# CHOICE OF THE METHOD OF TRANSMISSION, OF THE GEAR RATIO, OF THE MOTION CONVERSION TYPE, OF THE KEYING AND THE COUPLINGS.

The brushless motor, like any other motor, is built up on the delivered torque and not on the yielded power. As a consequence, in any application a low speed of the motor will correspond to a low specific power and a low yield. Nevertheless we must point out that the brushless motor contemplates no minimum speed (it purely depends on the sensor; some applications are available with axle speed of 1 revolution per year); consequently, the decision to act on the transmission to allow a high rotating speed of the motor is acceptable only when it is important to minimise the seize of the motor (i.e. with electric traction) or to maximise the yield; on the contrary, it does not represent a logical cost-effective solution or in consideration to the dynamic performances of the system. On the other hand, all the applications fitting a motor which is operated as direct drive on the load, are featured by the highest control pass-band, since the maximum stiffness of the transmission is experienced thus allowing to assure the highest precision in positioning or pursuing operations within the shortest time.

Before proceeding to select the correct drive for a certain system, it is indispensable to know the type of the mechanical transmission to be fitted in. The most common transmissions are the following:

**ROTATION-ROTATION CONVERSION**

- Toothed belt
- Helical gear and parallel axle reduction unit
- Cycloidal and epycyclic reduction units
- Harmonic Drive
- Endless screw or Gleason reduction units.

**ROTATION-RECTILINEAR MOTION CONVERSION**

- Toothed belts
- Ball screws
- Pinion – rack
- Metallic tape.

As a rule, for any drive gear system, the load parameters are related to the driving axle according to:

**n = gear ratio** (ratio between the motor speed and the load speed, in case of conversion from rectilinear motion rad/m), we will obtain:

- Torque to the motor = Torque (thrust) on the load / n
- Speed of the motor = Speed of the load n
- Inertia of the load on the driving axle = load inertia (or mass) / n².

Among all the drives listed above, the first ones, which are the cheapest, are at same time the lowest ones and they only allow low-average pass-bands (inferior to 10Hz, only upon the condition that a low stretching belt is used); for the same reason, ratios causing the inertia of the load referred to the motor shaft to become too high in comparison to the one of the motor itself must be avoided.

Definitely, belt drives can in no way be utilised for positioning operations with cycles below one second.

The gear reduction units do represent a correct solution only when their clearance is restricted to a considerably lower value than the precision rate required by the system; the best reducer (but most unfortunately the most expensive one, too) is always the epicyclic type; special ranges of cyclic and epicyclic reducers expressly designed for servo controls are available on the market, providing for the clearance of the outlet axis to be limited to a 1 3 arc minutes. These reducers are the only ones which can be used in applications with pass-bands superior to 10Hz.

The “servo range” reducers have been developed to be coupled directly to the motor by means of a conical fitting, without key.

The Harmonic Drive reducer too has been expressly designed to carry out positioning operations. Small in size, it features high ratio and low clearance. The angular stiffness is not excellent and the deriving pass-band is estimated around ten of Hz. Due to the limited energy efficiency, its use should be restricted to positioning operations, only.

A separate consideration must be devoted to the endless screw reducers. These reducers are absolutely unsuited to the application with variable speed motors. Indeed, the efficiency of the reduction units drastically collapses in proportion to the speed and strong static friction, thus causing the systems to loose in efficiency at low speed whereas the rise in speed will result in a strong wear of the reduction unit.

Regarding the linear conversion, the ball screws do offer a valid solution up to approximately 4 m/s, usually allowing to avoid any additional reduction. For extremely long drive mechanisms, it is necessary to verify both the bending and torsion stiffness of the screw, which may represent the limit to the band of the system. Longer drive mechanisms can be executed by means of racks which in any case always feature a significant clearance and they restrict the band to a few Hz.

The traditional clearance recovery mechanisms are not so efficient inside the control systems, since the static friction is high, thus causing the system to oscillate within a “limit cycle”.

Very quick and precise drive mechanisms can be obtained by means of metallic belts. This technique, which is not widely spread and therefore it has not been acquainted as standard procedure, allows to achieve superior performances in the control of small masses (some kgs).

The use of linear motors is anyway irreplaceable when we need to achieve the top performance in rectilinear motion.

In order to select the most suitable method and gear ratio for the application, we should distinguish between two kinds of applications:

- power applications, providing the motor to supply power to a process (spindles, traction, winding machines, etc.), featuring marginal dynamic performances, significant released power and where the cost of the motor is an important component in the cost of the whole system;
- Positioning or quick cycle applications (electronic cams), where most of the power is used to accelerate, to brake and to position objects quickly and at more or less high precision.

Traditionally, the two above mentioned groups are respectively named as applications type **spindles and shafts**.

