Characterization of Variable-sensitivity Compact Force Sensor using Stiffness Change of Shape-memory Polymer Based on Temperature


 In the present study, we propose a variable-sensitivity force sensor using a shape-memory polymer (SMP), the stiffness of which varies according to the temperature. Since the measurement range and sensitivity can be changed, it is not necessary to replace the force sensor to match the measurement target. Shape-memory polymers are often described as two-phase structures comprising a lower-temperature “glassy” hard phase and a higher-temperature “rubbery” soft phase. The relationship between the applied force and the deformation of the SMP changes depending on the temperature. The proposed sensor consists of strain gauges bonded to an SMP bending beam and senses the applied force by measuring the strain. Therefore, the force measurement range and the sensitivity can be changed according to the temperature. In our previous study, we found that a sensor with one strain gauge and a steel plate had a small error and a large sensitivity range. Therefore, in the present study, we miniaturize this type of sensor. Moreover, in order to describe the viscoelastic behavior more accurately, we propose a transfer function using a generalized Maxwell model. We verify the proposed model experimentally and estimated the parameters by system identification. In addition, we realize miniaturization of the sensor and achieve the same performance as in our previous study. It is shown that the proposed transfer function can capture the viscoelastic behavior of the proposed SMP sensor quite well.

T.M.: mukai@meijo-u.ac.jp 22 23 24 Introduction 25 Force sensors have been applied to various fields and are required to measure wider load ranges. One 26 example in industry is a manufacturing system that has the flexibility to cope with various kinds of 27 small-quantity production referred to as a flexible manufacturing system. Moreover, in rapidly aging 28 societies, robotic technology has been applied to various fields, including industrial fields as well as 29 nursing and welfare fields [1]. In these applications, a wide-range force sensor that can obtain load 1 information can measure multiple biosignals, such as heart rate, respiration cycle, and weight 2 transitions [2]. Most force sensors transform the mechanical deformation of the detection area under 3 an applied force into a change in resistance, capacitance, or reflectance that can be measured using 4 electric signals. For example, some force sensors consist of strain gauges bonded to a bending beam. 5 However, with this approach, it is difficult to change the measurement range or sensitivity of a sensor, 6 both of which depend on the material used, the type of strain gauge, and the measurement method. The 7 deformation range depends on the sensor material, and it is difficult to change these specifications 8 after the sensor is produced. For this reason, we previously developed a force sensor using a 9 shape-memory polymer (SMP), the measurement range and sensitivity of which can be changed [3,4]. 10 Shape-memory polymers [3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19] are increasingly being investigated as smart materials and are used 11 in various fields. Shape-memory polymers change their modulus around a glass transition temperature 12 (Tg), and are often described as two-phase structures comprising a lower-temperature "glassy" hard 13 phase and a higher-temperature "rubbery" soft phase. The hard and soft phases are characterized by 14 two different elastic moduli: an elastic modulus for the lower-temperature, higher-stiffness glassy 15 plateau and an elastic modulus for the higher-temperature, lower-stiffness rubbery plateau. The 16 reversible change in the elastic modulus between the glassy and rubbery states of SMPs can be as high 17 as several hundredfold. 18 Since the stiffness of the SMP can be changed according to the temperature, the measurable force 19 range determined based on the above strain range can also be changed. Moreover, even if the strain 20 resolution is the same, the force resolution can be changed in a similar manner. In this way, the 21 measurement range and sensitivity of the force sensor can be changed according to the temperature. 