Conference Paper · October 013 doi: 10. 1109/cobep. 2013. 6785223 citations reads 2,638 authors

¼. The performance parameters from the experimental 
results were found to be reasonable and within expected. 
The system presented in this paper is part of a CNC 
routing system. 
 
Keywords – Hybrid Stepper Motor, Motor Drive, 
Computer Numerical Control. 
I.
INTRODUCTION 
Stepper motors are a particular variation of variable 
reluctance machines and are designed to achieve higher 
compatibility and ease of use when interfacing with digital 
electronics systems. Its mechanical design has a main 
purpose: achieve a high positioning resolution. Both stator 
and rotor are built with a castle like structure, with tooth 
along their circumference and the final resolution of the 
system is proportional to this number of tooth. General 
purpose stepper motors are rated with resolutions as low as 
0.9 ˚. Precision, high end stepper motors are able to achieve 
up to 0.05 ˚. Increasing the resolution by means of 
mechanical design only also increases drastically the final 
cost of the machine. It is worth noting that stepper motors' 
weight and power ratio is high, from where arises a 
maximum achievable power as well. 
Due to its conception, stepper motors are one of the most 
employed mechanical drivers for positioning systems in 
various systems. Its application varies from low power 
systems, where only a few tenths of watts are necessary, to 
more power demanding systems, from a few watts to up to 
hundred of watts are needed. On low power systems, such as 
hard disk drives, CD, DVD and BD units, and ink-jet printer, 
these motors perform flawlessly and its application probably 
will not fade on next decades, because of the ease of 
development and use. 
Concerning to more power demanding applications, 
stepper motors are also employed on productive units, 
ranging from desktop, low productivity, units to industrial, 
entry level, units. On these systems, stepper motors have 
more issues on performing as well, due to issues that are not 
easy to address when using low-end electronics. Problems 
such as low-speed and high speed performance discrepancies 
and electro-mechanical resonance usually arises when 
dealing with higher power systems. 
The academic community put some effort towards better 
driving techniques to overcome these issues. On [1] and [2], 
it is explained a couple of modern and classic control 
techniques, based on Kalman Filters, Fuzzy control and 
Proportional-Integral, both being applied in a closed loop 
approach, based on high end electronics, i.e. FPGA. On [3], 
an open loop approach is presented, using micro step 
technique to reduce vibration - and, in consequence, 
resonance - and to enhance positioning precision. 
The purpose of this paper is to present a stepper motor 
drive system, which was applied for positioning control on a 
Computer Numerical Controlled router machine, which was 
briefly presented on [4] and [5]. This paper aims to provide 
basics insight on stepper motor driving technique and present 
the main elements of the developed system. 
II.
STEPPER MOTOR THEORY AND ITS DRIVERS 
Stepper motors are quite different from usual electrical 
machines. It can be regarded as a brushless DC motor, whose 
rotor rotates in discrete angular increments when its stators 
windings are programmatically energized [6]. The rotor has 
no electrical windings and can have: salient poles, relating to 
a variable reluctance machine; magnetized poles, relating to 
a permanent magnet DC motor; or can have both, in which 
case the motor is regarded as a hybrid stepper motor, being 
this the most common topology among the machines with 
higher power ratting. This work aims mostly at hybrid 
stepper motors and only this design will be regarded from 
now on. 
These motors are usually made of two or more stator 
windings, being more common two, four and five windings 
design. Each phase can be seen as a variable inductance, 

(), varying with the mechanical shaft angle, . This 
relation between 
 and 
() arises from the very conception 
of the motor. Figure 1 presents an example of the relation for 
a motor with the following characteristics: two phase, 90˚ per 
step, 
41  nominal inductance. 
As can be seen in Figure 1, the inductance of each phase 
has a periodic peeks in well-defined angular positions. That 
happens because the tooth of the stator align with tooth of 
rotor, hence, reducing the air gap and increasing accordingly 
the inductance. 

---

Figure 1 - Typical inductance profile plotted against 
, for 
each phase of a two phase stepper motor. 
It can be seen on Figure 1 that in no time the inductance 
falls to zero. Torque generated by such a motor is given by: 
=


2 ∙

()

(1)
where 
 is the current on the winding, 
(θ) is the inductance 
of the phase and 
 is the angular position of the shaft. 
Figure 2 presents the torque generated by the previously 
described stepper motor and such waveform is obtained by 
taking the derivative of inductance with respect to 
. It 
should be noted that magnetic saturation effect was not 
considered. 
Figure 2 - Typical torque exerted by a two phase stepper 
motor. 
The behavior seen in Figure 2 justifies why stepper motors 
are inherently used for position control: when a given 
winding is energized, the rotor aligns with the respective 
stator energized winding; if some external load torque tries to 
move the rotor from that position, an opposing torque will 
act in such a way to move back the rotor to the original rest 
position; if the load torque is higher than any opposing 
torque that the motor can generate, the shaft will enter an 
instability region and will move the rotor to another stable 
position. 
From Figures 1 and 2, it can be seen that stepper motors' 
resolution is related to its mechanical complexity, in a sense 
that the smaller distance between peeks for an inductance 
waveform, the higher will be its mechanical resolution. 
General purpose motors, with cylindrical rotor, the resolution 
can be as low as 0.9˚. Application specific motors, with disk 
rotor structure, resolution can be as low as 0.05˚. 
From that previous analysis, it can be observed that to 
control the position of a stepper motor, one only have to keep 
a constant current flowing through a stator winding. 
However, this position control is limited by three elements: 
its maximum torque driving capacity, known as holding 
torque; the number of phases a motor has; and the number of 
tooth that both stator and rotor have.