F l o r i a n P E T R E S C U\’ s B o o k s S t o r eThe Design of Gearings with High EfficiencyISBN 978-1-4467-9054-0A Short Book Description: Development and diversification of machines and mechanisms with applications in all areas of scientific research requires new systematization and improvement of existing mechanical systems by creating new mechanisms adapted to the modern requirements, which involve more complex topological structures. Modern industry, the practice of engineering design and manufacture increasingly rely more on scientific research results and practical. The processes

via The Efficiency of Gearings – THE DESIGN OF GEARINGS WITH HIGH EFFICIENCY.

 


F l o r i a n   P E T R E S C U’ s   B o o k s   S t o r e

The Design of Gearings with High Efficiency

ISBN 978-1-4467-9054-0


A Short Book Description:

Development and diversification of machines and mechanisms with applications in all areas of scientific research requires new systematization and improvement of existing mechanical systems by creating new mechanisms adapted to the modern requirements, which involve more complex topological structures. Modern industry, the practice of engineering design and manufacture increasingly rely more on scientific research results and practical.

The processes of robotisation of today define and influence the emergence of new industries, with applications in specific environmental conditions, handling of objects in outer space, and are leading teleoperator in disciplines such as medicine, automations, nuclear energetic, etc.

In this context this paper attempts to bring a contribution to science and technology applied in the kinematic and dynamic analysis and synthesis of mechanisms with gearings.

The book presents an original method to determine the efficiency of the gear. The originality of this method relies on the eliminated friction modulus. The work is analyzing the influence of a few parameters concerning gear efficiency. These parameters are: z1 – the number of teeth for the primary wheel of gear; z2 – the number of teeth of the secondary wheel of gear; ?0 – the normal pressure angle on the divided circle; ? – the inclination angle. With the relations presented in this paper, one can synthesize the gear’s mechanisms.

We begin with the right teeth (the toothed gear), with i=-4, once for z1 we shall take successively different values, rising from 8 teeth. One can see that for 8 teeth of the driving wheel the standard pressure angle, ?0=200, is too small to be used (it obtains a minimum pressure angle, ?m, negative and this fact is not admitted; see the first table). In the second table we shall diminish (in module) the value for the ratio of transmission, i, from 4 to 2. We will see how for a lower value of the number of teeth of the wheel 1, the standard pressure angle (a0=200) is too small and it will be necessary to increase it to a minimum value. For example, if z1=8, the necessary minimum value is a0=290 for an i=-4 (see the table 1) and a0=280 for an i=-2 (see the table 2). If z1=10, the necessary minimum pressure angle is a0=260 for i=-4 (see the table 1) and a0=250 for i=-2 (see the table 2). When the number of teeth of the wheel 1 increases, we can decrease the normal pressure angle, a0. We will see that for z1=90 it can take a less value for the normal pressure angle (for the pressure angle of reference), a0=80. In the table 3 we increases the module of i value (the ratio of transmission), from 2 to 6.

In the table 4, the teeth are bended (b?0). The module i takes now the value 2.

The efficiency (of the gear) increases when the number of teeth for the driving wheel 1, z1, increases, and when the pressure angle, ?0, diminishes; z2 and i12 have not so much influence about the efficiency value.

We can easily see that for the value ?0=200, the efficiency takes roughly the value ??0.89 for any values of the others parameters (this justifies the choice of this value, ?0=200, for the standard pressure angle of reference).

But the better efficiency may be obtained only for a ?0?200 (?0<200).

The pressure angle of reference, ?0, can be decreased, when in the same time, the number of teeth for the driving wheel 1, z1, increases, to increase the gears’ efficiency.

Contrary, when we desire to create a gear with a low z1 (for a less gauge), it will be necessary to increase the ?0 value, for maintaining a positive value for ?m (in this case the gear efficiency will be diminished).

When ? increases, the efficiency (?) increases too, but its growth is insignificant. We can see in the last part of the work, that in reality it (? increases) produces a decrease in yield.

The module of the gear, m, has not any influence on the gear’s efficiency value.

When ?0 is diminished one can take a higher normal module, for increasing the addendum of teeth, but the increase of the m at the same time with the increase of the z1 can lead to a greater gauge.

The gears’ efficiency (?) is really a function of ?0 and z1: ?=f(?0,z1); the two angles (?m and ?M) are just the intermediate parameters (intermediate variables).

