# Translation (technology)

In technology, translation is the process in which the value of a physical quantity is converted ( translated ) into another value of the same quantity . The quotient of both values ​​is the dimensionless transmission ratio ( symbol ). ${\ displaystyle i}$

When converting speeds with mostly a gear train , the gear ratio is the quotient between incoming and outgoing speed, where i. d. As a rule, the speed of a work machine (e.g. an automobile ) is adapted to the engine driving it (e.g. the engine of the automobile).

According to DIN , the quotient of the speed of the prime mover (gear input) and the speed of the driven machine (gear output) is defined as the transmission ratio. If i> 1, the speed is reduced, but the transmitted torque is increased. With i> 1, the colloquial use is reduction or translation into slow speed and with i <1 translation into fast .

## Basics

Unlike a converter , a translator does not convert any physical quantity . Rather, the result of the translation is of the same size type as the input.

A translation can only be done in such a way that the main principles of thermodynamics are adhered to. This applies in particular to the conservation of energy (first law) and the increase in entropy (second law).

## mechanics

A mechanical translation is always based on the principle of a simple machine ( rope / rod , roller , lever , inclined plane ). In the idealized case, these simple machines and their combinations, of which any machine, no matter how complex (in the sense of physics) consists, are transmitters of forces - in practical application, however, only translators because there are no real "ideal bodies" and losses inevitably arise. Subsequently, components of machines - or translate in real terms - then transfer movement ( dynamic machine or as load balancing in the structure ), energy or power .

Transmission in mechanical engineering describes the transmission of power through construction elements such as rods, belt drives (especially the historical transmissions of industrialization), shafts , gears and the like, as well as through combinations of these elements. The transmission ratio refers to a single pair of construction elements or the entire transmission.

### The gear ratio

2-stage spur gear .
Left drive, right output:
z 1 = 14 (red); z 2 = 42 (blue);
z 3 = 14 (yellow); z 4 = 28 (green).
i Level 1 = z 2 / z 1 = 42/14 = 3
i stage 2 = z 4 / z 3 = 28/14 = 2
i Ges = i Step 1 · i stage 2 = 6

The transmission ratio of individual pairings can be calculated using various relationships between the driving structural element ( drive ) and the driven structural element ( output ), for example for: ${\ displaystyle i}$

• Belt-driven via the effective diameter of the pulleys:${\ displaystyle d}$
${\ displaystyle i = {\ frac {d _ {\ text {output}}} {d _ {\ text {drive}}}}}$
${\ displaystyle i = {\ frac {z _ {\ text {output}}} {z _ {\ text {drive}}}}}$
• If losses are neglected, this results in the transmitted torque :${\ displaystyle M}$
${\ displaystyle i = {\ frac {M _ {\ text {output}}} {M _ {\ text {drive}}}}}$

The speeds of the gear wheels and their angular speeds behave in reverse to the torques . The higher the torque, the lower they are. ${\ displaystyle n}$ ${\ displaystyle \ omega}$

${\ displaystyle i = {\ frac {n _ {\ text {drive}}} {n _ {\ text {output}}}} = {\ frac {\ omega _ {\ text {drive}}} {\ omega _ { \ text {output}}}}}$

The following also applies:

• If the input speed is greater than the output speed (i.e. the magnitude of the gear ratio ), one speaks of a gear ratio to slow speed , sometimes colloquially also of a gear reduction .${\ displaystyle | i |> 1}$
• In epicyclic gears with parallel shafts, ratios are given as negative if the gears rotate in opposite directions.
• When several gear units are connected in series, the total ratio is calculated as:
${\ displaystyle i _ {\ text {Ges}} = \ prod _ {k = 1} ^ {n} i_ {k} = i_ {1} \ cdot i_ {2} \ cdot i_ {3} \ cdot \ ldots \ cdot i_ {n}}$
• The term gear corresponds to the transmission ratio of the pitch of the revolution to the feed rate in helical lines ( threads ) - in multi-stage gear designs one speaks of gears for the gradations of the transmission ratios. If the amount is small , one speaks of a high gear, and a large one of a low gear (in vehicle and drive technology, for example, crawler gear with an extremely high gear ratio).${\ displaystyle i}$${\ displaystyle i}$

## Electrical engineering

A simple transformer consists of two coils and converts an alternating voltage applied to one coil into a lower or higher alternating voltage in the other coil. The transmission ratio of the two voltages corresponds to the ratio of the number of turns of the two coils.

Specific types of transformers, such as transducers are used for adjustment of high electrical voltages or currents used at low cost measuring instruments. Despite the term "converter", these are converters.

## special cases

• Gears do not necessarily have to be round: To convert a rotary movement into a pendulum movement with an almost constant speed outside the turning points, a pair of gears consisting of two elliptical gears can be used. The transmission ratio is then dependent on the current angle of rotation of the drive gear.
• A somewhat curious application of gear ratios is the infinity machine .

## Individual evidence

1. ^ Karl-Heinrich Grote, Jörg Feldhusen: Dubbel - paperback for mechanical engineering . 20th edition. Springer, 2001, ISBN 3-540-67777-1 , 8.1.2, pp. G 123 .
2. ^ Karl-Heinrich Grote, Jörg Feldhusen: Dubbel - paperback for mechanical engineering . 20th edition. Springer, 2001, ISBN 3-540-67777-1 , 8.9.3, pp. G 150 .
3. Steinhilper, Sauer (ed.): Construction elements of mechanical engineering 2: Fundamentals of machine elements , excerpt
4. Elliptical gear pair , described on the radar tutorial.