1 Introduction

In most machines, at least two shafts must be connected to each other, e.g. between drive motor and gear box or between driven unit and gear box. For this purpose, elastic couplings are often used. They are located directly in the power flow, promoting them to be the ideal components for measuring process data, such as the transmitted torque or the operating temperature. Data acquisition using sensor-integrating machine elements (SiME) is becoming increasingly important in both research and industry [1]. The aim of the current work is to develop a concept for a sensor-integrating jaw coupling. Therefore, dielectric elastomer sensors (DES) are integrated into every tooth of the gear rim of the coupling. This allows to measure the transmitted torque. Additional sensors are integrated to measure the temperature and the rotational speed. The significant advantage of the present concept is that only the gear rim needs to be replaced to include sensory functions. The design of the other parts of the coupling is maintained. Hence, the developed sensor-integrating coupling is space neutral.

Possible fields of application for sensor-integrating couplings are the commissioning of machines, the evaluation of the data based performance of prototypes and industry 4.0 applications. Furthermore, a sensor-integrating coupling can enable the validation of load assumptions or the measurement of a load spectrum for load carrying calculations. Possible industrial applications of a sensor-integrating coupling are the detection of (i) misalignments [2], (ii) the spontaneous settling of foundations [3] and, (iii) sudden peaks in temperature. The former is of particular importance, since misalignments are one of the main causes of damage in automobile shafts [4].

A first concept for a sensor-integrating elastic jaw coupling was proposed by Schork et al. [3]. In order to measure the deformation of the tooth of the gear rim, a bending plate with strain gauges was applied. Due to this modification, the stiffness of the gear rim was reduced. The companies R+W Antriebselemente GmbH [5] and KTR Systems GmbH [6] manufacture sensor-integrating couplings, in which the sensors are integrated into the hubs or in a hollow shaft connection between two couplings. According to the R+W brochure [5], they are able to measure the torque, the rotational speed, the acceleration in all three axes, the temperature, the axial force, and the bending. The power supply is realized either via a battery, induction or energy harvesting. The signal from the sensor is transmitted wireless to a receiver, e.g. a tablet or a smartphone.

The novelty of this work lies in the fact that only the compliant gear rim is modified in a space neutral approach, to provide sensory functions. The integration of sensors in a compliant environment imposes special requirements on the electronics and the used sensors. The gear rims are typically made of a thermoplastic polyurethane (TPU) with a Shore hardness of 92A, 98A or 64D [5,6,7]. In contrast to the linear elastic behavior of steel, TPU exhibits a hyperviscoelastic behavior, see Ref. [8, 9]. This, in combination with the high deformations, limits the use of classic strain gauges as strain sensors. To overcome this issue, compliant DES are applied. Nevertheless, measuring in a coupling is not trivial. Within the present work a prototype of the sensor-integration coupling was developed addressing the following challenges: (i) the viscoelastic behavior, resulting in a non-linear dependency between torque and deformation, further subjected to a hysteresis, (ii) the energy management of the sensor system and (iii) the electrical contacting of the sensors.

The present paper is structured as follows: Sect. 2 outlines the most important requirements for the sensor-integrating coupling and the mechanical conception. Subsequently, the applied measurement chains for the measurement tasks are described in Sect. 3 and the electrical conceptualization in Sect. 4. Additionally, Sect. 5 outlines the taken steps for creating a sensor-integrating jaw coupling and their results. Finally, Sect. 6 concludes the main findings and provides an outlook into further development steps.

2 Mechanical conceptualization

The present Section outlines the most important requirements for the sensor-integrating jaw coupling and the developed sensor-integration concept. The main focus lies on the mechanical modification of the gear rim and the associated design considerations.

