蛇行带式输送机转弯处稳定性及非线性特性分析
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摘要
为分析系统转弯处的稳定性及非线性特性,以三节运输小车为研究对象,区别传统分析方法,兼顾横摆运动和侧倾运动对小车进行力学特性分析,列出各节小车的运动方程,从而建立起蛇行带式输送机四自由度非线性动力学模型;进一步分析蛇行带式输送机转弯处非线性特性,通过Jacobian矩阵A探究输送机非线性系统的临界稳定性;因系统在奇异点处具有复杂的动力学行为,利用Hurwitz判据判断稳定性;运用Matlab进行输送机小车轨迹仿真,得出小车加速过程中存在侧滑、侧倾、侧翻失稳三种情况,将实验结果与仿真结果对比分析得出临界稳定值。结果表明:当机头小车纵向速度vx1=1.5m/s,前轮转角幅值Ad=0.36rad时,其它小车稳定跟随;当机头小车纵向速度vx1=1.5m/s,前轮转角幅值Ad=0.38rad时,小车基本能稳定跟随,但在转弯时开始出现侧滑失稳现象;当机头小车纵向速度vx1=2m/s,前轮转角幅值Ad=0.36rad时,小车不能良好跟随,产生失稳现象。研究成果为蛇行带式输送机的布置、运行提供理论依据。
Three cars are taken as an example system, its stability and nonlinear characteristics are analyzed. Three transport cars are taken as the research object, being different from the traditional analysis methods, combining horizontal pendulum motion and roll motion mechanical characteristics, a quarter of each car is modeled, and eventually a four degrees of freedom nonlinear dynamic model of serpentine belt conveyor is built up. By analyses the force on turning of the tape, the model of adhesive tape in the process of turning is established. The nonlinear characteristics of the turning of the serpentine belt conveyor are further investigated. Through the Jacobian matrix A, the critical stability of the nonlinear system is explored. As the system has complex dynamic behavior at the singular point, the stability of the system is judged by the Hurwitz criterion. Using Matlab to simulate the track of the conveyor cars, we can get three kinds of situation that there is sideslip, tilting and side turning instability in the process of acceleration, and the experimental results are compared with the simulation results to get the critical stability value: when the longitudinal speed of the head car is vx1=1.5 m/s and the front wheel angle is Ad = 0.36 rad, other cars are steadily followed by the vehicle; When the longitudinal speed of the head car is vx1=1.5 m/s and the front wheel angle is Ad =0.38 rad, the car can basically follow the basic stability, but the side slip instability begins when the turn is turned. When the longitudinal speed of the head car is vx1=2 m/s and the front wheel corner amplitude is Ad =0.36 rad, the car can not follow well and produce the instability phenomenon. The research results provide theoretical basis for the layout and operation of the snake belt conveyor.
Three cars are taken as an example system, its stability and nonlinear characteristics are analyzed. Three transport cars are taken as the research object, being different from the traditional analysis methods, combining horizontal pendulum motion and roll motion mechanical characteristics, a quarter of each car is modeled, and eventually a four degrees of freedom nonlinear dynamic model of serpentine belt conveyor is built up. By analyses the force on turning of the tape, the model of adhesive tape in the process of turning is established. The nonlinear characteristics of the turning of the serpentine belt conveyor are further investigated. Through the Jacobian matrix A, the critical stability of the nonlinear system is explored. As the system has complex dynamic behavior at the singular point, the stability of the system is judged by the Hurwitz criterion. Using Matlab to simulate the track of the conveyor cars, we can get three kinds of situation that there is sideslip, tilting and side turning instability in the process of acceleration, and the experimental results are compared with the simulation results to get the critical stability value: when the longitudinal speed of the head car is vx1=1.5 m/s and the front wheel angle is Ad = 0.36 rad, other cars are steadily followed by the vehicle; When the longitudinal speed of the head car is vx1=1.5 m/s and the front wheel angle is Ad =0.38 rad, the car can basically follow the basic stability, but the side slip instability begins when the turn is turned. When the longitudinal speed of the head car is vx1=2 m/s and the front wheel corner amplitude is Ad =0.36 rad, the car can not follow well and produce the instability phenomenon. The research results provide theoretical basis for the layout and operation of the snake belt conveyor.
引文
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[13]曲辉.T型带带式输送机分散摩擦驱动的理论研究[D].辽宁:辽宁工程技术大学,2006.(QU Hui.Research on decentralized friction drive of T-belt conveyor in theory[D].Liaoning:Liaoning Technical University,2006(in Chinese)).
