Design and Testing of a Device to Investigate Dynamic Performance of Aero-Engine Rotor–Stator Rubbing Dynamics

Abstract

To analyze the wear performance induced by rotor–stator rubbing in an aero-engine sealing structure under authentic operating conditions, a transonic rotor system with double bearing is constructed. This system incorporates the disk, shaft, blades, joint bolts, and auxiliary support structure. The system was evaluated in terms of its critical speed, vibration characteristics, component strength under operational conditions, and response characteristics in abnormal extreme scenarios. A ball screw-type feeding system is employed to achieve precise rotor–stator rubbing during rotation by controlling the coating feed. Additionally, a quartz lamp heating system is used to apply thermal loads to coating specimens, and the appropriate heat insulation and cooling measures are implemented. Furthermore, a high-frequency rubbing force test platform is developed to capture the key characteristics caused by rubbing. The test rig can conduct response tests of the system with rotor–stator rubbing and abrasion tests with tip speeds reaching 425 m/s, feed rates ranging from 2 to 2000 μm/s, and heating temperatures up to 1200 °C. Test debugging has confirmed these specifications and successfully executed rubbing tests, which demonstrate stability throughout the process and provide reliable rubbing force test results. This designed test rig and analysis methodology offers valuable insights for developing high-speed rotating machinery.

1. Introduction

During operation across the entire flight envelope, an aero-engine undergoes multiple transient processes, including start-up, acceleration, deceleration, afterburner engagement, and disengagement, as well as thrust vectoring. These transitions involve the rotor tip speed passing through transonic regimes. The parameters during these transient states directly reflect the performance of both the engine and its control system. Failures such as surge and flameout frequently occur during transients [1,2]. Moreover, the operating conditions of components that are critical to engine performance and service life—such as structural integrity, seal clearances, and blade tip and inter-blade gaps—are all influenced by changes in rotor dynamics and aerodynamic performance during these non-steady-state processes [3].

To enhance performance and increase the thrust-to-weight ratio, it is common practice to reduce the clearance between the rotating and stationary components [4,5]. However, this reduction in clearance significantly increases the risk of rotor–stator rubbing incidents, which can lead to rotor imbalance, shaft fracture, or, in severe cases, complete mechanical seizure. A widely adopted solution in modern advanced aero-engines is the application of abradable seal coatings in critical regions of the flow path [6,7]. These coatings are designed to come into contact with the blades during transient-state rubbing events, thereby preventing blade wear while maintaining minimal flow path clearances to improve engine performance. The typical application of abradable seal coatings in an aero-engine is illustrated in Figure 1.

Improvements in aero-engine performance have resulted in increasingly high linear velocities at blade tips and elevated service temperatures, among other indicators. Consequently, the comprehensive performance requirements for coatings have become more stringent. The abradability of sealing materials is closely correlated with operating conditions, which presents challenges for effective evaluation through conventional rubbing and wear tests. In 2014, the Federal Aviation Administration (FAA) stated in the FAR 33.15 support document AC 33-11 that coatings need to be verified for compliance under test conditions analogous to those of the operating environment [8,9,10]. CCAR33.63 stipulates that “each type of engine design …… throughout its stated flight envelope …… shall not result in excessive stress on any component of the engine due to vibration” [11]. The Civil Aviation Administration of China (CAAC) also explicitly states in the advisory circular on aero-engine validation that “the applicant should demonstrate by analysis, test, or experience that the fan casing and fan rotor are insensitive to rotor-casing interactions and that there are no conditions that would lead to the occurrence of such phenomena.” [12]. Therefore, the rubbing dynamic properties of the rotor–stator rubbing coupling and the abradable properties of the sealing coatings are essential subjects that must be addressed for engine development. Furthermore, these properties must be assessed using experimental devices that closely simulate the service conditions of the engine prior to installation.

Enhancing the performance of aero-engines results in increasingly higher blade tip speeds and operating temperatures, which pose more stringent demands on the comprehensive performance of abradable seal coatings. The abradability of sealing materials is closely related to operating conditions, so it is difficult to effectively evaluate them using conventional friction and wear tests. The FAA’s Advisory Circular AC33-11, issued in support of FAR 33.15 in 2014, states that coatings must undergo conformity verification under test conditions that closely resemble the actual service environment [8]. Similarly, CCAR 33.63 stipulates that “the design of each engine … throughout the declared flight envelope … must not result in excessive stress on any engine component due to vibration” [9]. The Civil Aviation Administration of China (CAAC) also emphasizes in its engine certification advisory circular that “the applicant shall demonstrate through analysis, testing, or experience that the fan case and rotor are not sensitive to rotor-to-case interaction, and that conditions leading to such interaction do not exist” [10]. Therefore, the coupled rotor–stator rubbing dynamics and the abradability performance of seal coatings are critical research topics in engine development. Before entering service, such coatings must be evaluated using test rigs that simulate engine-like operational conditions.