2.1 Requirements

In order to design a sensor-integrating machine element, the requirements and boundary conditions for the highly integrated mechatronic system must be specified first, cf. Kirchner et al. [1]. The basic requirements for the sensor-integrating coupling are (i) to fulfill the functions of the unmodified coupling, (ii) to measure the torque, rotational speed and temperature and (iii) to integrate these functionalities in a space neutral way. The former mentioned functions of the unmodified coupling include the transmission of power between input- and output-hub, the compensation of shaft misalignment and dampening of shocks. Furthermore, the main dimensions and linkage dimensions must remain unaltered. The transmittable nominal torque may be reduced by the sensor integration. Nevertheless, the influence of the modifications on the performance shall be minimized. Similar to the approach by Herbst et al. [10], the aim is to weaken the gear rim only to the extent that it either reaches the properties of a smaller gear rim size or of a softer gear rim material.

Acquisition, evaluation and transmission of data should be done autonomous and energy-neutral. Furthermore, the measurement task and the data transmission must be feasible in a rotating system. The measurement resolution should be at least 8‑bit for the torque and the rotational speed, covering the range from zero to the maximum nominal value. The measurement frequencies depend on the size of the coupling and the expected rotational speed, and should be defined based on the use case. If components and their masses are unevenly distributed in a rotating system, critical imbalances can occur, which must be minimized. Finally, the sensor-integrating coupling needs to be deployable in the same environments as the conventional coupling.

If the aforementioned requirements are not met by the sensor-integrating coupling, its applicability is significantly limited. This reduces the importance of the system and limits its broad use.

2.2 Sensor-integration

An overview of the developed sensor-integrating jaw coupling is shown in Fig. 1a. It illustrates the currently smallest feasible coupling with an outer diameter \(d_{\textrm{outer}}\) of \(d_{\textrm{outer}}=65\,\text{mm}\). The coupling is composed of the two hubs (1) and the sensor-integrating gear rim (2). The internal structure of the gear rim is shown in the cross-sectional views in Fig. 1b and c. The dielectric elastomer sensor (3) is placed between two strain amplifiers (4). A DES and two amplifiers are inserted into a counter bore in every tooth of the gear rim. The resulting cavity is hereinafter referred as bore hole. The central electronics (5) with data transmission unit, capacitance sensor, power management system and microcontroller (MCU) are located in the inner ring of the gear rim, see Fig. 1b. The electrical connection between the DES and the central electronics is realized by a cable in the cavity (6).

Fig. 1
figure 1

Exploded view of the sensor-integrating coupling with an outer diameter \(d_{\textrm{outer}}\) of \(d_{\textrm{outer}}=65\,\text{mm}\). a Components of the coupling with the hubs (1) and a sensor-integrating gear rim (2). b Sectional view of the gear rim with the central electronics (5). c Cross-section of a tooth with a DES (3), two amplifiers (4) and the cavity for the electrical connections (6)

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A DES is typically a thin layer of a dielectric elastomer sandwiched between two compliant electrodes [11,12,13,14]. Thereby, the DES can undergo large deformations as it consists of compliant materials. Electrically, the DES behaves like a plate capacitor. Further information about dielectric elastomer sensors can be found in Refs. [15,16,17,18]. If the tooth and thus the sensor are compressed, a capacitance and an electrical resistance change can be measured, see Refs. [19,20,21]. This enables the determination of the applied torque. To maintain its functionality, the sensor must withstand a substantial compression, e.g. up to half of its initial height, in case of a maximum torque event. The height of the DES is constrained by the thickness of the tooth and the amplifiers. The diameter of the bore hole must allow radial expansion of the DES during compression. Therefore, the diameter of the bore hole is \(d_{\text{bh}}=d_{\text{DES}}\,+\,\text{1\,mm}\), see Fig. 1c. The diameter of the DES is \(d_{\text{DES}}=\,\text{5\,mm}\). Please refer to Prokopchuk et al. [19, 22] for more detailed information concerning the dimensions and structure of the used DES. Additionally, the bigger diameter of the counter bore \(d_{\text{cb}}\) is one millimeter larger than the diameter \(d_{\text{bh}}\).

In principle, DES must be integrated in at least two neighboring teeth, as in a jaw coupling only every second tooth is subjected to a load. Thereby, the sign of the torque, i.e. the direction of rotation, determines which teeth are loaded. However, to prevent an asymmetrical weakening and imbalances, a DES and two strain amplifiers are integrated into every tooth. Another advantage of this is, that redundancy is created in the case that one or more DES fail during use. If the shafts are perfectly aligned, all loaded teeth have the same deformation. However, if shaft misalignments occur, the teeth will be loaded differently, which can be measured when a DES is present in each tooth [2].

