An implementation of class D inverter for ultrasonic transducer mixed powder mixture

Graphical abstract

An ultrasonic mixer that appeals to the field of powder metallurgy was designed by driving an ultrasonic transducer, which is negatively affected by changes in mechanical load or changes, by a high-frequency DC-AC converter. 2% graphene was added to the aluminum alloy in ethanol and mixed, and the mixture was obtained homogeneous. The superiority of the designed mixing method is supported by SEM (scanning electron microscope) images. Block diagram of the UT for Al powder and graphene.

Highlights

• •The most important innovation: In powder metallurgy, an ultrasonic matrix mixer is designed to form alloys with a homogeneous and stable structure.
• •A summary of the main result: The consistency of simulation and experimental results of the ultrasonic matrix mixer is demonstrated.
• •Impact and significance on the research area: An ultrasonic transducer was driven by a class D half-bridge resonant inverter. A new strategy for obtaining homogeneous mixtures has been developed.

Abstract

Ultrasonic transducers (UTs) are the main components for generating sonic waves. These types of transducers are nonlinear loads, and they are adversely affected by changes in mechanical load or temperature. UTs are operated in the region close to the resonant frequency. An ultrasonic transducer needs to be driven by a high-frequency inverter. In this paper, a Class D resonant inverter circuit is implemented for ultrasonic mixer application. The proposed circuit operates at 34306 Hz at 140 V and has low cost and size. The simulation results of Class D inverter verified with the prototype experimental circuit. Al (Aluminum) alloy with ethanol and graphene is mixed in order to show the mixing performance of the resonant inverter fed transducer with probe. The system achieved the fine particles and homogen mixture according to the SEM images and EDX analysis.

1. Introduction

Transducers with 5–10 µm vibration amplitude that convert electrical energy into ultrasonic waves are called Piezoceramic (PC) [1]. Soft ceramics stretch easily. Although they are resistant to high voltage and mechanical loads, hard ceramics have low current permeability. UTs operating below the resonant frequency act like capacitors. This type of operation causes the UT to heat up and the power conversion to weaken. The capacitance of PCs varies up to 200 % of the signal value depending on voltage amplitude, temperature, and mechanical load. The lowest impedance value of UTs is at resonance. At all other frequencies, the impedance rises rapidly. Additionally, choosing an excitation method other than a sinusoidal signal may cause PCs to be damaged, increase power consumption, crack, and shorten their lifespan [2], [3].

UTs are used extensively in ultrasonic welding for the assembly and bonding of different materials, ultrasonic cleaning for cleaning surgical instruments, glasses, and machine parts from bacteria and viruses, distance measurement, non-destructive testing, medical imaging, and sensor technologies [4], [5], [6].

The resonant converter is used to send a sinusoidal driver signal to the UTs. Power switches used in the converter are usually controlled by PWM (Pulse-width Modulation), Ps-PW (Phase shifted Pulse-width Modulation) or PDM (Pulse-density modulation) type driving signal [7]. Zero voltage switching (ZVS) technique and resonance frequency tracking methods are used to prevent losses and increase efficiency [8], [9], [10]. Various simulation and control studies have been carried out to reduce harmonics during the control of the power switches [11].

Composites using nanoparticles in their production have properties such as high strength and low thermal conductivity by adding various reinforcements. Proper distribution of nanoparticles in the matrix is very difficult and takes a long time with ball systems. In traditional systems, problems such as agglomeration and clustering are frequently encountered. Agglomerations in graphene and aluminum nano powders can cause cracks. Mixing the matrix and reinforcement powders homogeneously is very important in obtaining the desired properties. The combination of the electrical properties of aluminum with the thermal conductivity and lightness of graphene is used in a wide range of applications such as defense, aviation, spacecraft, and chip production [12], [13], [14].

In this study, it is aimed to examine and implement the design stages of an ultrasonic mixer with Class D resonant inverter to overcome the problems that arise during the mixing of alloys and reinforcements during the manufacturing process. Mathematical modeling of the design stages was made and tested in a simulation environment. Finally, thanks to the obtained data, the experimental setup was prepared and tested. Theoretical and simulation results have been experimentally verified.

