Experimental Determination of the Mass Moment of Inertia of a Flywheel Using Dynamics and Statistical Methods

2015 ◽  
Author(s):  
Pezhman Hassanpour ◽  
Monica Weaser ◽  
Ray Colquhoun ◽  
Khaled Alghemlas ◽  
Abdullah Alrashdan
Keyword(s):  
Experimental Determination ◽  
Accurate Result ◽  
Moment Of Inertia ◽  
The Other ◽  
Experimental Measurements ◽  
Ball Bearings ◽  
Experiment Data ◽  
Mass Moment ◽  
Mass Moment Of Inertia

This paper presents the analysis of the mass moment of inertia (MMI) of a flywheel using experiment data. This analysis includes developing two models for determining the MMI of the flywheel. The first model considers the effect of mass moment of inertia only, while the second model takes the effect of friction in the ball bearings into consideration. The experiment results have been used along with both models to estimate the MMI of the flywheel. It has been demonstrated that while the model with no friction can be used for estimating the MMI to some extent, the model with friction produces the most accurate result. On the other hand, an effective application of the model with friction requires several experimental measurements using different standard masses. This translates into more expensive method in terms of experiment time and equipment cost.

Natural Frequencies of Nonuniform Beams on Multiple Elastic Supports

1958 ◽  
Vol 25 (1) ◽  
pp. 57-63
Author(s):  
R. A. Di Taranto
Keyword(s):  
Natural Frequencies ◽  
Forced Vibrations ◽  
Moment Of Inertia ◽  
Elastic Supports ◽  
Mass Moment ◽  
End Conditions ◽  
Mass Moment Of Inertia ◽  
Gyroscopic Effects

Abstract A method is presented for the determination of the natural frequencies of nonuniform beams on two or more torsionally and linearly elastic supports, including the effect of rotary mass moment of inertia. The method employed is an extension of the Myklestad method. The cases of two supports with varied end conditions and three supports with a torsional and linear restraint at each support are formulated. It is indicated how this method may be used for problems concerning forced vibrations of beams on multiple elastic supports and for the determination of critical rotor speeds including gyroscopic effects.

Determination of a missile polar mass moment of inertia

1993 ◽  
Vol 30 (6) ◽  
pp. 777-779
Author(s):  
Hsing-Juin Lee ◽  
Yang-Chung Lee ◽  
Hsing-Wei Lee
Keyword(s):  
Moment Of Inertia ◽  
Mass Moment ◽  
Mass Moment Of Inertia

scholarly journals Determination of the dimensions of the cylindrical weight at the end of the rod

2019 ◽  
Vol 14 (3) ◽  
pp. 214-217
Author(s):  
A.A. Aitbaeva
Keyword(s):  
Differential Equation ◽  
Spectral Problem ◽  
Natural Frequencies ◽  
Moment Of Inertia ◽  
Unknown Parameters ◽  
Transverse Vibrations ◽  
Mass Moment ◽  
Mass Moment Of Inertia ◽  
The Right

This article discusses free transverse vibrations of a homogeneous rod. The left end of the rod is clamped, and a cylindrical weight is concentrated at the right end. The eigenfrequencies of the rod vibration are known. The purpose of this work is to determine the parameters of the end cylindrical weight of the rod (mass, moment of inertia, length and radius) by the natural frequencies of the rod vibrations. We use a partial differential equation derivative of the fourth order to solve this problem. This equation and boundary conditions are reduced to a spectral problem. To find the mass and moment of inertia of the weight, the «Method of an additional unknown» was applied. In the characteristic determinant of the spectral problem, there are terms that contain products of unknown coefficients. The essence of the «Method of an additional unknown» is that some of these products are proposed to be considered new additional unknowns, through which the rest can be expressed. It is shown that the mass and moment of inertia of the weight can be found using the three natural frequencies of the rod vibrations. Formulas for finding the length and radius of a cylindrical weight are obtained, and corresponding examples of finding unknown parameters are considered.

Modeling and validation of crankshaft speed fluctuations of a single-cylinder four-stroke diesel engine

2021 ◽  
pp. 095440702110262
Author(s):  
Mustafa Babagiray ◽  
Hamit Solmaz ◽  
Duygu İpci ◽  
Fatih Aksoy
Keyword(s):  
Diesel Engine ◽  
Dynamic Model ◽  
Moment Of Inertia ◽  
Mass Motion ◽  
Cylinder Pressure ◽  
Motion Equations ◽  
Single Cylinder ◽  
Mass Moment ◽  
Mass Moment Of Inertia ◽  
Speed Fluctuations