One aim of the sensor-integration is to find a balance between the required space for the DES and the obtained capacitance change. Increasing the size of the DES enables the measurement of higher capacitance differences. However, larger bore holes are necessary, which weaken the gear rim and decrease the stiffness. To gain an understanding of the influence of the size of the bore hole on the stiffness, numerical simulations were conducted by Menning et al. [9]. As shown in Fig. 2, the results of the simulation indicate that the transmittable torque decreases with an increasing bore hole diameter. Hence, the gear rim is weakened by the sensor integration. However, the main functionality of the coupling is ensured, as torque is transmitted and a hysteresis is present. The DES developed by Prokopchuk et al. [19, 22] has a diameter of \(d_{\text{DES}}\,=\,\text{5\,mm}\), therefore, the bore hole diameter of \(d_{\text{bh}}\,=\,\text{6\,mm}\) was chosen in order to allow the DES to expand during compression and to minimize the effect on the torsion-torque characteristic. When scaling up this concept for larger coupling sizes, comparable sensor-dimensions can be integrated into bigger gear rims. This would lead to a smaller influence of the sensor-integration process on the torsion-torque characteristic of the coupling.

Fig. 2
figure 2

Numerically simulated torque \(\bar{T}\), normalized by the torque of the unmodified coupling at the angle of \(\phi\,=\,3.2^{\circ}\), for varying bore hole diameters \(d_{\textrm{bh}}\). The results are based on the model presented in Menning et al. [9]

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Mechanical amplifiers, see Henke et al. [23], are employed to increase the measured capacitance change during loading of the DES. Thus, the accuracy and sensitivity of the measurement are increased. One amplifier is placed on both sides of the DES. They are made of a stiffer material than the gear rim, leading to a higher absolute deformation of the sensor. Here, Polymethylmethacrylate (PMMA) is used for the amplifiers. Additionally, the strain amplifiers serve as an electrical and mechanical connection point to the DES and provide an interface to the central electronics. The connection between the amplifier and the DES is enabled by a conductive copper pad glued to the surface of the amplifier. Due to an oversized height of the DES, a stable electrical connection between the two components is ensured. Additionally, the strain amplifiers protect the DES from e.g. abrasive wear. The amplifiers are assembled by pressing them into the undersized counter bores with an oversized fit. Additional securing, e.g. by gluing, is not necessary as only compression loads occur and a form fit at the shoulder is present.

The electrical connection between the DES and the central electronics are done with flexible copper wires, see Fig. 1c. Using numerical simulations, the position of the cavities for the cables were optimized in regard to a minimal bending of the cables. The long-term goal is to replace the cable with a conductive elastomer glue or a comparable compliant material, e.g. by 3D printing the entire gear rim with different materials.

Additionally, temperature sensors are needed, as the mechanical properties of TPU are strongly temperature-dependent. They must be integrated close to the point of interest, which limits the possible positions. A placement of the temperature sensors on the amplifiers is favorable, since they are located centrally in the teeth. Please refer to Sect. 3 for detailed information regarding the importance and implementation of measuring the temperature.

Embedding the necessary electronics should not reduce the load-bearing capacity of the gear rim. Additionally, protection from the environment is advantageous. Therefore, integrating the electronics in an amplifier or in the inner ring is possible. With respect to the benefits of (i) centralized computing, (ii) data transmission and (iii) the available space, the electronics were placed in the inner ring of the gear rim, see Fig. 1. For a coupling with an outer diameter of \(d_{\textrm{outer}}=65\,\text{mm}\) the available design space for the central electronics corresponds to a cylinder with a diameter \(d_{\mathrm{cyl}}\) of \(d_{\mathrm{cyl}}=30\,\text{mm}\) and a maximum height of \(h=15\,\text{mm}\).

3 Measurement chain

The present section outlines the utilized measurement chains in the sensor-integrating coupling. First, the measurement chain for the determination of the transmitted torque is described. This includes the measurement of the capacitance of the dielectric elastomer sensor and the temperature of the teeth. Afterward, the measurement chain for the rotational speed is described.

