Predictive Energy Stability Margin: Prediction of Heavy Machine Overturning Considering Rotation and Translation

Abstract

Fatal accidents caused by the overturning of heavy machines still happen, so the prediction and prevention of overturns are urgently needed. Indicators to evaluate overturn, such as the energy stability margin (ESM), have been proposed but are limited to a non-slip ground surface. Even if ESM is above zero, the machine may overturn due to additional manipulator operation or hitting an obstacle while sliding down a slope. This study thus proposes a predictive energy stability margin, <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">${\bm{p}}$</tex-math></inline-formula>-ESM, that focuses on kinetic energy in the translational and rotational directions for overturn prediction. Rotational kinetic energy <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">${{{\bm{E}}}_{\bm{R}}}$</tex-math></inline-formula> accelerates overturning, and the translational kinetic energy <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">${{{\bm{E}}}_{\bm{T}}}$</tex-math></inline-formula> in the slope direction is converted to <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">${{{\bm{E}}}_{\bm{R}}}$</tex-math></inline-formula>. Both are calculated from the mass and the position and acceleration of the center of gravity (COG) for each part of the machine. ESM <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">${\bm{U}}$</tex-math></inline-formula> is defined as the difference between the height of COG just before overturn and the current height of the COG. Thus, <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">${\bm{p}}$</tex-math></inline-formula>-ESM is defined as <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">${\bm{U}}$</tex-math></inline-formula> minus the sum of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">${{{\bm{E}}}_{\bm{R}}}$</tex-math></inline-formula> and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">${{{\bm{E}}}_{\bm{T}}}$</tex-math></inline-formula>. We also developed an operation support system to limit the manipulator operation by using <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">${\bm{p}}$</tex-math></inline-formula>-ESM. The results of experiments using a hydraulically driven scale model (1/14) with different combinations of operations, loading weights, and ground surfaces confirmed that <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">${\bm{p}}$</tex-math></inline-formula>-ESM can predict overturns early and accurately, which conventional ESM cannot do. We also found that the support system using <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">${\bm{p}}$</tex-math></inline-formula>-ESM can prevent inappropriate operations and avoid overturns.