*Article* **Design and Analysis of Solid Rocket Composite Motor Case Connector Using Finite Element Method**

**Lvtao Zhu 1,2,\* , Jiayi Wang <sup>1</sup> , Wei Shen <sup>3</sup> , Lifeng Chen <sup>3</sup> and Chengyan Zhu <sup>1</sup>**


**Abstract:** The connector is an essential component in the solid rocket motor case (SRMC), and its weight and performance can directly affect the blasting performance of SRMC. Considering the lightweight design of these structures, fiber-reinforced composite materials are used for the major components. In this study, the finite element analysis of the SRMC connector was performed. The lay-up design and structure optimum design of the connector were studied. Furthermore, the strain distribution on the composite body was compared with experimental measurements. The results demonstrate that the calculated value of the final preferred solution was within the allowable range, and at least 31% weight loss was achieved, suggesting that the performance of the optimum design was optimized. The comparison between the finite element calculation and the test results suggests that the design was within the allowable range and reasonable.

**Keywords:** solid rocket motor case (SRMC) connector; carbon fiber; lay-up; mechanical properties; finite element

### **1. Introduction**

Composite materials can be classified according to the type of strengthening material into particle-reinforced and fiber-reinforced composite materials. Furthermore, fiber-reinforced composite materials can be divided into short fiber-reinforced and long fiber-reinforced composite materials [1]. A solid rocket composite shell is a kind of long fiber-reinforced composite material, which is pre-impregnated with carbon fiber (or glass fiber) and wound around the core mold layer by layer, before solidification at a certain temperature. The solid rocket motor case (SRMC) is mainly composed of a tube structure, head, insulation layer, and skirt, and it has been widely applied in space vehicles, missile weapons, and other fields as a crucial part of the rocket motor. An SRMC connector is employed to connect the engine nozzle and ignition device, as shown in Figure 1. The design of the case connector structure significantly contributes to the development of the composite case. Moreover, its performance directly affects the blasting performance of the composite case. Due to their light weight, high strength, and high stiffness, fiber-reinforced composites can efficiently decrease the structure mass of the SRMC and increase the range of the rocket, providing great military and economic benefits [2]. For example, the range of a strategic missile can be increased by 16 km if the mass of the third structure of the solid rocket engine is reduced by 1 kg [3].

At present, carbon fiber-reinforced composites are widely used for strategic missiles and delivery systems, with several related papers published in this field. Ramanjaneyulu et al. [4] explored the SRMC using the finite element method, revealing that the hoop stress was gradually increased from the outer layer to the inner layer in all parts of the SRMC. Özaslan et al. [5] designed and analyzed a filament wound composite SRMC with

**Citation:** Zhu, L.; Wang, J.; Shen, W.; Chen, L.; Zhu, C. Design and Analysis of Solid Rocket Composite Motor Case Connector Using Finite Element Method. *Polymers* **2022**, *14*, 2596. https://doi.org/10.3390/ polym14132596

Academic Editor: Yang Zhou

Received: 1 May 2022 Accepted: 15 June 2022 Published: 27 June 2022

**Publisher's Note:** MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations.

**Copyright:** © 2022 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

finite element analysis and compared burst tests regarding the fiber direction strain distribution through the outer surface of the motor case to verify the analysis. Niharika et al. [6] used the simulation software ANSYS (R 18.0, ANSYS Inc., Canonsburg, PA, USA) to design a composite rocket motor casing. Hossam et al. [7] proposed that filament winding was the best technique for the production of composite pressure vessels (CPVs) in a short time, and different materials (including conventional and composite materials) were suitable for the design of SRMC structures. They also studied and summarized the optimum design of SRMC structures. Shaheen et al. [8] developed a 3D model of SRMC using CATIA V5R16 software (V5R16, Dassault Systems, Waltham, MA, USA) and conducted static structural analysis and linear buckling analysis for different stack-ups of a unidirectional carbon–epoxy composite and D6AC steel material rocket motor casing to specify the more efficient material. Prakash et al. [9] successfully designed and developed VEGA SRMC and discussed the effect of material mismatch on the static behavior of the flex seal, which contributed imperatively to the development of composite rocket motor casings. *Polymers* **2022**, *14*, x FOR PEER REVIEW 2 of 12

**Figure 1.** Schematic of SRMC connector and shell: (**a**) the connector to the shell body (**b**) the shell body of the rocket. **Figure 1.** Schematic of SRMC connector and shell: (**a**) the connector to the shell body (**b**) the shell body of the rocket.

At present, carbon fiber-reinforced composites are widely used for strategic missiles and delivery systems, with several related papers published in this field. Ramanjaneyulu et al. [4] explored the SRMC using the finite element method, revealing that the hoop stress was gradually increased from the outer layer to the inner layer in all parts of the SRMC. Özaslan et al. [5] designed and analyzed a filament wound composite SRMC with finite element analysis and compared burst tests regarding the fiber direction strain distribution through the outer surface of the motor case to verify the analysis. Niharika et al. [6] used the simulation software ANSYS (R 18.0, ANSYS Inc., Canonsburg, PA, USA) to design a composite rocket motor casing. Hossam et al. [7] proposed that filament winding was the best technique for the production of composite pressure vessels (CPVs) in a short time, and different materials (including conventional and composite materials) were suitable for the design of SRMC structures. They also studied and summarized the optimum design of SRMC structures. Shaheen et al. [8] developed a 3D model of SRMC using CATIA V5R16 software (V5R16, Dassault Systems, Waltham, MA, USA) and conducted static structural analysis and linear buckling analysis for different stack-ups of a unidirectional carbon–epoxy composite and D6AC steel material rocket motor casing to specify the more efficient material. Prakash et al. [9] successfully designed and developed VEGA SRMC and discussed the effect of material mismatch on the static behavior of the flex seal, which contributed imperatively to the development of composite rocket motor casings. A large number of studies related to CERP have been carried out in other sectors. Juan [10] accurately modeled the winding layer of composite pressure vessels using the fiber winding pressure vessel plug-in WCM, as well as carried out a finite element simulation and blasting test verification on a type IV high-pressure hydrogen storage cylinder with the designed pressure of 70 MPa. Johansen et al. [11] designed a fiber winding analysis program and realized the winding analysis of any axisymmetric rotating body and its combination through an integrated CAD/CAE/CAM design method. Ambach [12] combined CFRP with steel and applied it to the manufacturing of an automobile roof, revealing that the mechanical properties of the material achieved good performance in terms of the crushing resistance of the automobile roof. Wang [13] explored the use of carbon fiber composite materials in biomedical science. Using barium titanate–hydroxyapatite (BT–HA) composite material as the matrix, Cf/BT–HA composite material was prepared to improve the artificial bone due to poor mechanical properties. Liang [14] studied the application of carbon fiber composite materials in bogies of rail transit vehicles, considering the properties of carbon fiber composite materials, such as high strength, high toughness, fatigue resistance, high temperature resistance, corrosion resistance, and light weight; he proposed a rectification plan for the use of carbon fiber composite material as a safety support in current vehicles. In terms of the spinning process, Kovarskii et al. [15] analyzed the structure of carbon fibers such as T800HB using EPR spectroscopy and X-ray diffraction, and they found that the microstructure of carbon fibers is directly related to their mechanical properties.

A large number of studies related to CERP have been carried out in other sectors. Juan [10] accurately modeled the winding layer of composite pressure vessels using the fiber winding pressure vessel plug-in WCM, as well as carried out a finite element simulation and blasting test verification on a type IV high-pressure hydrogen storage cylinder with the designed pressure of 70 MPa. Johansen et al. [11] designed a fiber winding analysis program and realized the winding analysis of any axisymmetric rotating body and its combination through an integrated CAD/CAE/CAM design method. Ambach [12] combined CFRP with steel and applied it to the manufacturing of an To date, many theoretical models related to SRMCs have been reported [16–19]. However, research on SRMC connectors is still insufficient. Generally, the case connector is the main force component, and the loading condition is complex. Meanwhile, the case connector is extremely sensitive to internal imperfections, necessitating methods to effectively improve its mechanical properties and dimensional accuracy. As is known, the SRMC connector operates in a high-temperature environment. Although the connector's external layer is protected by an insulating layer, the surface temperature can still reach up to a maximum of 250 ◦C. Furthermore, the dimensional stability of the connector is another

automobile roof, revealing that the mechanical properties of the material achieved good performance in terms of the crushing resistance of the automobile roof. Wang

