Curves of Minimum Moment of Inertia with Respect to a Point

1906 ◽  
Vol 7 (4) ◽  
pp. 165 ◽  
Author(s):  
Max Mason
Keyword(s):  
Moment Of Inertia ◽  
Minimum Moment

Stability of a Rigid Body With an Oscillating Particle: An Application of MACSYMA

1985 ◽  
Vol 52 (3) ◽  
pp. 686-692 ◽  
Author(s):  
L. A. Month ◽  
R. H. Rand
Keyword(s):  
Angular Velocity ◽  
Rigid Body ◽  
Classical Problem ◽  
Moment Of Inertia ◽  
Model Parameters ◽  
Stability Chart ◽  
The Stability ◽  
Transition Curves ◽  
Minimum Moment ◽  
Small Angular Velocity

This problem is a generalization of the classical problem of the stability of a spinning rigid body. We obtain the stability chart by using: (i) the computer algebra system MACSYMA in conjunction with a perturbation method, and (ii) numerical integration based on Floquet theory. We show that the form of the stability chart is different for each of the three cases in which the spin axis is the minimum, maximum, or middle principal moment of inertia axis. In particular, a rotation with arbitrarily small angular velocity about the maximum moment of inertia axis can be made unstable by appropriately choosing the model parameters. In contrast, a rotation about the minimum moment of inertia axis is always stable for a sufficiently small angular velocity. The MACSYMA program, which we used to obtain the transition curves, is included in the Appendix.

An Elastorelaxometer for Large Reversible Deformation of Elastomeric Systems and Polymer Solutions

1961 ◽  
Vol 34 (1) ◽  
pp. 165-175 ◽  
Author(s):  
A. A. Trapeznikov
Keyword(s):  
Polymer Solutions ◽  
Coaxial Cylinder ◽  
Moment Of Inertia ◽  
Colloidal Systems ◽  
Elastic Recoil ◽  
Elastic Deformations ◽  
Yield Value ◽  
New Instrument ◽  
Colloidal Gel ◽  
Minimum Moment

Abstract 1. A new instrument, the elastorelaxometer (based on the coaxial-cylinder principle) has been developed, for studies of large high-elastic deformations in relaxing colloidal gel systems and polymer solutions. 2. The effects of the following were investigated : a) width of the gap between the cylinders ; b) moment of inertia of the cylinder (with rapidly relaxing colloidal systems, cylinders of the minimum moment of inertia must be used) ; c) nature of the liquid in the bottom of the cylinder ; d) nature of the motion of the inner cylinder at different ultimate deformations. 3. Values of elastic recoil εc for different predetermined deformations ε have been determined in dilute aluminum naphthenate gels in decalin. It is shown that εc passes through a maximum, associated with transition beyond the yield value of the structure, with increase of ε. It is shown that εc can reeah 6000% in 2% gels.

Perception of the moment of inertia of hand tools

1982 ◽  
Author(s):  
Carol Zahner ◽  
M. Stephen Kaminaka
Keyword(s):  
Moment Of Inertia ◽  
Hand Tools ◽  
The Moment

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.

Research on the identification of the moment of inertia of PMSM for industrial robots

2020 ◽  
Author(s):  
Chuanwen Zhang ◽  
Guangxu Zhou ◽  
Ting Yang ◽  
Ningran Song ◽  
Xinli Wang ◽  
...  
Keyword(s):  
Industrial Robots ◽  
Moment Of Inertia ◽  
The Moment
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