Study on a Fault Mitigation Scheme for Rub-Impact of an Aero-Engine Based on NiTi Wires

The aim of this study was to solve the frequently occurring rotor-stator rub-impact fault in aero-engines without causing a significant reduction in efficiency. We proposed a fault mitigation scheme, using shape memory alloy (SMA) wire, whereby the tip clearance between the rotor and the stator is adjusted. In this scheme, an acoustic emission (AE) sensor is utilized to monitor the rub-impact fault. An active control actuator is designed with pre-strained two-way SMA wires, driven by an electric current via an Arduino control board, to mitigate the rub-impact fault once it occurs. In order to investigate the feasibility of the proposed scheme, a series of tests on the material properties of NiTi wires, including heating response rate, ultimate strain, free recovery rate, and restoring force, were carried out. A prototype of the actuator was designed, manufactured, and tested under various conditions. The experimental result verifies that the proposed scheme has the potential to mitigate or eliminate the rotor-stator rub-impact fault in aero-engines.


Introduction
The efficiency of a rotating machine such as an aero-engine is strongly dependent on the tip clearance between the stationary and rotating parts [1]. In order to improve the efficiency of an aero-engine, the clearance should be designed as small as possible. It has been reported that a 0.0254 mm reduction in the tip clearance of a high-pressure turbine may lead to a decrease of 0.1 percent in specific fuel consumption [2,3]. However, minimizing the clearance is usually associated with undesired rub-impact phenomena occurring between the rotor and the casing due to mechanical, aerodynamic excitation, or thermal gradience during engine operation [4,5]. This leads to material or structural damage, e.g., plastic deformations, changes in the microstructure on the blade tips, crack initiation, and the break out of liner material at the rubbing zone [6], and, sometimes, catastrophic accidents [7].
Researchers have strived to understand the rub-impact fault, for example, exploring the fault mechanism [8][9][10], the fault feature extraction method [11][12][13], source localization [14,15], and intelligent fault diagnosis [16,17], etc. These studies contributed to the development of rub-impact fault diagnosis and to practical applications. However, most studies focused on how to monitor the occurrence of a fault and analyze its type or location; few were concerned with the mitigation or elimination of the rub-impact phenomenon. Unfortunately, rub-impact is a fault which may induce disastrous accidents, if it cannot be mitigated in time.
In order to protect the rotor from rub-impact from the casing of an aero-engine, a feasible solution is to adjust the tip clearance when it occurs. The most popular scheme to achieve this that is used in the design of aero-engines is based on the active clearance control (ACC) method [18]. For example, Bucaro et al. designed a new gas turbine engine This paper presents a promising solution for rub-impact fault detection and mitigation for an aero-engine. An active control scheme, based on two-way SMA wires actuation is proposed. The rub-impact fault is monitored by an acoustic emission (AE) sensor. An SMA wire-based actuator prototype operated by an Arduino control board is established. A series of tests to establish the material properties of NiTi wires, including heating response rate, ultimate strain, free recovery rate, and restoring force, were carried out. The mechanism and design of the actuator are described in detail in this paper. The feasibility of the proposed model for rub-impact fault is verified by our experimental research and our results show that the proposed active control actuator can effectively mitigate rub-impact fault when it occurs. Therefore, the main contribution of this paper is that it provides a potential way to mitigate or even eliminate the accidental rub-impact fault, without a significant reduction in the engine's efficiency.

Mechanical Behaviors of SMA Wires
Typical SMA, such as NiTi, is capable of recovering its original shape after plastic deformation by heating above its characteristic transition temperature via the shape memory effect (SME) [29]. This unique mechanical behavior results from a phase transformation between high-temperature austenite and low-temperature martensite phases [30] and has led to many actuation applications [31,32]. In this study, NiTi wires with a two-way shape memory effect [30] were used in our design to drive the actuator through the application of an electric current. As the primary functional component of the actuator, the SME mechanical behaviors of NiTi wires were analyzed in a series of tests prior to design assembly. The material properties of the NiTi wires used in this study and their transition temperatures are listed in Tables 1 and 2, respectively.