22 Generally, environmental stability is a very important requirement for sensors. For example, special 23 compensating elements are often incorporated either directly into sensors or into signal conditioning 24 circuits in order to compensate for temperature errors [20]. Note that, inverting the above idea, the 25 proposed sensor uses the temperature-dependent changes positively. 26 In previous studies [3,4], we made several prototypes of this sensor by attaching a strain gauge to 27 an SMP sheet with an embedded electrical heating wire and evaluated their basic characteristics. 28 Through experiments with these prototypes, which use the stiffness change of the SMP based on the 29 temperature, we showed that the measurement range and sensitivity can be changed without replacing 30 the actual sensor [3]. On the other hand, the changes in measurement range and sensitivity (ranging 31 from a hundredfold to a thousandfold) depend on the Young's modulus of the SMP and are not 1 adjustable. However, the change may be too large for some applications. We also affixed a thin steel 2 plate to reduce the influence of the difference in elastic modulus between the strain gauges and the 3 SMP sheet. This made it possible to reduce the discrepancy between the theoretical values and the 4 measured values. Moreover, SMP force sensors with either one or two strain gauges and steel plates 5 were fabricated, and their accuracy and sensitivity were investigated under the same conditions [4]. 6 Experiments using the prototypes demonstrated that a sensor with one steel plate had a small error and 7 a large sensitivity range although the dimensions of the sensors were not optimized. 8 Therefore, in the present study, we miniaturized this type of sensor for practical use. A prototype of 9 this sensor was made by attaching a strain gauge to an SMP sheet with an embedded electrical heating 10 wire, and we evaluated the basic characteristics of the prototype sensor. 11 In a previous study, we proposed a theoretical formula that took the viscosity of the SMP into 12 consideration, which made it possible to reduce the effect of stress relaxation [4]. However, since the 13 first derivative of the measurement values was used to estimate the force (see "Basic concept of the 14 force sensor" and "Generalized Maxwell model" sections for additional details), the measurement 15 errors could be large. Therefore, in the present study, we propose a transfer function method using a 16 generalized Maxwell model. We verified the proposed model experimentally and estimated the 17 parameters by system identification. where x is the distance between the strain gauge and the position at which the force is applied, Ep and 28 Es are the elastic moduli of the SMP and steel, respectively, and Ip' and Is' are the area moments of 29 inertia for the SMP and steel, respectively, about the neutral axis of the composite beam. Here, Ip' and 30 where b is the width of the beam, hp and hs are the thicknesses of the SMP and steel plates, 6 respectively, and h1 is the distance between the neutral axis and the SMP surface and is expressed as 7 follows: 8 9 (4) 10 11 As described "Introduction" section, Ep can be changed according to the temperature. Therefore, the 12 relationship between ε and W given in Eq.
(1) can also be changed. Therefore, the change in the 13 measurement range based on temperature can be modified. Moreover, as shown in Eq. (1), by 14 changing the thickness of the steel plate, the measurement range and the sensitivity of the sensor can 15 be modified. In order to understand the mechanisms producing such unique properties and to design products 20 including SMPs, various mathematical models have been proposed [5,6,[12][13][14][15][16][17][18][19]22]. To investigate 21 relaxation processes in polymers, combinations of elements, including springs and dashpots, are 22 widely used for modeling under isothermal conditions [12][13][14][15][16][17][18]22]. For example, Tobushi et al. 23 proposed a linear constitutive model by modifying a three-element viscoelastic model combining two 24 springs and a dashpot to represent the deformation characteristics of the SMP [12]. Similarly, in our 25 previous study [4], considering the viscosity of the SMP, we assumed that the relationship between W 26 and ε is given by 27

