Cutting force is one of the most basic signals that can reflect the information of the cutting process, so it is very necessary to study the strain elastic element of strain gauge wireless rotating dynamometers. This paper proposes a strain elastic element with a double-layer cross floating beam that can be applied to the strain gauge wireless rotating dynamometer, which can simultaneously obtain the four-component cutting force/torque information of $F_X$, $F_Y$, $F_Z$, and $M_Z$. Based on the proposed strain elastic element, a compact strain gauge wireless rotating dynamometer is designed, which is composed of a tool holder, upper connection flange, strain elastic element, lower connection flange, tool base, and data acquisition and wireless transmission system. The static model of the double-layer cross floating beam on the strain elastic element is established by the segmented rigid body method, and the relationships between the material, force, structural parameters, and the strain and deformation of the floating beam are obtained. The static model is consistent with the finite element solution, which proves the rationality of the static model. Based on the established static model, the sequential quadratic programming algorithm is used to optimize the structural parameters of the double-layer cross floating beam to maximize the sensitivity of the floating beam. The overall structure of the strain elastic element is analyzed by finite element software, and the strain of the structure under simulation conditions is obtained, which provides a reference for subsequent calibration tests and circuit design. The calibration matrix and dynamic performance of the strain elastic element are obtained by the static calibration test, dynamic calibration test, and cutting test. The results show that the proposed strain elastic element has high sensitivity and low cross-sensitivity error, and can be applied to the strain gauge wireless rotating dynamometer to measure medium- and low-speed cutting forces.

The accurate measurement of dynamic forces is pivotal for advancing manufacturing process monitoring and enhancing equipment intelligence. To address the challenges of contact interface force field nonlinearity in existing PVDF piezoelectric film force sensors and the inability of a monolithic PVDF piezoelectric film to measure multi-dimensional forces, this study designs a uniform-load double-bossed elastic force-transmitting diaphragm to achieve contact interface force field reconstruction between the sensor’s elastic sensing structure and the sensitive element group. Building upon the load-bearing surface domain segmentation technique, the silver ink electrode on the front surface of a complete circular PVDF piezoelectric film is segmented into four independent sector-shaped rings. Each sector ring, together with its underlying PVDF piezoelectric film, constitutes a sensitive element, and these four sensitive elements are integrated to form the sensitive element group. The three-dimensional force measurement method of this sensitive element group in the Cartesian coordinate system is investigated. The measurement of three-dimensional force is realized by leveraging the tensile-compressive piezoelectric effect of each sensitive element in conjunction with a pre-stressed assembly structure. Quasi-static calibration test results indicate that the charge sensitivities of the force sensor in the X-, Y-, and Z-directions are 52.63 pC/N, 55.96 pC/N, and 9.02 pC/N, respectively, with a linearity ≤4.6%. Dynamic calibration test results reveal that the force measurement module exhibits a natural frequency of 4675.5 Hz. Experimental investigations into the response of triaxial cutting forces to variations in cutting speed, feed rate, and cutting depth were conducted, which verified the sensor’s ability to capture dynamic three-dimensional cutting forces. This study provides an effective solution for the structural design and three-dimensional force measurement methodology of PVDF piezoelectric film force sensors.