HA composite material was prepared to improve the artificial bone due to poor mechanical properties. Liang [14] studied the application of carbon fiber composite materials in bogies of rail transit vehicles, considering the properties of carbon fiber composite materials, such as high strength, high toughness, fatigue resistance, high temperature resistance, corrosion resistance, and light weight; he proposed a rectification plan for the use of carbon fiber composite material as a safety support in current vehicles. In terms of the spinning process, Kovarskii et al. [15] analyzed the structure of carbon fibers such as T800HB using EPR spectroscopy and X-ray diffraction, and they found that the microstructure of carbon fibers is directly related

to their mechanical properties.

basic item, and titanium alloy with excellent comprehensive properties has been broadly used in the connector. However, titanium alloy is expensive with high density, making it a single component with a large mass. The metal connector accounts for more than 15% of the total mass of the case. Furthermore, the process of manufacturing the metal connector is rather complex with a long cycle and high cost. Thus, it is urgent to develop a new material that can replace the metal material in the SRMC connector. broadly used in the connector. However, titanium alloy is expensive with high density, making it a single component with a large mass. The metal connector accounts for more than 15% of the total mass of the case. Furthermore, the process of manufacturing the metal connector is rather complex with a long cycle and high cost. Thus, it is urgent to develop a new material that can replace the metal material in the SRMC connector. In this study, finite element analysis of the SRMC connector was performed. The lay-

*Polymers* **2022**, *14*, x FOR PEER REVIEW 3 of 12

To date, many theoretical models related to SRMCs have been reported [16–19]. However, research on SRMC connectors is still insufficient. Generally, the case connector is the main force component, and the loading condition is complex. Meanwhile, the case connector is extremely sensitive to internal imperfections, necessitating methods to effectively improve its mechanical properties and dimensional accuracy. As is known, the SRMC connector operates in a high-temperature environment. Although the connector's external layer is protected by an insulating layer, the surface temperature can still reach up to a maximum of 250 °C. Furthermore, the dimensional stability of the connector is another basic item, and titanium alloy with excellent comprehensive properties has been

In this study, finite element analysis of the SRMC connector was performed. The layup and optimum structure designs of the connector were exported. The FEM simulation results were shown to be similar to experimental results. Thus, the performance of the optimum design was successfully improved. up and optimum structure designs of the connector were exported. The FEM simulation results were shown to be similar to experimental results. Thus, the performance of the optimum design was successfully improved.

#### **2. Experimental Analysis** The SRMC connector RS05A was made by using the mold pressing process with

**2. Experimental Analysis** 

The SRMC connector RS05A was made by using the mold pressing process with carbon fiber T300 fabric prepreg (Toray Inc., Lacq, France). The thickness and density of the single layer were 0.235 mm and 1.55 g/cm<sup>3</sup> , respectively. Toray T700SC (12K, Toray Inc., Lacq, France)) carbon fiber was employed to produce a motor case with fiber winding technology. The fiber winding shell of the solid rocket motor was made of T700 fiber/epoxy resin composite material (Kosan Inc., Tokyo, Japan)" with a resin content of 32% and fiber content of 150 g, a viscosity of 300 mPa·s at room temperature, an opening period of 8–12 h, a curing temperature of 150 ◦C for 4 h, and a glass transition temperature of 170 ◦C. The bushing was embedded in the composite made of aluminum (AL7075-T6, Moju Inc., Shanghai, China) material, as shown in Figure 2b. The mechanical properties of carbon fiber, P700-1M resin, and AL are presented in Table 1. carbon fiber T300 fabric prepreg (Toray Inc., Lacq, France). The thickness and density of the single layer were 0.235 mm and 1.55 g/cm3, respectively. Toray T700SC (12K, Toray Inc., Lacq, France)) carbon fiber was employed to produce a motor case with fiber winding technology. The fiber winding shell of the solid rocket motor was made of T700 fiber/epoxy resin composite material (Kosan Inc., Tokyo, Japan),, with a resin content of 32% and fiber content of 150 g, a viscosity of 300 mPa·s at room temperature, an opening period of 8–12 h, a curing temperature of 150 °C for 4 h, and a glass transition temperature of 170 °C. The bushing was embedded in the composite made of aluminum (AL7075-T6, Moju Inc., Shanghai, China) material, as shown in Figure 2b. The mechanical properties of carbon fiber, P700-1M resin, and AL are presented in Table 1.

**Figure 2.** Profile of the RS05A front connector: (**a**) primary front connector (**b**) after first-round optimization. **Figure 2.** Profile of the RS05A front connector: (**a**) primary front connector (**b**) after first-round optimization.

**Table 1.** Mechanical properties of the materials.


### **3. Structural Design**

The primary connector structure of the RS05A front connector is illustrated in Figure 1a. After the first round of optimization using the finite element method, the length of the connector was adjusted to make the street longer, so as to fit more closely with the shell wall, as exhibited in Figure 1b. The primary front connector was 10 mm from the opening cut, while the optimized one was 20 mm from the opening cut.

Since the connector was fixed on the case using bolts, the primary RS05A metal connector was designed with M28 × 1.5 threaded hole in the middle. The bushing made of AL-7075-T6 was embedded in the composite connector to solve the problem of the composite being difficult to use as the metal connector.

According to the actual prepreg lay-up effect, the RS05A composite connector was designed to reduce the number of multilayer step structures during the production process, facilitating the insertion of the prepreg in the step structures. Meanwhile, the AL bushing embedded in the composite structure was adjusted into trapezoidal modes in order to ensure the flatness of the inner surface of the case and the thickness of the bushing root. In this way, an optimal design could be achieved.

### **4. RS05A Lay-Up Mode**

Considering the operability of the actual production process, the final optimized layup is illustrated in Figure 3a. The optimized lamination of the composite was cured by a secondary co-curing process. The lamination was laid on the core die, and the lower half of the connector was cured by a molding process after lamination was completed. The secondary co-curing treatment was conducted when the top end face of the connector was laid up again. After curing, the connector was machined to the theoretical shape. Finally, the intermediate insert was embedded into the composite connector body using an adhesive. *Polymers* **2022**, *14*, x FOR PEER REVIEW 5 of 12

**Figure 3.** Lay-up diagram of the preferred scheme: (**a**) lay-up diagram (**b**) cutting opening mode. **Figure 3.** Lay-up diagram of the preferred scheme: (**a**) lay-up diagram (**b**) cutting opening mode.

**Table 2.** The layering table of the connector structure. **Serial Number Lay Up Thickness (mm) Angle (°) Layer Number** 1 Twill weaves of carbon fiber T300 0.225 0/90 1001 2 Twill weaves of carbon fiber T300 0.225 45/−45 1002 The material used for the composite connector was carbon fiber T300 biaxial fabric, which was spread as an isotropic material in the form of a patchwork butt. The prepreg layering table of the connector structure is shown in Table 2. Given the large radian shape of the front connector, it was necessary to shear the pavement. The cutting opening mode is presented in Figure 3b.

3 Twill weaves of carbon fiber T300 0.225 0/90 1003 4 Twill weaves of carbon fiber T300 0.225 45/−45 1004 5 Twill weaves of carbon fiber T300 0.225 0/90 1005 6 Twill weaves of carbon fiber T300 0.225 45/−45 1006 … … … … … 163 Twill weaves of carbon fiber T300 0.225 0/90 1163

166 Prepreg of carbon fiber T300 0.145 45 2002 167 Prepreg of carbon fiber T300 0.145 −45 2003 168 Prepreg of carbon fiber T300 0.145 90 2004 169 Prepreg of carbon fiber T300 0.145 0 2005 170 Prepreg of carbon fiber T300 0.145 45 2006 171 Prepreg of carbon fiber T300 0.145 −45 2007 172 Prepreg of carbon fiber T300 0.145 90 2008 … … … … … 285 Prepreg of carbon fiber T300 0.145 0 2021 286 Prepreg of carbon fiber T300 0.145 45 2122 287 Prepreg of carbon fiber T300 0.145 −45 2123 288 Prepreg of carbon fiber T300 0.145 90 2124 289 Prepreg of carbon fiber T300 0.145 0 2125

The shell layer was designed by grid theory [20], and the designed burst pressure was 15 MPa. The finite element computer software, ABAQUS (V6.13, Dassault Systems, Waltham, MA, USA), was employed for SRMC burst pressure simulation. The dimensions of the finite element model were the actual dimensions. The SRMC and connector were meshed with linear reduced integration solid elements (C3D8R), with a mesh size of

Total thickness 55.025 mm

**5. Finite Element Model** 


**Table 2.** The layering table of the connector structure.

### **5. Finite Element Model**

The shell layer was designed by grid theory [20], and the designed burst pressure was 15 MPa. The finite element computer software, ABAQUS (V6.13, Dassault Systems, Waltham, MA, USA), was employed for SRMC burst pressure simulation. The dimensions of the finite element model were the actual dimensions. The SRMC and connector were meshed with linear reduced integration solid elements (C3D8R), with a mesh size of approximately 10 mm. The model had a total of 23,355 cells and 29,020 nodes. Table 3 presents the front connector weight of different schemes. It can be seen that the front connector weight of the initial plan was 0.41 kg, while that of the optimized scheme was 0.408 kg; the corresponding weights of the AL insert were 0.056 kg and 0.0613 kg, respectively. The percentage weight loss of the optimized plan, final scheme, and experimental measurement was 31.4%, 31.0%, and 30.6%, respectively.

