# Ultrasound transducers modeling

## Performed calculations

If you have materials parameters and geometry of the piezo transducer, with consent the Engineering Solutions, it is possible to order the following works:

- calculation of the amplitude-frequency characteristic (AFC) and phase-frequency characteristic (PFC) of the conductivity and the impedance of the transducer / piezoelectric element;
- calculation of AFC and PFC of the sensitivity of the transducer;
- calculation of AFC and PFC of average displacement of the radiating surface of the transducer;
- determination of oscillation modes of the transducer.

We also have a database of materials consisting of more than 100 components, including metals, polymers, composites, piezoceramic materials, etc.

## Piezoelectric transducer modeling

- Modeling of physical processes allows to calculate the characteristics of the sensor and its output parameters with high accuracy (error not more than 5%), such as:
- amplitude of oscillation (displacement);
- resonant frequencies;
- voltage on the piezo element, etc.

The developer can be more flexible at the conceptual design stage. Thus, prototypes creating and experimental tests conducting required only after calculating the optimal design of the sensor. This makes it possible to significantly reduce costs during the R&D phase and anticipate in advance the pitfalls.

## Piezoelectric element FEA

The most difficult in the calculation of ultrasonic piezoelectric sensors is the simulation of the piezoelectric element. For a correct calculation of the piezoelectric element, it is required to know a large number of piezoceramic parameters. The graph (Fig. 1) shows the AFC of the piezoelectric element taken experimentally with help of impedance analyzer and calculated AFC of the piezoelectric element. The frequency error is 2.3% (at the first resonance) and 0.34% (at the second resonance).

Scale of oscillations 200000: 1

Scale of oscillations 10000:1

Scale of oscillations 10000:1

# Portfolio

## Ice sensor

Scale of oscillations 10000:1

- Task:
- calculation of resonance frequency;
- determination of the frequency dependence on the amount of ice;
- calculation of spurious oscillations at the attachment point;
- determining the sensor sensitivity area.

## Densimeter

Determination of parasitic oscillations in a density meter.

### Model of a piezo package used in a density meter

## Dispergator

№ | Version | Frequency of the first resonance f1, Гц | Frequency of the second resonanceа f2, Гц | Mechanical amplitude of tip oscillations | |

at f1, µm | at f2, µm | ||||

1 | initial | 18971 | 45295 | 36,29 | 24,55 |

2 | with a whole piezoelectric element | 19318 | 46189 | 42,46 | 28,08 |

3 | with reduced length of mass | 24697 | 40213 | 38,37 | 36,65 |

4 | with increased mass radius | 19226 | 39691 | 35,25 | 32,11 |

5 | with a modified horn | 20194 | 48475 | 40,33 | 37,03 |

6 | with 4 whole piezo elements | 18126 | 43230 | 46,85 | 33,94 |

## Flowmeter

# Contacts

E-mail: info@engineering-solutions.ru, info@ooo-up.ru

Phone: +7 (831) 423-90-07