## Workings of a Brush DC Motor

### BRUSHED DC MOTOR BASICS

Portescap's Brush DC technology originates from a design based on an ironless rotor (self-supporting coil) combined with a precious metal or carbon copper commutation system and a rare earth or Alnico magnet. It offers distinct advantages for high-performance drive and servo systems: low friction, low starting voltage, absence of iron losses, high efficiency, good thermal dissipation, linear torque-speed function. All these factors facilitate use and simplify the servo loop. For incremental motion systems where the low rotor inertia allows for exceptional acceleration, and for all battery-powered equipment where efficiency is a major concern, brush DC motors offer optimum solutions.

#### DC Motor Diagram

### BRUSHED MOTOR DESIGN - THE THREE MAIN SUB-ASSEMBLIES

All DC motors are composed of three main sub-assemblies:

- the stator
- the brush holder end cap
- the rotor

**1. Stator**

The stator consists of the central and cylindrical two-pole permanent magnet, the core that supports the bearings, and the steel tube that closes the magnetic circuit. High-quality rare earth magnets ensure outstanding performance in a small envelope. Sintered bearings and ball bearings are available depending on your application loads and requirements.

**2. Brush holder endcap**

The brush holder endcap is made of a plastic material. Depending on the intended use of the motor, the brush could be of two different types; carbon or multi-wire. Carbon types use copper graphite or silver graphite and perfectly suit incremental motion applications where high continuous and peak torque are required. Multi-wire type uses precious metal and will guarantee low starting voltage and improved efficiency, a perfect match for portable battery-powered applications. Portescap's engineer can design endcaps that reduce electromagnetic noise to meet EMC requirements.

**3. Rotor**

The rotor is the heart of Portescap's DC motor. The coil is directly and continuously wound onto a cylindrical support that is later removed, eliminating excessive air gaps and inactive coil heads that bring no contribution to the torque creation. The self-supporting coil does not require an iron structure and therefore offers low moment of inertia and no cogging (the rotor will stop in any position). Unlike other conventional DC coil technologies, due to the absence of iron there are no hysteresis, eddy current losses or magnetic saturation. The motor has a perfectly linear speed-torque behavior and the running speed depends only on supply voltage and load torque. Portescap, through its proprietary know-how, has developed multiple automated winding machines for different frame sizes and continues to innovate on the winding method to increase power output.

The brushes/collectors combination is optimized to withstand a long operational lifetime at up to 12,000 rpm and provide high reliability. Portescap DC products can deliver a torque range from 0.6 mNm up to 150 mNm continuously and from 2.5 mNm up to 600 mNm in intermittent operation.

### PORTESCAP BRUSHED MOTOR DESIGN FEATURES: IRONLESS ROTOR DC MOTORS

The rotor of a conventional iron core DC motor is made of copper wire which is wound around the poles of its iron core. Designing the rotor in this manner has the following results:

- A large inertia due to the iron mass which impedes rapid starts and stops
- A cogging effect and rotor preferential positions caused by the attraction of the iron poles to the permanent magnet.
- A considerable coil inductance producing arcing during commutation. This arcing is responsible on one hand for an electrical noise, and on the other hand for the severe electro—erosion of the brushes. It is for the latter reason that carbon type brushes are used in the conventional motors.
- Ironless Rotor Coil Enables High Acceleration

A self supporting ironless DC motor from Portescap has many advantages over conventional iron core motors:

- high torque to — inertia ratio
- absence of preferred rotor positions
- very low torque and back EMF variation with armature positions
- essentially zero hysteresis and eddy current losses
- negligible electrical time constant
- almost no risk of demagnetization, thus fast acceleration
- negligible voltage drop at the brushes (with multi wire type brushes)
- lower viscous damping
- linear characteristics

### Portescap REE System proven to increase motor life up to 1000 percent

The two biggest contributors to the commutator life in a brush DC motor are the mechanical brush wear from sliding contacts and the erosion of the electrodes due to electrical arcing. The superior surface finish, commutator precision along with material upgrades such as precious metal commutators with appropriate alloys has helped in reducing the mechanical wear of the brushes. To effectively reduce electro erosion in while extending commutator life Portescap innovated its proprietary REE (Reduced Electro Erosion) system of coils. The REE system reduces the effective inductivity of the brush commutation by optimization of the mutual induction of the coil segments. In order to compare and contrast the benefits of an REE system Portescap conducted tests on motors with and without REE coil optimization. The commutator surface wear showed improvements ranging from 100 -300 percent as shown in Figure 5. Coils 4, 5 and 6 are REE reinforced while 1, 2 & 3 are without REE reinforcement.

