Measurement of the Moment of Inertia for a Zero Turning Radius Mower

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The moment of inertia (MI) is one of the important factors that affect the continuous roll behavior of a zero turning radius (ZTR) mower, and therefore, an accurate measurement or calculation of the MI is required. Previous research focused on the estimation techniques for vehicle MIs, and the measurements included a car, pickup truck, sport utility vehicle, and van, all of which have a small front/rear axle load distribution difference (i.e., the front/rear axle load distribution ratio ranges from 0.67 to 1). However, little research has investigated the MI of a ZTR mower, which has a large front/rear axle load distribution difference (i.e., the front/rear axle load distribution ratio is approximately 0.33); thus, the load distribution of a ZTR mower is more nonhomogeneous than that of the other vehicles. The primary objectives of this research were to investigate a mathematical model and a suitable MI measurement method for the ZTR mower, which is a vehicle with a large difference in front/rear axle load distribution. A mathematical model was developed based on the principle of the pendulum method for measuring the MI in the x-, y-, and z-axes. Three ZTR mowers were used as test vehicles: a mower without a deck, a 1.2 m swath mower, and a 1.8 m swath mower. The test results were compared with the results obtained using the empirical formulas. Based on the comparison of the MIs, the results of the tests were within the range of 6.7% to 16.5% of the relative error from the values calculated using the empirical formulas. The test results indicated that the relative errors increased for mowers with a large difference in the front/rear axle load distribution. © 2016 American Society of Agricultural and Biological Engineers.

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... Together with mass, centre of mass, product of inertia etc., it constitutes mass characteristics (properties) [1,2]. All machines with rotational behaviour, such as aircraft, satellites, automobiles and robots, need to be tested for inertia properties to verify their rotational performance [3][4][5][6][7][8][9][10]. Precision measurement of inertia properties is of significance for air vehicles, which need precise attitude and orbit control, such as missile, high supersonic aircraft, interceptor and satellite [11,12]. ...
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Oscillation method is the most effective approach to determine the inertia properties of rigid bodies. This paper proposes a new signal processing method to determine the moment of inertia (MoI) accurately in the presence of high frictional damping when using a torsion pendulum setup. A mathematical model of damped oscillation is established, and the analytic form of Fourier transformation of the damped torsional oscillation is derived. A formula for calculating the MoI in relation to the dominant frequency and damping ratio is also derived. An algorithm regarding periodic extension and normalization of torsional oscillation signal is proposed to calculate the dominant frequency and damping ratio of torsional oscillation in the frequency domain. The feasibility and accuracy of this algorithm are verified by both numerical simulations and measurement experiments. The experimental results show that the proposed method has good measurement repeatability, and the relative error of measurement is within 0.80%.
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