 2025, 42(8): 144-152.

图/表 12

图1 螺母柱传力系统结构简图

Fig.1 Structure of nut column force transmission system

图2 螺母柱传力系统双弹性耦合地基梁力学模型

Fig.2 Mechanical model of double elastic coupling founda-tion beam for nut column force transmission system

图3 载荷传递计算示意图注:h0为螺母柱螺牙节线至螺母柱中性轴的距离;h1为螺母柱螺牙节线至螺母柱和调整梁凸齿传力中心线的距离;h2为螺母柱和调整梁凸齿中心线至调整梁向二期混凝土传力界面的距离。

Fig.3 Schematic diagram of load transfer calculation

图4 螺母柱和调整梁微段静力平衡简图

Fig.4 Illustration of static equilibrium of the micro segments of the nut columns and adjusting beams

表1 计算输入参数

Table 1 Input parameters for calculation

H₁/mm	H₂/mm	b₁/mm	b₂/mm	L/mm
180	1 130	1 600	1 020	4 950
I₁ /mm⁴	I₂ /mm⁴	h₀/mm	h₁/mm	h₂/mm
5.79×10⁹	4.15×10¹⁰	200	196	1 080

图5 轴向界面分布力函数曲线

Fig.5 Curves of axial interfacial distribution force functions

图6 螺母柱轴向内力分布函数

Fig.6 Axial internal force distribution function of nut column

表2 主要中间计算参数

Table 2 Main intermediate calculation parameters

K₁/ (N·mm^-2)		K₂/ (N·mm^-2)		s/mm	ξ₁		ξ₂		η/mm
3.65×10⁵		1.89×10⁴		-0.188 2	-3.562 3		0.969 8		-0.164 8
a/mm^-4	b/mm^-8		c/(N^-1·mm^-5)			β₁/mm^-1		β₂/mm^-1
3.88×10^-10	7.48×10^-22		5.08×10^-22			3.314×10^-3		8.341 4×10^-4

表3 2种轴向界面分布力假定下的系数A、B、C和D

Table 3 Values of coefficients A, B, C, and D under two assumptions of axial interfacial distribution force

α	A/mm	B/mm	C/mm	D/mm
π	-0.121 4	-0.314 5	0.129 2	1.254 8
2π	-0.121 6	-0.978 1	0.137 2	1.848 8

图7 螺母柱和调整梁挠度、弯矩及剪力分布函数曲线

Fig.7 Distribution function curves of deflections, bending moments, and shear force in nut column and adjustment beam

表4 2种轴向界面分布力假定下螺母柱和调整梁的挠度和内力最大值或最小值

Table 4 Maximum or minimum values of deflections and internal forces in nut column and adjustment beam under two assumptions of axial interfacial distribution force

α	y_1max/ mm	y_2max/ mm	M_1max/ (kN·m)	M_2max/ (kN·m)	V_1max/ kN	V_2min/ kN
π	1.163	0.876	2 870	5 618	5 963	7 398
2π	1.321	1.025	2 954	8 515	6 413	8 971

表5 计算应力、容许应力与试验结果的比较

Table 5 Comparison between calculated stresses, allowable stresses, and experimental results

条件	σ_1max/ (N·mm^-2)	σ_2max/ (N·mm^-2)	τ_1max/ (N·mm^-2)	τ_2max/ (N·mm^-2)
α=2π	219.30	128.00	20.30	93.40
α=π	213.90	84.50	18.80	77.10
物模试验	70.48	71.06	15.58	41.61
容许应力	567.00	203.00	334.00	119.00

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