# Study on elevator vibration problem升降机振动问题研究

## As an important overhead working machine, the vibration analysis of the elevator system has been widely concerned. In this paper, the vibration of the lift is analyzed, the system vibration mechanical model is established, the natural frequency of each stage of the system is obtained in different loads and different positions, the change trend of natural frequency of each stage with load and cargo position is analyzed, and the system response to the given initial conditions is determined. Elevator is an important vertical conveyor machinery, its cargo vibration and lift operation at the same time produced.

With the development of high-rise buildings, the lift speed is accelerated and the lift height is increased. This paper takes the rack and pinion elevator as the object, establishes the vibration mechanics model and vibration equation, and analyzes the response of the system to the given initial conditions by calculating the natural frequency of the system under different loads and different positions, providing reference for the vibration analysis of the elevator. Vibration model is established in this paper, vibration mechanics model in freight elevator, for example, by a pulley, the pulley frame, frame, steel wire rope, attached to the wall rack, guide rack, cargo, cab, the heavy, bottom cage and basis of the gear transmission device on the arrangement of the goods and arrange engages in guide rail on the shelf rack, make the goods make up and down along the guide rail, complete personnel and material transport, the actual structure as shown below. The structure features that the guide frame is mostly single, composed of standard sections, and the section form can be divided into rectangle and triangle. The guide rail is connected with the building by the wall bracket, and the rigidity is better. Cargo distribution is divided into two cages and a single cage, which generally balance the weight of the cargo and improve the balance of operation. The guide frame assembled by the standard joint has a large stiffness in the vertical direction. It can be considered that the pulley is installed on the rigid foundation, and the vibration mechanical model is established as shown. Physical meaning of each parameter in the vibration model: it is the rotating member in the cargo, load, steel wire rope and drive device. Since the natural vibration frequency of the system is only related to the mass and stiffness of the system, it is the natural frequency of the system in the characteristic equation rewritten as the vibration equation.

Since the elevator in operation is a system changing at any time, the parameters in the stiffness matrix are changing at any time, so the natural frequency of the system is changing at any time. According to the system parameters and software programming, the variation trend of natural frequencies of the aluminum alloy hoist under three working conditions of no-load, load-bearing and full-load is calculated. In the case of no-load, load-bearing and full-load, the change of natural frequency of the third order of the system has little influence, and its frequency curve basically coincides with each other. The maximum and minimum values of the first order natural frequency of the system (no load, load and full load) are located at the top and bottom of the cargo respectively; The maximum and minimum values of second order natural frequency are located at the position of 50m and top of the cargo when no load, at the position of bottom when load, and at the position of 60m and bottom when full load. The maximum and minimum values of the third order natural frequencies are at the bottom of the cargo. The results show that the natural frequency of the system is related to the load size and the change of the cargo position. High order natural frequency is greatly affected by the position of the cargo, but little affected by the load. Initial conditions at the time of the brake system response lifts in the process of work often start and brake, substitution to sum to the weight and wire rope combined respectively in the quality of heavy gear and rack tooth mesh composite stiffness and damping of stiffness and damping of wire rope pulley respectively respectively around the center of mass moment of inertia, the pulley rope and pulley wheel radius Angle displacement and velocity for the corresponding quality; As an incentive to act on goods. According to the vibration model, the vibration equation has 3 degrees of freedom. The coordinates are the position of each particle and the rotation Angle of the crown wheel.

The vibration equation is deduced as follows: the total dissipation energy of the total kinetic energy of the system is obtained from the equation. In order to understand the vibration characteristics of goods, to calculate the response of goods when braking, the free vibration of lift system under given initial conditions is solved. The response of the system to the initial condition is the mode of the main vibration of each order when t=0. When braking, the initial condition of the system is, and the system response to the initial condition is calculated. When the cargo is in different positions, the system has different responses to the initial conditions. When the cargo is near 40m, the system response does not change with the load, and the response under 40m is greater than that under full load, and the response under 40m is less than that under full load.

Conclusion: low order natural frequency is not sensitive to the position of the cargo. The minimum no-load first and second order natural frequencies do not change much with the change of cargo height. The higher natural frequency varies greatly with the change of the cargo position. The third natural frequency varies with the increase of the cargo height. The lower natural frequency decreases as the load increases, while the higher natural frequency is not affected by the load. The response of the system to the initial condition decreases with the increase of the height of the cargo when it is empty, increases with the increase of the height when it is full, and the response of the system to the initial condition is maximum when the fully loaded cargo is at the top of the lift.

