Pressure sensor and method for measuring a pressure

1. A pressure sensor comprising:

a main body comprising:

a piezoelectric material; and

at least two internal electrodes arranged in the piezoelectric material, wherein the at least two internal electrodes are arranged such that a voltage arises between the at least two internal electrodes when a pressure acts on a side surface of the main body that is provided for an application of pressure, and wherein a polarization direction of the piezoelectric material changes under action of the pressure;

wherein the pressure sensor is configured to calculate a mechanical stress T acting on the main body based on equations (1) and (2):

s=d 33 E+s 33 T   (1)

D=ε 33 ε0 E+d 33 T   (2),

wherein s indicates a mechanical strain of the main body, D indicates a displacement density, E indicates an electrical field strength of an electrical field that arises owing to a piezoelectric effect, d indicates a piezo constant of the piezoelectric material of the main body, ε33 and ε0 indicate relative permittivities and s33 indicates compliance, and wherein it is assumed that a pressure axis, a polarization axis and a detection axis each correspond and lie in a stacking direction.

2. The pressure sensor according to claim 1 , wherein the side surface of the main body that is provided for the application of pressure consists of the piezoelectric material.

3. The pressure sensor according to claim 1 , further comprising:

a first external electrode arranged on a first side surface of the main body; and

a second external electrode arranged on a second side surface of the main body,

each of the at least two internal electrodes connecting to the first external electrode or the second external electrode, and

wherein neither the first side surface nor the second side surface is the side surface that is provided for the application of pressure.

4. The pressure sensor according to claim 3 , wherein the first external electrode is arranged perpendicularly to the at least two internal electrodes, and wherein the second external electrode is arranged perpendicularly to the at least two internal electrodes.

5. The pressure sensor according to claim 4 , wherein the first and second external electrodes comprise a partial vitreous firing metallization composed of silver, silver-palladium or copper.

6. The pressure sensor according to claim 4 , wherein the first and second external electrodes comprise a sputtering layer composed of CuAg or CrNiAg.

7. The pressure sensor according to claim 1 , wherein the side surface of the main body that is provided for the application of the pressure is arranged parallel to the at least two internal electrodes.

8. The pressure sensor according to claim 1 , further comprising an evaluation unit connected to the at least two internal electrodes, the evaluation unit being configured to determine the pressure acting on the main body.

9. The pressure sensor according to claim 8 , wherein the at least two internal electrodes are electrically contacted with one another via the evaluation unit, and wherein the evaluation unit is configured to measure a current flowing between the at least two internal electrodes and to determine therefrom the pressure acting on the main body.

10. The pressure sensor according to claim 8 , wherein the evaluation unit is configured to measure a voltage present between the at least two internal electrodes and to determine therefrom the pressure acting on the main body.

11. The pressure sensor according to claim 1 , wherein the piezoelectric material comprises a lead zirconate titanate ceramic.

12. The pressure sensor according to claim 1 , wherein the internal electrodes comprise silver, silver-palladium or copper.

13. A method for measuring a pressure with a pressure sensor, wherein the pressure sensor comprises a main body comprising a piezoelectric material, at least two internal electrodes arranged in the piezoelectric material, a first external electrode and a second external electrode, wherein each of the at least two internal electrodes is connected to the first external electrode or the second external electrode, wherein the first external electrode is arranged on a first side surface of the main body, wherein the second external electrode is arranged on a second side surface of the main body, and wherein the main body further comprises a third side surface, which is free of the first external electrode and the second external electrode, the method comprising:

measuring the pressure on the third side surface, wherein a polarization direction of the piezoelectric material changes under action of the pressure;

wherein a mechanical stress T acting on the main body is calculated based on equations (1) and (2):

s=d 33 E+s 33 T   (1)

D=ε 33 ε0 E+d 33 T   (2),

wherein s indicates a mechanical strain of the main body, D indicates a displacement density, E indicates an electrical field strength of an electrical field that arises owing to a piezoelectric effect, d indicates a piezo constant of the piezoelectric material of the main body, ε33 and ε0 indicate relative permittivities and s33 indicates compliance, and wherein it is assumed that a pressure axis, a polarization axis and a detection axis each correspond and lie in a stacking direction.

14. The method according to claim 13 , wherein the pressure sensor further comprises an evaluation unit connected to the at least two internal electrodes, and wherein the method further comprises:

generating a voltage between the at least two internal electrodes based on the pressure detected on the third side surface;

measuring a current intensity or the voltage by the evaluation unit; and

determining the pressure acting on the main body based on the current intensity or the voltage.