**Table 3.** Front connector weight of different schemes.


### *5.1. Lay-Up Information Table*

The lay-up of the front connector of the RS05A composite was quasi-isotropic, the lay-up of the RS05A composite connector was divided into five directions (0◦ , 22.5◦ , 45◦ , 67.5◦ , and 90◦ ), and the lay-up ratio was 1. In the actual lay-up, each layer was rotated by a certain angle to disperse the lap position and angle.

#### *5.2. Loading and Constraints 5.2. Loading and Constraints*

*5.1. Lay-Up Information Table* 

**Location**

Abaqus was used for linear loading calculation to achieve progressive failure analysis. In the finite element analysis, at each incremental step, the first equilibrium equation was solved, and the stress and strain of each layer of the element covered the stress and strain of the previous step. According to the damage mode, the stiffness could be reduced by changing the material parameters of the integral point. The equilibrium equation was reestablished, and the next load increment step was substituted. If the structure relative stiffness value of the current load step (the ratio of the current stiffness to the initial stiffness) tended to zero and began to soften and enter the unloading state, the structure was considered to have lost the bearing capacity, necessitating the progressive failure analysis of the wound shell [21]. Abaqus was used for linear loading calculation to achieve progressive failure analysis. In the finite element analysis, at each incremental step, the first equilibrium equation was solved, and the stress and strain of each layer of the element covered the stress and strain of the previous step. According to the damage mode, the stiffness could be reduced by changing the material parameters of the integral point. The equilibrium equation was reestablished, and the next load increment step was substituted. If the structure relative stiffness value of the current load step (the ratio of the current stiffness to the initial stiffness) tended to zero and began to soften and enter the unloading state, the structure was considered to have lost the bearing capacity, necessitating the progressive failure analysis of the wound shell [21].

The RS05A Motor Case mainly bears internal pressure. Axial displacement constraints were applied to the middle part of the shell to avoid rigid body displacement in the finite element calculation, and cyclic symmetry conditions were applied to the sides of the shell and joint model. Uniformly distributed pressure was applied on the inner surface of the shell, increasing from 0 to 15 MPa. The boundary conditions for the SRMC and connector in ABAQUS are defined below. The *X*-axis translation of the RS05A motor case was constrained, in addition to the Y-direction translation of the upper and lower surface elements and the Z-direction translation of the front and rear surface elements. In other words, symmetric constraints were imposed on the motor case. The constraints are illustrated in Figure 4. The RS05A Motor Case mainly bears internal pressure. Axial displacement constraints were applied to the middle part of the shell to avoid rigid body displacement in the finite element calculation, and cyclic symmetry conditions were applied to the sides of the shell and joint model. Uniformly distributed pressure was applied on the inner surface of the shell, increasing from 0 to 15 MPa. The boundary conditions for the SRMC and connector in ABAQUS are defined below. The *X*-axis translation of the RS05A motor case was constrained, in addition to the Y-direction translation of the upper and lower surface elements and the Z-direction translation of the front and rear surface elements. In other words, symmetric constraints were imposed on the motor case. The constraints are illustrated in Figure 4.

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**Table 3.** Front connector weight of different schemes.

a certain angle to disperse the lap position and angle.

experimental measurement was 31.4%, 31.0%, and 30.6%, respectively.

**AL Front Connector Scheme**

**Front connector weight (kg)** 0.68 0.41 0.408 0.411 **AL insert weight (kg)** - 0.056 0.0613 0.0613 **Total weight (kg)** 0.68 0.466 0.469 0.472 **Percentage weight loss (%)** - 31.4% 31.0% 30.6%

The lay-up of the front connector of the RS05A composite was quasi-isotropic, the lay-up of the RS05A composite connector was divided into five directions (0°, 22.5°, 45°, 67.5°, and 90°), and the lay-up ratio was 1. In the actual lay-up, each layer was rotated by

approximately 10 mm. The model had a total of 23,355 cells and 29,020 nodes. Table 3 presents the front connector weight of different schemes. It can be seen that the front connector weight of the initial plan was 0.41 kg, while that of the optimized scheme was 0.408 kg; the corresponding weights of the AL insert were 0.056 kg and 0.0613 kg, respectively. The percentage weight loss of the optimized plan, final scheme, and

> **The Initial Configuration**

**Optimized Scheme**

**Experimental Measurements**

The load condition was 15 MPa of internal blasting press.

Contact: Since the front connector and the insert are two parts, there may be relative friction between them. In this study, the contact constraint conditions were imposed on the bottom end face, the side of the front connector, and the bushing. The friction form was set using a friction coefficient of 1.5.

The SRMC failure criteria proposed by Hashin criteria [22] were applied to detect the failure modes in the fiber and matrix under both tension and compression failures, which involve four failure modes. The failure modes included in Hashin's criteria are expressed below.

Tensile fiber failure for *σ*<sup>11</sup> ≥ 0:

$$
\left(\frac{\sigma\_{11}}{X\_T}\right)^2 + \frac{\sigma\_{12}^2 + \sigma\_{13}^2}{S\_{12}^2} \ge 1. \tag{1}
$$

Compressive fiber failure for *σ*<sup>11</sup> < 0:

$$\left(\frac{\sigma\_{11}}{X\_{\mathfrak{C}}}\right)^2 \ge 1.\tag{2}$$

Tensile matrix failure for *σ*<sup>22</sup> + *σ*<sup>33</sup> > 0:

$$\frac{\left(\sigma\_{22} + \sigma\_{33}\right)^2}{Y\_T^2} + \frac{\sigma\_{23}^2 - \sigma\_{22}\sigma\_{33}}{S\_{23}^2} + \frac{\sigma\_{12}^2 + \sigma\_{13}^2}{S\_{12}^2} \ge 1. \tag{3}$$

Compressive matrix failure for *σ*<sup>22</sup> + *σ*<sup>33</sup> < 0:

$$\mathbb{E}\left[\left(\frac{Y\_{\mathbb{C}}}{2S\_{23}}\right)^2 - 1\right] \left(\frac{\sigma\_{22} + \sigma\_{33}}{Y\_{\mathbb{C}}}\right) + \frac{(\sigma\_{22} + \sigma\_{33})^2}{4S\_{23}^2} + \frac{\sigma\_{23}^2 - \sigma\_{22}\sigma\_{23}}{S\_{23}^2} + \frac{\sigma\_{12}^2 + \sigma\_{13}^2}{S\_{12}^2} \ge 1. \tag{4}$$

Interlaminar tensile failure for *σ*<sup>33</sup> > 0:

$$\left(\frac{\sigma\_{33}}{Z\_T}\right)^2 \ge 1.\tag{5}$$

$$\left(\frac{\sigma\_{33}}{Z\_{\mathbb{C}}}\right)^2 \ge 1.\tag{6}$$

Here, the *σij* terms are components of the stress tensor, *i* and *j* are local coordinate axes parallel and transverse to the fibers in each ply, respectively, and the *z*-axis coincides with the through-thickness direction.

Statical analysis using FEM was performed for the RS05A Motor Case, where the connector received complicated stress under high internal pressure. The mechanical responses and damage morphology of the FE models were obtained.

### **6. Results and Discussion**

### *6.1. Analysis Results of the RS05A Front Connector*

Pressure was applied on the shell; then, the shell was enlarged and deformation occurred in the middle of the front connector. This phenomenon was due to the existence of the pressure exerted internally. The deformation and maximum shear stress diagrams of the front connector under 15 MPa of blasting pressure are exhibited in Figure 5. It can be seen that the magnitude deformation of the front connector reached 5.376 mm. The maximum shear stress in the *XY*-direction was 2.57 MPa. Table 4 presents the displacement and shear stress results of the design. *Polymers* **2022**, *14*, x FOR PEER REVIEW 8 of 12 maximum shear stress in the *XY*-direction was 2.57 MPa. Table 4 presents the displacement and shear stress results of the design.

**Figure 5.** Deformation and maximum shear stress diagrams of the front connector: (**a**) deformation diagram; (**b**) maximum shear stress in *XY*-direction (τxy = 257 × 10<sup>−</sup>2 MPa). **Figure 5.** Deformation and maximum shear stress diagrams of the front connector: (**a**) deformation diagram; (**b**) maximum shear stress in *XY*-direction (τxy = 257 <sup>×</sup> <sup>10</sup>−<sup>2</sup> MPa).