In the first case, dynamics is rarely important and therefore it is possible to utilize low cost reducers and, since the required power is often relevant, it would be better to use a mechanic driving gear with a reduction stage. In order to choose the ideal transmission ratio, we must consider that the size and the cost of the motor, up to a speed of the motor lower than 4000 r.p.m., drop in a linear way parallel to the transmission ratio. On the contrary, the cost of the driving gear will increase according to the number of the gear or pulley couples; as a rule, the excellent cost-effective condition can be found only for a restricted number of points and more in detail:

- or in direct drive
- or at the highest ratio achievable by means of one reduction couple, only
- or at the highest ratio achievable with two reduction couples, etc.

The best cost-effective solution, in such a case, can be achieved by verifying these points and summing up the costs of the motors and to the reduction units.

Concerning the high dynamics applications (shafts), the situation is completely different. If the torque required by the driving cycle is controlled by the inertia torque of both the motor and the load, it follows that, by increasing the reduction ratio, the importance of the load inertia will be reduced whereas the importance of the motor will rise up. Therefore we can demonstrate that, for an application where the torque is purely inertial, the reduction ratio causing the load inertia referred to the motor shaft to be equal to the motor inertia (inertial coupling), corresponds to the minimum torque (and as a consequence the smallest motor).

For this reason, the inertial coupling has been long considered as the only and unique correct coupling. Nevertheless, such a rule is purely a useful suggestion.

Indeed, the minimum dimension of the motor, considering that the cost of the reduction unit is as a rule at least double of the motor, does not absolutely correspond to the most cost-effective version of the application. Furthermore, if we consider that the dynamics of the application will mostly depend on the elasticity and the clearance of the transmission, it has no sense to optimise the drive devoting our most attention exclusively to the motor.

**From a general point of view, we can remark that:**

- any transmission ratio superior to the ratio of inertia is wrong;
- the ideal and excellent ratio is always lower or equal to the ratio of inertia, and it is obtained taking into consideration the cost both of the motor and the reducer;
- huge rates will always correspond to a pass-band and to an inferior accuracy (and to a higher energy consumption) of what you could obtain with more reduced ratio.

These considerations explain the present tendency to eliminate the reducers in order to operate in a straight way. Despite this, when the load inertia considerably exceeds the inertia of the motor, it will be necessary to take the necessary precautions since the inertia of the motor is no more in a condition to exert a stabilizing action on the eventual mechanic resonances of the system.

Consequently, in such applications, a top quality mechanic system, rigid and with no clearance is required and the coupling to be without key (namely with conic fitting). If you are operating in direct drive, it is necessary to check the torsion rigidity of the system. In particular, also the torsion elasticity of the motor must be taken in due consideration as it is most significant in case of motors longer than any usual size. The ranges of brushless motors are superimposed, so as that same torque can be obtained either with a long and narrow motor or with a short motor with higher geometry, exactly for this reason:

- the long motors feature a minimum moment of inertia and they must be utilised for high accelerations with low inertia loads;
- the shorter motors feature the highest torsion rigidity and they must be utilised with loads at an inertia by far superior to the one of the motor.

As pure reference, we are quoting the formula expressing the torsion rigidity of a steel shaft with D diameter and L length:

whereas the first frequency of torsion resonance of a load with JI inertia connected to an axis with Sm torsion rigidity is given by the following formula:

If you opt for an application contemplating reduced times and high load inertia, it will be indispensable to plan a check of the first mechanic resonance of the system.

**CORRELATED PAGES**

# DECLARATION OF CE CONFORMITY

Referred to EC Low Voltage Directive 73/23/CEE

We hereby certify that the motors of the ULTRACT and LYRA line have been designed, manufactured and tested according to the EC Low Voltage Directive 73/23/CEE under the responsibility of:

R.C.V. s.r.l.

V. Cavour, 7 z.i.

10070 ROBASSOMERO (TO)

Applied standards are the following:

IEC 72/1, 34/1, 34/5, 34/11

EN 60034 – 1 + VAR A1 + VAR A2

EN 60529

EN 50262

CEE 73/23

## HOW TO REACH R.C.V.

R.C.V. is conveniently located in the industrial area of Robassomero, a town on the outskirts of Turin.

Coming from Aosta (A5) and Milan (A4) motorway, take the Turin highway – southward direction, if arriving from the Fréjus (A32), from Piacenza (A21) or from Savona (A6), drive north.

Exit “Venaria – stadio” and turn left at the lights, direction to Lanzo.

Cross the built-up area of Venaria and drive the S.P. (Provincial Road) No. 1 for 8 km approximately, you will run along the perimeter wall of the Regional Parc of “La Mandria”, up to the lights of the industrial area of Robassomero.

Turn right, at the first street turn right again and you will reach Cavour street where R.C.V. is located.