Design of compact sensor 3
The dimensions of the prototype SMP sensors used in our previous study [4] and the present study are 4 shown in Table 1. Here, l' is the length of the sensor. The dimensions of the prototype sensor 5 constructed in the present study are similar to those of the commercial force sensor (LVS-2KA (T < Tg), 6 LVS-200GA (T > Tg), Kyowa Electronic Instruments Co., Ltd.) used in the experiment. The volume of 7 the proposed sensor was reduced by 87% compared with that in our previous study. In our previous 8 study, we applied a deformation of 5 mm to the tip of the sensor. In the present study, we determined b 9 and hp so that the reaction force W is the rated capacity of a commercial load cell (20 N) when the 10 deformation is 1 mm below Tg. The ratio of the sensor length (14 mm) to the deformation (1 mm) is 11 approximately the same as that in the previous study, because the large creep strain of the SMP below 12 Tg is not recovered [7]. The thickness of the steel plate (hs = 0.07 mm) is similar to that in our previous 13 study [4]. The relationship between the applied force W and the deflection y is expressed as follows: where l (= 11 mm) is the distance between the fixed end and the position at which the force is applied. 18 In the present study, we chose a polyurethane SMP (SMP Technologies Inc., MP4510, Tg = 45C). The 19 fundamental characteristics of this material taken from the product catalogue are listed in Table 2 The prototype SMP force sensor is shown in Fig. 2. In the present study, we prepared an SMP sheet 27 with an embedded electrical heating wire in a manner similar to that described in our previous studies 28 [4,8]. The shape and dimensions of the heating wire (outer diameter: 0.26 mm, electrical resistivity: 29 108×10 6 Ω•cm) are shown in Fig. 3. The underlined lengths in the figure were smaller than those in 30 our previous study. The total electrical resistivity was 1.8 Ω. 31 We bonded the SMP sheet and steel plate (SUS304H, thickness: 0.07 mm) using an adhesive (PPX,5 Cemedine Co., Ltd.). We attached one strain gauge (KFGS-2-120-C1-16 L1M2R, Kyowa Electronic 6 Instruments Co., Ltd.) to the steel plate and measured the strain on the surface of the steel plate. The 7 distance between the strain gauge position and the position at which the force was applied (x) was 7 8 mm. We used a cyanoacrylate adhesive (CC-36, Kyowa Electronic Instruments Co. Ltd., operating 9 temperature range: -30 to 100°C). 10 The heating wire was connected to a power supply (PE18-1.3AT, KENWOOD) with a stable direct 11 current, and voltages of 5 V were supplied to the prototype sensor. With a thermocouple attached to 12 the surface of the SMP sheet (red circle in Fig. 2), we heated the sheet and maintained a temperature of 13 70°C, as in our previous study [4]. When the SMP was heated from room temperature to 70°C, we set 14 the duty ratio to 100% and then modified it to compensate for the heat loss and maintain the SMP 15 temperature at 70°C A thermogram of the heated SMP sheet captured by an infrared thermal camera 16 (NEC Avio Infrared Technologies Co., Ltd., F30W) is shown in Fig. 4. The entire sheet was heated 17 uniformly to approximately 70°C. One reason for the temperature uniformity is the reduced distance 18 between the heating wire segments. Since the tape covered the surface to attach the thermocouple, the 19 center of the SMP sheet is shown in blue. We created a base, a presser plate, and a cover using a 3D printer (Fig. 5). The prototype force 24 sensor in Fig. 2 was fixed between the presser plate and the base. As shown in Fig. 5(b), the total 25 sensor dimensions including these parts are almost same as those of a commercial load cell 26 Kyowa Electronic Instruments Co., Ltd.). The experimental apparatus is shown in Fig. 6. The applied force was measured at temperatures above 1 and below Tg. The experiments below Tg were performed at room temperature. The relationship 2 between the strain and the force applied using an indenter connected to the load cell was then 3 evaluated. The indenter was placed in contact with the steel plate of the prototype sensor in order to 4 prevent SMP surface deformation. The load cell and the sensor were attached to a manual stage and an 5 automatic stage (OSMS20-85, Sigma Koki Co., Ltd.), respectively. The prototype sensor was 6 automatically displaced using the automatic stage. The strain gauge was connected to a PC through a 7 bridge box (DB-120A, Kyowa Electronic Instruments Co., Ltd.) and a strain amplifier 8 Kyowa Electronic Instruments Co., Ltd.). The load cell was also connected to the PC through a strain 9 amplifier. The sampling frequency was 1 kHz. We resampled the obtained 1-kHz signal at 100 Hz 10 using the resample() function in MATLAB.

