twopt_normal.m

Matlab中实现轮对分析的程序以及相关的程序包,可以实现火车轮轨接触关系的分析

% M-file name: twopt_normal.m
% M-file type: Function file

% This function file computes the normal forces acting on the left and the right wheels due to
% the interaction between wheel and rail. This calculation is valid for a two-point contact
% condition between the wheel and the rail. The inputs to the function are the longitudinal,
% lateral, and vertical creep forces, the lateral creep moments, rolling radii and contact angles at
% the left and the right wheel contact patches, and the wheelset lateral and yaw displacement
% and velocity. The outputs are the normal forces on the left and the right wheels resolved in
% longitudinal, lateral, and vertical directions.

% The outputs given by this function are called by the function file 'wheelset.m'.

function [Fny1,Fnz1,Fny2,Fnz2,Fny3,Fnz3]=twopt_normal(x1,x2,x3,x4,delta1,delta2,delta3,r1,r2,r3,Fcx1,Fcy1,Fcz1,Fcx2,Fcy2,Fcz2,Fcx3,Fcy3,Fcz3,Mcy1,Mcy2,Mcy3)

% Parameters used for simulation

% V: Forward velocity of wheelset (m/sec)
% a: Half of track gage (m)
% r0: Centered rolling radius of the wheel (m)
% mw: Mass of wheelset (kg)
% Iwy: Pitch principal mass moment of inertia of wheelset (kg-m2)

% g: Acceleration due to gravity (m/s2)
% yfc: Flange clearance or flange width (m)
% krail: Effective lateral stiffness of rail (N/m)
% crail: Effective lateral damping of rail (N/m)
% N: Axle load (N)

% Indicating the global nature of the variables. This means that the value of the variables need
% not be specified in this function file. This value is automatically obtained from the main file
% 'single_wheelset.m'.

global V a r0 mw Iwy g yfc krail crail N;

% Computing the normal forces at the left and right wheel-rail contact patches

F2=-Fcz1-Fcz2-Fcz3+N+mw*g;
M1=-a*(Fcz1+Fcz2-Fcz3)-r1*(Fcy1-x2*Fcx1)-r2*(Fcy2-x2*Fcx2)-r3*(Fcy3-x2*Fcx3)-x2*(Mcy1+Mcy2+Mcy3)-Iwy*(V/r0)*x4;
Vt=F1*(2*a*cos(delta2)*cos(delta3)-r2*sin(delta2)*cos(delta3)-r3*cos(delta2)*sin(delta3))+F2*(sin(delta2)*(a*cos(delta3)-r3*sin(delta3)))+M1*sin(delta2)*cos(delta3);
vf=F1*(-2*a*cos(delta1)*cos(delta3)+r1*sin(delta1)*cos(delta3)+r3*cos(delta1)*sin(delta3))-F2*(sin(delta1)*(a*cos(delta3)-r3*sin(delta3)))-M1*sin(delta1)*cos(delta3);
v=F1*(r2*cos(delta1)*sin(delta2)-r1*sin(delta1)*cos(delta2))+F2*(a*(cos(delta1)*sin(delta2)-sin(delta1)*cos(delta2))+(r2-r1)* sin(delta1)*sin(delta2))-M1*(cos(delta1)*sin(delta2)-sin(delta1)*cos(delta2));
del2=(2*a*cos(delta3)-r3*sin(delta3))*(cos(delta1)*sin(delta2)-sin(delta1)*cos(delta2))+(r2-r1)*sin(delta1)*sin(delta2)*cos(delta3);
Fnt=vt/del2;
Fnf=vf/del2;
Fn=v/del2;

% The normal forces calculated above are normal to the contact patch plane. These forces are
% resolved in the longitudinal, lateral, and vertical directions in the track coordinate system. The
% variables calculated below are passed to the function 'wheelset'.

% Resolving normal forces at the left and right wheel contact patches

Fny1=-Fnt*sin(delta1);
Fnz1=Fnt*cos(delta1);
Fny2=-Fnf*sin(delta2);
Fnz2=Fnf*cos(delta2);
Fny3=Fn*sin(delta3);
Fnz3=Fn*cos(delta3);