2. Frequency response and equivalent circuit of ultrasonic transducer

In order to determine the equivalent circuit parameters of UT, resonance and anti-resonance frequencies must be known. One of the best ways to determine this is large signal impedance measurement. The large-signal impedance measurement scheme of UT is shown in Fig. 1. Large signal voltage-current measurements can be used to measure the impedance Zt, resonant frequency (fs) and anti-resonant frequency (fp). It will be sufficient to drive the UT with a 20 Vpp sine wave to measure the frequency response. Fig. 1 shows the large signal measurement scheme. The value of the resistor Rs should be sufficient (usually 50 Ω) to drop a small voltage across it [15].

Fig.1.

Large-signal impedance measurement scheme of UT.

The current flowing through the UT can be calculated using Eq. (1), while its impedance and angle can be calculated using Eqs. (2), (3). Where T is the measured period, t is the phase difference between the applied voltage and the measured resistor voltage. It is assumed that ∠a from the signal generator is 0[15].

$$\mathrm{I}=\frac{{\mathrm{U}}_2\angle \mathrm{\alpha }}{{\mathrm{R}}_{\mathrm{s}}}$$ (1)

$${\mathrm{Z}}_{\mathrm{t}}\angle -\mathrm{\alpha }=\frac{{\mathrm{U}}_1\angle 0-{\mathrm{U}}_2\angle \mathrm{\alpha }}{{\mathrm{U}}_2\angle \mathrm{\alpha }}\mathrm{x}{\mathrm{R}}_{\mathrm{s}}$$ (2)

$$\mathrm{\alpha }=\frac{\mathrm{t}}{\mathrm{T}}\mathrm{x}360$$ (3)

Test frequency is increased from 0 to 40 kHz by 10 Hz steps. The points where the impedance of the UT is pure resistance are the resonance and anti-resonance frequencies. Impedance values at ${\mathrm{\omega }}_{\mathrm{s}}$ and ${:\mathrm{\omega }}_{\mathrm{p}}$ are presented in Table 1. Table 2, Table 3.

Table 1.

Impedance Values.

Frequency (Hz)	Impedance (ohm)
${\mathrm{\omega }}_{\mathrm{s}}$ = 34460	${\mathit{Z}}_{\mathrm{w}\mathrm{s}}$ = 1 $\angle 0$
${\mathrm{\omega }}_{\mathrm{p}}$ = 34750	${\mathit{Z}}_{\mathrm{w}\mathrm{p}}$ = 36350 $\angle 0$

Table 2.

Equivalent circuit parameters obtained from Equations (4), (5), (6), (7).

Equivalent elements	Values
${\mathrm{R}}_{\mathrm{m}}$(Ω)	1
${\mathrm{C}}_{\mathrm{m}}$(nF)	2.553
${\mathrm{L}}_{\mathrm{m}}$(mH)	330
$C_e$(nF)	151.04
$C_q$(nF)	2.510

Table 3.

Simulation and Experimental results.

	Simulation	Experimental
${\mathrm{f}}_{\mathrm{s}}(\mathrm{H}\mathrm{z})$	34,460	34,306
${\mathrm{f}}_{\mathrm{p}}(\mathrm{H}\mathrm{z})$	34,750	34,510
${\mathrm{V}}_{\mathrm{a}\mathrm{b}}$(V)	140	169
i (mA)	165	132

Design studies and parameter extraction of UT can be done based on the Butterworth-Van Dyke (BVD) model. In the BVD equivalent circuit shown in Fig. 2, Rm, Lm and Cm refer to the mechanical losses, mass and flexibility of the UT, respectively. Ce is used to represent the static capacitance of the UT and the external coupling capacitances. Rm and Lm are dynamic and affected upwards by load and temperature [16].

Fig.2.

Unloaded piezoelectric ultrasonic transducer electrical equivalent circuit.