**Calculated Value** 

**Final Preferred Solution Experimental Measurements**

**Factor Experimental Value** 

**Safety** 

The stress distribution of the front connector is presented in Figures 6 and 7. As can be seen, the maximal tensile and compressive stress calculated using FEM was 492 MPa and −537 MPa, respectively. As shown in Table 4, the FEM results and experimental

measurements were in agreement with the practical values.

(**a**) (**b**)

**Tensile stress in** *X***-direction (MPa)** 500 492.0 1.24 496.4 **Compressive stress in** *X***-direction (MPa)** −665 −158.9 1.02 −172.8 **Tensile stress in** *Y***-direction (MPa)** 552 450.2 1.23 463.6 **Compressive stress in** *Y***-direction (MPa)** −500 −212.6 3.16 −235.8 **Shear stress in** *XY***-plane (MPa)** 118 2.574 45.91 6.431 **Von Mises stress of AL inserts (MPa)** 505 332.4 1.52 362.3

**Table 4.** Finite element calculation results.

**Allowable Value [23,24]** 


(**a**) (**b**)

diagram; (**b**) maximum shear stress in *XY*-direction (τxy = 257 × 10<sup>−</sup>2 MPa).

*Polymers* **2022**, *14*, x FOR PEER REVIEW 8 of 12

displacement and shear stress results of the design.

maximum shear stress in the *XY*-direction was 2.57 MPa. Table 4 presents the

**Figure 5.** Deformation and maximum shear stress diagrams of the front connector: (**a**) deformation

**Table 4.** Finite element calculation results. **Table 4.** Finite element calculation results.

The stress distribution of the front connector is presented in Figures 6 and 7. As can be seen, the maximal tensile and compressive stress calculated using FEM was 492 MPa and −537 MPa, respectively. As shown in Table 4, the FEM results and experimental measurements were in agreement with the practical values. The stress distribution of the front connector is presented in Figures 6 and 7. As can be seen, the maximal tensile and compressive stress calculated using FEM was 492 MPa and −537 MPa, respectively. As shown in Table 4, the FEM results and experimental measurements were in agreement with the practical values.

**Figure 6.** Maximal tensile and compressive stress diagrams in the *X*-direction: (**a**) Tensile stress (σ<sup>x</sup> = 4.92 <sup>×</sup> <sup>10</sup><sup>2</sup> MPa); (**b**) Compressive stress (σ<sup>x</sup> <sup>=</sup> <sup>−</sup>1.589 <sup>×</sup> <sup>10</sup><sup>2</sup> MPa). **Figure 6.** Maximal tensile and compressive stress diagrams in the *X*-direction: (**a**) Tensile stress (σ<sup>x</sup> = 4.92 × 102 MPa); (**b**) Compressive stress (σx = −1.589 × 102 MPa).

**Figure 7.** Maximal tensile and compression stress diagram in the *Y*-direction: (**a**) Tensile stress (σ<sup>y</sup> = 4.502 × 102 MPa); (**b**) Compression stress (σy = −2.126 × 102 MPa). **Figure 7.** Maximal tensile and compression stress diagram in the *Y*-direction: (**a**) Tensile stress (σ<sup>y</sup> = 4.502 <sup>×</sup> <sup>10</sup><sup>2</sup> MPa); (**b**) Compression stress (σ<sup>y</sup> <sup>=</sup> <sup>−</sup>2.126 <sup>×</sup> <sup>10</sup><sup>2</sup> MPa).

Figure 8 shows that the Von Mises stress of AL inserts was 332.4MPa. As shown in Table 4, the stress–strain values obtained from the simulations were all within the

**Figure 8.** Von Mises stress of AL inserts (σy = 332.4 MPa): (**a**) Von Mises stress (overall view); (**b**)

A water pressure blasting experiment is designed for the shell to monitor the strain displacement change of the shell during blasting. Strain monitoring points were uniformly set on the shell and front connector, as shown in Figure 9. Deformation was relatively larger in the process of the booster, with resin shell cracking. Due to some damage of the strain gauge, the strain value could not be displayed. The complete results of the test points were generated, with each strain measuring point monitoring strain changes in both directions. The strain of point 8 at the small polar hole generated a sudden

 (**a**) (**b**)

Von Mises stress (partial view).

*6.2. Experimental Results* 

Figure 8 shows that the Von Mises stress of AL inserts was 332.4MPa. As shown in Table 4, the stress–strain values obtained from the simulations were all within the permissible limits obtained from the experiments. Figure 8 shows that the Von Mises stress of AL inserts was 332.4MPa. As shown in Table 4, the stress–strain values obtained from the simulations were all within the permissible limits obtained from the experiments.

**Figure 7.** Maximal tensile and compression stress diagram in the *Y*-direction: (**a**) Tensile stress (σ<sup>y</sup>

**Figure 6.** Maximal tensile and compressive stress diagrams in the *X*-direction: (**a**) Tensile stress (σ<sup>x</sup>

*Polymers* **2022**, *14*, x FOR PEER REVIEW 9 of 12

= 4.92 × 102 MPa); (**b**) Compressive stress (σx = −1.589 × 102 MPa).

(**a**) (**b**)

= 4.502 × 102 MPa); (**b**) Compression stress (σy = −2.126 × 102 MPa).

**Figure 8.** Von Mises stress of AL inserts (σy = 332.4 MPa): (**a**) Von Mises stress (overall view); (**b**) Von Mises stress (partial view). **Figure 8.** Von Mises stress of AL inserts (σy = 332.4 MPa): (**a**) Von Mises stress (overall view); (**b**) Von Mises stress (partial view).

#### *6.2. Experimental Results 6.2. Experimental Results*

A water pressure blasting experiment is designed for the shell to monitor the strain displacement change of the shell during blasting. Strain monitoring points were uniformly set on the shell and front connector, as shown in Figure 9. Deformation was relatively larger in the process of the booster, with resin shell cracking. Due to some damage of the strain gauge, the strain value could not be displayed. The complete results of the test points were generated, with each strain measuring point monitoring strain changes in both directions. The strain of point 8 at the small polar hole generated a sudden A water pressure blasting experiment is designed for the shell to monitor the strain displacement change of the shell during blasting. Strain monitoring points were uniformly set on the shell and front connector, as shown in Figure 9. Deformation was relatively larger in the process of the booster, with resin shell cracking. Due to some damage of the strain gauge, the strain value could not be displayed. The complete results of the test points were generated, with each strain measuring point monitoring strain changes in both directions. The strain of point 8 at the small polar hole generated a sudden change. Two points were set for displacement change monitoring, which coincided with strain monitoring points 2 and 5. The results of extracting the two point shifts are shown in Figure 10. When the pressure reached 33 MPa, displacement occurred at both points. Combined with the strain displacement test results in the experiment, it can be seen that the actual burst pressure was 33 MPa. The hydrostatic test showed that the cylinder could meet the internal pressure of 15 MPa in working conditions and 33 MPa in blasting conditions. *Polymers* **2022**, *14*, x FOR PEER REVIEW 10 of 12 change. Two points were set for displacement change monitoring, which coincided with strain monitoring points 2 and 5. The results of extracting the two point shifts are shown in Figure 10. When the pressure reached 33 MPa, displacement occurred at both points. Combined with the strain displacement test results in the experiment, it can be seen that the actual burst pressure was 33 MPa. The hydrostatic test showed that the cylinder could meet the internal pressure of 15 MPa in working conditions and 33 MPa in blasting conditions.

> The calculation results of typical schemes are summarized in Table 4. As shown, the experimental measurements, such as the front connector deformation, tensile and compressive stress in the *XY*-direction, shear stress in *XY*-plane, and Von Mises stress of

> The winding angle used in the calculation (18.5°) was the average winding angle, while the actual winding angle at the equator was about 26°, i.e., the winding angle from the middle part of the barrel to the equator of the back head changed from 18.5° to 26°, resulting in an increase in the actual torsional stiffness of the cylinder near the back head. Therefore, the measured circumferential strain value was small. In the actual working condition, the stress of the shell would be better than that of the proposed design, and no damage would occur with the calculated value. Both calculated stresses were within the range of allowable design values. The design scheme and calculation met the

> 1. In this study, finite element analysis of the SRMC connector was performed. The layup and optimum structure designs of the connector were investigated. An experimental design was established, and the FEM simulation value was calculated. Loading and constrains were implemented in the FEM model. The actual

**Figure 9.** Stress measurement point. **Figure 9.** Stress measurement point.

**Figure 10.** Tendency of displacement.

**7. Conclusions** 

AL inserts, were preferred as the final solution.

requirements, and the design proposal was reasonable.