[14]周立彬.大型带式输送机拉紧装置的动态分析与优化设计[D].辽宁:辽宁工程技术大学,2002.(ZHOU Libin.Large belt take-ups’dynamic analysis and their optimization design[D].Liaoning:Liaoning Technical University,2002(in Chinese)).
[15]STEVEN R B.Belting the world’s longest single flight conventional overland belt conveyor[J].Bulk solids handling,2008,28(3):172-181.
[16]徐国华.带拖车的轮式移动机器人系统的研究[D].天津:南开大学,1998.(XU Guohua.Research of tractor-trailer robot systems’kinematics[D].Tianjin:Nankai University,1998(in Chinese)).
[2]WOODWARD W D H,WOODSIDE A R,JELLIE J H.Reducing stockpile segregation and degradation using telescopic conveyor technology[J].Bulk solids handling,2003,23(2):114-115.
[3]ALSPAUGH M A.The evolution of intermediate driven belt conveyor technology[J].Bulk solids handling,2003,23(3):168-172.
[4]张国胜.大型可弯曲带式输送机静态设计理论研究[D].辽宁:辽宁工程技术大学,2001.(ZHANG Guosheng.Research about the static design theory of belt[D].Liaoning:Liaoning Technical University,2001(in Chinese)).
[5]范晓宁.钢绳芯带式输送计算机辅助选型设计及参数绘图[D].太原:太原理工大学,2003.(FAN Xiaoning.Computer-aided selection design and parametric drawing of steel-core belt conveyor[D].Taiyuan:Taiyuan University of Technology,2003(in Chinese)).
[6]潘鹏.蛇行带式输送机转向动力学特性研究[D].辽宁:辽宁工程技术大学,2015.(PAN Peng.Sinusoidal belt conveyor turning dynamics research[D].Liaoning:Liaoning Technical University,2015(in Chinese)).
[7]王东杰.半挂汽车列车弯道行驶横向稳定性分析[D].青岛:青岛理工大学,2008.(WANG Dongjie.Analysis on lateral stability of semi-trailer train running along a curve[D].Qingdao:Qingdao University of Technology,2008(in Chinese)).
[8]刘宏飞.半挂汽车列车横摆动力学仿真及控制策略研究[D].吉林:吉林大学,2005.(LIU Hongfei.Study on the simulation and control strategy for yaw motion dynamics of tractor-semitrailer[D].Jilin:Jilin University,2005(in Chinese)).
[9]刘丽.车辆三自由度平面运动稳定性的非线性分析及控制策略评价[D].吉林:吉林大学,2010.(LIU Li.Three degrees of freedom vehicle plane movement stability of nonlinear analysis and control strategy evaluation[D].Jilin:Jilin University,2010(in Chinese)).
[10]杨达文,鲍师云.常用带式输送机的现状[J].起重运输机械,2003(1):4-6.(YANG Dawen,BAO Shiyun.Current situation of common belt conveyor[J].Lifting the transport machinery,2003(1):4-6(in Chinese)).
[11]战悦晖.平面转弯带式输送机变坡转弯理论的研究[D].沈阳:东北大学,2006.(ZHAN Yuehui.Research on theory of variational curve of belt conveyor with horizontal curves[D].Shenyang:Northeastern University,2006(in Chinese)).
[12]彭涛.半挂汽车列车非线性稳定性控制研究[D].吉林:吉林大学,2012.(PENG Tao.A study on control of nonlinear stability for tractor-semitrailer[D].Jilin:Jilin University,2012(in Chinese)).
[13]曲辉.T型带带式输送机分散摩擦驱动的理论研究[D].辽宁:辽宁工程技术大学,2006.(QU Hui.Research on decentralized friction drive of T-belt conveyor in theory[D].Liaoning:Liaoning Technical University,2006(in Chinese)).
[14]周立彬.大型带式输送机拉紧装置的动态分析与优化设计[D].辽宁:辽宁工程技术大学,2002.(ZHOU Libin.Large belt take-ups’dynamic analysis and their optimization design[D].Liaoning:Liaoning Technical University,2002(in Chinese)).
[15]STEVEN R B.Belting the world’s longest single flight conventional overland belt conveyor[J].Bulk solids handling,2008,28(3):172-181.
[16]徐国华.带拖车的轮式移动机器人系统的研究[D].天津:南开大学,1998.(XU Guohua.Research of tractor-trailer robot systems’kinematics[D].Tianjin:Nankai University,1998(in Chinese)).