The resulting equations for the BVD equivalent circuit parameters are the following [16], [17].

$${\mathrm{C}}_e=\sqrt{\frac{{{\mathrm{Z}}_{\mathrm{w}\mathrm{s}}}^2\left({{\mathrm{\omega }}_{\mathrm{p}}}^2-{{\mathrm{\omega }}_{\mathrm{s}}}^2\right)+\sqrt{{\left({{2\mathrm{\omega }}_{\mathrm{p}}}^2{\mathrm{Z}}_{\mathrm{w}\mathrm{s}}{\mathrm{Z}}_{\mathrm{w}\mathrm{p}}\right)}^2+{{\mathrm{Z}}_{\mathrm{w}\mathrm{s}}}^4{\left({{\mathrm{\omega }}_{\mathrm{p}}}^2-{{\mathrm{\omega }}_{\mathrm{s}}}^2\right)}^2}}{2{\left({{\mathrm{\omega }}_{\mathrm{p}}}^2{\mathrm{Z}}_{\mathrm{w}\mathrm{s}}{\mathrm{Z}}_{\mathrm{w}\mathrm{p}}\right)}^2}}$$ (4)

$${\mathrm{R}}_{\mathrm{m}}=\sqrt{\frac{{{\mathrm{Z}}_{\mathrm{w}\mathrm{s}}}^2}{1-{\left({{\mathrm{C}}_0\mathrm{Z}}_{\mathrm{w}\mathrm{s}}{\mathrm{\omega }}_{\mathrm{s}}\right)}^2}}$$ (5)

$${\mathrm{C}}_{\mathrm{m}}={\mathrm{C}}_0\left[{\left(\frac{{\mathrm{\omega }}_{\mathrm{p}}}{{\mathrm{\omega }}_{\mathrm{s}}}\right)}^2-1\right]$$ (6)

$${\mathrm{L}}_{\mathrm{m}}=\frac{1}{{\mathrm{C}}_{\mathrm{m}}{{\mathrm{\omega }}_{\mathrm{s}}}^2}$$ (7)

where the values of the impedance magnitude measured in ${\mathrm{\omega }}_{\mathrm{s}}$ and ${\mathrm{\omega }}_{\mathrm{p}}$ are ${\mathrm{Z}}_{\mathrm{\omega }\mathrm{s}}$ and ${\mathrm{Z}}_{\mathrm{\omega }\mathrm{p}}$, respectively [16], [17].

UTs are capacitive elements and may operate under heavy loads. Driving capacitive loads requires high energy. UTs require a sinusoidal high voltage due to their capacitive impedance although they low resistance at the resonant frequency. PCs may damage as high current flows through them at resonant frequency during operation. For this reason, it would be appropriate to work near the resonance frequency [17].

3. Class D resonant inverter for ultrasonic transducer

UTs have a nonlinear and variable load characteristic. The operating time, temperature, and working areas cause to get different impedance values. In addition, the waves generated by powerful transducers are reflected, negatively affecting the transducer's impedance and the driving circuit's operation [18].

Fig. 3 shows an ultrasonic transducer and circuit diagram of the proposed UT system for Al powder and graphene with resonant inverter.

Fig.3.

Power circuit of the UT for Al powder and graphene.

The rectified AC voltage is filtered and applied to the Class D inverter. The driving signal with 50 % duty cycle is applied to the power switches. The high-frequency square wave voltage is converted into sinusoidal shape by the resonant circuit. High power ultrasounds are applied to the metal powder mixture over the horn.

Advantage of the Class D inverter is that it can be used in high voltage applications as the stress on the switches are low. Inverter can operate above or below resonance frequency. Since the load is capacitive, there is a phase difference less than zero between the load current and voltage. When switch S1 is in conduction, resonance current flows through the resonance circuit. Before switch S1 is closed and switch S2 is opened, current i flows through the antiparallel diode D1 of switch S1. When switch S2 turns on, diode D1 closes and the current of the resonant circuit is directed to S2. Under these operating conditions, diodes D1 and D2 close at high voltage. Operating above or below the resonant frequency will reduce the power delivered to the load [19]. Fig. 4 shows equivalent circuit of ultrasonic mixer. Here, ${\mathbf{Z}}_{\mathrm{t}}$ is the equivalent impedance of UT and ${\mathbf{Z}}_{\mathrm{a}\mathrm{b}}$ is the input impedance of the circuit.

Fig.4.

Equivalent circuit of ultrasonic mixer.

The circuit shown in Fig. 4 can be analyzed according to some assumptions given below [20], [21].

All circuit elements are ideal.

The quality factor of the resonant circuit is high enough to get sinusoidal current.