### BRUSHED MOTOR THEORY - IRONLESS ROTORS

The electromechanical properties of motors with ironless rotors can be described by means of the following equations:

1. The power supply voltage U0 is equal to the sum of the voltage drop produced by the current I in the ohmic resistance RM of the rotor winding, and the voltage Ui induced in the rotor:

U0 = I x RM + Ui (1)

2. The voltage Ui induced in the rotor is proportional to the angular velocity ω of the rotor: Ui = kE x ω (2)

It should be noted that the following relationship exists between the angular velocity ωexpress in radians per second and the speed of rotation n express in revolutions per minute: ω = (2π n)/60

3. The rotor torque M is proportional to the rotor current I:

M = kT x I (3)

It may be mentioned here that the rotor torque M is equal to the sum of the load torque ML supplied by the motor and the friction torque Mf of the motor:

M = ML + Mf

By substituting the fundamental equations (2) and (3) into (1), we obtain the characteristics of torque/angular velocity for the dc motor with an ironless rotor:

U0 = M x RM + kE x ω (4)

By calculating the constant kE and kT from the dimensions of the motor, the number of turns per winding, the number of windings, the diameter of the rotor and the magnetic field in the air gap, we find for the direct-current micromotor with an ironless rotor:

M/I = Ui /ω = k (5)

Which means that k = kE = kT

The identity kE = kT is also apparent from the following energetic considerations:

The electric power Pe = U0 x I which is supplied to the motor must be equal to the sum of the mechanical power Pm = M x ω produced by the rotor and the dissipated power (according to Joule’s law) Pv = I2 x RM:

Pe = U0 x I = M x ω + I2 x RM = Pm + Pv

Moreover, by multiplying equation (1) by I, we also obtain a formula for the electric power Pe :

Pe = U0 x I = I2 x RM + Ui x I

The equivalence of the two equations gives M x ω = Ui x I or Ui /ω = M/I and kE = kT = k

Quod erat demonstrandum. Using the above relationships, we may write the fundamental equations (1) and (2) as follows:

U0 = I x RM + k x ω (6)

and:

U0 = M x RM/ + k x ω (7)

Graphic express “speed-torque” characteristic:

To overcome the friction torque Mf due to the friction of the brushes and bearings, the motor consumes a no-load current I0. This gives

Mf = k x I0

and:

U0 = I0 x RM + k x ω0 where

ω0 = 2π/60 x n0 hence:

k = U0 - I0 /ω0 x RM (8)

Is it therefore perfectly possible to calculate the motor constant k with the no-load speed n0, the no-load current I0 and the rotor resistance RM.

The starting-current Id is calculated as follows:

Id = U0 /RM

It must be remembered that the RM depends to a great extent on the temperature; in other words, the resistance of the rotor increases with the heating of the motor due to the dissipated power (Joule’s law):

RM = RM0 (1 + γ x ∆T)

Where γ is the temperature coefficient of copper (γ = 0.004/°C).

As the copper mass of the coils is comparatively small, it heats very quickly through the effect of the rotor current, particularly in the event of slow or repeated starting. The torque Md produced by the starting-current Id is obtained as follows:
Md = Id x k - Mf = (Id - I0 )k (9)

By applying equation (1), we can calculate the angular velocity ω produced under a voltage U0 with a load torque Mi. We first determine the current required for obtaining the torque M = ML + Mf :

I = (ML + Mf)/k Since Mf /k = I0 we may also write

I = (ML /k)+ I0 (10)

For the angular velocity ω, we obtain the relationship

ω = (U0 − I x RM )/k (11)

= U0 /k − RM /k2 (ML + Mf )

In which the temperature dependence of the rotor resistance RM must again be considered; in other words, the value of RM at the working temperature of the rotor must be calculated. On the other hand, with the equation (6), we can calculate the current I and the load torque ML for a given angular velocity ω and a given voltage U0:

I = (U0 − k x ω)RM = Id − k/RM ω (12)

And with equation (10)

ML = (I − I0 )k

We get the value of ML:

ML = (I − I0 )k − k2/RM ω

The problem which most often arises is that of determining the power supply voltage U0 required for obtaining a speed of rotation n for a given load torque ML (angular velocity ω = n x 2π/60). By introducing equation (10) into (6) we obtain:

U0 = (ML + I0)/k RM + k x ω (13)

**Practical examples of calculations
**

Please note that the International System of Units (S.I.) is used throughout.

1. Let us suppose that, for a Portescap® motor 23D21-216E, we wish to calculate the motor constant k, the starting current Id and the starting torque Md at a rotor temperature of 40°C. With a power supply voltage of 12V, the no-load speed is n0 is 4900 rpm (ω0 = 513 rad/s), the no-load current I0 = 12 mA and the resistance RM0 = 9.5 Ω at 22°C.

By introducing the values ω0 , I0 , RM0 and U0 into the equation (8), we obtain the motor constant k for the motor 23D21-216E: k = 12 − 0.012 x 9.5 = 0.0232 Vs 15

Before calculating the starting-current, we must calculate the rotor resistance at 40°C. With ∆T = 18°C and RM0 = 9.5Ω, we obtain RM = (1 + 0.004 x 18) = 9.5 x 1.07 = 10.2Ω

The starting-current Id at a rotor temperature of 40°C becomes

Id = (U0/RM) = (12/10.2) = 1.18A

and the starting-torque Md , according to equation (9), is Md = k(Id − I0) = 0.0232 (1.18 − 0.012) = 0.027 Nm

2. Let us ask the following question: what is the speed of rotation n attained by the motor with a load torque of 0.008 Nm and a power supply voltage of 9V at a rotor temperature of 40°C?