Heating Response Rate of NiTi Wires
The heating response rate of the NiTi wire is used as a measure of how fast the wire's SME function works. This function is represented by the phase transformation spending time, which is the time it takes the wire to reach its austenite finish temperature Af from its starting state. The shorter the phase transformation spending time, the higher the

Mechanical Behaviors of SMA Wires
Typical SMA, such as NiTi, is capable of recovering its original shape after plastic deformation by heating above its characteristic transition temperature via the shape memory effect (SME) [29]. This unique mechanical behavior results from a phase transformation between high-temperature austenite and low-temperature martensite phases [30] and has led to many actuation applications [31,32]. In this study, NiTi wires with a two-way shape memory effect [30] were used in our design to drive the actuator through the application of an electric current. As the primary functional component of the actuator, the SME mechanical behaviors of NiTi wires were analyzed in a series of tests prior to design assembly. The material properties of the NiTi wires used in this study and their transition temperatures are listed in Tables 1 and 2, respectively.

Heating Response Rate of NiTi Wires
The heating response rate of the NiTi wire is used as a measure of how fast the wire's SME function works. This function is represented by the phase transformation spending time, which is the time it takes the wire to reach its austenite finish temperature A f from its starting state. The shorter the phase transformation spending time, the higher the heating response rate. In order to investigate the heating response rate of NiTi wires, a series of tests under various temperatures were conducted. The experimental setup is schematically shown in Figure 2. The test rig consisted of a DC power supply, a tension test platform, NiTi wire, a thermocouple, and a data acquisition system.
The length and diameter of the NiTi wire were 100 mm and 0.8 mm, respectively. During the tests, the wire was clamped on a tension test platform and one thermocouple was attached to the wire to measure its surface temperature. At room temperature T 0 = 21 • C, the wires were heated by 2, 3, 4, and 5 A electric currents provided by the DC power supply. The temperature variations of the wires are shown in Figure 3. The temperature of the NiTi wire rose slowly initially, becoming almost invariable, with an increased electric current. This means that the rising temperature rate of the NiTi wire gradually decreases, and tends to become stable when subjected to a continuous electric current. Figure 3 also indicates that the rising temperature rate of the wire is dependent on the amplitude of the electric current. A large current amplitude is associated with a high rising temperature rate. In order to evaluate the response of the NiTi wires to different electric currents, the phase transformation spending time, which is the time that it takes for the wire to reach A f from its starting state, was measured, using various currents. The comparison results are shown in Table 3. The heating response rate rose with an increased electric current, but an increase in the response rate was not obvious when the electric current increased beyond 6 A. heating response rate. In order to investigate the heating response rate of NiTi wires, a series of tests under various temperatures were conducted. The experimental setup is schematically shown in Figure 2. The test rig consisted of a DC power supply, a tension test platform, NiTi wire, a thermocouple, and a data acquisition system. The length and diameter of the NiTi wire were 100 mm and 0.8 mm, respectively. During the tests, the wire was clamped on a tension test platform and one thermocouple was attached to the wire to measure its surface temperature. At room temperature T0 = 21 °C, the wires were heated by 2, 3, 4, and 5 A electric currents provided by the DC power supply. The temperature variations of the wires are shown in Figure 3. The temperature of the NiTi wire rose slowly initially, becoming almost invariable, with an increased electric current. This means that the rising temperature rate of the NiTi wire gradually decreases, and tends to become stable when subjected to a continuous electric current. Figure 3 also indicates that the rising temperature rate of the wire is dependent on the amplitude of the electric current. A large current amplitude is associated with a high rising temperature rate. In order to evaluate the response of the NiTi wires to different electric currents, the phase transformation spending time, which is the time that it takes for the wire to reach Af from its starting state, was measured, using various currents. The comparison results are shown in Table 3. The heating response rate rose with an increased electric current, but an increase in the response rate was not obvious when the electric current increased beyond 6 A.   The length and diameter of the NiTi wire were 100 mm and 0.8 mm, respectively. During the tests, the wire was clamped on a tension test platform and one thermocouple was attached to the wire to measure its surface temperature. At room temperature T0 = 21 °C, the wires were heated by 2, 3, 4, and 5 A electric currents provided by the DC power supply. The temperature variations of the wires are shown in Figure 3. The temperature of the NiTi wire rose slowly initially, becoming almost invariable, with an increased electric current. This means that the rising temperature rate of the NiTi wire gradually decreases, and tends to become stable when subjected to a continuous electric current. Figure 3 also indicates that the rising temperature rate of the wire is dependent on the amplitude of the electric current. A large current amplitude is associated with a high rising temperature rate. In order to evaluate the response of the NiTi wires to different electric currents, the phase transformation spending time, which is the time that it takes for the wire to reach Af from its starting state, was measured, using various currents. The comparison results are shown in Table 3. The heating response rate rose with an increased electric current, but an increase in the response rate was not obvious when the electric current increased beyond 6 A.