## 升降机作为重要的高空作业机械，其系统振动分析一直受到广泛关注。本文对升降机的振动进行分析，建立系统振动力学模型，利用计算获得在不同载重和不同位置时系统的各阶段固有频率，分析各阶段固有频率随载重和货物位置的变化趋势，确定了系统对于给定初始条件的响应。升降机是一种重要的垂直输送机械，其货物振动与升降机运行同时产生。

## 随着高层建筑物的发展，升降机速度加快，提升高度增加，振动的问题越来越突出。本文以在用齿轮齿条式升降机为对象，建立振动力学模型和振动方程，通过计算不同载重和不同位置时系统的固有频率，分析系统对给定初始条件的响应，为升降机振动分析提供参考。振动模型建立：振动力学模型以货物升降机为例，由天轮、天轮架、附墙架、钢丝绳、齿条、导轨架、货物、司机室、对重、底笼和基础组成，通过布置在货物上的传动装置中的齿轮与布置在导轨架上的齿条相啮合，使货物沿导轨架做上下运动，完成人员和物料的输送，实际结构如所示。结构特点是导轨架多为单根，由标准节组成，截面形式可分为矩形和三角形两种；导轨架多由附墙架与建筑物相连，刚性较好；货物布置分为双笼和单笼，一般有对重来平衡货物重量，提高运行平衡性。由标准节组装而成的导轨架在竖直方向上刚度较大，可认为天轮安装在刚性基础上，建立振动力学模型如所示。振动模型中各参数物理意义：为货物、载重、钢丝绳及驱动装置中转动构件，由于系统的固有振动频率只与系统的质量和刚度有关，则是改写为振动方程的特征方程式中系统的固有频率。

## 由于运行中的升降机是一个时刻变化的系统，刚度矩阵中的参数是时刻变化的，因而系统的固有频率也是随时变化的。根据系统参数，利用软件编程，计算获得铝合金升降机在空载、载重以及满载三种工况下系统各阶固有频率的变化趋势中，在空载、载重和满载时，系统三阶固有频率变化影响较小，其频率曲线基本重合。系统的一阶固有频率的最大值和最小值（空载、载重和满载时）分别位于货物处于顶部和底部的位置；二阶固有频率的最大值和最小值空载时位于货物处于50m和顶部的位置，载重时位于和底部的位置，满载时也出现在60m和底部的位置；三阶固有频率的最大值和最小值位于货物处于底部的位置。结果所示,系统固有频率与载荷大小和货物的位置变化有关，低阶固有频率受货物位置的影响不大，受载荷的影响较大；高阶固有频率受货物位置影响较大，受载荷的影响不大。系统对制动时初始条件的响应升降机在工作过程中经常启动和制动，总和为对重及钢丝绳代换到对重的质量总和分别为齿轮齿条轮齿啮合综合刚度及阻尼分别为钢丝绳的刚度及阻尼分别为天轮绕质心的转动惯量、天轮绳轮半径及天轮转角为相应质量的位移及速度；为作用于货物的激励。振动方程根据振动模型可知其具有3个自由度，坐标分别为各质点的位及天轮的转角。

## 振动方程推导如下位移矢量：系统总动能系统总势能系统总耗散能由方程可得振动方程式中外力列阵给系统带来较大的冲击和振动。为了解货物的振动特性，计算制动时货物的响应，求解给定初始条件下升降机系统的自由振动。系统对初始条件的响应即是当t=0时各阶主振动的振型。制动时系统的初始条件为，计算系统对制动时初始条件的各阶响应变化。货物处于不同位置时，系统对初始条件有不同的响应，货物靠近40m时系统响应不随载荷的变化而变化，低于40m时空载响应大于满载响应，高于40m时空载响应小于满载时的响应。

## 结论：低阶固有频率对货物处在的位置不敏感，不同载重时系统固有频率最大值最小值最大值。最小值空载第一、二阶固有频率随货物高度的改变变化不大；高阶固有频率随着货物位置的改变其数值存在较大的差异，第三阶固有频率随货物高度的增加呈不规则抛物线变化。低阶固有频率随着载荷的增加而减小，高阶固有频率受载荷的影响不大。空载时系统对初始条件的响应随货物高度的增加而减小，满载时随高度的增加而增大，满载的货物处于升降机顶部时，系统对初始条件的响应最大。