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浙江大学学报(工学版)
浙江大学学报(工学版)  2025, Vol. 59 Issue (1): 109-119    DOI: 10.3785/j.issn.1008-973X.2025.01.011
机械工程、能源工程     
电梯安全钳制动块与导轨接触应力的有限元计算方法
吴洋1(),肖磊2,王玮彦2,许金鑫2,杜原2,杨泊莘1,安琦1,*()
1. 华东理工大学 机械与动力工程学院，上海 200237
2. 迅达（中国）电梯有限公司，上海 201807
Finite element calculation method of contact stress between elevator safety gear brake block and guide rail
Yang WU1(),Lei XIAO2,Weiyan WANG2,Jinxin XU2,Yuan DU2,Boxin YANG1,Qi AN1,*()
1. School of Mechanical and Power Engineering, East China University of Science and Technology, Shanghai 200237, China
2. Schindler (China) Elevator Limited Company, Shanghai 201807, China
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摘要：

为了研究电梯安全钳的制动块与导轨接触应力的分布规律，结合有限单元法与赫兹接触公式提出精确且高效的计算方法. 通过非线性刚度矩阵建立楔块-滚子-导轨平衡方程，应用接触理论及牛顿-拉夫逊（N-R）法求解平衡方程. 考虑制动楔块与导轨的相对运动，进行热传导方程修正，采用伽辽金法求解瞬态温度场. 通过热力耦合迭代精确计算摩擦面接触应力分布. 结果表明，制动摩擦面的最高温度约为72.7 ℃，最大接触应力约为35 MPa，热效应对摩擦面接触应力的影响程度为两端区域大于中间区域；滚子位置上移会减小下端滚子的压力和摩擦面下端的接触应力；弹簧位置的下移或摩擦面位置的上移均会增大摩擦面下端的接触应力，摩擦面位置的上移会减小摩擦面上端的接触应力.
关键词： 安全钳制动块;  力学性能;  热力学分析;  接触应力;  有限元法    
Abstract:

An accurate and efficient calculation method was proposed by combining the finite element method and Hertz contact formula, to study the contact stress distribution between elevator safety gear brake block and guide rail. A balance equation among wedges, rollers and guide rail was established with a nonlinear stiffness matrix, and the equation was solved by the Newton-Raphson (N-R) method combined with contact theory. The heat conduction equation was modified because of the relative motion between the wedge and the guide rail, and the transient temperature field was calculated by the Galerkin method. The accurate calculation of the contact stress distribution of the friction surface was realized through thermal-mechanical coupling iteration. Results showed that the maximum temperature of the friction surface was about 72.7 ℃ during the braking process, while the maximum contact stress was about 35 MPa. The thermal effect influence on the contact stress was greater at both ends of the friction surface than at the middle area. When the rollers’ position was moved up, both the pressure of the lower roller and the contact stress of the lower-end friction surface were reduced. When the position of the spring was moved down or the position of the friction surface was moved up, the contact stress at the lower end of the friction surface was increased, and the contact stress at the upper end of the friction surface was reduced by the upward movement of the friction surface.
Key words: safety gear brake block    mechanical performance    thermal analysis    contact stress    finite element method
收稿日期: 2023-11-24 出版日期: 2025-01-18
CLC:  TU 857  
通讯作者: 安琦     E-mail: 1269039606@qq.com;anqi@ecust.edu.cn
作者简介: 吴洋（1999—），男，硕士生，从事工程摩擦学与流体润滑研究. orcid.org/0009-0000-7684-913X. E-mail：1269039606@qq.com
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吴洋
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杜原
杨泊莘
安琦

引用本文:

吴洋,肖磊,王玮彦,许金鑫,杜原,杨泊莘,安琦. 电梯安全钳制动块与导轨接触应力的有限元计算方法[J]. 浙江大学学报(工学版), 2025, 59(1): 109-119.

Yang WU,Lei XIAO,Weiyan WANG,Jinxin XU,Yuan DU,Boxin YANG,Qi AN. Finite element calculation method of contact stress between elevator safety gear brake block and guide rail. Journal of ZheJiang University (Engineering Science), 2025, 59(1): 109-119.