Ultimate Strain of NiTi Wires
A tension test was conducted using an Instron 5565 Universal Testing Machine. The length of the wire specimen used was 750 mm. Because the wire is very fine, it is difficult to accurately measure the ultimate strain directly during its deformation. As such, a loaddisplacement curve was plotted from the tension test results, as shown in Figure 4. The wire underwent elastic deformation from 0 to point A, plastic deformation from point A to B, a hardening stage from point B to C, and it fractures at point C. The elongations at points A, B, and C are 0.68%, 4.89%, and 13.33% of the original length of the wire, respectively. We found that the NiTi wire behaved well in terms of plasticity and its pre-strain was not allowed to exceed 13.33% due to its ultimate strain. displacement curve was plotted from the tension test results, as shown in Figure 4. The wire underwent elastic deformation from 0 to point A, plastic deformation from point A to B, a hardening stage from point B to C, and it fractures at point C. The elongations at points A, B, and C are 0.68%, 4.89%, and 13.33% of the original length of the wire, respectively. We found that the NiTi wire behaved well in terms of plasticity and its prestrain was not allowed to exceed 13.33% due to its ultimate strain.

Free Recovery Rate of NiTi Wires
The free recovery rate of NiTi wires under different pre-strain was investigated using the same experimental setup as was used in the heating response rate tests. The initial length of the wire specimens was 100 mm and they were trained to have the characteristic of two-way SME. The wires were stretched with pre-strains of 2%, 3%, 4%, 5%, 6%, and 7%, and were heated to recover their deformations, then cooled to room temperature. As shown in Figure 5, L0, L1, L2, and L3 represent the original length of the wire, the length of the wire after being stretched and unloaded, the length of the wire after being heated, and the length of the wire after being cooled to room temperature, respectively. The elongations of the wires were measured to calculate the two-way free recovery rate η, which is defined by:

Free Recovery Rate of NiTi Wires
The free recovery rate of NiTi wires under different pre-strain was investigated using the same experimental setup as was used in the heating response rate tests. The initial length of the wire specimens was 100 mm and they were trained to have the characteristic of two-way SME. The wires were stretched with pre-strains of 2%, 3%, 4%, 5%, 6%, and 7%, and were heated to recover their deformations, then cooled to room temperature. As shown in Figure 5, L 0 , L 1 , L 2 , and L 3 represent the original length of the wire, the length of the wire after being stretched and unloaded, the length of the wire after being heated, and the length of the wire after being cooled to room temperature, respectively. The elongations of the wires were measured to calculate the two-way free recovery rate η, which is defined by: Based on Equation (1), the variation in the free recovery rate with respect to the cycle number at different pre-strain levels is plotted in Figure 6. The two-way free recovery rate initially increased with increased training cycles and then tended to stabilize after 60 cycles. Additionally, the large pre-tension strain resulted in a low free recovery rate. However, the largest free recovery rate appeared when the pre-strain was 4%. Therefore, a median deformation of 4% is preferred in order to obtain the maximum recovery rate of the NiTi wire used in a two-way SME.