Experiment 1 15
We performed two types of experiments in order to characterize the proposed sensor. We first applied a 16 random force to the prototype sensor in order to estimate the optimum transfer function and compare 17 the proposed sensor with that used in our previous study [4]. The sensor was deformed as follows: 18

19
Step 1: The sensor was held motionless in the unloaded state (just before touching). 20 Step 2: After the unloaded state, the sensor was moved in the direction of the blue arrow in Fig. 6 and 21 was brought into contact with the load cell to apply a deformation of 1 mm to the tip of the 22

sensor. 23
Step 3: Leaving the tip deformed, the sensor was held motionless. 24 Step 4: The sensor was returned to the initial position. 25 Steps 1 through 4 were repeated. The number of repetitions was 5, 10, and 20, which were larger 26 than in our previous study [4]. For system identification, the input should be persistently exciting, i.e., 27 it should contain many distinct frequencies [23]. Therefore, in the present study, considering the 28 potential applications of our sensor (i.e., a wide range of inputs), we randomly set the velocity in Steps 29 2 and 4 from 0 to 5 mm/s, and the rest time in Steps 1 and 3 from 0 to 10 s. For each condition, the 30 measurements were conducted six times. We evaluated two prototype sensors (samples 1 and 2).

Experiment 2 2
We then evaluated the dynamic response of the proposed sensor to a step deformation. Similarly to 3 experiment 1, the sensor was deformed as follows: 4 5 Step 1: The sensor was held motionless in the unloaded state (just before touching) for 10 s. 6 Step 2: After the unloaded state, the sensor was moved in the direction of the blue arrow in Fig. 6 and  7 was brought into contact with the load cell in order to apply a deformation to the tip of the 8 sensor. 9 Step 3: Leaving the tip deformed, the sensor was held motionless for 300 s. 10 We set the deformation in Step 2 to 0.25, 0.5, 0.75, or 1 mm in order to check whether the force 11 increases with increasing deformation. For each condition, the measurements were conducted three 12 times. We evaluated two prototype sensors (samples 1' and 2'). In our previous study [4], after performing this procedure multiple times, the force measured using the 23 load cell was compared with W obtained based on the strain measured using the strain gauge, and the 24 error was calculated. Then, W was determined by combining the theoretical equations in "Basic 25 concept of the force sensor" section. In MATLAB, the least-squares method was then used to 26 determine the optimum values of L, M, and N in Eq. (5). 27 In the present study, in order to describe the viscoelastic behavior more accurately, we derived a 28 transfer function using the generalized Maxwell model, as shown in Fig. 7 [13]. Westbrook developed 29 a generalized Maxwell model to capture the shape-memory effect using two sets of nonequilibrium 30 branches for two fundamentally different modes of relaxation: the glassy mode and the Rouse modes [13]. Since the temperature of our sensor is fixed above and below Tg, we neglected the thermal 1 expansion of the SMP. Then, using the transfer function, we calculated the force from the strain. The derivation process is shown below. As shown in Fig. 7, the forces applied to each element 0 ， 6 ( = 1 ⋯ ) are expressed as follows: After Laplace transformation of Eq. (10), by substituting Eqs. (13) and (14) an input U(s) and an output F(s), is expressed as follows: 7 8 1 ( ) = 0 ( 1 + 1 )( 2 + 2 ) ⋯ ( + ) As shown in Eq. (18), the numbers of poles and zeros are n. In the present study, we assumed that the 11 transfer function G(s) with an input ε(s) and an output W(s) had a structure similar to G1(s) and n poles 12 and n zeros. Namely, G(s) is expressed as follows: 13 14 ( ) = + ⋯ + 1 + 0 + ⋯ + 1 + 0 (19) 15

16
Since the temperature of the proposed sensor is fixed above or below Tg, we assumed that (i = 17

0⋯ ) and
(i = 0⋯ ) are constants in the rubbery and glassy states. Note that by Laplace 18 transformation of Eq. (5), G(s) with n = 1 can be obtained. We determined n using the experimental 19 results. Furthermore, using the method in our previous study [4] (namely Eqs. (5) and (7), method 2) and 10 the results of experiment 1, we estimated W, calculated FIT, and compared the obtained results with 11 those measured by Method 1. The procedure is as follows. 12  Method 2 (used in our previous study): Using Eqs. (5) and (7)