**Figure 9.** Stress measurement point.

**Figure 10.** Tendency of displacement. **Figure 10.** Tendency of displacement.

conditions.

The calculation results of typical schemes are summarized in Table 4. As shown, the experimental measurements, such as the front connector deformation, tensile and compressive stress in the *XY*-direction, shear stress in *XY*-plane, and Von Mises stress of AL inserts, were preferred as the final solution. The calculation results of typical schemes are summarized in Table 4. As shown, the experimental measurements, such as the front connector deformation, tensile and compressive stress in the *XY*-direction, shear stress in *XY*-plane, and Von Mises stress of AL inserts, were preferred as the final solution.

change. Two points were set for displacement change monitoring, which coincided with strain monitoring points 2 and 5. The results of extracting the two point shifts are shown in Figure 10. When the pressure reached 33 MPa, displacement occurred at both points. Combined with the strain displacement test results in the experiment, it can be seen that the actual burst pressure was 33 MPa. The hydrostatic test showed that the cylinder could meet the internal pressure of 15 MPa in working conditions and 33 MPa in blasting

The winding angle used in the calculation (18.5°) was the average winding angle, while the actual winding angle at the equator was about 26°, i.e., the winding angle from the middle part of the barrel to the equator of the back head changed from 18.5° to 26°, resulting in an increase in the actual torsional stiffness of the cylinder near the back head. Therefore, the measured circumferential strain value was small. In the actual working condition, the stress of the shell would be better than that of the proposed design, and no damage would occur with the calculated value. Both calculated stresses were within the range of allowable design values. The design scheme and calculation met the requirements, and the design proposal was reasonable. The winding angle used in the calculation (18.5◦ ) was the average winding angle, while the actual winding angle at the equator was about 26◦ , i.e., the winding angle from the middle part of the barrel to the equator of the back head changed from 18.5◦ to 26◦ , resulting in an increase in the actual torsional stiffness of the cylinder near the back head. Therefore, the measured circumferential strain value was small. In the actual working condition, the stress of the shell would be better than that of the proposed design, and no damage would occur with the calculated value. Both calculated stresses were within the range of allowable design values. The design scheme and calculation met the requirements, and the design proposal was reasonable.

#### **7. Conclusions 7. Conclusions**


**Author Contributions:** Conceptualization, L.Z.; methodology, L.Z.; software, W.S. and J.W.; validation, L.Z., J.W. and L.C.; formal analysis, L.Z.; investigation, L.Z. and J.W.; resources, W.S. and L.C.; data curation, L.Z.; writing—original draft preparation, L.Z.; writing—review and editing, L.Z. and J.W.; visualization, W.S. and L.C.; supervision, C.Z.; project administration, L.Z.; funding acquisition, L.Z. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was funded by Zhejiang Provincial Natural Science Foundation of China (LGG21E050025), Fundamental Research Funds of Zhejiang Sci-Tech University, (20202113-Y) and Fundamental Research Funds of Shaoxing Keqiao Research Institute of Zhejiang Sci-Tech University, (KYY2021001G).

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** Data sharing not applicable.

**Acknowledgments:** The authors acknowledge the financial support from the Zhejiang Provincial Natural Science Foundation of China under Grant No. LGG21E050025, the Fundamental Research Funds of Zhejiang Sci-Tech University (Project Number: 20202113-Y), and the Fundamental Research Funds of Shaoxing Keqiao Research Institute of Zhejiang Sci-Tech University (Project number: KYY2021001G).

**Conflicts of Interest:** The authors declare no conflict of interest.

### **References**


**Xinhua Liang, Honglian Cong \*, Zhijia Dong and Gaoming Jiang**

Engineering Research Center for Knitting Technology, Ministry of Education, Jiangnan University, Wuxi 214122, China; liangxh18861852560@163.com (X.L.); dongzj0921@163.com (Z.D.); jgm@jiangnan.edu.cn (G.J.) **\*** Correspondence: cong-wkrc@163.com; Tel.: +86-186-2631-3622

**Abstract:** Benefitting from the multifunctional properties of knitted fabrics with elasticity, flexibility, and high resilience, knitted strain sensors based on structure and strain performance are widely utilized in sports health due to their adaptability to human movements. However, the fabrication process of common strain sensors mainly relies on experienced technicians to determine the best sensor size through repeated experiments, resulting in significant size errors and a long development cycle. Herein, knitted strain sensors based on plain knit were fabricated with nylon/spandex composite yarn and silver-plated nylon yarn using a flat knitting process. A size prediction model of knitted strain sensors was established by exploring the linear relationship between the conductive area size of samples and knitting parameters via SPSS regression analysis. Combined with stable structures and high performance of good sensitivity, stability, and durability, the knitted strain sensors based on size prediction models can be worn on human skin or garments to monitor different movements, such as pronunciation and joint bending. This research indicated that the reasonable size control of the knitted strain sensor could realize its precise positioning in intelligent garments, exhibiting promising potential in intelligent wearable electronics.

**Keywords:** knitted fabrics; strain sensors; size prediction; precise positioning; human motion detection

### **1. Introduction**

With the foreseeable prosperity and integration of medical electrical devices, textile equipment, and human health monitoring equipment, wearable devices have attracted considerable attention from investigators due to their promising applications in human motion detection, soft robotics, electronic skins, and sensors [1–7]. Knitted strain sensors with the attributes of being lightweight, having good flexibility, and with a wide strain range have been emerging, promising a myriad of applications in the development of wearable sensing devices [8–13]. So far, plenty of knitted strain sensors are coated with conductive materials, such as graphene [14–16], polypyrrole [17,18], PEDOT: PSS [19], and nano-silver [20,21], showcasing the advantages of good stability, high sensitivity, and fast response. Various novel fabrication methods [22–24] have been proposed to knit the conductive yarn into the conductive fabric directly, forming an intelligent wearable device with sensing performance. However, these types of sensors are structurally unstable and have a small strain range, which definitely impedes their practical application [25,26].

In addition, yarn type, structure, and the interaction between loops are also important factors affecting the knitted sensor's performance. Production parameters, such as structural changes, spandex content, and the washing and ironing processes, play a fundamental role in determining the sensors' physical behavior and sensing performance [27–29]. Most strain sensors based on knitted structures rely on resistance changes [30–32]. For instance, Liu et al. proposed a geometric model incorporated with a simplified resistive network, determining the resistance effect of conductive float stitches on knitted structures with different courses and wales [33]. To evaluate the overall degree of plane anisotropy of knitted fabrics, a new measurement procedure was established using the van der Pauw electrode configuration to solve the issue of measuring the edge resistance of fabrics [34].

**Citation:** Liang, X.; Cong, H.; Dong, Z.; Jiang, G. Size Prediction and Electrical Performance of Knitted Strain Sensors. *Polymers* **2022**, *14*, 2354. https://doi.org/10.3390/ polym14122354

Academic Editors: Yang Zhou and Zhaoling Li

Received: 5 May 2022 Accepted: 6 June 2022 Published: 10 June 2022

**Publisher's Note:** MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations.

**Copyright:** © 2022 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

Knitting elements with different proportions also have a considerable impact on the conductive fabric resistance [35]. Li et al. produced a resistance model of conductive knitted fabric under unidirectional stretching, superimposing length resistance and contact resistance to simulate the fabric resistance [36]. The as-developed resistance calculation systems reveal the discipline of resistance variation in conductive knitted fabrics, offering a theoretical reference in conductive fabric design.

The size prediction of knitted fabric is a considerable segment in the garment design and production process. For example, Liu et al. developed the size prediction model of warp-knitted Jacquard fabric to investigate the relationship between the yarn count, tensile density, and the size shrinkage rate, utilizing JavaScript and WebGL technologies to automatically generate clothing templates [37]. A structural model correlating the size of tubular knitted fabric with the loop geometric parameters was produced, deducing yarn-feeding parameters according to the elasticity and size requirements of the fabric [38]. Ulson et al. put forward a prediction system of circular-knitted cotton fabric, introducing an approach that saves time and money while improving knitted fabric quality for customers [39].

To date, the study on knitted strain sensors has mainly focused on the influence of elements of resistance, the resistance calculation model, and the sensor design and application, whereas there are few researches on size control and prediction. Intelligent garments monitoring human movements require that sensors be able to respond instantly and sensitively to changes in human joints and skin. In the actual development process, samples should be designed at least 2–3 times to determine the sensors' sizes at different parts of the human body, and the finishing process is also more complicated, resulting in a significant increase in cost and product losses. This makes the size control the focus and nodus in the design and fabrication of knitted strain sensors.