Ultimate Strain of NiTi Wires
A tension test was conducted using an Instron 5565 Universal Testing Machine. The length of the wire specimen used was 750 mm. Because the wire is very fine, it is difficult to accurately measure the ultimate strain directly during its deformation. As such, a loaddisplacement curve was plotted from the tension test results, as shown in Figure 4. The wire underwent elastic deformation from 0 to point A, plastic deformation from point A to B, a hardening stage from point B to C, and it fractures at point C. The elongations at points A, B, and C are 0.68%, 4.89%, and 13.33% of the original length of the wire, respectively. We found that the NiTi wire behaved well in terms of plasticity and its prestrain was not allowed to exceed 13.33% due to its ultimate strain.

Free Recovery Rate of NiTi Wires
The free recovery rate of NiTi wires under different pre-strain was investigated using the same experimental setup as was used in the heating response rate tests. The initial length of the wire specimens was 100 mm and they were trained to have the characteristic of two-way SME. The wires were stretched with pre-strains of 2%, 3%, 4%, 5%, 6%, and 7%, and were heated to recover their deformations, then cooled to room temperature. As shown in Figure 5, L0, L1, L2, and L3 represent the original length of the wire, the length of the wire after being stretched and unloaded, the length of the wire after being heated, and the length of the wire after being cooled to room temperature, respectively. The elongations of the wires were measured to calculate the two-way free recovery rate η, which is defined by: (1) Figure 5. Two-way shape memory effects.

Restoring Force of NiTi Wires
The restoring forces of the NiTi wires, with various pre-strains and which were subjected to 3, 4, 5, and 6 A of electric current, were tested and measured. Figure 7 shows that the restoring force of each wire, at a given electric current, begins to rise sharply and then tends to stabilize. In addition, the maximum restoring force of the NiTi wire with a given pre-strain is dependent on the amplitude of the electric current applied. The restoring force rose with increased current. To compare the heating efficiency of the wires subjected to different electric currents, the response time required to reach the maximum restoring force of each wire was measured and is listed in Table 4. The results indicate that the heating response time to reach the maximum force under a large current does not change significantly. Moreover, the wire with a 4% pre-strain presents the largest restoring force at 6 A. Thus, the designed actuator, installed with a NiTi wire with a 4% pre-strain, may obtain the largest restoring force in an acceptable response time under such conditions. Based on Equation (1), the variation in the free recovery rate with respect to the cycle number at different pre-strain levels is plotted in Figure 6. The two-way free recovery rate initially increased with increased training cycles and then tended to stabilize after 60 cycles. Additionally, the large pre-tension strain resulted in a low free recovery rate. However, the largest free recovery rate appeared when the pre-strain was 4%. Therefore, a median deformation of 4% is preferred in order to obtain the maximum recovery rate of the NiTi wire used in a two-way SME.

Restoring Force of NiTi Wires
The restoring forces of the NiTi wires, with various pre-strains and which were subjected to 3, 4, 5, and 6 A of electric current, were tested and measured. Figure 7 shows that the restoring force of each wire, at a given electric current, begins to rise sharply and then tends to stabilize. In addition, the maximum restoring force of the NiTi wire with a given pre-strain is dependent on the amplitude of the electric current applied. The restoring force rose with increased current. To compare the heating efficiency of the wires subjected to different electric currents, the response time required to reach the maximum restoring force of each wire was measured and is listed in Table 4. The results indicate that the heating response time to reach the maximum force under a large current does not change significantly. Moreover, the wire with a 4% pre-strain presents the largest restoring force at 6 A. Thus, the designed actuator, installed with a NiTi wire with a 4% pre-strain, may obtain the largest restoring force in an acceptable response time under such conditions.  restoring force of each wire was measured and is listed in Table 4. The results indicate that the heating response time to reach the maximum force under a large current does not change significantly. Moreover, the wire with a 4% pre-strain presents the largest restoring force at 6 A. Thus, the designed actuator, installed with a NiTi wire with a 4% pre-strain, may obtain the largest restoring force in an acceptable response time under such conditions.