The first main measurement task is the measurement of the transmitted torque \(T\). The approach presented here pursues the approximation of the torque by measuring the deformation and temperature of the teeth of the gear rim. Thus, the torque can be calculated using the temperature-dependent torque-deformation characteristic. Therefore, two measurement paths are necessary: one for the deformation of a tooth and one for the temperature. With increasing temperature the stiffness of the TPU decreases. Thus, the transmitted torque decreases at the same torsion angle of the coupling. Consequently, the measurement of the temperature is required to incorporate the temperature-dependent behavior of the surrounding elastomer.

The measurement chain for the torque is shown in Fig. 3. During nominal torque loads, the hubs are twisted against each other by a torsion angel of \(\phi=3.2^{\circ}\) [7]. This leads to a compressive deformation of the teeth. Following the top measurement path in Fig. 3, the deformation applied on the DES is further enforced by the strain amplifiers. Since the amplifiers are not compressed, the absolute deformation of the DES is increased. The most popular measurands for the determination of deformation with a DES are resistance and capacitance. Resistance based strain sensors have been developed e.g. by Amjadi et al. [24] using a silver nanowire-elastomer nanocomposite, by Liu et al. [25] using conductive and non-conductive yarns and by Jiang et al. [26] using 3D porous reduced graphene oxide fiber fabrics. Capacitance based compliant sensors have been proposed e.g. by Ruhhammer et al. [27] using a conductive polymer and polydimethylsiloxane (PDMS) based strain gauge, by Wang et al. [28] using 3D interdigital electrodes fabricated by vertically aligned carbon nanotubes, and by Qiu et al. [29] using an elastomeric nanocomposite dielectric. Furthermore, an extensive review of capacitive strain sensors was done by Nesser and Gilles [30]. In the present work, a capacitance based strain measurement was chosen, see Prokopchuk et al. [19]. The current capacitance of the DES can subsequently be evaluated with a capacitance-to-digital converter. Here, the FDC1004 from Texas Instruments is used, see Sect. 4.

Fig. 3 further illustrates the measurement path for the temperature. Dynamic torque excitations lead to dynamic deformations, which cause the elastomeric material of the gear rim to heat up [31]. Due to thermal conduction, the temperature of the amplifiers increases. Since the temperature sensors are placed on the amplifiers, they heat up as well. The current local temperature of a tooth can thus be measured using e.g. thermoelectric or electrical resistance devices. Please refer to Childs et al. [32] for an extensive review on further temperature measurement methods. Here, the electrical resistance based temperature sensors HS3003 are used.

Fig. 3
figure 3

Measurement chain of the sensor-integrating coupling for the measurement of torque. The measurement requires two measurement paths, one for the deformation, and one for the temperature of the coupling. The structure is based on Kirchner et al. [1]

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The digital capacitance and temperature signals are subsequently supplied to the MCU for the torque approximation. Please note that the FDC1004 and the HS3003 are smart sensors, which measure the physical measurand, digitalize the value and transfer it to the MCU. The measurement procedure poses two main challenges: (i) the precise measurement of the capacitance of the DES and (ii) the description of the load, loading rate and temperature dependent torsion-torque characteristic of the coupling. Additionally, the aging of the material must be taken into account [31, 33]. Incorporating all relevant interactions, the torque \(T\) can be approximated as a function of the capacitance \(C\), previously measured capacities \(C_{{n-1}}\), the temperature \(\vartheta\) and the current age of the gear rim: \(T=T(C,\,C_{{n-1}},\,\vartheta,\,\text{age})\). Thereby, the determination of the current hysteresis branch is particularly important, as significantly different torques can be transmitted at the same deformation, see Fig. 2. For the torque approximation a regression model will be used, which incorporates the aforementioned dependency \(T=T(C,\,C_{\mathrm{n-1}},\,\vartheta,\,\text{age})\). The regression model is still under development.