Herein, knitted strain sensors based on plain knit were successfully fabricated with nylon/spandex composite yarn and silver-plated nylon yarn using a flat knitting process. By investigating the influence of different knitting parameters on a sensor's size, the size prediction model was established. To assess its potential to serve as a strain sensor, electrical performance tests were carried out to probe its sensitivity, hysteresis deviation, working sense range, and repeatability under various stretching rates. Furthermore, the as-prepared strain sensor based on the size prediction model was applied to monitor different human movements in order to verify its accuracy, indicating its promising potential for use in intelligent wearable devices.

### **2. Experimental Methods**

### *2.1. Materials*

In this experiment, silver-plated nylon yarn (222dtex/48F, the electrical resistance is 6.5 Ω/cm) was purchased from Qingdao Hengtong Weiye Special Fabric Technology Co., Ltd. (Qingdao, China). Nylon/spandex composite yarns (22/55dtex, 22/77dtex, and 44/77dtex) were purchased from Hubei Yutao Special Fiber Co., Ltd. (Chongyang, China). Elastic nylon filament (333dtex/24F) was obtained from Jiangsu Pingmei Yarn Industry Co., Ltd. (Hai'an, China).

### *2.2. Preparation of Knitted Strain Sensors*

The plain knit structure has been proved to be a promising candidate as the fabric substrate due to its merits of compact structure, considerable flexibility, and relatively excellent electrical performance [40]. Figure 1 exhibits the pattern design and knitting process of the strain sensors. The machine parameters of a sensor's compression pattern transformed into an expanded pattern via automatic control instructions were set in SDS-ONE APEX3 pattern design system matching with a computerized flat knitting machine. Three yarn feeders were used in the knitting process, working from bottom to top.

nylon/spandex composite yarns, respectively.

APEX3 pattern design system matching with a computerized flat knitting machine. Three

The preparation process of the knitted strain sensor is illustrated in Figure 2. The elastic nylon filament was knitted to form the non-conductive area as a fabric substrate. Every loop in the conductive area consisted of two overlapping yarns, in which the silverplated nylon yarn appeared at the technical surface of the strain sensors, with the nylon/spandex composite yarn at the back. The two areas were connected by a tuck loop. Considering the feasibility of knitting, the measurability, and the reduction in excess waste, the wales of the sensor's conductive area were set as 30, 40, and 50, and the courses were set as 10, 20, and 30, respectively. The specifications of all samples are shown in Table 1, where EN, SN, and NS are elastic nylon filament, silver-plated nylon yarn, and

yarn feeders were used in the knitting process, working from bottom to top.

The preparation process of the knitted strain sensor is illustrated in Figure 2. The elastic nylon filament was knitted to form the non-conductive area as a fabric substrate. Every loop in the conductive area consisted of two overlapping yarns, in which the silver-plated nylon yarn appeared at the technical surface of the strain sensors, with the nylon/spandex composite yarn at the back. The two areas were connected by a tuck loop. *Polymers* **2022**, *14*, x FOR PEER REVIEW 4 of 14

**Figure 2.** The fabrication process of the knitted strain sensor. **Figure 2.** The fabrication process of the knitted strain sensor.

**Fabric No. Wales Courses** 

30

40

50

10

20

30

10

20

30

10

F1

F4

F7

F10

F13

F16

F19

F22

**Table 1.** Knitting parameters of the experimental samples. **Yarn Composition Spandex**  Considering the feasibility of knitting, the measurability, and the reduction in excess waste, the wales of the sensor's conductive area were set as 30, 40, and 50, and the

**Non-Conductive Area Content (%) Conductive Area** 

**Plating Yarn Ground Yarn** 

20/50 NS 28.5

20/50 NS 28.5

20/50 NS 28.5

20/50 NS 28.5

20/50 NS 28.5

20/50 NS 28.5

20/50 NS 28.5

F3 40/70 NS 36.3

F5 20/70 NS 22.2 F6 40/70 NS 36.3

F8 20/70 NS 22.2 F9 40/70 NS 36.3

F11 20/70 NS 22.2 F12 40/70 NS 36.3

F14 20/70 NS 22.2 F15 40/70 NS 36.3

F17 20/70 NS 22.2 F18 40/70 NS 36.3

F20 20/70 NS 22.2 F21 40/70 NS 36.3

F23 20/70 NS 22.2

<sup>20</sup>20/50 NS 28.5

EN SN

courses were set as 10, 20, and 30, respectively. The specifications of all samples are shown in Table 1, where EN, SN, and NS are elastic nylon filament, silver-plated nylon yarn, and nylon/spandex composite yarns, respectively.

**Table 1.** Knitting parameters of the experimental samples.


*2.3. Characterization and Measurements*

### 2.3.1. Size-Change Test

Under the ironing condition of 150 ◦C and 0.4 MPa, the knitted strain sensors were ironed with a BOG energy-saving steam generator (Yancheng Xuanlang Machinery Equipment Co., Ltd., Yancheng, China). The size-change principle of the sensors was analyzed by SPSS regression analysis.

### 2.3.2. Electrical Performance Test

The electrical performance of a sensor largely depends on its strain. When the sensor is stretched, the contact conditions between the loops change, resulting in corresponding changes in its resistance [41]. In this paper, a sensor's resistance from 0−100% strain range was measured. The strain was implemented to the sensor by the electric stretching/compression test bench (Beijing Jipin Times Technology Co., Ltd., Beijing, China). The resistance was recorded using a CHI760 electrochemical analyzer (Shanghai Chenhua Instrument Co., Ltd., Shanghai, China), which presents the corresponding time-current (I-T) characteristic curve.

### **3. Results and Discussions**

### *3.1. Relationship between Knitting Factors and Sensor Size*

The horizontal and vertical sizes of the conductive area in the sensors with different knitting factors were measured, including the gray and the finished samples. Size shrinkage of the samples was calculated by Formulas (1) and (2).

$$S\_{\rm h} = (X\_{\rm h} - Y\_{\rm h}) / X\_{\rm h} \times 100\% \tag{1}$$

$$\mathbf{S}\_{\upsilon} = (\mathbf{X}\_{\upsilon} - \mathbf{Y}\_{\upsilon}) / \mathbf{X}\_{\upsilon} \times 100\% \tag{2}$$

where *X<sup>h</sup>* and *Y<sup>h</sup>* represent the horizontal size of the gray and the finished samples, respectively. *S<sup>h</sup>* represents the horizontal size shrinkage. *X<sup>v</sup>* and *Y<sup>v</sup>* represent the vertical size of the gray and the finished samples, respectively. *S<sup>v</sup>* represents the vertical size shrinkage.

### 3.1.1. The Effect of Knitting Factors on Sensors' Horizontal Size

Figure 3 reveals the change rate of the sensors' horizontal size. When the wales and courses were constant, the horizontal change rate of the samples increased gradually with the increase of spandex content. There was inevitable residual stress in the nylon and spandex fibers, producing a shrinkage phenomenon when heated at a high temperature. A sensor with a high spandex content had a large shrinkage rate. It also increased with the augmentation of the wales and courses under the uniform yarn composition. This resulted mainly from the increase in the length of the needle and sinker loops, causing a higher shrinkage rate during the process. *Polymers* **2022**, *14*, x FOR PEER REVIEW 6 of 14

**Figure 3.** Change rate of sensors' horizontal size. **Figure 3.** Change rate of sensors' horizontal size.

3.1.2. The Effect of Knitting Factors on Sensors' Vertical Size

3.1.2. The Effect of Knitting Factors on Sensors' Vertical Size The change rate of the sensors' vertical size, similar to that of the horizontal size, is shown in Figure 4. It increased with the addition of the spandex content, wales, and courses, which was mainly affected by the elastic shrinkage property of spandex and the The change rate of the sensors' vertical size, similar to that of the horizontal size, is shown in Figure 4. It increased with the addition of the spandex content, wales, and courses, which was mainly affected by the elastic shrinkage property of spandex and the number of leg yarn segments. The change rate of samples with vertical size exceeded that of those of horizontal size. The probable explanation is that the length of the

number of leg yarn segments. The change rate of samples with vertical size exceeded that of those of horizontal size. The probable explanation is that the length of the needle and

Therefore, the length change of the latter surpasses the former when subjected to heat

**Figure 4.** Change rate of sensors' vertical size.

contraction, leading to a higher vertical shrinkage rate.

needle and the sinker loop is shorter than the leg yarn segment in a loop with a compact arrangement. Therefore, the length change of the latter surpasses the former when subjected to heat contraction, leading to a higher vertical shrinkage rate. the sinker loop is shorter than the leg yarn segment in a loop with a compact arrangement. Therefore, the length change of the latter surpasses the former when subjected to heat contraction, leading to a higher vertical shrinkage rate.