Prototype of the Actuator
The proposed actuator was designed with the aim of mitigating or eliminating the rub-impact fault when it occurs between the rotor and casing during the operation of an aero-engine. A flowchart of the proposed fault mitigation scheme is shown in Figure 8. The design of the proposed actuator consists of a package, an electrode plate, an insulation layer, pre-stretched NiTi wires, a driving lever, a limit roller, a baffle, a spring, and external and internal casings, as is shown schematically in Figure 9.

Prototype of the Actuator
The proposed actuator was designed with the aim of mitigating or eliminating the rub-impact fault when it occurs between the rotor and casing during the operation of an aero-engine. A flowchart of the proposed fault mitigation scheme is shown in Figure 8. The design of the proposed actuator consists of a package, an electrode plate, an insulation layer, pre-stretched NiTi wires, a driving lever, a limit roller, a baffle, a spring, and external and internal casings, as is shown schematically in Figure 9.  The actuator works by using a driving lever that passes through the external casing. The two ends of the lever are fixed on the internal casing and the bottom electrode plate, respectively, which forces the internal casing to deform when the lever moves. Two insulation layers are placed between the electrode plates and the other parts of the actuator for the insulation and protection of the entire structure. The two ends of NiTi wires are bolted at each end to two electrode plates and are heated by an electric current during the operation of the actuator. A baffle is welded onto the driving lever and a spring is installed between the baffle and the external casing to generate a restoring force. In addition, one limiter with three rollers, circumferentially threaded and installed on the driving lever, act to improve the accuracy of the motion. The prototype of the actuator is shown in Figure 10. To allow us to observe the behavior of the actuator, the package was not completely sealed, as shown in Figure 10d. The actuator works by using a driving lever that passes through the external casing. The two ends of the lever are fixed on the internal casing and the bottom electrode plate, respectively, which forces the internal casing to deform when the lever moves. Two insulation layers are placed between the electrode plates and the other parts of the actuator for the insulation and protection of the entire structure. The two ends of NiTi wires are bolted at each end to two electrode plates and are heated by an electric current during the operation of the actuator. A baffle is welded onto the driving lever and a spring is installed between the baffle and the external casing to generate a restoring force. In addition, one limiter with three rollers, circumferentially threaded and installed on the driving lever, act to improve the accuracy of the motion. The prototype of the actuator is shown in Figure 10. To allow us to observe the behavior of the actuator, the package was not completely sealed, as shown in Figure 10d.
The two ends of the lever are fixed on the internal casing and the bottom electrode p respectively, which forces the internal casing to deform when the lever moves. insulation layers are placed between the electrode plates and the other parts o actuator for the insulation and protection of the entire structure. The two ends of wires are bolted at each end to two electrode plates and are heated by an electric cu during the operation of the actuator. A baffle is welded onto the driving lever and a s is installed between the baffle and the external casing to generate a restoring forc addition, one limiter with three rollers, circumferentially threaded and installed o driving lever, act to improve the accuracy of the motion. The prototype of the actua shown in Figure 10. To allow us to observe the behavior of the actuator, the package not completely sealed, as shown in Figure 10d. Once a rub-impact fault is detected, the external direct current (DC) power su system begins to heat the SMA wires. When the temperature is beyond the austenite temperature of the wires As, the wire undergoes a martensite phase transformation a compressed due to the unique property of SME. This compression forces the int casing to move upwards via the driving lever. Due to the motion of the internal ca the tip clearance between the rotor and the casing is enlarged and, as a result, the impact phenomenon is mitigated or possibly eliminated. The aim of using two-way wires is to mitigate the rubbing fault, whilst guaranteeing engine efficiency, wh achieved when the clearance is reduced once the NiTi wires cool to the martensite p To verify the feasibility of the proposed model, a prototype of an SMA-based actuato designed and its geometric parameters are shown in Table 5.  Once a rub-impact fault is detected, the external direct current (DC) power supply system begins to heat the SMA wires. When the temperature is beyond the austenite start temperature of the wires A s , the wire undergoes a martensite phase transformation and is compressed due to the unique property of SME. This compression forces the internal casing to move upwards via the driving lever. Due to the motion of the internal casing, the tip clearance between the rotor and the casing is enlarged and, as a result, the rub-impact phenomenon is mitigated or possibly eliminated. The aim of using two-way NiTi wires is to mitigate the rubbing fault, whilst guaranteeing engine efficiency, which is achieved when the clearance is reduced once the NiTi wires cool to the martensite phase. To verify the feasibility of the proposed model, a prototype of an SMA-based actuator was designed and its geometric parameters are shown in Table 5.