The second main measurement task is the measurement of the rotational speed \(n\). Here, a concept with an external static transducer is not feasible, due to the requirement of a space neutral design. A rotation of the coupling leads to a radial acceleration \(a_{\mathrm{r}}\) of the components in the coupling. The acceleration can thus be measured using a micro-electromechanical systems (MEMS) based accelerometer, which is placed at a defined distance \(r\) from the rotational axis of the coupling. Using \(n=\frac{1}{2\pi}\sqrt{\frac{a_{\mathrm{r}}}{r}}\) the rotational speed can be calculated. Note that the acceleration due to gravity must be taken into account in the measurement of the radial acceleration. To additionally measure vibrations, a 3-axis accelerometer could be used. Within the measurement chain, the measured acceleration quantities are sent to the MCU for further data processing.

4 Electrical conceptualization

The present section describes the electrical conceptualization of the central electronics. Thereby, the focus is on the capacitance measurement unit. Additionally, investigations on the power consumption of the central electronics are conducted.

The components of the central electronics are illustrated by the block diagram in Fig. 4. Furthermore, the connections of the sensors, integrated in the teeth, are shown. The central electronics include the capacitance measurement unit (CMU), the data transmission unit, the accelerometer (ACS), the power supply, the energy harvesting system and the microcontroller (MCU). In each tooth of the gear rim, a dielectric elastomer sensor (DES) and a temperature sensor (TES) are integrated.

Fig. 4
figure 4

Block diagram of the electrical components of the sensor-integrating jaw coupling. The central electronics include the accelerometer (ACS), the capacitance measurement (CMU), the microcontroller (MCU), the data transmission unit and the energy management. In the teeth, temperature sensors (TES) and DES are integrated

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The DES can be abstracted as a RC-circuit with or without an additional parallel resistance [15]. Measuring the capacitance of a DES can be challenging due to the following factors: (i) changing resistance of the RC-circuit during deformation [20], (ii) occurrence of instability and stray capacitance of the carbon grease when contact damage or significant displacement occurs, (iii) change in contact conductivity due to drying of carbon grease over time. Various methods of capacitance measurement have been reviewed by Xu et al. [21], for instance (i) from gain and phase shift of a sinusoidal input [17, 34], (ii) using the impedance frequency response [15], (iii) using hyper-plane approximation [35] or (iv) by measuring charge using a current integrator [36]. Two further possibilities are the usage of (v) the time constant, by charging/discharging the capacitor, and (vi) the AC bridge method, in particular the modified Schering bridge network proposed by Bera and Chattopadhyay [37]. In addition, ready-made solutions are available. A capacitance-to-digital converter, for instance, measures the capacitance connected between its input pin and ground.

In the present work, various capacitance measurement options were evaluated. Based on the requirements for the available design space, capacitance measurement range and measurement frequency, four methods were chosen for further tests. Experimental investigations were conducted for the time constant approach, measuring charge using current integration and two ready-made solutions. As a result, the capacitance-to-digital converter FDC1004 from Texas Instruments [38] was selected. It has a small design space and measures on four channels, achieves high measurement accuracies and has a measurement frequency of \(f \textrm{= 100 Hz}\). Due to its measuring principle, the FDC1004 can handle changing resistance of the DES during deformation. Please refer to Refs. [38] for detailed information. The FDC1004 is connected in series to two analog pins of the MCU, a \(3.3\,\text{V}\) power pin and a ground pin. The DES is connected to two contacts of the FDC1004: \(C_{\text{in}}\) and ground.

Furthermore, the measurement of the radial acceleration is realized with the BMI270 by Bosch. The temperature of the teeth is measured with the aforementioned HS3003 by Renesas.

Power for the central electronics is provided by an accumulator. However, to increase the operating time of the entire system, it is necessary to implement an energy harvesting system. For example, in an experiment with a loading frequency of \(f=\mathrm{20\,Hz}\), a constant sinusoidal amplitude \(\hat{\phi}\) of \(\hat{\phi}=0.75^{\circ}\) and a mean amplitude \(\phi\) of \(\phi=1.5^{\circ}\) the loaded teeth showed an equilibrium temperature of \(\vartheta={45}^{\circ}\text{C}\). Whereas the non-loaded teeth reached \(\vartheta={26}^{\circ}\text{C}\). This operation point is chosen, because it resembles a typical frequency of an electric motor and likely dynamic torsional loads. However, with a decreasing amplitude and frequency, the temperature difference will decrease too. It is thus possible to, temporarily, use the Seebeck effect and convert the temperature differences of the teeth to electric voltage. Moreover, the rotational motion of the coupling and its rotational inertia can be used to harvest energy. However, the integration of an energy harvester and its detailed evaluation of energy output needs to be investigated further.