For a good projection of the gear, it’s necessary a z1 and a z2 greater than 30-60; but this condition may increase the gauge of mechanism; when the numbers of teeth z1 and z2 beyond the 30 value, the efficiency of the gearing are greater, and the values of the two different efficiencies leveled; this can be a great advantage in transmissions, especially in planetary transmissions, where the moments may come from both directions; will result a better and more equilibrated functionality (But these are the subject of a future work).

In the second (and last) part the book presents shortly an original method to obtain the efficiency of the geared transmissions in function of the contact ratio. With the presented relations one can make the dynamic synthesis of the geared transmissions having in view increasing the efficiency of gearing mechanisms in work (the accuracy of calculations will be high).

One calculates the efficiency of a geared transmission, having in view the fact that at one moment there are several couples of teeth in contact, and not just one.

The start model has got four pairs of teeth in contact (4 couples) concomitantly.

The first couple of teeth in contact has the contact point i, defined by the ray ri1, and the pressure angle ai1; the forces which act at this point are: the motor force Fmi, perpendicular to the position vector ri1 at i and the force transmitted from the wheel 1 to the wheel 2 through the point i, Fti, parallel to the path of action and with the sense from the wheel 1 to the wheel 2, the transmitted force being practically the projection of the motor force on the path of action; the defined velocities are similar to the forces (having in view the original kinematics, or the precise kinematics adopted); the same parameters will be defined for the next three points of contact, j, k, l (see fig. 2).

The best efficiency can be obtained with the internal gearing when the drive wheel 1 is the ring; the minimum efficiency will be obtained when the drive wheel 1 of the internal gearing has external teeth. For the external gearing, the best efficiency is obtained when the bigger wheel is the drive wheel; when one decreases the normal angle a0, the contact ratio increases and the efficiency increases as well. The efficiency increases too, when the number of teeth of the drive wheel 1 increases (when z1 increases).

Generally we use gearings with teeth inclined (with bended teeth). For gears with bended teeth, the calculations show a decrease in yield when the inclination angle increases. For angles with inclination which not exceed 25 degree the efficiency of gearing is good (see the table 6). When the inclination angle (?) exceeds 25 degrees the gearing will suffer a significant drop in yield (see the tables 7 and 8).

The calculation relationships (33-35) are general (Have a general nature). They have the advantage that can be used with great precision in determining the efficiency of any type of gearings.

1 Introduction

In this paper the authors present an original method to calculating the efficiency of the gear.

The originality consists in the way of determination of the gear’s efficiency because one hasn’t used the friction forces of couple (this new way eliminates the classical method). One eliminates the necessity of determining the friction coefficients by different experimental methods as well. The efficiency determined by the new method is the same like the classical efficiency, namely the mechanical efficiency of the gear.

Some mechanisms work by pulses and are transmitting the movement from an element to another by pulses and not by friction. Gears work practically only by pulses. The component of slip or friction is practically the loss. Because of this the mechanical efficacy becomes practically the mechanical efficiency of gear.

The paper is analyzing the influence of a few parameters concerning gear efficiency. With the relations presented in this paper, one can synthesize the gear’s mechanisms. Today, the gears are present every where in the mechanical’s world.


 

Author: Florian Ion TIBERIU-PETRESCU Company: UPB POLYTECHNIC UNIVERSITY OF BUCHAREST TMR Department Residence: BUCHAREST – ROMANIA – EUROPE Websites:

dynamics.ro expertdyna Cars

Memorable Quote 1: Drivetrain Expert (Gear And Gearing Expert) Memorable Quote 2: Otto Engines Expert (Powertrain Expert)

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Florian Ion PETRESCU\’s Books and Publications Spotlight.

 

http://www.lulu.com/spotlight/petrescuflorian

 

First Book:

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THE DESIGN OF GEARINGS WITH HIGH EFFICIENCY

Development and diversification of machines and mechanisms with applications in all areas of scientific research requires new systematization and improvement of existing mechanical systems by creating new mechanisms adapted to the modern requirements; the gearing mechanisms are found today everywhere: in the industry of machinery construction, in energy industry, in aeronautics and aerospace, in electronics& Electrical, in oil industry, in mechatronics and robotics, etc. In this context this book attempts to bring a contribution to science and technology applied in the kinematic and dynamic analysis and synthesis of mechanisms with gearings. The book presents an original method to determine the efficiency of the gearing; the originality of this method relies on the eliminated friction modulus. With the relations presented in this paper, one can synthesize the gear’s mechanisms; the best efficiency can be obtained with the internal gearing when the drive wheel 1 is the ring.

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Gear Expert

January 15, 2011

Gear Expert.

 

 

© 2010 Florian Ion PETRESCU and Relly Victoria PETRESCU – Gears Design

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About Energy

January 15, 2011

About Energy.

Obtaining Energy by the Annihilation of an Electron with a Positron

The subject is all about getting energy, renewable, clean, friendly (not dangerous), cheaper, by annihilation(for example, the annihilation of an electron with an anti electron (positron)). The Electron and the positron are obtained by extracting them from atoms; the extraction, consumes a negligible amount of energy. Then, the two particles are brought near one another (collision).The phenomenon of annihilation occurs, when the rest mass is converted totally into energy (gamma photons). Occuring gamma photons, as many as needed to retrieve the total energy of the electron and positron (rest energy and kinetic energy); usually one can get two or three gamma particles (when we have a lower annihilation, ie two antiparticles with lower energy, each with a little beyond rest mass, i.e. the particles are accelerated at a low-speed motion), but we can get more particles when we have a high annihilation (i.e. when the particle energy is high and the particles were strongly accelerated before the collision). The rest energy of an electron-positron pair exceeds slightly 1 MeV (what is an extremely large energy from some as small particles, comparable energy with that achieved by the merger of two much larger particles, having rest mass of about 2000 times higher). Hence the first great advantage of the new method proposed, namely that if the most complex physical phenomenon so far tried to get inside the material energy (hot or cold fusion), draw only about a thousandth part of the rest mass of the particle, resulting in the fusion of two particles practically only the energy gap between energy particles being free and their energy when they are united, the proposed method extract virtually all the internal energy of the particles annihilated. We started with the electron positron pair because these small particles are more easily extracted from the atoms (the atoms are then immediately regenerated naturally, which determines the nature of renewable energy from the annihilation of particles). Next step is to test the annihilation between a proton and an antiproton, because their mass is about 1800 times higher than that of the electron and positron, resulting in their annihilation as an energy by about 1000 times higher, i.e. instead of 1 MeV, 1 GeV (is considered as the only real obtained energy, the energy donated by the proton of the hydrogen ion; but the energy of an antiproton is considered to be donated by us almost entirely, for now, because to obtain today an antiproton we must accelerate some particles at very high-energy and then collide them). So the real comparison must to be made between the deuterons fusion and annihilation process of a hydrogen ion (proton) with an antiproton. It will be a difference of energy of about 1000 times higher per pair of particles used, in favor of the annihilation process. Practically it achieves the dream of extracting energy from all the substance. Another great advantage of this method is that no radioactive substances occur and no radioactive wastes come out of the process. From this process we obtain only gamma photons (i.e. energy) and possibly other energetic mini particles. The process does not pose any threat to humans and the environment. The energy produced is clean. The technology required is much simpler than nuclear (fission or fusion), cheaper and easier to maintain. Enough energy is given by the annihilation process (virtually unlimited), cheap, clean, safe, renewable immediately (sustainable), with technology made simple.

We can extract the energy of the rest mass of an electron. For a pair of an electron and a positron this energy is circa 1 MeV. The “synchrotron radiation (synchrotron light source)” produces deliberated a radiation source. Electrons are accelerated to high speeds in several stages to achieve a final energy (that is typically in the GeV range). We need two synchrotrons, a synchrotron for electrons and another who accelerates positrons. The particles must to be collided, after they are being accelerated to an optimal energy level. All the energies are collected at the exit of the Synchrotrons, after the collision of the opposite particles. We will recover the accelerating energy, and in addition we also collect the rest energy of the electrons and positrons.

At a rate of 10^19 electrons/s we obtain an energy of about 7 GWh / year, if even are produced only half of the possible collisions. This high rate can be obtained with 60 pulses per minute and 10^19 electrons per pulse, or with 600 pulses per minute and 10^18 electrons per pulse. If we increase the flow rate of 1,000 times, we can have a power of about 7 TWh / year. This type of energy can be a complement of the fusion energy, and together they must replace the energy obtained by burning hydrocarbons.

Advantages of the annihilation of an electron with a positron, compared with the nuclear fission reactors, are disposal of radioactive waste, of the risk of explosion and of the chain reaction.

Energy from the rest mass of the electron is more easily controlled compared with the fusion reaction, cold or hot.

Now, we don’t need enriched radioactive fuel (as in nuclear fission case), by deuterium, lithium and of accelerated neutrons (like in the cold fusion), of huge temperatures and pressures (as in the hot fusion), etc.

 

Renewable Energy, Sustainable Energy, Cheap Energy, Green Energy, Friendly Energy, New Energy, Annihilation Energy

Bio:

PhD. Eng. Florian Ion PETRESCU,

Senior Lecturer at Bucharest Polytechnic University