Control Scheme of the Actuator
In order to realize the self-healing of rub-impact faults, a control system based on an Arduino control board was investigated for the proposed actuator. This system consists of an Arduino Uno R3 control board, an RB-02S082A piezoelectric sensor, and an SRD-05VDC-SL-C 5V electromagnetic relay, as shown in Figure 11. When the system is running, the AE signals are acquired by the piezoelectric sensor and are then transferred to the Arduino Uno R3 control board, which is capable of identifying whether the acquired signals are fault signals. The electric circuit switching function is implemented by compiled coding. In normal conditions, the current circuit is shut down and the actuator does not work. Once a rub-impact fault is identified by the board, an order is sent to the electromagnetic relay to switch on the current circuit to heat the NiTi wires. A flowchart depiction of the algorithm of the control scheme is shown in Figure 12.

Control Scheme of the Actuator
In order to realize the self-healing of rub-impact faults, a control system based on an Arduino control board was investigated for the proposed actuator. This system consists of an Arduino Uno R3 control board, an RB-02S082A piezoelectric sensor, and an SRD-05VDC-SL-C 5V electromagnetic relay, as shown in Figure 11. When the system is running, the AE signals are acquired by the piezoelectric sensor and are then transferred to the Arduino Uno R3 control board, which is capable of identifying whether the acquired signals are fault signals. The electric circuit switching function is implemented by compiled coding. In normal conditions, the current circuit is shut down and the actuator does not work. Once a rub-impact fault is identified by the board, an order is sent to the electromagnetic relay to switch on the current circuit to heat the NiTi wires. A flowchart depiction of the algorithm of the control scheme is shown in Figure 12. Figure 11. Configuration of the control system. Figure 11. Configuration of the control system. Figure 11. Configuration of the control system.

Experimental Verification of the Clearance Control Mechanism
In order to evaluate the effectiveness of the clearance control actuator, the mechanism was verified by an experimental study. Figure 13 shows the experimental setup, which

Experimental Verification of the Clearance Control Mechanism
In order to evaluate the effectiveness of the clearance control actuator, the mechanism was verified by an experimental study. Figure 13 shows the experimental setup, which consisted of a rotor test rig, a rotor power supply, an accelerator, an electromagnetic relay, an Arduino control board, a piezoelectric sensor, an AE sensor, a preamplifier, a signal acquisition instrument, a DC power supply, and a PC and data analysis system. consisted of a rotor test rig, a rotor power supply, an accelerator, an electromagnetic relay, an Arduino control board, a piezoelectric sensor, an AE sensor, a preamplifier, a signal acquisition instrument, a DC power supply, and a PC and data analysis system. The NiTi wires with 4% pre-strain were installed on the clearance control actuator, and the actuator was fixed on the external casing of the aero-engine. The power of the rotor test rig was provided by a rotor power supply and the rotational speed of the rotor was controlled by an accelerator. The piezoelectric sensor was attached to the upper surface of the internal casing and was connected to the Arduino control board to identify the rubbing and control the electromagnetic relay operation. An AE sensor was attached to the surface of the external casing to acquire the AE signals. These AE signals were processed by a signal preamplifier and then transmitted to the PC.