The chosen microcontroller for the central electronics is the nRF52840 from Nordic Semiconductor. Programming of the MCU is carried out in the Arduino IDE development environment via a USB cable. The data transmission is realized with the build in Bluetooth® Low Energy (BLE) module of the MCU.

In order to determine how much energy the entire measurement system consumes, the electrical setup was tested while measuring with all sensors and transmitting the data. Therefore, the digital multimeter DMM6500 by Keithley for the current measurement and the laboratory power supply BASE Tech BT-305 were used. The measurement system includes a FDC1004, two HS3003 and a BMI270. The results for the power consumption \(P\) over the time \(t\) are shown in Fig. 5. The power consumption \(P=U\cdot I\) is calculated with the supply voltage of \(U=5\,\text{V}\) and the measured current \(I\). The current was recorded via a \(1\,\text{Ohm}\) measuring resistor with a sample rate of \(100\,\text{kHz}\). Please note that the results are shown for a measurement duration of \(t=0.1\,\text{s}\), as the course of the power repeats periodically over time. In Fig. 5 four power spikes are visible. They occur when the BLE module is active, either for an advertising to other BLE devices or during data transmission. This correlates with the program on the MCU, which sends the measured data every 30 ms and advertises the BLE module every 100 ms. Considering one period of the power consumption of the employed BLE cycle, an advertising event is used to establish the connection to external BLE devices. At the same time, data is measured and processed. Additionally, communication is carried out via the Inter-Integrated Circuit (I2C) bus system and the data is sent via BLE to an external device. The measurements show, that the largest energy consumption of \(15\,\text{mW}\) occurs during data transfer.

Fig. 5
figure 5

Power consumption \(P\) of the measuring system versus time \(t\) for a period of \(t=0.1\,\text{s}\). The system includes the BLE module, a FDC1004, two temperature sensors, and an accelerometer

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5 Development process of the sensor-integrating jaw coupling

This section summarizes the necessary working steps for the sensor integration into the jaw coupling. The development process from the concept to a SiME coupling is illustrated in Fig. 6.

Fig. 6
figure 6

Central development steps of the development process of the sensor-integrating coupling and their dependencies

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First, a material model for the gear rim is parameterized. Therefore, temperature- and strain rate-dependent material tests of the TPU are conducted. At the same time, a new type of DES are developed, see [19]. It consists of multiple smaller DES, which are stacked upon each other and are electrically connected in parallel. As demonstrated by Prokopchuk et al. [18], it is thus possible to easily adjust the base capacitance, by decreasing or increasing the number of layers. A first combined proof of concept is conducted using a minimal working example. Therefore, the developed DES are integrated into a hollow TPU cylinder. This setup is placed in a tensile test machine for a deformation controlled loading test. The obtained experimental data is then used to validate a numerical model for the DES and the surrounding TPU [39].

In the next step, a concept for the integration of the central electronics is developed, as described in Sect. 4. Furthermore, a numerical model for the conventional coupling is created, Ref. [9]. Using numerical simulations, a deeper understanding of the behavior of a jaw coupling under different loads is obtained. In order to develop a first prototype, additional component tests and simulations are conducted. With the component test, different load cases for the coupling are tested. Experiments are carried out for the standard and the modified coupling. When testing the modified coupling, however, only the amplifiers are integrated. Thus, the DES and the central electronics are neglected. To simulate the sensor-integrating jaw coupling, the models of the conventional jaw coupling and the DES are combined [40]. It is thus possible to simulate (i) different load cases, (ii) sensor positions and (iii) sensor configurations.

