Sensor device for determining a displacement of a shaft

An exhaust gas recirculation valve arranged in the exhaust gas train of an internal combustion engine in order to control an exhaust gas flow, the recirculation valve comprising:

• an inlet;
• an outlet;
• a valve seat with a valve disk coupled to a shaft comprises a valve rod;
• wherein the position of the valve disk with respect to the valve seat can be adjusted by means of a displacement of the shaft along a longitudinal axis of the shaft;
• wherein the exhaust gas recirculation valve controls the exhaust gas flow from the inlet to the outlet as a function of the position of the valve disk with respect to the valve seat;
• a sensor unit disposed at a first radial distance from the longitudinal axis, wherein the shaft moves in relation to the sensor unit along the longitudinal axis;
• a detection element arranged between the shaft and the sensor unit and fixedly coupled to the shaft at a second radial distance from the longitudinal axis;
• wherein a first side of the detection element facing away from the longitudinal axis comprises a convex shape with respect to a plane perpendicular to the longitudinal axis and a gap distance defined between the detection element and the sensor unit varies over an extent of the sensor unit perpendicularly with respect to the longitudinal axis and independently of a tilting angle of the shaft;
• wherein the sensor unit generates a shaft displacement signal dependent on a displacement of the detection element in relation to the sensor unit along the longitudinal axis.