*by Dr. Martin Doppelbauer, SEW Eurodrive*

**The current trend towards slow-running direct drives is driven by ****a demand for precision, reliability and low maintenance, among others. This article provides a theoretical comparison of diriect drives and gearmotors based on known growth laws and a few practical assumptions.**

When comparing direct drives and geared motors, it must be ensured that both contestants are based on the same motor principle (e.g. permanent magnet synchronous motors), or the differences of the motor principles overshadow the differences between the direct drive and the gearbox, making it clear results impossible.

In the following comparison the shaft power of the motor part of the geared motor is kept constant regardless of the gear unit reduction ratio.

The reduction ratio reduces the power output of the gear unit slightly due to the efficiency of the gear unit. This is accounted for in the formulas for the geared motor and the direct drive in equal measure.

For a fair comparison, the use of both motor types, i.e. the power density in the air gap *t* and the pole distance of the rotating field *T _{p}*, must also be equal.

**General basic equations**

The torque of the motor part of the geared motor is related to the power density in the air gap, the rotor diameter and the rotor length as follows:

EQN 1 HERE.

At the output shaft, the gearbox reduction and efficiency must be considered:

EQN 2 HERE

The same basic equation applies to the direct drive, obviously without the gearbox:

EQN 3 HERE

As the power density in the air gap is assumed to be constant, the torque of the direct drive increases linearly with the air gap length and with the square of the diameter (circumference multiplied by the lever arm).

As the pole distance *T _{P}* remains constant, the pole pair number of the direct drive depends directly on the diameter.

For the output speed, both increase in pole pair number and the reduced line frequency of the direct drive must be taken into account where applicable. The slenderness ratio L is useful for further analysis. It represents the ratio of active part length l?? to air gap diameter *D*.

**Case distinction **

It is useful to narrow down the different design alternatives for direct drives by considering two extreme variants.

The S type designates the design principle in which the supply frequency of the motor is kept constant and the lower speed is achieved by means of changing the diameter only. As much as these motors are designed for slower speeds, the active parts are shortened more and more and finally assume a disk shape.

The K type represents the other extreme: here, the slenderness ratio L of the motor constantly has an ideal value of 1??. To reduce the speed, the motor designer will increase the motor diameter and also reduce the supply frequency.

Each practical implementation of a torque motor will have to range somewhere between these design extremes.

Some manufacturers offer motor assembly kits in which the rotor is a hollow ring similar to a bent-up linear motor. This is a special kind of S type and will also be examined here as a separate type (*R* = ring motor).

Based on a motor with slenderness ratio L = l / *D* = 1, Fig. 2 shows an example of the basic dimensions of these three direct motor types for a speed reduction by 50%.

This distinction of cases allows for direct expression of the frequency ratio, diameter ratio and length ratio, depending on the intended speed reduction *i* compared to a standard motor:

EQN 4 HERE

By definition, the frequency is only reduced in the compact direct drive (K type). If 5 Hz is chosen as the lower limit frequency with regard to the load of the power semiconductors and smooth running, this drive can deliver reduction ratios up to *i* = 30.

Frequency does not limit the bottom speed of the ring motor (S and R types). This motor can therefore be designed larger and larger in theory.

**Practical comparison **

Two torque motor series from different manufacturers (A and B) were compared with servo geared motors from SEW Eurodrive to test the theoretically-derived formulas for their practicality.

The servomotors are salient pole synchronous drives with ten or twelve poles, depending on size. Single or two-stage planetary gear units were used where output torque allowed. The largest torque ratings could only be realised with low backlash helical gear units.

The torque motors of manufacturer A are water-cooled ring drives (R type) with 22 to 176 poles and an outer diameter of 0,2 m to approximately1 m. For a fair comparison with the non-ventilated servomotors, the continuous torque ratings of the torque motors were reduced by 40%. Peak torque ratings are not reduced.

The drives of manufacturer B are also water-cooled, diameter-emphasized torque drives, but they are delivered complete with housing, end shields and solid shaft. Depending on diameter, the number of poles is between 20 and 40. Here, too, the thermal continuous torque ratings are converted for non-ventilated operation.

The gear units were dimensioned for the respective peak torque ratings of the direct drives and their size does not change with the adaptation of the continuous torque ratings, which is why the following comparison is not affected by this measure.

The ratio of pole numbers of the direct drive and the servomotor respectively was used as the gear unit reduction ratio *i*. For example, Fig. 3 shows that a direct drive which runs ten times slower than to a standard motor (and has a ten-times higher torque) will have a rotor diameter between 1 and 0,5 times (type S) and between 1 and 0,1 times (type-K) larger than that of a standard motor.

Since the triangles in Fig. 3 are close to the blue curve, it can be seen that both manufacturers designed their direct drives with large diameters to create as much torque as possible.

From a practical point of view, *i* = 10…20 would be a reasonable limit for direct drives. Above this ratio, the diameter would increase by too much.

**Volume, installation space and weight**

The ratio of volume of a geared motor and a direct drive simply depends on the desired speed reduction factor (and torque increase factor) *i*:

EQN 5 HERE

This equation applies to all types of direct drives except for ring drives (R type), as the internal space of the rotor must be subtracted here.