Based on the experimental and numerical results, a first prototype of the sensor-integrating coupling, that implements the concept described in Sect. 2, can be manufactured. An image of the prototype with integrated DES is shown in Fig. 7. The sensor-integrating gear rim (2) is inserted into the hub (1). Further, the amplifiers (3) and the wires (4) for the connection of DES are visible. However, the central electronics are not yet integrated.

Fig. 7
figure 7

Prototype of the sensor-integrating jaw coupling with the hubs (1), the sensor-integrating gear rim (2), the amplifiers (3) and wires for the connection to the electronics (4)

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The manufactured prototype is tested in a servo hydraulic test bench. The capacitance of the DES is measured using the FDC1004 and an LCR meter HIOKI IM3523. Thereby, the latter is used in order to validate the usage of the FDC1004.

Fig. 8 shows two measurement series for a number of loading and unloading cycles up to a torsional angel of \(\phi=1^{\circ}\) with a frequency of \(f=\text{0.25 Hz}\). This load point is chosen, to test the sensitivity of the measurement during small loads and to assure the comparability between both capacitance measurements. The torsion angle is regulated by the test bench. Fig. 8a shows the load excitations over the time. The increases in torque is due to the controller and the steady regulation of the torsional angle to the desired amplitude. The capacitance change of the DES \(\Delta C=C-C_{\mathrm{0}}\), based on the current capacitance \(C\) and the initial capacitance \(C_{\mathrm{0}}\), is shown for both methods over the time \(t\) in Fig. 8b. The FDC- and LCR-measurements are conducted on the same DES. The bottom left graph shows the torque \(T\) measured by the test bench over the torsion angle \(\phi\). The bottom right graph shows the torque \(T\) over the measured capacitance change \(\Delta C\). A comparable hysteresis is visible for both cases. For this setup, the sensitivity is close to \(1\,\text{Nm/pF}\). Both measurements correlate excellently with the torque. The correlation coefficient between \(T\) and \(\Delta C\) for the cycle in Fig. 8d is \(R=\text{0.9803}\) for measurements using the LCR meter and \(R=\text{0.9724}\) using the FDC.

Fig. 8
figure 8

a Experimentally measured load excitation for the specimen. The torque \(T\) is displayed over the time \(t\) b Experimentally measured capacitance change \(\Delta C\) for the FDC and LCR meter over time. c Torque \(T\) over the torsional angle \(\phi\) for the loading cycle displayed in the box in a and b. Loading is done with a frequency of \(f=\) 0.25 Hz. d Measured torque \(T\) over the capacitance change \(\Delta C\) for the loading cycle displayed in the box in a and b

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6 Conclusion and Outlook

Data acquisition in mechanical systems is becoming increasingly important. Thereby, sensor-integrating machine elements offer a considerable development potential. This work outlines a sensor-integrating jaw coupling for the measurement of torque, rotational speed and temperature. The sensor-integration concept is described and validated by a prototype.

Sensor-integration is done by integrating compliant dielectric elastomer sensors (DES) into every tooth of the gear rim of the coupling. This results in a space neutral sensor-integration, as no external sensors or peripherals are required. In order to measure the aforementioned values, two measurement chains are used. The torque can be determined by measuring the capacitance of the DES and the current temperature of the teeth. The second measurement chain enables the measurement of rotational speed.

The experimental validation of the concept shows that DES can successfully be used within a jaw coupling and fulfills the defined requirements. As the proposed sensor-integrating coupling is space neutral, it can be integrated into various existing designs without any modification to existing hardware.

However, there is potential for further development. This includes the investigation of the weakening of the gear rim and the effect of notches introduced by the sensor-integration. In order to enable the use of smaller DES, their sensitivity must be increased in the following development steps. This can be achieved by decreasing the layer height of the DES. Hence, the diameter of the bore hole \(d_{\mathrm{bh}}\) could be reduced, while maintaining the sensitivity of the DES and reducing the influence of the sensor integration on the gear rim. Furthermore, a model for the reliable estimation of the torque must be developed. The model could be based on higher order regression methods like recurrent neural networks. Lastly, a big development potential lies in the reduction of the power consumption of the central electronics and data transmission.