Setting of the Threshold and Sampling Frequency
The accuracy of the proposed control scheme is dependent on the selection of the signaling threshold and sampling frequency. The operation of an aero-engine is always accompanied by vibrations, whether or not rub-impact occurs. Therefore, the primary goal is to ascertain the appropriate threshold at which rub-impact faults occur, by reference to the amplitude of the vibration signal. Figure 14 shows the signals acquired by the piezoelectric sensor at rotational speeds of 1500, 2000, 2500, and 3000 rpm. The amplitudes of all vibration signals without the rub-impact fault are lower than 20. Therefore, the threshold may be set to 20 as the threshold for the occurrence of the rubimpact fault. Regarding the sampling, in our experience, it is generally better for the set The NiTi wires with 4% pre-strain were installed on the clearance control actuator, and the actuator was fixed on the external casing of the aero-engine. The power of the rotor test rig was provided by a rotor power supply and the rotational speed of the rotor was controlled by an accelerator. The piezoelectric sensor was attached to the upper surface of the internal casing and was connected to the Arduino control board to identify the rubbing and control the electromagnetic relay operation. An AE sensor was attached to the surface of the external casing to acquire the AE signals. These AE signals were processed by a signal preamplifier and then transmitted to the PC.

Setting of the Threshold and Sampling Frequency
The accuracy of the proposed control scheme is dependent on the selection of the signaling threshold and sampling frequency. The operation of an aero-engine is always accompanied by vibrations, whether or not rub-impact occurs. Therefore, the primary goal is to ascertain the appropriate threshold at which rub-impact faults occur, by reference to the amplitude of the vibration signal. Figure 14 shows the signals acquired by the piezoelectric sensor at rotational speeds of 1500, 2000, 2500, and 3000 rpm. The amplitudes of all vibration signals without the rub-impact fault are lower than 20. Therefore, the threshold may be set to 20 as the threshold for the occurrence of the rub-impact fault. Regarding the sampling, in our experience, it is generally better for the set to be greater than 5 times the highest frequency of the vibration signals, to ensure the reliability of the acquired data. Because the rotational frequency of the rotor at 3000 rpm was measured at 50 Hz in our tests, the sampling frequency in this study was set to 500 Hz, which was 10 times the highest frequency.

Verification of the Clearance Control Actuator
(1) Effect of rotational speed The effectiveness of the proposed clearance control actuator was verified at rotational speeds of 1500, 2000, 2500, and 3000 rpm, with a 6 A electric current, in our tests. Assuming that t0, t1, t2, t3, t4, t5 represent the points at which a rub-impact fault occurs, the amplitude of the AE signal reaches its maximum, the fault is eliminated, the second rub-impact fault begins, the amplitude of the AE signal reaches its maximum again, and the second fault is eliminated, consecutively. The specific durations are defined by:

Verification of the Clearance Control Actuator
(1) Effect of rotational speed The effectiveness of the proposed clearance control actuator was verified at rotational speeds of 1500, 2000, 2500, and 3000 rpm, with a 6 A electric current, in our tests. Assuming that t 0 , t 1 , t 2 , t 3 , t 4 , t 5 represent the points at which a rub-impact fault occurs, the amplitude of the AE signal reaches its maximum, the fault is eliminated, the second rub-impact fault begins, the amplitude of the AE signal reaches its maximum again, and the second fault is eliminated, consecutively. The specific durations are defined by: where T 1 is the duration from the start of rub-impact to its most serious state, T 2 denotes the rub-impact fault elimination time spent by the proposed actuator, T 3 represents the time interval between the rub-impact fault and the start of the following rub-impact fault event, T 4 is the duration from the start of the next fault to its most serious state, and T 5 denotes the time spent to eliminate the fault. Table 6 gives the spending times measured at various rotational speeds in the rotation test, at a 6 A electric current. The results show that the control times T 1 , T 2 , T 3 , T 4 , and T 5 are almost the same at different rotational speeds. This means the control time of the clearance control mechanism based on two-way NiTi wires is independent of the rotational speed of the rotor. A series of rotational rubbing tests were conducted under the condition of a 6 A current and a 1500 rpm rotational speed, and the AE signal during the operational process was measured. As shown in Figure 15, the amplitude of the AE signal continuously rises with increased rotor speed during the start-up process until it reaches the maximum at t 1 = 2.143 s, i.e., the rubbing becomes serious and a fault at this moment. At t 2 = 3.177 s, this rubbing fault is eliminated. The next rubbing fault occurs at t 3 = 17.49 s, becoming severe at t 4 = 18.77 s. At t 5 = 19.78 s, the fault is eliminated. event, T4 is the duration from the start of the next fault to its most serious state, and T5 denotes the time spent to eliminate the fault. Table 6 gives the spending times measured at various rotational speeds in the rotation test, at a 6 A electric current. The results show that the control times T1, T2, T3, T4, and T5 are almost the same at different rotational speeds. This means the control time of the clearance control mechanism based on two-way NiTi wires is independent of the rotational speed of the rotor. A series of rotational rubbing tests were conducted under the condition of a 6 A current and a 1500 rpm rotational speed, and the AE signal during the operational process was measured. As shown in Figure 15, the amplitude of the AE signal continuously rises with increased rotor speed during the start-up process until it reaches the maximum at t1 = 2.143 s, i.e., the rubbing becomes serious and a fault at this moment. At t2 = 3.177 s, this rubbing fault is eliminated. The next rubbing fault occurs at t3 = 17.49 s, becoming severe at t4 = 18.77 s. At t5 = 19.78 s, the fault is eliminated. Figure 15. AE signals acquired during the clearance control process based on two-way NiTi SMA wires.
(2) Effect of the electric current A series of rotational rubbing tests at 4, 5, and 6 A electric currents were conducted at rotational speeds of 1500 rpm. The rubbing fault eliminating time spent during the control process is recorded in Table 7. It was found that T2, T3, and T5 changed significantly with different electric currents. The durations of T2 and T5 gradually descended with (2) Effect of the electric current A series of rotational rubbing tests at 4, 5, and 6 A electric currents were conducted at rotational speeds of 1500 rpm. The rubbing fault eliminating time spent during the control process is recorded in Table 7. It was found that T 2 , T 3, and T 5 changed significantly with different electric currents. The durations of T 2 and T 5 gradually descended with increased current. Therefore, a large electric current contributes to a rapid control response time. In addition, the interval between one rub-impact fault and the next fault, T 3 , becomes larger at a higher current compared to lower currents, resulting from the fact that the NiTi wires need more time to cool. The proposed actuator is affected significantly by the electric current.

Conclusions
A fault mitigation scheme based on a two-way SMA wire system to mitigate and possibly eliminate the rotor-stator rub-impact of an aero-engine, by controlling the tip clearance between the rotor and stator, was proposed in this study. Based on the inherent characteristics of SMA, a prototype of an SMA-based actuator was designed, manufactured, and tested. Through our experimental study, the proposed scheme was verified and the following conclusions were drawn: (1) The mechanical properties of NiTi wire are highly dependent upon the heating electric current and on its pre-strain level. It is recommended to apply a 6 A electric current to heat the wires and to use wires with a 4% pre-strain in the design of an SMA wire-based actuator. (2) The time spent in the fault mitigation/elimination process is not significantly dependent on the rotational speed of the rotor. Institutional Review Board Statement: Not applicable.

Informed Consent Statement: Not applicable.
Data Availability Statement: Not applicable.

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

Abbreviations
The following abbreviations are used in this manuscript: SMA Shape memory alloy AE Acoustic emission ACC Active clearance control SME Shape memory effect DC Direct current