Using Eqs. (8), (9), series resonance frequency ${\omega }_s$ and parallel resonance frequency ${\omega }_p$ can be calculated. Where ${\mathrm{C}}_{\mathrm{e}\mathrm{q}}={(\mathrm{C}}_{\mathrm{e}}{\mathrm{C}}_{\mathrm{m}})/({\mathrm{C}}_{\mathrm{e}}+{\mathrm{C}}_{\mathrm{m}})$ [20], [21].

$${\mathrm{\omega }}_{\mathrm{s}}=\frac{1}{\sqrt{{\mathrm{L}}_{\mathrm{m}}{\mathrm{C}}_{\mathrm{m}}}}$$ (8)

$${\mathrm{\omega }}_{\mathrm{p}}=\frac{1}{\sqrt{{\mathrm{L}}_{\mathrm{m}}{\mathrm{C}}_{\mathrm{e}\mathrm{q}}}}$$ (9)

A quality factor (${\mathrm{Q}}_{\mathrm{L}}$) greater than 2.5 is required for the load current to be sinusoidal. The quality factor can be calculated by Eq. (10) [20], [21].

$${\mathrm{Q}}_{\mathrm{L}}=\frac{1}{{\mathrm{\omega }}_{\mathrm{s}}{\mathrm{C}}_{\mathrm{e}\mathrm{q}}\mathrm{R}}$$ (10)

The input impedance of the resonance circuit of the circuit shown in Fig. 5 is given in Eq.11 [20], [21].

$${\mathbf{Z}}_{\mathit{ab}}={\mathbf{Z}}_t+{\mathrm{j}\mathbf{Z}}_{\mathit{Ls}}$$ (11)

$${\mathbf{Z}}_{\mathit{ab}}={\mathrm{R}}_{\mathrm{e}}-j{\mathrm{X}}_{\mathrm{e}}+\mathrm{j}{\mathrm{\omega }}_{\mathrm{s}}{\mathrm{L}}_{\mathrm{s}}$$ (12)

The impedance of the BVD equivalent circuit can be calculated using Eq. (12). The parameters calculated with the help of equations are approximate to real values. The exact points of resonance and anti-resonance values are not known. Where ω values are assumed to be the points where the impedance is maximum and minimum [20], [21].

$${\mathbf{Z}}_{\mathrm{t}}=\frac{{(\mathrm{L}}_{\mathrm{m}}{\mathrm{C}}_{\mathrm{m}}{\omega }^2-1)-\mathrm{j}({\mathrm{L}}_{\mathrm{m}}{\mathrm{C}}_{\mathrm{m}}\mathrm{\omega })}{{({\mathrm{R}}_{\mathrm{m}}\mathrm{C}}_e{\mathrm{C}}_{\mathrm{m}}{\omega }^2)+\mathrm{j}[{{\mathrm{R}}_{\mathrm{m}}\mathrm{C}}_e{\mathrm{C}}_{\mathrm{m}}{\omega }^3-\mathrm{\omega }\left({\mathrm{C}}_0+{\mathrm{C}}_m\right)]}$$ (13)

$${\mathbf{Z}}_{\mathrm{t}}=\frac{{{\mathrm{R}}_{\mathrm{m}}}^2}{1+{{\mathrm{R}}_{\mathrm{m}}}^2{C_e}^2{\mathrm{\omega }}^2}-\mathrm{j}\frac{{{\mathrm{R}}_{\mathrm{m}}\mathrm{C}}_{\mathrm{e}}\omega }{1+{{\mathrm{R}}_{\mathrm{m}}}^2{C_e}^2{\mathrm{\omega }}^2}$$ (14)

$${\mathbf{Z}}_{\mathrm{t}}={\mathrm{R}}_{\mathrm{e}}-j{\mathrm{X}}_{\mathrm{e}}$$ (15)

Fig.5.

Simulation output waveforms A) resonance circuit voltage, B) resonant circuit current.

The design of Ls is designed so that the resonance frequency and switching frequency of PS are equal [20], [21].

