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Research Papers

Lagrangian Formulation and Numerical Solutions to Dump Truck Vibrations Under HISLO Conditions

[+] Author and Article Information
Nassib Aouad

Assistant Professor of Mining Engineering,
Missouri S&T,
Rolla, MO 65401
e-mail: narzf@mst.edu

Samuel Frimpong

Robert Quenon Endowed Chair and Professor of Mining Engineering,
Missouri S&T,
Rolla, MO 65401
e-mail: frimpong@mst.edu

The product QR is computed where Q is an orthonormal matrix and R is an upper-triangular matrix.

Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF VIBRATION AND ACOUSTICS. Manuscript received November 5, 2012; final manuscript received January 7, 2014; published online February 5, 2014. Assoc. Editor: Dr. Corina Sandu.

J. Vib. Acoust 136(2), 021020 (Feb 05, 2014) (8 pages) Paper No: VIB-12-1307; doi: 10.1115/1.4026479 History: Received November 05, 2012; Revised January 07, 2014

Heavy mining machinery has exposed the human body to extreme vibrations that may limit the performance of operators and further impact the overall system performance. Large capacity shovels and dump trucks have been deployed in surface mines to achieve economic, bulk production operations. The high-impact shovel loading operation (HISLO) causes severe truck vibrations that expose operators to whole-body vibrations (WBV) levels that may exceed ISO standards. The effects of these shockwaves on the human body are severe resulting in long-term lower-back disorders and other health problems. There is a need for fundamental and applied research to determine HISLO vibration levels, their comparisons to ISO 2631 limits, and the safety of operators under these conditions. A fundamental research has been carried to model these HISLO shockwave generation and propagation through the truck body and attenuated via the suspension mechanism and within the rollover protective structures (ROPS) cabin. The Lagrangian mechanics technique has been used to formulate the equations of motions governing the HISLO problem. The Fehberg fourth–fifth order Runge–Kutta (RKF45) numerical method in maple environment (maple classic Version 10.00, 2006, Maplesoft, a division of Waterloo Maple Inc., Waterloo, ON, Canada) is used to solve the equations of motions symbolically. The Lagrangian formulation and the RKF45 solutions provide efficient solutions to complex functions with stability, convergence, and minimum errors. The results of this analysis show that the vertical root mean square (rms) accelerations are equal to 3.56, 1.12, and 0.87 m/s2 for the operator's seat, lower-back, and cervical regions, respectively. These vibration levels also fall within the extremely uncomfortable zone compared to the ISO 2631-1 comfort zone (less than 0.315 m/s2), which pose severe health threats to truck operators over long-term exposure to these vibrations.

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Figures

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Fig. 3

Free body diagram of each mass

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Fig. 5

Operator's seat vertical rms acceleration in the z direction

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Fig. 6

Human lumbar region rms acceleration in the z direction

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Fig. 7

Human cervical region rms acceleration in the z direction

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Fig. 4

Flow chart of the numerical methods for the solution

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Fig. 2

Free body diagram of a 9-DOF system

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Fig. 1

High impact shovel loading of a dump truck in surface mining

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