Effects of Sensor Geometry on the Stress-Averaged Output of PVDF Sensors in Tires Available to Purchase

Polyvinylidene fluoride (PVDF) sensors are attractive for use in tires due to their high sensitivity, fast response time, low cost, and ability to operate without power supplies or signal amplification. Based on sensor design, placement, and signal processing techniques, they may be used to determine tire parameters such as tire revolutions, footprint size, and cornering and traction conditions. PVDF sensors generate a voltage output that is related to the average stress acting on the sensor. For non-uniform distributions of stress over the sensor area, there can be a significant difference between the stress at a point and the average sensor stress calculated from the measured voltage. Understanding the effects of sensor geometry on sensor output is important for designing sensors for specific applications, such as tires. This paper presents analytical and numerical models for PVDF voltage output that are developed from the linear piezoelectric constitutive equations, with the average sensor stress modeled using a convolution of the stress input and the PVDF electrode shape. Parametric studies on rectangular, stepped, and triangular sensor shapes show the effects of sensor geometry on voltage output for PVDF sensors under sinusoidal and tire stress inputs.