This means that design details of the direct drive (such as length, diameter, number of poles and supply frequency) do not affect the rotor volume ratio as long as the power is kept constant in relation to the geared motor.

Strictly speaking, Equation 5 gives the ratio of the rotor volumes and not the overall motor (stator) volume. It also disregards the volume required for the gear unit.

The overall volume can be regarded as a measure for the installation space, the weight and the cost.

Assuming that the stator height (teeth plus yoke) is not different between the direct drive and the geared motor, a good estimation for the total volume (still excluding the gear unit) can be given:

- S type direct drive:

EQN 6 HERE

- K type direct drive:
EQN 7 HERE

- R type direct drive:

EQN 8 HERE

In these equations, *k* is the ratio of active rotor parts compared to shaft diameter in standard motors (not direct drives!). Typically, *k* is close to 0,5 for asynchronous motors and 0,4 for synchronous motors; *m* is the ratio of the stator diameter compared to the rotor diameter (typically 1,5 in standard motors).

The gear unit cannot be left out in a fair comparison. This is a problem here, as there are too many possible gear unit variants for a simple, compact formula.

The following assessments can at least be made for the field of single and multi-stage planetary servo gear units. These are most likely to be replaced by direct drives:

For *i* = 1, no gear unit is needed (*m _{gear unit}* = 0), for

This results in the following estimation for the overall drive:

EQN 9 HERE

Summing all up, Fig. 4 shows the volume ratio between direct drives and geared motors for different speed ratios i taking the estimated volume of the gear unit into account.

Even when considering that the influence of the gear unit in this diagram was only estimated very roughly, it can be determined that at *i* = 5 and above, a direct drive is decidedly inferior to a geared motor in terms of volume, and therefore also in terms of installation space, weight and price.

The ring-shaped assembly kit motor (R type) offers better results here as expected. For this motor, however, the higher amount of effort for the customer for structural integration must be taken into account, as there is no housing, bearing, encoder, precise air gap control, etc. The “system responsibility” must be clarified as well, since not every plant manufacturer can engage in motor design details.

The practical comparison between the motors of manufacturers A and B yields even worse results than the theoretical consideration. For this purpose, the ratio in Fig. 4 is not based on volume but on the overall weight.

Even the ring torque motor (manufacturer A) is not lighter on average than a geared motor of the same torque. The direct drive motor (manufacturer B) is between 1,5 and 3,5 times as heavy.

The gear unit dimensioning was based on the peak torque ratings. For applications which are rated on continuous torque rather than on acceleration, the gear units can be selected one or two sizes smaller. This shifts the weight ratio even further to the disadvantage of direct drives.

**Moment of inertia **

The moment of inertia and acceleration characteristics are regarded as the key advantages of direct drives. Generally, the following applies for the moment of inertia of solid cylinders (S and K types):

EQN 10 HERE

and of hollow cylinders (R type):

EQN 11 HERE

As the output shaft of the geared motor can either be a solid shaft or hollow shaft, the same moment of inertia is assumed for the shafts of these drive types. Only the ring torque motor (R type) is considered separately.

The ratio of the moments of inertia of the direct drives to that of the geared motor can be given as follows:

For the S type:

EQN 12 HERE

For the K type:

EQN 13 HERE

For the R type:

EQN 14 HERE

Equations 12 to 14 are based on a comparison of the motors without considering the inertia of the gear unit. The moment of inertia at the gear unit shaft can be determined with the square of the reduction ratio: *J _{2,G} *=

Theoretically, the moment of inertia of the gear unit itself (gears and shafts) must be added to this. This is not necessary in practice as the smaller diameters and lower speed of the gears result in an inertia which is only a few per mill of the motor inertia.

Fig. 5 shows a comparison of the moments of inertia at the motor and output shafts.

It might be surprising that both the moment of inertia of the short and thick direct drive (S type) as well as that of the ring motor (R type) are higher than that of a comparable geared motor.

Only the compact direct drive (K type) has a lower inertia than the geared motor, but the difference is not pronounced (at *i* = 7 the direct drive has about half as much moment of inertia than the geared motor).

The conclusion would be to design motors for small moments of inertia as slender as possible, that is l / *D *= L > 1, but this contradicts with demands placed on high torque direct drives, where large diameters are used for high torque ratings.

Only a few variants of the ring torque motor (manufacturer A) achieve a moment of inertia as low as that of a comparable geared motor.

**Acceleration capacity**

The factor of inertia *FI* describes the ratio of the overall inertia (external load plus rotor) to the rotor inertia alone:

EQN 15 HERE

*FI* =1 means that there is no external inertia, *FI* = 2 means that internal and external inertia are the same, and *FI* > 2 means that the external inertia predominates.

With the general equation for the acceleration capacity of the geared motor,

EQN 16 HERE

and that of the direct drive,

EQN 17 HERE

the specific acceleration capacity is calculated as follows:

EQN 18 HERE

It is assumed that the overload factors of the geared motor and the direct drive are equal. This is true as long as the same motor technology is used.

