Universidade Federal do Rio Grande do Sul (UFRGS)
Programa de Pós-Graduação em Engenharia Civil (PPGEC)
Prof. Marcelo M. Rocha, Dr.techn. (ORCID)
Porto Alegre, RS, Brazil
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1. Introduction
2. Reduced model scaling
3. Typical soil
4. The R4 studless 120mm chain
5. Dynamic load definition
6. Design of chain anchoring system
7. Design of uniaxial load cell with inclinometer
8. Location of experimental sites
# Importing Python modules required for this notebook
# (this cell must be executed with "shift+enter" before any other Python cell)
import numpy as np
import pandas as pd
import matplotlib.pyplot as plt
The uniaxial load cell is designed for a 7.1kN bottom scale times a safety margin 2, hence maximum admissible load is 15.2kN. Conditioning electronics shall map this maximum load to approximatelly 3V.
The chain under test is connected to the chain anchor (see section 6) through a bottom load cell (BLC) and to the loading hoist through the a top load cell (TLC). Both BLC and TLC shall have exactly the same design. All connections are accomplished with steel shackles of compatible strength. Each cell is provided with strain gages in full bridge configuration and also with a MEMS accelerometer ADXL203. The accelerometer will provide the chain angle to vertical direction.
The basic cell geometry is presented in the following figure:
Special attention must be drawn to the following features:
The script below provides the expected stress levels:
Fmax = 2*7.1 # bottom scale design load (kN)
t = 0.0125 # maximum thickness
H = 0.0220 + 0.0250 # maximum width equals chain link width (m)
r = 0.00625 # radius of lateral notches
b = t - 2*0.004 # central thickness
h = H - 2*r # central width
σn = Fmax/(b*h) # central nominal stress
print('Ratio H/h is: {0:6.2f} '.format(H/h))
print('Ratio r/h is: {0:6.2f} '.format(r/h))
print('Nominal stress is: {0:6.2f}MPa'.format(σn/1000))
ks = 2.0
σmax = ks*σn/1000
print('Stress concentration is {0:6.2f} '.format(ks))
print('Concentrated stress is: {0:6.2f}MPa'.format(σmax))
Ratio H/h is: 1.36 Ratio r/h is: 0.18 Nominal stress is: 91.47MPa Stress concentration is 2.00 Concentrated stress is: 182.93MPa
Hence the maximum stress is less than 200MPa, what is acceptable for a stainless steel of any grade.
A Poisson ration $\nu = 0.3$ is used for the two gages disposed orthogonally to the loading axis. The strain gages are assumed to have a $k = 2.1$ gage factor (with $R = 350\Omega$ for minimizing current). Young's modulus for steel is assumed as $E = 205$GPa. Expected bridge voltage unbalance is given by:
$$ \frac{\Delta V}{V} = \left(2 + 2\nu\right) \frac{k \sigma_{\max}}{4E}$$The bridge source voltage will be approximatelly 5V. The script below is used to estimate the required amplification gain for maping the maximum force to 3V.
k = 2.1 # gage factor
nu = 0.3 # Poisson ratio
E = 205000 # Young's modulus (MPa)
dV = 5.*(2 + 2*nu)*k*σmax/E/4
G = 3./ dV
print('Maximum bridge unbalance: {0:8.5f}V'.format(dV))
print('Required amplification gain: {0:8.0f}x'.format( G))
Maximum bridge unbalance: 0.00609V Required amplification gain: 493x
According to the INA118 datasheet, the required gain of approximatelly 500x can be achieved without frequency attenuation problems:
All calculations are approximated, and the load cell will require a careful calibration.