68 lines
2.1 KiB
Mathematica
68 lines
2.1 KiB
Mathematica
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%% Clear Workspace and Close figures
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clear; close all; clc;
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%% Intialize Laplace variable
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s = zpk('s');
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% Finite Element Model
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% From the Finite Element Model, the stiffness and stroke of the flexible joint have been computed and summarized in Tables [[tab:axial_shear_characteristics]] and [[tab:bending_torsion_characteristics]].
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%% Stiffness
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ka = 94e6; % Axial Stiffness [N/m]
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ks = 13e6; % Shear Stiffness [N/m]
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kb = 5; % Bending Stiffness [Nm/rad]
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kt = 260; % Torsional Stiffness [Nm/rad]
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%% Maximum force
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Fa = 469; % Axial Force before yield [N]
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Fs = 242; % Shear Force before yield [N]
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Fb = 0.118; % Bending Force before yield [Nm]
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Ft = 1.508; % Torsional Force before yield [Nm]
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%% Compute the corresponding stroke
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Xa = Fa/ka; % Axial Stroke before yield [m]
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Xs = Fs/ks; % Shear Stroke before yield [m]
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Xb = Fb/kb; % Bending Stroke before yield [rad]
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Xt = Ft/kt; % Torsional Stroke before yield [rad]
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% Setup
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% The setup is schematically represented in Figure [[fig:test_bench_flex_side_bis]].
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% The force is applied on top of the flexible joint with a distance $h$ with the joint's center.
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% The displacement of the flexible joint is also measured at the same height.
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% The height between the joint's center and the force application point is:
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h = 25e-3; % Height [m]
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% Estimation error due to force sensor compression
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% The measured displacement is not done directly at the joint's location.
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% The force sensor compression will then induce an error on the joint's stiffness.
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% The force sensor stiffness $k_F$ is estimated to be around:
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kF = 50/0.05e-3; % [N/m]
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sprintf('k_F = %.1e [N/m]', kF)
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% Estimation error due to height estimation error
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% Let's consider an error in the estimation of the height from the application of the force to the joint's center:
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% \begin{equation}
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% h_{\text{est}} = h (1 + \epsilon)
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% \end{equation}
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% The computed bending stiffness will be:
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% \begin{equation}
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% k_\text{est} \approx h_{\text{est}}^2 \frac{F_x}{d_x}
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% \end{equation}
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% And the stiffness estimation error is:
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% \begin{equation}
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% \frac{k_{\text{est}}}{k_{R_y}} = (1 + \epsilon)^2
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% \end{equation}
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h_err = 0.2e-3; % Height estimation error [m]
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