Shock simulation of engine mounting system transient modal dynamic analysis and response spectrum analysis

1、 Reference resources

python Decoupling calculation of engine mount - Decouple according to the coordinate system of the whole vehicle at the center of gravity

Engine mount python Simulation calculation - Calculation of engine overturning torque excitation and vibration

Abaqus System impact simulation example - Transient modal method and response spectrum method Refer to Zhihu

Theoretical reference Baidu library writes well , The more you look, the less you can see

2、 Simulation ideas

• use Abaqus First establish 6 Degree of freedom rigid body system , Conduct transient time domain simulation based on mode Modal dynamics And response spectrum simulation Response spectrum,4 Three mounting points plus mass points form a rigid body , The center of mass is the reference point ,4 Support point constraint （ exert base motion incentive ） The mounting point and the supporting point are connected by springs . The data of the model comes from reference 1 ,Abaqus Refer to the above Zhihu for the operation process of .
  
• Motivation is base motion Acceleration , Use half sine wave , from Python Programming is complete , Maximum acceleration 10g, Maximum displacement 80mm about , Then use the anti - （ ring ） Strain spectrum calculation software , Generate acceleration response spectrum with half sine wave .
• Modal dynamics The dynamic response process of the whole time domain can be obtained , But it's time consuming ,Response spectrum The algorithm is very characteristic , from base motion Acceleration excitation （ There can be many ） After multiple One degree of freedom The system of , The maximum response value under different frequencies is obtained through the action of the system , Make response spectrum curve （look up table）. then , According to base motion Unit displacement of , Get system Participation factor of each mode , namely 1 Company base Displacement of , How much displacement change will be caused by each mode , Or what is the modal displacement , It can also be said that modal coordinates , It can also be said that the modal weighting factor , It is actually a unit base The projection of the displacement vector on the modal coordinate system .1* Modal participation factor =1 The unit of base motion The resulting modal displacement （ Displacement excitation of a single degree of freedom system ）, Then according to the modal frequency look up Response spectrum, Interpolation , Get the maximum value of the response under this mode , Then through the modal shape coordinate transformation , Transform to various physical coordinate systems , Get the physical coordinate system The maximum response value of the visible physical quantity . therefore , Its calculation speed is very fast , If you only care about the maximum response value of the system , Do not care about the process of system dynamic response , use Response spectrum, It is a very cost-effective Algorithm .

3、python Data processing

Impact excitation generation

• python Program to generate half cycle sine wave , Sampling interval 0.001s, Sampling frequency 1000hz, Analysis frequency 500hz, And save to 2 individual txt In file , One is used to calculate the response spectrum , One for transient simulation excitation .

import numpy as np
y_t=lambda f,t,A:A*np.sin(2*np.pi*f*t)*(t<=0.5/f)
ti=np.array(np.linspace(0,1,1000,False))#0:0.001:1;
y_ti=y_t(10,ti,10)
#np.savetxt(r'data.txt', np.c_[np.mat([ti,y_ti]).T], fmt='%f', delimiter=',')
np.savetxt(r'data.txt', np.c_[ti,y_ti], fmt='%f', delimiter=',')
np.savetxt(r'data_t_Y.txt', np.c_[ti,y_ti][:int(1*(0.5/10)*1000+1)], fmt='%f', delimiter=',')

Response spectrum processing

python hold excel The period of the response spectrum is changed to the frequency , And increase modal damping , write in txt in , be used for Abaqus Response spectrum analysis data import

import numpy as np
import pandas as pd
import matplotlib.pyplot as plt

plt.rcParams['font.sans-serif']=['SimHei'] # Used to display Chinese labels normally 
plt.rcParams['axes.unicode_minus']=False # Used to display negative sign normally 

file_path = r'data_RS.xls'
dataFrame =pd.read_excel(file_path)
#data=dataFrame.values[:,1:] # Two dimensional array 
f=1/dataFrame.values[0:,0]
y=dataFrame.values[0:,1]
f=f[::-1][:np.size(f)-1]
y=y[::-1][:np.size(y)-1]
plt.plot(f,y,label='Response Spectra')
plt.legend()
plt.show()

damp=np.ones(int(np.size(f)))*0.02
np.savetxt(r'data_f_RS.txt', np.c_[y,f,damp], fmt='%f', delimiter=',')

4、 result

Transient response , You can see 4 The second mode contributes the most , Vertical direction y towards , The same as the direction of motivation .

Response spectrum results , The result is only one point , It is very close to the maximum value of transient calculation .