Results and discussion
18 Identification of transfer function (experiment 1, method 1) 19 Typical transitions of the force below and above Tg are shown in Fig. 8. As shown in Fig. 8, the two 20 measured forces are almost identical. Moreover, by considering the viscosity of the SMP, the estimated 21 force can reproduce the stress relaxation phenomenon. The maximum force and strain for different 22 conditions are shown in Fig. 9. Although we applied a similar displacement below and above Tg, the 23 measured force range is significantly different. Based on the above results, it was shown that the 24 miniaturized sensor achieved the same performance as in our previous study. On the other hand, the 25 maximum strain below and above Tg are similar. The measured force below Tg is smaller than 26 expected (27 N, see "Design of compact sensor" section for additional details) and both the maximum 27 force and strain are different for the two prototype sensors. These differences may be attributed to 28 errors during sensor manufacture. 29 [Insert Fig. 9 here] 1 2 On the other hand, when the sensor was returned to the initial position, the force measured by the 3 load cell became zero although the estimated values were not zero. One reason is that the SMP sheet 4 could not recover to the initial shape quickly because of its viscosity, and the indenter of the load cell 5 could not contact the prototype sensor. Above Tg, a fluctuation of the estimated force can be seen. The 6 transitions of the measured strain are shown in Fig. 10. Similarly to Fig. 8, fluctuations can also be 7 seen, and are attributed to electrical noise in the heating wire. Using Method 1 (n = 1-5), we calculated FIT. The mean ± the standard deviation below and above 12 Tg are shown in Figs. 11(a) and 11(b), respectively. When n = 4 and 5, by imposing the condition that 13 αi and βi are positive, an error occurred during the calculation in MATLAB. Therefore, the results are 14 not shown in Fig. 11. The values of FIT below Tg are larger than those above Tg. One reason would be 15 the electrical noise shown in Figs. 8 and 10. We then calculated the average values of the coefficients in Eq. (19) below and above Tg, and 20 determined G(s) with n = 1, 2, and 3. Using the same experimental results, we calculated the mean and 21 the standard deviation of FIT below and above Tg for each n. The calculated FIT values are shown in 22 Fig. 12; the largest value was obtained for n = 3. As shown in Fig. 12(a), when n = 2 below Tg, FIT 23 was the smallest. This could be attributed to factors such as the mass and shape of the sensor, which 24 were not considered in the proposed model. The FIT values determined using Method 2 are shown in Fig. 14. As shown in Figs. 11 and 14, the 6 largest values of FIT determined using Method 1 were larger than those determined using Method 2. 7 Using the proposed transfer function model, the FIT values became larger than those in our previous 8 studies. Step deformation response (Experiment 2) 19 Using Method 1 (n = 1-3) and the results of experiment 2, we calculated FIT for different conditions. 20 The mean ± the standard deviation below and above Tg are shown in Figs. 16(a) and 16(b), 21 respectively. When n = 4 and 5, an error occurred during the calculation in MATLAB. Similarly to 22 experiment 1, Figure 16 shows excellent agreement between the model estimations and the 23 experimental data, although the deformations of the SMP sensors were not the same. As shown in Figs. 24 11(b) and 16(b), above Tg, the values of FIT in experiment 2 were smaller than those in experiment 1. 25 One reason would be the changes in the temperature and the sensor characteristics over time because 26 experiment 2 (more than 310 s) was longer than experiment 1 (about 130 s). 27 28 [Insert Fig. 16 here] 29 30 determined G(s) for n = 1, 2, and 3. Using the same experimental results, we calculated the mean and 1 the standard deviation of FIT below and above Tg for each n. The calculated values of FIT are shown 2 in Fig. 17, and are seen to be much lower than those in Fig. 16. The main reason is that the coefficients 3 in Eq. (19) are different for each deformation. Therefore, for practical applications of the proposed 4 sensor, it would be necessary to set the optimum coefficients according to the operating conditions. We have developed a variable-sensitivity force sensor using an SMP sheet with an embedded electrical 10 heating wire. In the present study, we miniaturized this type of sensor while referencing the 11 dimensions and rated capacity of a commercial load cell. The volume was decreased by 87% 12 compared with that in our previous study. The entire sheet of the prototype sensor was heated 13 uniformly to approximately 70°C. 14 Moreover, we proposed a transfer function using a generalized Maxwell model. Using identification 15 experimental results, we determined the numbers of poles and zeros and compared the FIT value 16 between our previous and present studies. Models were introduced and were validated experimentally, 17 and there was excellent agreement between the model estimations and the experimental data. A 18 transfer function with n = 3 was found to be optimal. Using the proposed model, the FIT value became 19 larger than in our previous studies.

Competing interests 26
The authors declare that they have no competing interests.   Prototype force sensor using an SMP sheet with an embedded electrical heating wire. We attached a thermocouple to the surface of the SMP sheet at the position indicated by the red circle Figure 3 Heating wire. The underlined lengths are smaller than those in our previous study Figure 4 Thermogram of SMP force sensor when heated and maintained at 70°C  Experimental apparatus for evaluating force sensor. The prototype sensor was automatically displaced using an automatic stage   Maximum force (a) and strain (b) for different conditions