The change rate of the sensors' vertical size, similar to that of the horizontal size, is shown in Figure 4. It increased with the addition of the spandex content, wales, and courses, which was mainly affected by the elastic shrinkage property of spandex and the number of leg yarn segments. The change rate of samples with vertical size exceeded that of those of horizontal size. The probable explanation is that the length of the needle and

**Figure 3.** Change rate of sensors' horizontal size.

3.1.2. The Effect of Knitting Factors on Sensors' Vertical Size

*Polymers* **2022**, *14*, x FOR PEER REVIEW 6 of 14

**Figure 4.** Change rate of sensors' vertical size. **Figure 4.** Change rate of sensors' vertical size.

3.1.3. Size Prediction Model of the Sensors

To probe the relationship between the spandex content, wales, courses, and sensor size, SPSS was utilized for regression analysis of the sorted data. S represents significance, which is the basis for judging whether R (correlation coefficient) is of statistical significance. The correlation coefficient between the two variables has no statistical significance when S > 0.05. The S and R values of the samples are shown in Table 2. The three knitting parameters are highly correlated with the size shrinkage of the sensors, and all have a significant effect.



In the light of the analysis by SPSS, the horizontal and vertical shrinkage rate of the sensor size was calculated using the following Formulas (3) and (4), respectively.

$$S\_h = -3.617 + 0.044x + 0.064y + 31.567z,\tag{3}$$

$$S\_{\upsilon} = -37.552 + 0.101x + 0.215y + 83.334z,\tag{4}$$

where *x* represents the wales, *y* represents the courses, and *z* represents the spandex content. It can be observed from the equation that the dependent coefficients of the horizontal and vertical shrinkage rates are all positive, indicating that the size shrinkage in two directions of the samples increases with the three parameters. In combination with Formulas (1) and (2), the calculation methods of the horizontal and vertical sizes of the sensors can be described as Formulas (5) and (6), respectively.

$$Y\_h = \frac{\mathbf{x}}{P\_\mathbf{x}} - \frac{(-3.617 + 0.044\mathbf{x} + 0.064y + 31.567\mathbf{z}) \cdot P\_\mathbf{x}}{\mathbf{x}}\tag{5}$$

$$Y\_v = \frac{y}{P\_y} - \frac{(-37.552 + 0.101x + 0.215y + 83.334z) \cdot P\_y}{y} \tag{6}$$

In conclusion, the size prediction and control of the sensors can be realized by changing the number of wales, courses, and the spandex content, providing a certain guiding significance for future research. *Polymers* **2022**, *14*, x FOR PEER REVIEW 8 of 14

#### *3.2. Electrical Performance of the Knitted Strain Sensor* data processing software matched with the electrochemical analyzer, the applied AC voltage was set to 0.1 V. Then, the current data was processed by Excel software according to

To illustrate the electrical properties of the knitted strain sensor, the sensing mechanism was systematically explored by simulating the relationship between resistance and deformation under the stretching–releasing process. As shown in Figure 5a, the knitting strain sensor connected to the CHI760 electrochemical analyzer through two collets (red wire and blue wire) was held at both ends of the ESM303 electric stretching/compression test bench along the horizontal direction. The sensor was stretched 0–100% at the stretching rate of 100 mm min−<sup>1</sup> . Furthermore, a computer was affiliated to the CHI760 electrochemical analyzer through a multifunctional communication cable (black wire) to output the current change with time during the stretching–releasing process in real time. In the data processing software matched with the electrochemical analyzer, the applied AC voltage was set to 0.1 V. Then, the current data was processed by Excel software according to the formula: R = V/I, and the corresponding data of resistance change with time was obtained. the formula: R = V/I), and the corresponding data of resistance change with time was obtained. The loop structure of the knitted strain sensor can be regarded as a complex series and parallel electrical network involving the resistance of each yarn segment and contact resistance [42]. Figure 5b expounds on the loop changes of the sensor during the cycle test. The contact resistance change played a governing function in the horizontal stretching of the fabric, whereas the resistance change caused by loop transfer had little effect on the sensor's resistance. In the initial stage of stretching, the leg yarn segments transferred to the needle and sinker loops [43], and the number of contact points changed rapidly, accounting for the higher sensitivity of the sensor. With the further increase in external stretching, the transfer of the yarn segment was no longer evident, resulting in a smaller change in the number of contact points. Herein, lower sensitivity was observed for higher stretching.

**Figure 5.** Research on sensing mechanism of the knitted strain sensor, (**a**) illustration of the measuring device, and (**b**) loop change of the strain sensor during the horizontal stretching process. **Figure 5.** Research on sensing mechanism of the knitted strain sensor, (**a**) illustration of the measuring device, and (**b**) loop change of the strain sensor during the horizontal stretching process.

Sensitivity is one of the critical parameters in determining a sensor's performance. It usually represents the ratio of sensor output to input, elaborating the accuracy and effectiveness of the sensor [44]. GF is traditionally described as the gauge factor, which is defined as the following Formula (7). = ( − )/ <sup>=</sup> / , (7) where *R*0 is the initial resistance, *R* refers to the real-time resistance of the sensor in the stretching–releasing process, and ε represents the strain applied to the sensor. The loop structure of the knitted strain sensor can be regarded as a complex series and parallel electrical network involving the resistance of each yarn segment and contact resistance [42]. Figure 5b expounds on the loop changes of the sensor during the cycle test. The contact resistance change played a governing function in the horizontal stretching of the fabric, whereas the resistance change caused by loop transfer had little effect on the sensor's resistance. In the initial stage of stretching, the leg yarn segments transferred to the needle and sinker loops [43], and the number of contact points changed rapidly, accounting for the higher sensitivity of the sensor. With the further increase in external stretching,

> As depicted in Figure 6a, the variation of ∆*R*/*R*0 with strain in the horizontal stretching of the sensor can generally be divided into two phases. The ∆*R*/*R*0 of the sensor shows a rapid upward trend in phase Ⅰ when the strain <25% (GF = 1.1452), whereas it slows

> This is consistent with the fabric-sensing mechanism described in Figure 5b. The more significant the change of contact points during stretching, the higher the sensitivity.

> Figure 6b reveals the variation curves of ∆*R*/*R*0 and strain with time, which change almost synchronously, indicating a good response of the knitted strain sensor to the applied strain. The signal is from F1 for the following electrical performance test. The stretching–releasing curves of the sensor are revealed in Figure 6c. They almost overlap, although the two have a specific height difference. The maximum hysteresis of about 1.78%

the transfer of the yarn segment was no longer evident, resulting in a smaller change in the number of contact points. Herein, lower sensitivity was observed for higher stretching.

Sensitivity is one of the critical parameters in determining a sensor's performance. It usually represents the ratio of sensor output to input, elaborating the accuracy and effectiveness of the sensor [44]. GF is traditionally described as the gauge factor, which is defined as the following Formula (7). *Polymers* **2022**, *14*, x FOR PEER REVIEW 9 of 14

$$\text{GF} = \frac{(R - R\_0) / R\_0}{\varepsilon} = \frac{\Delta R / R\_0}{\varepsilon} \,\tag{7}$$

where *R*<sup>0</sup> is the initial resistance, *R* refers to the real-time resistance of the sensor in the stretching–releasing process, and *ε* represents the strain applied to the sensor. sor under strain (0–100%). Evidently, the value of ∆*R*/*R*0 is practically identical under the same strain and increases gradually with the continuous augmentation of strain, demon-

As depicted in Figure 6a, the variation of ∆*R*/*R*<sup>0</sup> with strain in the horizontal stretching of the sensor can generally be divided into two phases. The ∆*R*/*R*<sup>0</sup> of the sensor shows a rapid upward trend in phase I when the strain <25% (GF = 1.1452), whereas it slows down and gradually becomes gentle in phase II in the strain range 25–100% (GF = 0.2673). This is consistent with the fabric-sensing mechanism described in Figure 5b. The more significant the change of contact points during stretching, the higher the sensitivity. strating great repeatability of the sensor under different strains. Figure 6e declares the ∆*R*/*R*0 curve of the knitted strain sensor under four different stretching rates of 0.5, 1, 2.5, and 5 mm/s with a strain of 40%. The ∆*R*/*R*0 is highly consistent with the stretching curve and remains stable at each stretching rate. To illustrate the repeatability and durability of the sensor, 500 stretching–releasing cycles at 100% strain are shown in Figure 6f. It can be observed that the knitted strain sensor shows good repeatability and stability in electrical performance tests.