In this study, a dynamic model of a single-cylinder four-stroke diesel engine has been created, and the crankshaft speed fluctuations have been simulated and validated. The dynamic model of the engine consists of the motion equations of the piston, conrod, and crankshaft. Conrod motion was modeled by two translational and one angular motion equations, by considering the kinetic energy resulted from the mass moment of inertia and conrod mass. Motion equations involve in-cylinder gas pressure forces, hydrodynamic and dry friction, mass inertia moments of moving parts, starter moment, and external load moment. The In-cylinder pressure profile used in the model was obtained experimentally to increase the accuracy of the model. Pressure profiles were expressed mathematically using the Fourier series. The motion equations were solved by using the Taylor series method. The solution of the mathematical model was performed by coding in the MATLAB interface. Cyclic speed fluctuations obtained from the model were compared with experimental results and found compitable. A validated model was used to analyze the effects of in-cylinder pressure, mass moment of inertia of crankshaft and connecting rod, friction, and piston mass. In experiments for 1500, 1800, 2400, and 2700 rpm engine speeds, crankshaft speed fluctuations were observed as 12.84%, 8.04%, 5.02%, and 4.44%, respectively. In simulations performed for the same speeds, crankshaft speed fluctuations were calculated as 10.45%, 7.56%, 4.49%, and 3.65%. Besides, it was observed that the speed fluctuations decreased as the average crankshaft speed value increased. In the simulation for 157.07, 188.49, 219.91, 251.32, and 282.74 rad/s crankshaft speeds, crankshaft speed fluctuations occurred at rates of 10.45%, 7.56%, 5.84%, 4.49%, and 3.65%, respectively. The effective engine power was achieved as 5.25 kW at an average crankshaft angular speed of 219.91 rad/s. The power of friction loss in the engine was determined as 0.68 kW.

III. An experimental determination of the velocity of sound

1872 ◽  
Vol 20 (130-138) ◽  
pp. 34-35
Keyword(s):  
Experimental Determination ◽  
Cape Town ◽  
The Other ◽  
Velocity Of Sound ◽  
Successful Operation ◽  
Single Wire ◽  
Galvanic Current ◽  
Royal Observatory ◽  
Port Elizabeth

A galvanic current passes from the batteries at the Royal Observatory, Cape Town, at 1 o’clock, and discharges a gun at the Castle, and through relays drops a time-ball at Port Elizabeth. It appeared to the author that a valuable determination of the velocity of sound might be obtained by measuring upon the chronograph of the Observatory the interval between the time of the sound reaching some point near the gun and that of its arrival at the Observatory. As there is only a single wire between the Observatory and Cape Town, some little difficulty was experienced in making the necessary arrangements, without any interference with the 1 o’clock current to Port Elizabeth; but this difficulty was overcome by a plan which the author describes, and which was brought into successful operation on Feb. 27, 1871. The experiments could not have been carried out, on account of the encroachment they would have made on the time of the Observatory staff, had it not been for the assistance of J. Den, Esq., the acting manager of the Cape Telegraph Company, to whom the author is indebted for the preparation of a good earth-connexion near the gun, for permission to Mr. Kirby, a gentleman attached to the telegraph office, to assist in the experiments, and for a general superintendence of the arrangements at Cape Town. The observed times of hearing the sound were recorded on the chronograph by two observers, situated one (Mr. Kirby) at a distance of 641 feet from the gun, the other (Mr. Mann) at the Observatory, at a distance of 15,449 feet from the gun. The former distance was sufficient to allow the connexion of the main wire to be broken at the telegraph office after the gun had been fired, but before the sound reached the first observer.

scholarly journals Pengaruh Variasi Radius-Dalam Rim Terhadap Pengurangan Massa dan Momen Inersia Massa Dengan Studi Kasus Benda Putar Berdiameter 10 cm

2018 ◽  
Vol 1 (1) ◽  
Author(s):  
Eka Taufiq Firmansjah
Keyword(s):  
Outer Radius ◽  
Moment Of Inertia ◽  
Mass Reduction ◽  
Inner Radius ◽  
Mass Moment ◽  
Mass Moment Of Inertia ◽  
Machine Elements ◽  
The Moment ◽  
The Masses

