2.2. Calibration and electrical–mechanical benchmarking

Electrical–mechanical benchmarking was performed in two steps (Fig. 2). First, calibration was performed to establish the conversion from voltage to pressure. Subsequently, the FEM was employed to analyse the relationship between the pressure on the sensor units and the applied force. All five sensors were encapsulated within a bracket and responded simultaneously to an applied force (F) by providing output voltages (V₁, V₂, V₃, V₄, and V₅). Using the linear relationship obtained in the first step, the output voltages were converted into pressure values (P₁, P ₂, P ₃, P ₄, and P ₅). The pressure on each sensor was also acquired through FEM simulation and recorded as P₁’, P ₂’, P ₃’, P ₄’, and P ₅’. The electrical output of the sensors and the actual applied force were benchmarked by the ratio P’/P. Thus, the output voltages could be converted into pressure values, which were further multiplied by P’/P, and subsequently, through a reversed procedure of the FEM, the applied force (F’) could be simulated.

Flowchart of calibration and electrical-mechanical benchmarking.

In step 1, five sensor units were calibrated with atmospheric pressure separately. Pressure values and output voltages were analysed with linear regression. In step 2, all five sensors were encapsulated within a bracket and responded simultaneously to one applied force (F) by giving output voltages (V₁, V₂, V₃, V₄, V₅). Using the linear relationship gained in step 1, the output voltages were converted into pressure values (P₁, P ₂, P ₃, P ₄, P ₅). At the same time, the applied force (F) was loaded onto the sensor chip FEM model, through simulations of stress distribution, thus obtaining pressure on sensors (P₁’, P ₂’, P ₃’, P ₄’, P ₅’). P and P′ were compared to establish associations between electrical and mechanical systems. Thus, the output voltages could be converted into pressure values, which should be further multiply ratio P’/P, and then through a reversed procedure of the FEM, the exerted force could be simulated (F′). Finally, the simulated force (F′) and the actual applied force (F) were compared, and the error of electrical-mechanical conversion was calculated.

The first step, calibration with barometric pressure was performed before the chips were assembled onto the brackets. A direct-current powered analyser (N6705C, Keysight, Beijing, China) was used as the power supply, and was set to 3.3 V. An Agilent 34401A 6 1/2 Digit Multimeter was used to read the output voltage. The wired, unpackaged chip was placed in a sealed, airtight testing box (Supplementary Fig. 3), and a GE Druck DPI 104 digital standard pressure gauge (Supplementary Fig. 3) was used to adjust the pressure in the testing box.

By loading the atmospheric pressure (60, 84, 101.03, 110.47, 129.78, and 145.76 kPa) on the chip, six output voltages were recorded from each sensor. The pressure was maintained static when the results were recorded. Linear regression of the output voltage with the pressure was performed for each sensor to establish the conversion from voltage to pressure.

After the encapsulation, the relationship between the pressure on each of the five sensors in the stress-monitoring bracket and the force exerted was determined. The bracket base was placed upward and fixed parallel to the horizontal plane on a universal test bench. A digital force meter with a range of 10 N and a resolution of 0.001 N (SH–10 N, Nscing Es Su Test, Nanjing, Jiangsu) was used to apply force to the bracket base. Thirteen different sites were selected for force exertion using 13 operating modes (OM). A static pressing force of 0–0.784 N (0–80 gf) was used for each OM, and the load was increased by 0.098 N per test, and this was repeated thrice. The five channels of output voltage data of each OM were acquired at a frequency of 800 Hz for 6.4 s in each test. A coordinate system was established with the centre of the bracket base plate as the origin, with the X-axis in the medial-distal direction and the Y-axis in the gingival-incisal direction.

In this step, an FEM with a second-order hexahedral mesh was utilised to simulate the stress contour when the force boundary was set on the force detection bracket. The simulations considered the stress distribution on the force detection bracket when an applied force was loaded onto the sensor chip model, which consisted of a bracket baseplate, medical silicone, epoxy bonding vinyl, silicone on the sensitive film surface, a sensor element, and PI-reinforced FPC boards (Supplementary Fig. 4 and Supplementary Table 2). The resulting stress and pressure values were used to establish the relationship with an electrically collected pressure using linear regression obtained from the calibration.

Finally, the output voltage was converted to pressure, and subsequently to the resultant force after correcting for the actual applied force.

Afterwards, a second test was conducted to verify the accuracy of the electrical–mechanical benchmarking. The random forces were applied twice at each action point. The random forces and output voltages were recorded separately. The simulated force (F’) and actual applied force (F) were compared, and the error of the electrical-mechanical conversion was calculated.

Using the collected voltage data and the conversion relationship established above, the synthesized force acting on the chip and the coordinates of the action point were calculated. The calculated force value and coordinates were compared with the actual force magnitude and position of the action point, and the error of the stress chip was analysed.