A
B
C
D 12
34
walking principle different waveforms
phase shifted signals for an exemplary waveform
arrangement of the 4 phases in the legs
A B C D
U
t 0 1
0 0 0
2 3 4
pair 1 pair 2
Figure 19: Drive principle of walking piezoelectric motors. One walking cycle is shown for an exemplary sine-shaped driving waveform.
The drive signal consists of four phase-shifted electrical phases (numbered1-4). The phases are connected to the legs as shown in the encircled region. The four legs are arranged in two pairs, each pair receiving the same driving signals (e.g. first and third leg from the left). The capital letters next to the walking stages correspond to the sampling time of the drive signal. Darker shad-ing indicates higher drive voltage, arrows indicate the direction of motion of leg tips and of the slider.
In a walking cycle, the legs alternately establish contact to a movable slider which is pressed against them with some kind of preload (see next section). The contact to the slider is maintained by those legs which are most extended and while in contact, these legs advance the slider in the direction of their bending motion due to friction. This alternating contact sequence is a necessary condition for the walking principle to work (cf. sect.3.4.1). It follows that at least two legs are required in a walking type motor. However, in order to ensure static stability of the slider, it has to be supported at least at two different points along its length at any given time. For this reason, four legs in two pairs are employed in practical designs; also in the PiezoLegs motor considered in this work. Each leg in a pair receives the same control signals – two signals per leg for each of the longitudinal mode actuators. Thus, a four phase signal is necessary to drive the motor consisting of two pairs of legs.14 The higher the driving signal (i.e.
voltage) the higher the electric field and consequently the elongation of a given actuator. In the walking sequence of Fig.19, an exemplary sine-shaped four phase drive signal is used. There is a 90◦ phase shift between phase 1 and 2. Phase3 and 4 are phase shifted 180◦ with
14A pair, or an m-tuple, can consist of m legs in a theoretical design of the walking motor. This fact is accounted for in the general motor modeling strategy of chapt.3.
regard to phase1and2, respectively. The effect is as follows. At the time point marked with an A , phases1and4are relatively low while phases2and 4relatively high. Thus all legs are bent – pair1 to the left and pair 2 to the right. Pair2 is at the moment slightly higher than pair1 and thus maintains contact to the slider which has been forwarded by its bending motion to the right. In the next step, B , pair2contracts while pair1has taken over the contact to the slider and advances it while bending to the right. At time point C , pair1 reaches its maximal bending to the right while pair2being now bent to the left expands to take over the contact to the slider. Finally, in D , pair1has retracted and pair2being now in frictional contact with the slider moves it to the right. The next time step in this sequence would again be A completing one walking cycle. During this cycle, the slider has been all the time advanced to the right. In order to change the direction of motion phase1would need to be swapped with phase 2and phase3with phase4or the sequence A - D be reversed. In any case, in order for the motor to move in a given direction both pairs of legs need to move most of the time in the same direction while contacting the slider. The non-contact times are used to reposition the legs before contacting the slider again. This requirement together with the alternating leg contacts to the slider provides the basic rules of the walking principle.
Besides the sine-shaped driving signals (waveforms), other peri-odic waveforms as well as phase relations between them are conceiv-able [145,146] and employed in order to optimize particular aspects of motor performance (e.g. speed, maximal stall force, etc.). By using different waveforms, important insights into the internal workings of the motor can be gained. In the following chapter (chapt.3), the forcewaveform, which improves the stall force characteristics of the motor, will be used additionally to thesinewaveform. This will prove useful in identifying a nonlinearity in leg deflection characteristics (sect.3.3.3). It will be also shown that in reality there are overlap-ping contact times between both pairs of the legs and the slider and how these contact times are influenced by the choice of a particular waveform (sect.3.4.1). Finally, in chapt.5, a bio-inspired waveform generation strategy is proposed. In simulation, this strategy proves to be superior to any particular fixed periodic waveform. Its practical application would require an independent control over each of the four legs as opposite to the pairwise control. Before proceeding to the chapters concerned with motor modeling and waveform generation, the last section of this chapter provides details on motor construction and leg fabrication process.
1 2
6 7 8 9
3 4 5
1
4 5 7
6
9
8 3
2 10
11
Figure 20: Computer rendering of the walking piezo motor (PiezoLegs).
The motor consists of only a few parts which are numbered and displayed in separate boxes. Inside of the lower housing (1) the drive unit (2) with four piezoelectric leg elements (10) is placed.