An inductance (Ls) matching the imaginary part of the impedance is connected in series. For resonance to occur, the condition given in Eq.17 must be met [20], [21].

$${\mathrm{X}}_{\mathrm{L}}{=\mathrm{X}}_{\mathrm{e}}$$ (16)

$${\mathrm{L}}_{\mathrm{s}}=\frac{{{\mathrm{R}}_{\mathrm{m}}}^2{\mathrm{C}}_{\mathrm{e}}}{1+{{\mathrm{R}}_{\mathrm{m}}}^2{{\mathrm{C}}_{\mathrm{e}}}^2{\mathrm{\omega }}^2}$$ (17)

Eqs. (18) and (19), R represents the total impedance generated during the mixing process. The maximum current of the resonant circuit is given in Eq. (17) [20], [21].

$${\mathrm{I}}_{\mathrm{m}}=\frac{2{\mathrm{V}}_{\mathit{DC}}}{\mathrm{\pi }\mathrm{R}}$$ (18)

4. Simulation study

The 140 V DC source is used in the simulation. The filter inductor (Ls) is 150.11µH and is designed for 34306 Hz which is the resonant frequency of the UT with horn. The load is capacitive during operation. Due to the high variability of the load, the Ls inductor can be increased or by around 10–15 %. A phase difference occurs between the load current and voltage. During the mixing process, the total impedance is limited to 500 Ω due to the mechanical strength of heat, liquid, and metal powders. The value of the resonance current is 165 mA. Matlab simulation results of ultrasonic mixer system for inverter current and inverter voltage are presented in Fig. 5.

5. Experimental study

Fig. 6 shows the scheme of the proposed application. The circuit consists of a full bridge rectifier and a Class D resonant inverter. In the diagram, the measurement points for the 4-channel oscilloscope are CH1-CH4. Fig. 7 shows test set up of the ultrasonic transducer system for powder mixer.

Fig.6.

Proposed inverter with ultrasonic transducer equivalent circuit.

Fig.7.

Experimental setup.

Fig. 8 shows the waveforms obtained as a result of the experimental study. Non-ideal circuit elements cause differences in experimental and simulation results. The peak voltage and ultrasonic transducer current of the Vab point reach 169 V, 0.132A. During the experiments, the temperature of the solution was measured as 95 °C. The temperature of UT is 145 °C.

Fig.8.

Waveforms obtained as a result of the experimental study.

Working conditions are very effective on UTs. Non-linear circuit elements, jumps in temperature and switching transitions caused the I current to drop. The resonance and anti-resonance frequencies of the mechanical distribution have been changed.

6. Microstructural examination of produced composite powder

After the design and electronic process of the device was completed, its application in the field of powder metallurgy was examined. In this context, the aluminum alloy (Al7075) was chosen as the matrix material at the micron level (80–100 µm with 99.9 % purity). This matrix alloy includes 6 wt% Zn, 1.8 wt% Cu, 2.5 wt% Mg and remaining part Al. For the reinforcement, Graphene nanoplatelets (GNPs) with 99.9 % C content, 5–8 nm thickness and 750 m²/gr surface area were chosen as the reinforcement element. In this context, the aluminum alloy was chosen as the matrix material at the micron level. Graphene nanoparticles (GNP) were chosen as the reinforcement element. In the production of these types of nanocomposites with traditional methods, homogeneity, and agglomeration problems are experienced in terms of chemical composition as seen in Fig. 9A.

Fig.9.

Powder mixture (Al-GNPs) for A) traditional alloying, B) ultrasonic mixer.

For this purpose, in addition to traditional mechanical alloying, mixing methods in liquid-based solutions using magnetic and mechanical stirrers have been tried in recent years. However, these processes take a serious time to evaporate the solution from the system and generally more than 1 wt% reinforcement added composites cannot be fabricated easily [22], [23].

With the proposed system, the mixing process in the liquid is carried out much faster than traditional ball systems. The solution is rapidly evaporated with the heat generated as a result of the movement of the system, and as a result, a homogeneously mixed powder is obtained. In this study, 2 % by weight which can be considered high in powder metallurgy graphene was added to the aluminum alloy and the mixture was carried out in a small amount of ethanol. Microstructure image of this composite is presented in Fig. 9B. When Fig. 9A and 9B are examined, it is understood that the matrix-reinforcement powder becomes thinner and more homogeneous with the high impact applied by the ultrasonic mixer. It has been observed that in the mixing process carried out with traditional methods, the powder sizes and shapes are not homogeneous, and a good metallurgical bond may not be formed. While composites powder grain size is about 50 µm after the traditional method (ball milling), this value decreases to 15–20 µm when ultrasonic mixer developed in this study is applied.

