The impact angle dependency of a piezoelectric impact sensor – a conceptual study

Piezoelectric impact sensors are designed to trigger an immediate or delayed detonation when they sense that the projectile impacts a desired target. The initial voltage signal of a piezoelectric element (PE) in a projectile depends on several conditions: the target (material properties, thickness etc.) and terminal ballistic parameters (impact speed and impact angle). This report presents a conceptual study of the PE generated (PEG) charge as function of the impact angle. The PEG charge signal will be derived in the case when a longitudinal, plane, square-shaped stress pulse enters the PE. A pulse of that form resembles the simplest form of shock waves, and it will simplify the piezoelectric equations. Four factors that reduce the PEG charge and PE voltage as the impact angle increases, are considered: (1) the collision impulse which generates the stress pulse at impact, (2) the transmission coefficient, (3) the electric field dependence on the stress pulse’s amplitude and direction as described by the piezoelectric equations, and (4) the proportion of the PE’s volume effectively being stressed by the stress pulse that traverses it. Other effects are discussed qualitatively, but are either regarded as negligible or too complex for this simple analytical study to be included in the final PEG charge formula. The derived PEG charge formula is applied to a simple scenario where all the assumptions in the derivation are true, and where the stress pulse’s incident angle equals the impact angle. Though this scenario is mainly for conceptual study purposes, it also resembles a special case: when the side of a (e.g. conically shaped) projectile nose collides with a flat and equally angled target plate and generates a plane shock wave. The projectile nose shape ensures that a plane, square pulse is produced at the impact interface and propagates unchanged into a PE made of a PZT material, where the stress generates an electric field. In this scenario the relative PEG charge amplitude decreases approximately linearly (though with a contribution from a cosine factor), as the impact angle increases. The PEG charge at 60° impact angle is (60°) ≈ 0.2 · 𝑄(0°). We also learn that the angle dependency of a closed circuited PE is quite similar to that of an open circuited PE. The shape of the PEG charge signal’s rising edge as a stress pulse enters it at an angle, is also studied. As the transmission angle increases, the rising edge changes from a straight line to an S-shape.