ABSTRAK Mesin terdiri dari sekumpulan elemen mesin yang diam dan bergerak. Elemen mesin yang bergerak dengan gerakan berputar disebut benda putar. Pada beberapa kasus seringkali diinginkan pengurangan massa dari benda putar tersebut untuk alasan ekonomis, biasanya untuk elemen mesin yag diproduksi massal. Namun pengurangan massa berakibat pada pengurangan momen inersia massa benda putar bersangkutan. Jika tuntutan perancangan tidak mempermasalahkan perubahan tersebut, maka pengurangan massa tidak menjadi masalah. Namun jika momen inersia massa tidak boleh terlalu rendah, maka harus dicari kompromi dimana pengurangan massa sebesar-besarnya namun penurunan momen inersia massa sekecil-kecilnya. Pada penelitian ini dilakukan studi kasus terhadap benda putar berjari- jari 10 cm jari-jari dalam hub 2 cm dan jari-jari luar hub 4 cm. Jumlah jari-jari ada 4 dengan lebar 1 cm dan tebal benda putar 0,5 cm. Variasi pengurangan massa dilakukan dengan memvariasikan jari-jari- dalam rim. Untuk tiap variasi, dilakukan perhitungan untuk mendapatkan jumlah massa yang dapat dikurangi dan momen inersia massa dari benda putar. Ternyata pada nilai jari-jari dalam tertentu, dapat diperoleh nilai kompromi dari permasalahan diatas. Kata kunci: benda putar, penghematan bahan, momen inersia massa.  ABSTRACT Machine consists of a set of machine elements that still and moving. Machine elements that move in a circular motion called rotary object. In some cases it is often desirable reduction in the mass of the rotating object for economic reasons, usually for a mass production of machine elements. But the mass reduction results in a reduction in moment of inertia of the mass. If the demands of the design allow this decrease of moment of inertia, mass reduction is not a problem. But if the moment of inertia of the masses should not be too low, it must find a compromise in which a mass reduction profusely but the decrease in the mass moment of inertia of the smallest. In this research conducted a case study of rotating element radius of 10 cm, radius of the hub 2 cm and outer radius hub 4 cm. The number of spoke are 4 with a width of 1 cm and uniform thickness 0.5 cm all over rotating element. Variations mass reduction is done by varying the inner radius of the rim. For each variation, calculation is performed to obtain the amount of mass that can be reduced and the mass moment of inertia of the rotating object. It turned out that in the certain value of inner radius of the rim in particular, can compromise the values obtained from the above problem. Keywords: rotating element, reducing material, mass moment of inertia.

An Analysis of the Simplified Two-Mass System of the Connecting Rod in Spark Ignition Engines

2002 ◽  
Author(s):  
Richard Stanley
Keyword(s):  
Statistical Study ◽  
Cylinder Liner ◽  
Moment Of Inertia ◽  
Average Error ◽  
Spark Ignition Engines ◽  
Connecting Rod ◽  
Mass System ◽  
Rolling Moment ◽  
Mass Moment ◽  
Mass Moment Of Inertia

Replacing the connecting rod with a lumped two-mass system causes an error, which influences the inertia rolling moment, the thrust force between the piston and the cylinder liner, and the loading on the main bearings. Dimensionless relationships have been found that relate the inertia error due to the connecting rod simplification (the inertia error) to the errors of the forces and moments that are created by it. Additionally, the results of a statistical study of 19 SI connecting rods indicate that the mass moment of inertia of the two mass system is −2.65% to 22% higher than that the experimentally measured moment of inertia of the connecting rod, with an average error value of 9.65%.

scholarly journals Quantification of vibrissal mechanical properties across the rat mystacial pad

2019 ◽  
Vol 121 (5) ◽  
pp. 1879-1895 ◽  
Author(s):  
Anne En-Tzu Yang ◽  
Hayley M. Belli ◽  
Mitra J. Z. Hartmann
Keyword(s):  
Mechanical Properties ◽  
Center Of Mass ◽  
Distal Region ◽  
Density Variation ◽  
Average Density ◽  
Proximal Region ◽  
Moment Of Inertia ◽  
Radius Of Gyration ◽  
Mass Moment ◽  
Mass Moment Of Inertia

Recent work has quantified the geometric parameters of individual rat vibrissae (whiskers) and developed equations that describe how these parameters vary as a function of row and column position across the array. This characterization included a detailed quantification of whisker base diameter and arc length as well as the geometry of the whisker medulla. The present study now uses these equations for whisker geometry to quantify several properties of the whisker that govern its mechanical behavior. We first show that the average density of a whisker is lower in its proximal region than in its distal region. This density variation appears to be largely attributable to the presence of the whisker cuticle rather than the medulla. The density variation has very little effect on the center of mass of the whisker. We next show that the presence of the medulla decreases the deflection of the whisker under its own weight and also decreases its mass moment of inertia while sacrificing <1% stiffness at the whisker base compared with a solid whisker. Finally, we quantify two dimensionless parameters across the array. First, the deflection-to-length ratio decreases from caudal to rostral: caudal whiskers are longer but deflect more under their own weight. Second, the nondimensionalized radius of gyration is approximately constant across the array, which may simplify control of whisking by the intrinsic muscles. We anticipate that future work will exploit the mechanical properties computed in the present study to improve simulations of the mechanosensory signals associated with vibrissotactile exploratory behavior. NEW & NOTEWORTHY The mechanical signals transmitted by a whisker depend critically on its geometry. We used measurements of whisker geometry and mass to quantify the center of mass, mass moment of inertia, radius of gyration, and deflection under gravity of the whisker. We describe how variations in these quantities across the array could enhance sensing behaviors while reducing energy costs and simplifying whisking control. Most importantly, we provide derivations for these quantities for use in future simulation work.

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