Synchronous and decoupling calibration of tri-axial impact force transducers based on a Hopkinson bar and an artificial neural network

The impact force transducers are widely used in aerospace, national defense engineering, auto industry and other important fields involving national security and people livelihood. Those transducers usually need to be calibrated before being put into practical use. Realizing synchronous loading and developing an accurate mathematical model to describe the input-output relationship are the major challenges in the calibration of triaxial impact force transducers at this stage. In this paper, a method for the synchronous excitation of three-dimensional impact force loads was established based on a modified Hopkinson bar technique and the principle of vector decomposition. The triaxial impact force transducer being calibrated was mounted at an angle to the axis of the Hopkinson bar, the one-dimensional force excited in the Hopkinson bar was then decomposed onto each sensitive axis of the transducer, thus realizing its synchronous loading. The coupling effect between the sensitive axes of the transducer was assumed to be linear. A linear decoupling calibration model of the triaxial impact force transducer was built based on a sensitivity matrix containing three main sensitivity coefficients and six transverse sensitivity coefficients. The sensitivity matrix was solved using the least squares method. The amplitude and pulse width of the impact force pulses excited in the Hopkinson bar were adjusted by varying the structure and the impact velocity of the bullet. Reference impact force pulses with varied amplitudes and pulse widths were then used to calibrate the triaxial impact force transducer. Characteristics were revealed that both the main sensitivity coefficients and the transverse sensitivity coefficients of the transducer are related to the amplitude and the pulse width of the reference impact force. The amplitude and pulse width information of the input force pulses that the transducer was subjected to can be reflected by the output voltage pulses of the transducer. Therefore, the amplitude and pulse width of the output voltages of the sensitive axes of the transducer were taken as influencing factors and added to the input layer of the artificial neural network (ANN) in form of artificial neurons. A nonlinear decoupling calibration model for the tri-axial impact force transducer was then built based on an ANN model. The calibration results show that the ANN model has higher calibration accuracy compared to the least squares model. It is feasible and valid to use ANNs to calibrate the tri-axial impact force transducers. © 2022 Explosion and Shock Waves. All rights reserved.