链接本文:

https://www.zjujournals.com/eng/CN/10.3785/j.issn.1008-973X.2025.01.011    或    https://www.zjujournals.com/eng/CN/Y2025/V59/I1/109

图 1  楔形渐进式安全钳的结构示意图
图 2  安全钳的工作过程示意图
图 3  六节点三角单元及面积坐标
图 4  楔块的边界条件
接触对状态约束条件校核条件
传动楔块上
表面?钳体		接触$ {g_1} = {V^j_{\text{C}}} = 0$$ {{\boldsymbol{F}}^j_{\text{N}}}\cdot {\boldsymbol{n}} < 0 $
分离$ {{\boldsymbol{F}}^j_{\text{N}}} = {\boldsymbol{0}} $$ {{{V}}^j_{\text{C}}} < 0 $
传动楔块下
表面?钳体		接触$ {g_2} = {V^j_{\text{C}}}+w = 0 $$ {{\boldsymbol{F}}^j_{\text{N}}}\cdot {\boldsymbol{n}} < 0 $
分离$ {{\boldsymbol{F}}^j_{\text{N}}} = {\boldsymbol{0}} $$ -{{{V}}^j_{\text{C}}} - w < 0 $
制动楔块上
表面?钳体		接触$ {g_3} = {V^j_{\text{A}}} = 0 $$ {{\boldsymbol{F}}^j_{\text{N}}}\cdot {\boldsymbol{n}} < 0 $
分离$ {{\boldsymbol{F}}^j_{\text{N}}} = {\boldsymbol{0}} $$ {{{V}}^j_{\text{A}}} < 0 $
制动楔块右
表面?导轨		接触$ \begin{array}{c} {g_4} = {U^j_{\text{A}}} - {U^j_{\text{G}}} = 0,\\ {{\boldsymbol{F}}^j_{\text{f}}} = - f({{\boldsymbol{F}}^j_{\text{N}}}\cdot {\boldsymbol{n}}) {\boldsymbol{n}}_{\mathrm{v}}\end{array}$$ {{\boldsymbol{F}}^j_{\text{N}}}\cdot {\boldsymbol{n}} < 0 $
分离$ {{\boldsymbol{F}}^j_{\text{N}}} = {\boldsymbol{0}} $,$ {{\boldsymbol{F}}^j_{\text{f}}} = {\boldsymbol{0}} $$ {{{{U}}^j_{\text{A}}} - {{{U}}^j_{\text{G}}}} < 0 $
传动楔块?
滚子?制动楔块		接触$ {g_4} = {U^{j}_{\text{A}}} - {U^{j}_{\text{C}}} - {Y^{j}} = 0 $$ {{\boldsymbol{F}}^j_{\text{N}}}\cdot {\boldsymbol{n}} < 0 $
分离$ {{\boldsymbol{F}}^j_{\text{N}}} = {\boldsymbol{0}} $$ {Y^j} = 0 $
表 1  安全钳的接触类型
图 5  制动过程中导轨单元控制体中的内能变化
图 6  安全钳热力耦合的求解流程
图 7  安全钳和导轨的几何参数
材料E/GPaμα/10?6kxy/(W·m?1·℃?1)c/(J·kg?1·℃?1)
Q235(20 ℃)2110.3010.651.6450
Q235(100 ℃)2070.3012.248.9483
QT600(20 ℃)1690.2711.152.2503
QT600(100 ℃)1660.2713.257.2537
GCr15(20 ℃)2100.30———
表 2  安全钳和导轨的材料参数
图 8  温度与接触力的关系曲线
图 9  制动时间为80 ms时的温度、位移与应力云图
图 10  不同滚子位置下的力与温度分布图
图 11  工作后的制动楔块实物图
图 12  不同弹簧位置下的滚子压力与摩擦面接触应力分布图
图 13  不同摩擦面位置的滚子压力与摩擦面接触应力分布图
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