Each leg has a wear-resistant cap made of aluminum oxide on its top face (11). The description of all parts can be found in the running text.
2.4.2 Walking motor construction
The different drive strategies used in piezoelectric motors including the walking principle can be understood easily. The actual construction of a device utilizing these principle is a more demanding technological challenge. On overview of this process is sketched below.
The commercially available walking piezo motor PiezoLegs considered here is produced by the Swedish company PiezoMotor Uppsala AB.
Similar motors are offered by the German company Physik Instru-mente GmbH. The motor consists of only a few parts which are shown in Fig.20. Inside of a steel lower housing marked with 1 there is a drive unit 2 consisting of four leg elements made of a soft-type PZT.
Each leg is a piezoceramic multilayer bimorph 10 covered with a wear-resistant aluminum oxide cap 11. Backfaces of the legs are coated with electrodes and soldered to a flexible printed circuit board (flex circuit, PCB) 9 on which a5-pin socket 8 (JST SH BM05B-SRSS TB) is mounted. The socket is the interface to the driving circuitry (see chapt.6) which provides the legs with a4-phase signal and a common ground. A 50 mm long ceramic bar 3 (drive rod, slider) is placed on top of the legs and pressed against them by means of two roller bearings 5 whose outer ring can roll freely on the slider. The inner ring is elongated and supported by the upper steel housing 4 . The
upper and lower parts of the motor housing are screwed together with M1.6hexagon cap or torque screws 7 . The preload force required to press the slider against the legs is generated by a stack of cross-shaped leaf springs 6 . The central part of the springs has a whole in it and is screwed to the upper housing while the arms of the springs lay on the elongated parts of the bearings pressing them against the slider.
The preload level can be adjusted with the central screw.
Especially interesting from the technological point of view is the fabrication process of the drive elements (legs). According to the classification from sect.2.3.1, the drive elements are composite actu-ators because they are both multilayer and bending mode actuactu-ators.
Multilayer structure is chosen in order to increase the displacement and decrease the driving voltage at cost of a higher current and lower structural rigidity. There are two basic techniques for the fabrication of a multilayer structure –cut-and-bondandtape-castingmethod [209,208] which is also used for multilayer capacitors. In the first method, mul-tiple polished ceramic discs are prepared and stacked together with metal foils in-between the layers serving as electric leads. The minimal layer thickness in this method is limited to about 1 mm and thus it is not suited for small-sized, low-voltage actuators.15 In the second method, ceramic green sheets with printed electrodes are prepared, laminated and co-fired with internal electrodes.16,17 Much thinner layers below 100µm and lower driving voltages are possible with this method. A variation of the tape-casting method [185,186] is used to produce the drive elements of the walking motor. Several steps which the method consists of are described in detail in appendixA.
This chapter provided the reader with the basic knowledge about the piezoelectric technology in general and the construction as well as the working principle of the walking piezoelectric motor in particular.
The next chapter opens the main part of this work concerned with modeling of the walking motor.
15A multilayer actuator with90 1mm layers would have to be 9cm long and would generate ten times smaller displacement in relation to its length for the same amount of applied voltage as compared to a9mm long actuator consisting of 90 100µm thick layers.
16“Green” refers to the approximate color of the ceramic slurry, i.e. a mixture of ceramic powder and organic binders, formed in the shape of a flat sheet by a forming machine.
17Co-firing refers to the fact that electrodes can be applied already to the green material and sintered in one step. A prerequisite for this process is a ceramic material which can be sintered at relatively low temperatures below the melting point of the electrodes.
3 P H Y S I C A L M O D E L O F M O T O R D Y N A M I C S
abstract
In this chapter a novel dynamic model of a contemporary linear piezoelectric motor is presented. The model is based on physically meaningful parameters and macroscopically measured data in fully assembled state. The model describes the frictional interaction between multiple piezoelectric legs and a ceramic rod. It consists of two orthogonal dynamics which are coupled together by means of preload and frictional forces. Linearity of the model is maintained through most of the modeling stages with clear indication of nonlinear effects due to hysteresis, friction and impact dynamics of the legs. Unknown model parameters are estimated within a global optimization procedure and bounds on parameter values are indicated. The presented model explains the linear drive frequency/velocity as well as the nonlinear load force/velocity characteristics of the motor within its full operational range. The insights gained throughout the modeling process indicate the possibilities of design improvements. Moreover, the model is able to explain the resonance phenomena limiting the range of motor operation and is used to develop an alternative drive strategy in chapt.5. The content of this chapter is based on publicationI.