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浙江大学学报(工学版)
Journal of ZheJiang University (Engineering Science)  2025, Vol. 59 Issue (1): 109-119    DOI: 10.3785/j.issn.1008-973X.2025.01.011
    
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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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     
Received: 24 November 2023      Published: 18 January 2025
CLC:  TU 857  
Corresponding Authors: Qi AN     E-mail: 1269039606@qq.com;anqi@ecust.edu.cn
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Yang WU
Lei XIAO
Weiyan WANG
Jinxin XU
Yuan DU
Boxin YANG
Qi AN
Cite this article:

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.

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


电梯安全钳制动块与导轨接触应力的有限元计算方法

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 
Fig.1 Construction schematic of wedge-shaped progressive safety gear
Fig.2 Diagram working process of safety gear
Fig.3 Six-node triangular element and area coordinates
Fig.4 Boundary condition of wedges
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 $
Tab.1 Contact type of safety gear
Fig.5 Internal energy change in control unit of guide rail during braking
Fig.6 Solution process of thermodynamic coupling of safety gear
Fig.7 Geometric parameters of safety gear and guide rail
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———
Tab.2 Material parameters of safety gear and guide rail
Fig.8 Curves of temperature and contact force
Fig.9 Nephogram of temperature, displacement and stress at braking time of 80 ms
Fig.10 Distribution of force and temperature at different rollers positions
Fig.11 Picture of brake wedge after work
Fig.12 Distribution of rollers pressure and friction surface contact stress at different spring positions
Fig.13 Distribution of rollers pressure and friction surface contact stress at different friction surface positions
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