Using equation (10) we first calculate the current which is supplied to the motor under these conditions:

I = (ML /k)+ I0 = (0.008/0.0232) + 0.012 = 0.357A

Equation (11) gives the angular velocity ω:

ω = (U0 − I x RM )/k = (9 − 0.357 x 10.2)/0.0232 = 231 rad/s

and the speed of rotation n: n = 60/2π ω = 2200 rpm

Thus the motor reaches a speed of 2200 rpm and draws a current of 357 mA.

3. Let us now calculate the torque M at a given speed of rotation n of 3000 rpm (ω = 314 rad/s) and a power supply voltage U0 of 15V; equation (12) gives the value of the current:

I = (U0 − k x ω)/RM = Id − k/RM x ω

= 1.18 − (0.0232/10.2) x 314 = 0.466A

and the torque load ML:

ML = k(I − I0)

= 0.0232 (0.466 − 0.012)

= 0.0105 Nm

(ML = 10.5 mNm)

4. Lastly, let us determine the power supply voltage U0 required for obtaining a speed rotation n of 4000 rpm (ω = 419 rad/s) with a load torque of ML of 0.008 Nm, the rotor temperature again being 40°C (RM = 10.2Ω).

As we have already calculated, the current I necessary for a torque of 0.008 Nm is 0.357 A

U0 = I x RM + k x ω

= 0.357 x 10.2 + 0.0232 x 419

= 13.4 volt

### BRUSHED MOTOR APPLICATIONS

**MEDICAL
**

- Powered surgical instruments
- Dental hand tools
- Infusion, Volumetric & Insulin Pumps
- Diagnostic & scanning equipment

Benefits: Reduced footprint analyzers with high efficiency & precision sample positioning

**SECURITY & ACCESS**

- Security cameras
- Locks
- Bar code readers
- Paging systems

Benefits: Low Noise & Vibration, High Power & Superior Efficiency

**AEROSPACE & DEFENSE**

- Cockpit gauge
- Indicators
- Satellites
- Optical scanners

Benefits: Low Inertia, Compactness and Weight, High Efficiency

**ROBOTICS & FACTORY AUTOMATION**

- Conveyors
- Remote controlled vehicles
- Industrial robots

Benefits: High Power & Low Weight

**POWER HAND TOOLS**

Shears Pruning hand tools Nail guns

Benefits: High Efficiency, Compactness and Weight, Low Noise

**OTHER**

Office equipment Semiconductors Model railways Document handling Optics Automotive Transportation Audio & video

Benefits: Low Noise, High Power, Better Motor Regulation

#### Application spotlight

**MEDICAL ANALYZERS** Portescap solves multiple application needs in analyzers, from sample draw on assays to rapid scanning and detection of molecular mechanisms in liquids and gases, with its coreless brush dc motors. For high throughput applications—those where over 1,000 assays are analyzed in an hour—high efficiency and higher speed motors such as brush DC coreless motors are a suitable choice. Their low rotor inertia along with short mechanical time constant makes them ideally suited for such applications. As an example, a Portescap 22-mm motor brush coreless DC motor offers no-load speed of 8,000 rpm and a mechanical time constant of 6.8 milliseconds. Another analyzer function that plays a vital role in their output is collecting samples from the vials or assays, and serving them up to measurement systems based on photometry, chromatography, or other appropriate schemes. Here again, a brush DC coreless motor is highly applicable due to the power density it packs in a small frame size. You can maximize your application’s productivity with a 16 or 22mm workhorse from Portescap.

#### Application spotlight

**INFUSION PUMPS** Coreless brush DC motors offer significant advantages over their iron core brush counterparts for some of the critical care pump applications where, the benefits range from improved efficiency to higher power density, in a smaller frame size. One of the factors that deteriorates motor performance over long term usage is the heating of the motor with associated Joule loss. In motor terminology this is governed by the motor regulation factor determined by the coil resistance, R, and the torque constant, k. The lower the motor regulation factor (R/k2 ) the better would the motor perform over its life while sustaining higher efficiencies. With some of the lowest motor regulation factors Portescap’s latest innovation in Athlonix motors is already benefiting applications in the infusion pump space by offering a choice of a higher performance motor with less heat loss, higher efficiency and power density in compact packages.

#### Application spotlight

**ELECTRONICS ASSEMBLY SURFACE MOUNT EQUIPMENT **How Portescap’s versatile 35mm coreless motors with carbon brush commutation excel in electronic assembly, robotics and automated machinery equipment and have been a workhorse in some of the pick and place machinery used in surface mount technology. Our 35mm low inertia motors can provide high acceleration, low electromagnetic interference, and frequent start stops that the machines need while maintaining smaller and lightweight envelopes.

#### ADDITIONAL INFORMATION

Rotor Assembly

Brush DC motor cutaway