In Fig. 10, a much larger image was taken and the: chemical composition:of the alloy was examined using the Energy Dispersive:X-ray (EDX) technique. As a result, when the analysis was performed in large powder grains (caused by being stuck to each other during the analysis) and small powder grains, values close to each other were found in the carbon ratio, and this revealed the stability of the chemical composition. When the structure is examined in general, it is observed that macro pores and defects do not occur, and it is seen that the production method does not cause any problems on the powders.

Fig.10.

EDX analysis of composites powder.

7. Conclusion

In this study, a ultrasonic transducer was used in the mixing process to constitute metal composites. The designed circuit was simulated in Matlab and showed great similarities with the experimental results. The system designed to drive the ultrasonic transducer has a minimum number of components. In this way, volume and cost have been reduced.

With the large-signal impedance measurement scheme of the ultrasonic transducer, the resonance frequency during no-load operation was determined as 34460 Hz and the anti-resonance frequency was determined as 34750 Hz. Due to the change in temperature and impedance values due to the nature of UT during mixing, the resonance frequency was 34306 Hz and the anti-resonance frequency was 34510 Hz. System is tested at 34306 Hz operating frequency at 140 V supply voltage. The maximum value of the ultrasonic transducer voltage is 169 V, its current is 0.13A. Operating the UT below its resonance frequency and increasing temperature negatively affected its impedance, causing the current to be lower than the theoretical and simulation values. Evaporation of ethanol is approximately 85 °C. The temperature of the solution was measured as 95 °C and the temperature of UT was 145 °C.

With the designed system, aluminum powder and graphene flakes were mixed in ethanol. Evaporation of ethanol is ensured by the temperature that occurred during mixing. A homogeneous mixture is obtained. More successful results were obtained than traditional systems. The results are presented comparatively with SEM images and EDX analysis.

Ultrasonic mixers have been used in various studies in the field of powder metallurgy, but for the first time, the design stages have been examined theoretically, simulation and experimentally for use in the relevant field. The driving circuit of the ultrasonic transducer is made with a Class D resonance inverter with a half-bridge topology, which enriches the ultrasonic mixer design path. In future studies, the effects of different transducer types and circuit topologies on obtaining a homogeneous mixture will be investigated.

Author Contribution Statements.

Name-Surname of the Authors	Affiliation details	Authors’ Contributions
1- Dr. Mehmet TAŞLIYOL (Corresponding Author)	Karabük University, Eskipazar Vocational School	-Contributed to the design and implementation of the research, to the analysis of the results and to the writing of the manuscript. -Discussed the results and commented on the manuscript. -Aided in interpreting the results and worked on the manuscript. -Developed the theoretical framework. -Processed the experimental data, performed the analysis, drafted the manuscript, and designed the figures. -Made the simulations. -Provided critical feedback and helped shape the research, analysis, and manuscript.
2- Prof. Dr. Selim ÖNCÜ	Karabük University, Faculty of Engineering	-Discussed the results and commented on the manuscript. -Aided in interpreting the results and worked on the manuscript. -Involved in planning and supervised the work. -Provided critical feedback and helped shape the research, analysis, and manuscript.
3- Associate Prof. Muhammet Emre TURAN	Karabük University, Eskipazar Vocational School	-Discussed the results and commented on the manuscript. -Aided in interpreting the results and worked on the manuscript. -Performed SEM and EDX analyses. -Provided critical feedback and helped shape the research, analysis, and manuscript.

CRediT authorship contribution statement

Mehmet Taşlıyol: Writing – review & editing, Writing – original draft, Visualization, Validation, Software, Investigation, Formal analysis, Data curation, Conceptualization. Selim Öncü: Writing – original draft, Visualization, Validation, Supervision, Data curation, Conceptualization. Muhammet E. Turan: Visualization, Validation, Methodology, Conceptualization.

Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Appendix A. Supplementary data

The following are the Supplementary data to this article: