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

### February 1, 2011

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:**

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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: z_{1} – the number of teeth for the primary wheel of gear; z_{2} – 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 z_{1} 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}=20^{0}, 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 (a_{0}=20^{0}) is too small and it will be necessary to increase it to a minimum value. For example, if z_{1}=8, the necessary minimum value is a_{0}=290 for an i=-4 (see the table 1) and a_{0}=28^{0} for an i=-2 (see the table 2). If z_{1}=10, the necessary minimum pressure angle is a_{0}=26^{0} for i=-4 (see the table 1) and a_{0}=25^{0} for i=-2 (see the table 2). When the number of teeth of the wheel 1 increases, we can decrease the normal pressure angle, a_{0}. We will see that for z_{1}=90 it can take a less value for the normal pressure angle (for the pressure angle of reference), a_{0}=8^{0}. 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, z_{1}, increases, and when the pressure angle, ?_{0}, diminishes; z_{2} and i_{12} have not so much influence about the efficiency value.

We can easily see that for the value ?_{0}=20^{0}, the efficiency takes roughly the value ??0.89 for any values of the others parameters (this justifies the choice of this value, ?_{0}=20^{0}, for the standard pressure angle of reference).

But the better efficiency may be obtained only for a ?_{0}?20^{0} (?_{0}<20^{0}).

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

Contrary, when we desire to create a gear with a low z_{1} (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 z_{1 }can lead to a greater gauge.

The gears’ efficiency (?) is really a function of ?_{0} and z_{1}: ?=f(?_{0},z_{1}); the two angles (?_{m} and ?_{M}) are just the intermediate parameters (intermediate variables).

For a good projection of the gear, it’s necessary a z_{1} and a z_{2} greater than 30-60; but this condition may increase the gauge of mechanism; when the numbers of teeth z_{1} and z_{2} 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 r_{i1}, and the pressure angle a_{i1}; the forces which act at this point are: the motor force F_{mi}, perpendicular to the position vector r_{i1} at i and the force transmitted from the wheel 1 to the wheel 2 through the point i, F_{t}_{i}, 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* *a*_{0}*, 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 z

_{1}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:

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

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.