✅作者简介：热爱科研的Matlab仿真开发者，修心和技术同步精进，matlab项目合作可私信。
🍎个人主页：Matlab科研工作室
🍊个人信条：格物致知。
更多Matlab仿真内容点击👇
⛄ 内容介绍
This MATLAB code can reproduce some results in: “Fault tracing of gear systems: An in-situ measurement-based transfer path analysis method” [1]. This paper focuses on transfer path analysis (TPA) for gear systems. A virtual decoupling method is proposed to realize the in-situ measurement-based TPA. An identification of the bearing force is performed based on the Tikhonov regularization theory.
A gear dynamic model is adopted as the numerical example to illustrate the procedure of the transfer path analysis. Details about the proposed TPA algorithm can be seen in Ref. [1]. The complementary information of the time-varying mesh stiffness and dynamic modelling can be seen in Refs. [2, 3].
⛄ 部分代码
function [X,Xd,Xdd] = newmark(M,C,K,f,dt,gamma0,beta0,Xi,Xdi,Xddi)
%% ================================================================
% This function is intended to perform the numerical integration of a structural system
% subjected to an external dynamic excitation such as a wind or earthquake.
% The structural model is assumed to be a lumped mass shear model.
% The integration scheme utilized for this analysis is the newmark alpha-beta method.
% The newmark alpha-beta method is an implicit time steping scheme so stability of the system need not be considered.
%% ================================================================
% Input Variables:
% [M] = Mass Matrix (nxn)
% [C] = Damping Matrix (nxn)
% [K] = Stiffness Matrix (nxn)
% {f} = Excitation Vector (nx1)
% dt = Time Stepping Increment
% beta= Newmark Const (1/6 or 1/4 usually),alpha
% gamma = Newmark Const (1/2) ,delta
% Xi = Initial Displacement Vector (nx1)
% Xdi = Initial Velocity Vector (nx1)
% ------*------*------*------
% Output Variables:
% {t} = Time Vector (mx1)
% [X] = Response Matrix (mxn)
%% ================================================================
% %% Check Input Excitation
% n = size(M,1);
% fdimc = size(f,2);
% % fdimr = size(f,1);
% if(fdimc==n)
% f=f';
% end
% % m=size(f,2);
%% ================================================================
%% Coefficients
c0 = 1/(beta0*dt*dt) ;
c1 = gamma0/(beta0*dt) ;
c2 = 1/(beta0*dt) ;
c3 = 1/(beta0*2) - 1 ;
c4 = gamma0/beta0 - 1 ;
c5 = 0.5*dt*(gamma0/beta0 - 2 ) ;
c6 = dt*(1 - gamma0 ) ;
c7 = dt* gamma0 ;
%% ==============================
%% Initialize Stiffness Matrix Equivalent
Keff = c0*M + c1*C + K ;
%% ==============================
%% Perform First Step
f= f+ M*(c0*Xi+c2*Xdi+c3*Xddi)+C*(c1*Xi+c4*Xdi+c5*Xddi) ;
% X=Keff\f;
[L,U]=lu(Keff); % LU decomposition can speed up if Keff is in sparse
X=U\(L\f);
Xdd= c0*(X-Xi) - c2*Xdi - c3*Xddi ;
Xd= Xdi + c6*Xddi + c7*Xdd;
⛄ 运行结果
⛄ 参考文献
[1]Y.F. Huangfu, X.J. Dong, X.L. Yu, K.K. Chen, Z.W. Li, Z.K. Peng, Fault tracing of gear systems: An in-situ measurement-based transfer path analysis method, Journal of Sound and Vibration 553 (2023) 117610.1-26.
[2]K.K. Chen, Y.F. Huangfu, H. Ma, Z.T. Xu, X. Li, B.C. Wen, Calculation of mesh stiffness of spur gears considering complex foundation types and crack propagation paths, Mechanical Systems and Signal Processing 130 (2019) 273-292.
[3]Y.F. Huangfu, K.K. Chen, H. Ma, X. Li, H.Z. Han, Z.F. Zhao, Meshing and dynamic characteristics analysis of spalled gear systems: A theoretical and experimental study, Mechanical Systems and Signal Processing 139 (2020) 106640.1-21.
