Journal of Zhejiang University-SCIENCE A

, Volume 19, Issue 9, pp 719–734

# Static analysis of a stepped main shaft in a mine hoist by means of the modified 1D higher-order theory

• Wen-xiang Teng
• Zhen-cai Zhu
Article

## Abstract

The analysis of a stepped main shaft by 1D refined beam theories in cylindrical coordinate system is presented. High-order displacement fields are achieved by employing the Carrera unified formulation (CUF), which takes direct implementation of any-order theory without the requirement of considering special formulations. The classical beam theories can be derived from the formulation as particular cases. The principle of minimum potential energy is used to obtain the governing differential equations and the related boundary conditions in a cylindrical coordinate system. These explicit terms of the stiffness matrices are exhibited and a global stiffness matrix is then obtained by matrix transformation. For the special working condition in a mining hoist and stepped shaft, the resulting global stiffness matrix and the loading vector are modified and applied with the boundary conditions in the static analysis of shaft parts. The accuracy of static analysis based on the refined beam theory is confirmed by comparing ANSYS solid theory and classical beam theories. An experiment for verifying the availability of the modified 1D refined beam model on the surface strain of segment 9 of the main shaft is conducted in a field experiment at Zhaojiazhai Coal Mine, China. Experimental results demonstrate the practicability of the present theory in predicting the strain field on the surface of the stepped main shaft of a mining hoist.

## Key words

Carrera unified formulation (CUF) 1D higher-order theory Finite element method Strain field Stepped main shaft Main hoist

# 基于一维高阶理论的矿井提升机阶梯主轴静力分析

## 摘要

### 方 法

1. 1.

引入基于 Carrera 通用表达式的一维高阶理论, 克服传统梁理论的局限性和三维有限元法计算经济性差等问题;

2. 2.

通过理论计算、 软件仿真和现场试验(图14 和15), 验证改进的主轴一维高阶模型的有效性和可用性。

### 结 论

1. 1.

基于 Carrera 通用表达式的一维高阶理论模型能够以较少的计算量得出与 ANSYS 三维实体模型相近的结果;

2. 2.

改进的提升机主轴一维高阶模型能够准确地监测矿井提升系统的工况。

## 关键词

Carrera 通用表达式 一维高阶理论 有限元法 应变场 阶梯主轴

TD444

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