The graphs of the acceleration capacity (see Fig. 6) are similar to that of the moment of inertia (see Fig. 5). Only if the direct drive has a relatively slender design can it outperform the geared motor (K type) in terms of acceleration.

Short, thick direct drives (S type) accelerate more slowly than geared motors do. A ring-shaped rotor (R type) can improve this, but cannot reverse the ratio completely.

In general, the acceleration capacity of the direct drives is below that of servo geared motors of the same torque. The few exceptions are only marginal improvements without practical significance.

**Losses and efficiency**

The current flowing through the stator winding causes copper losses (*IÂ²R*). As the electromagnetic use and pole pitch are kept constant for this analysis, the losses only change with resistance, which in turn increases linearly with the core length and the number of poles, that is with the diameter.

Synchronous motors offer an advantage as they have no windings and therefore no copper losses in the rotor.

The magnetic losses caused by eddy currents also increase linearly with the rotor surface (i.e. the number of magnets).

Core losses depend on volume and frequency. They practically occur in the stator only. There is a quadratic dependency on the frequency for eddy current losses and a linear dependency for hysteresis losses. As both have about the same magnitude in practice, the dependency on the frequency can be estimated across the board with the exponent 1,5.

Stator fan losses are not significant for the speeds used here and are disregarded.

Friction is determined by bearings and seals; it depends linearly on the speed and the rotor weight.

Additional friction losses in the gear unit must be considered separately. The overall efficiency of planetary gear units is normally 98% or better, which means that these losses are hardly relevant. The efficiency of helical gear units is 96%.

Additional losses are another element. These depend mainly on the air gap surface, similar to the copper losses in this scenario (same utilisation).

For the relative losses of the three design variants of direct drives, the following set of formulas applies:

EQN 19 HERE

The relative proportions of the individual losses are required to determine the sum of all losses. They vary with motor size and the functional principle of the motor (asynchronous or synchronous) (see Fig. 7).

In practice, the relative overall losses are hardly different, so that Fig. 8 applies both to synchronous and asynchronous machines.

As long as the direct drive and the geared motor are operated on the same frequency (types S and R), their motor losses are almost equal. The direct drive does not entail gear unit losses but, as the efficiency of a high-quality gear unit is about 97% or better, these losses are hardly relevant.

Losses increase dramatically as soon as the direct drive is supplied with a lower frequency to achieve the required low speeds (K type), compared to the geared motor. Halving the frequency (in the diagram: K type with* i* = 2,8) means 50% more losses.

**Conclusion **

In conveying technology, a domain of classical geared motors, the required reduction ratios are usually i > 30. The speed is therefore very low and for direct drives practically unachievable; more than *i *= 10 is hardly possible. Servo drive technology often uses smaller reduction ratios, the focus is on roughly *i *= 5…10. Here, direct drives are an alternative that is worth thinking about. The same applies for large pump and fan drives in principle.

The results of this analysis illustrate the dilemma of direct drive design. On the one hand, small inertia and a good acceleration capacity are desirable (K type direct drive). This makes a slender design necessary, which means that the geared motor outperforms the direct drive in terms of weight, price, installation space and losses/efficiency.

If, on the other hand, weight and installation space are the decisive design factors, the result will be a short design direct drive with a large diameter (S type direct drive).

However, both the theoretical considerations and a practical comparison of two direct drive series of well known manufacturers with comparable geared servo motors show that even short direct drives are inferior to the geared motor in terms of weight and volume, while they are marginally superior at best in terms of losses and motor efficiency.

The ring-shaped assembly kit motor (R type) is also subject to these constraints. This drive is unbeatable in terms of compactness wherever round objects with large diameters must be moved.

However, its weight is not generally lower than that of a geared motor, and its efficiency is only marginally higher, if at all. Contrary to common belief, the moment of inertia of ring torque motors is usually worse and the acceleration capacity is the same or even slightly lower than that of geared motors based on the same motor technology and fitted with high-quality gear units.

Added to this is the integration effort at the OEM (bearing arrangement, encoder mounting, sealing, …), the unanswered question of system responsibility and service disadvantages (disassembly/replacement).

Direct drives are useful wherever gear units are forbidden for special reasons. For example as drives for machine tools, where highest positioning and repetition accuracy without backlash is required or in applications on which great demands are placed in terms of service life and minimized maintenance (offshore wind parks, underwater pumps). Direct drives are also useful in applications where the transition between motor operation and regenerative operation must be realized with as small torque step changes as possible (printing rollers). In applications with special noise requirements, e.g. in TV studios or theaters, direct drives can also play their strength.

The special design of direct drives offers constructional advantages in a few other areas. The shaft-integrated elevator motor is a well-known example.

However, it is highly unlikely that direct drives will replace gear units across the board in slow-running standard applications in the future.

**References**

[1] K. Greubel, A. Storath: “Torquemotoren versus Getriebemotoren – ein technischer Vergleich hinsichtlich Beschleunigung und Energieeffizienz”, Internationaler ETG-Kongress 2007, Karlsruhe, Germany, 24 October 2007.

Contact René Rose, SEW Eurodrive, Tel ???, rrose@sew.co.za