**Figure 6.** Sensing performance of the knitted strain sensor, (**a**) the ∆*R*/*R*<sup>0</sup> curve of the sensor with strain, (**b**) the curves of ∆*R*/*R*<sup>0</sup> and strain varying with time, (**c**) single stretching–releasing curve of the sensor, (**d**) the curves of ∆*R*/*R*<sup>0</sup> under different strains (0–100%), (**e**) ∆*R*/*R*<sup>0</sup> of strain sensor under different stretching rates of 40% strain, (**f**) the stretching–releasing tests under a cyclic strain of 100%.

**Body Part** 

Figure 6b reveals the variation curves of ∆*R*/*R*<sup>0</sup> and strain with time, which change almost synchronously, indicating a good response of the knitted strain sensor to the applied strain. The signal is from F1 for the following electrical performance test. The stretching– releasing curves of the sensor are revealed in Figure 6c. They almost overlap, although the two have a specific height difference. The maximum hysteresis of about 1.78% occurs when the strain is about 25%, indicating that the sensor has low hysteresis and good sensing performance. The elastic hysteresis and the energy absorption in the loops will affect the hysteresis of the sensor. Figure 6d reveals the dynamic response of the sensor under strain (0–100%). Evidently, the value of ∆*R*/*R*<sup>0</sup> is practically identical under the same strain and increases gradually with the continuous augmentation of strain, demonstrating great repeatability of the sensor under different strains. Figure 6e declares the ∆*R*/*R*<sup>0</sup> curve of the knitted strain sensor under four different stretching rates of 0.5, 1, 2.5, and 5 mm/s with a strain of 40%. The ∆*R*/*R*<sup>0</sup> is highly consistent with the stretching curve and remains stable at each stretching rate. To illustrate the repeatability and durability of the sensor, 500 stretching–releasing cycles at 100% strain are shown in Figure 6f. It can be observed that the knitted strain sensor shows good repeatability and stability in electrical performance tests.

### *3.3. Application of the Size Prediction Model*

As illustrated in Figure 7, the as-designed knitted sensors under the size prediction model can be applied as a wearable device to four human body parts (wrist <sup>1</sup> , elbow <sup>2</sup> , throat <sup>3</sup> , and forefinger <sup>4</sup> ) of a female volunteer to detect human movements. The horizontal and vertical sizes of different body parts are displayed in Table 3. Taking into account the effect of size changes and electrical properties, the parameters of the sensors' conductive area based on nylon/spandex composite yarn with better elasticity (44/77dtex, *z* = 0.36) in different body parts are revealed in Table 4. The size deviation rates of the four knitted strain sensors are within the acceptable range of 5%, verifying the correctness of the size prediction model. *Polymers* **2022**, *14*, x FOR PEER REVIEW 11 of 14

**Figure 7.** Different body parts for motion detection. **Figure 7.** Different body parts for motion detection.

**Horizontal Direction** 

**Table 3.** Horizontal and vertical sizes of different body parts. **Table 3.** Horizontal and vertical sizes of different body parts.


**Horizontal Direction** 

**Predicted Size/cm Finished Sizes/cm Deviation Rate/%** 

The joint bending displayed in Figure 8a,b indicates that the sensor with a wide workable strain range can detect human movements. The ∆*R*/*R*0 of the sensor is consistent with the joint motions. In addition, the strain sensor can detect subtle movements. Figure 8c indicates that the sensor was attached to the throat with the continuous swallowing of food, and the ∆*R*/*R*0 of the sensor had a relatively consistent response. Pronunciation could also be discriminated by repeatedly reading the words 'Jiangnan', 'K', 'T', and 'C', as demonstrated in Figure 8d,e. To further probe the strain sensor's capabilities in series motion detection, it was adhered to the forefinger to collect signals. As revealed in Figure 8f, the finger bent from small to large degrees. The resistance changed synchronously with the finger deformation when it bent, indicating a good discernible ability for subtle motion. All these indicate that the as-designed knitted strain sensor exhibits a potential ap-

**Vertical Direction** 

**Horizontal Direction** 

**Vertical Direction** 

③ 46 32 0.36 2.97 1.74 3.07 1.81 3.26 3.87 ④ 38 28 0.36 1.72 1.80 1.79 1.87 3.91 3.74

plication prospect in smart wearable devices in the near future.

**Vertical Direction** 

**Table 4.** The predicted and finished sizes of the sensors in different body parts.


**Table 4.** The predicted and finished sizes of the sensors in different body parts.

The joint bending displayed in Figure 8a,b indicates that the sensor with a wide workable strain range can detect human movements. The ∆*R*/*R*<sup>0</sup> of the sensor is consistent with the joint motions. In addition, the strain sensor can detect subtle movements. Figure 8c indicates that the sensor was attached to the throat with the continuous swallowing of food, and the ∆*R*/*R*<sup>0</sup> of the sensor had a relatively consistent response. Pronunciation could also be discriminated by repeatedly reading the words 'Jiangnan', 'K', 'T', and 'C', as demonstrated in Figure 8d,e. To further probe the strain sensor's capabilities in series motion detection, it was adhered to the forefinger to collect signals. As revealed in Figure 8f, the finger bent from small to large degrees. The resistance changed synchronously with the finger deformation when it bent, indicating a good discernible ability for subtle motion. All these indicate that the as-designed knitted strain sensor exhibits a potential application prospect in smart wearable devices in the near future. *Polymers* **2022**, *14*, x FOR PEER REVIEW 12 of 14

**Figure 8.** Application of the knitted strain sensors under the size prediction model in detecting different human movements, (**a**) wrist bending, (**b**) elbow bending, (**c**) swallowing of food, (**d**) speaking the word 'Jiangnan', (**e**) pronouncing words 'K', 'T', and 'C', (**f**) responsive curve of the sensor on the finger under diverse bending degrees. **4. Conclusions**  In short, a knitted strain sensor of silver-plated nylon yarn and nylon/spandex com-**Figure 8.** Application of the knitted strain sensors under the size prediction model in detecting different human movements, (**a**) wrist bending, (**b**) elbow bending, (**c**) swallowing of food, (**d**) speaking the word 'Jiangnan', (**e**) pronouncing words 'K', 'T', and 'C', (**f**) responsive curve of the sensor on the finger under diverse bending degrees.

or clothing to monitor subtle and large-scale movements of the human body, such as pronunciation and joint bending, confirming the accuracy of the size prediction model. The results demonstrate that the sensor has a promising application prospect in intelligent

wearable garments.

posite yarn was successfully fabricated based on the knitting process. The numbers of wales, courses, and spandex content significantly affect the size of the knitted strain sensor. The change rate of samples with vertical size surpasses that of the horizontal size. The horizontal and vertical size prediction model of the knitted strain sensor was established. The sensor has a relatively good sensitivity of 1.1452 (strain ≤ 25%) with a rather large

### **4. Conclusions**

In short, a knitted strain sensor of silver-plated nylon yarn and nylon/spandex composite yarn was successfully fabricated based on the knitting process. The numbers of wales, courses, and spandex content significantly affect the size of the knitted strain sensor. The change rate of samples with vertical size surpasses that of the horizontal size. The horizontal and vertical size prediction model of the knitted strain sensor was established. The sensor has a relatively good sensitivity of 1.1452 (strain ≤ 25%) with a rather large workable strain range (0–100%), good hysteresis, durability and stability over 500 cycles, ability to distinguish various tensile rates and strains, and good synchronization between output resistance and strains. The knitted strain sensors with different conductive areas based on the established size prediction model were designed and applied to human skin or clothing to monitor subtle and large-scale movements of the human body, such as pronunciation and joint bending, confirming the accuracy of the size prediction model. The results demonstrate that the sensor has a promising application prospect in intelligent wearable garments.

**Author Contributions:** Conceptualization, X.L. and H.C.; data curation, X.L. and H.C.; investigation, X.L., H.C., Z.D. and G.J.; methodology, X.L., H.C. and Z.D.; project administration, H.C., Z.D. and G.J.; writing—original draft, X.L. and H.C.; writing—review and editing, X.L., H.C., Z.D. and G.J.; funding acquisition, H.C., Z.D. and G.J. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was funded by the National Science Foundation of China (61902150), the Fundamental Research Funds for the Central Universities (JUSRP122003) and the research fund of Postgraduate Research & Practice Innovation Program of Jiangsu Province (KYCX22\_2345).

**Informed Consent Statement:** Informed consent was obtained from all subjects involved in the study.

**Data Availability Statement:** The data presented in this study are available on request from the corresponding author.

**Acknowledgments:** We would like to express our gratitude to the editors and the reviewers for their constructive and helpful review comments.

**Conflicts of Interest:** The authors declare no conflict of interest.

### **References**