In the past half century or so, scholars have carried out a great deal of research around the rubbing problems. A systematic summary of relevant theoretical advances has been provided. For example, Muszynska [13] reviewed the research work on the modeling of rotor–stator rubbing and rotor response mechanisms before 1989. Jiang Jun et al. [14] categorized the local and system models of rubbing in the theoretical studies from the viewpoint of dynamics and control and summarized the research results on the nonlinear response of rubbing. Ma et al. [15,16] reviewed the research on the blade-casing rubbing-induced dynamic behaviors and emphasized the modeling of the casing coatings, the wear behavior, and the effect on the overall vibration characteristics of the rotor–stator system.

Overall, there exists a large body of literature addressing rotor–stator rubbing in aero-engines, encompassing a wide range of research perspectives and emphases. However, most existing studies primarily focus on elucidating the damage mechanisms of rubbing from the standpoint of nonlinear dynamics or on the development of rubbing force models. While some publications discuss the experimental validation of rubbing behavior, they typically present only test results, with relatively limited attention given to the design and development of test rigs that accurately replicate real engine operating conditions for rotor–stator rubbing assessments.

This paper presents the design and evaluation of a transonic rotor–stator rubbing test rig developed to investigate and analyze rubbing and wear phenomena relevant to aero-engines. The structure of the paper is organized as follows: following the introduction, Section 2 describes the overall structure of the rotor–stator rubbing test rig. Section 3 focuses on the design and analysis of the transonic rotor system. Section 4 details the design and analysis of the rubbing feed system, while Section 5 covers the design and analysis of the rubbing measurement system. Section 6 discusses the design of the heating system. Section 7 presents the testing and experimental validation of the rotor–stator rubbing test system. Finally, Section 8 summarizes the main conclusions.

2. The Structure of the Rotor–Stator Rubbing Experimental Device

The core structure of the rotor–stator rubbing test rig consists of a drive system, rotor system, rubbing feed system, heating system, and a vacuum shielding enclosure. The structural configuration of the test rig is shown in Figure 2. The rotating disk is connected to the motor via a speed-increasing gearbox and is driven to high rotational speeds by the motor, reaching a maximum speed of 12,500 rpm. Blade mounting slots are distributed along the circumference of the rotor disk, where blades are securely positioned. When the disk rotates at full speed, the blade tips can reach a maximum circumferential speed of 425 m/s. A precision micro-feed system is used to control the depth of blade intrusion into the casing’s coating layer, with feed rates adjustable between 2 and 2000 μm/s. This enables the controlled investigation of rotor blade–stator coating rubbing characteristics and the abradability performance of the coatings. Radiative heating is applied using quartz lamps, and the coating temperature can reach up to 1200 °C. Thus, the test rig can simulate the high-temperature and high-speed service conditions experienced by rotor–stator assemblies in operational aero-engines.

3. Design and Analysis of Transonic Rotor System

3.1. Design of Transonic Rotor System Configuration

In high-speed rotating machinery, to ensure that the critical speed is higher than the operating speed, the shaft is typically designed as a rigid shaft to guarantee the operational safety of the rotor system. Accordingly, the rotor in this study adopts a segmented, double-support, single-disk configuration, as shown in Figure 3. The rotor is supported by two journal bearings. To ensure the axial stability of the shaft system, the bearing located near the drive end is equipped with an axial thrust structure. The disk and blades are positioned between the two supports; the blades are mounted to the disk using dovetail joints, while the disk is axially positioned and bolted to the left and right shaft segments via rabbet joints. Vibration measuring bands are arranged on both sides of each bearing support segment, with sensors installed to monitor shaft vibration in real time. The rotor is connected to the speed-increasing gearbox via a diaphragm coupling, which is flanged to the shaft.

The rotor system employs pedestal-mounted high-speed tilting-pad journal bearings with a five-pad configuration and a width-to-diameter ratio of 1. At the maximum operating speed of 12,500 rpm, the bearings exhibit an axial stiffness of 2.45 × 10⁸ N/m and a radial stiffness of 2.59 × 10⁸ N/m. They are capable of withstanding a maximum radial load of 9800 N and a maximum axial load of 16,000 N, with a minimum oil film thickness of 0.052 mm. To ensure coaxial alignment and facilitate rotor centering, integrated bearing housing is adopted, with both bearing seats machined in a single operation to maintain precision. Oil seals are implemented on both sides of each bearing seat using oil baffles, while wind baffles are positioned outside the oil baffles to prevent oil suction caused by airflow. The free end is sealed with an end cap equipped with a manual barring mechanism.

Given that the rotor system is designed for rotor–stator rubbing experiments, which inherently generate unbalanced forces and require high precision in rotor–stator clearance, a high balancing accuracy is essential. Therefore, a balance grade of G1 is specified for this rotor system, indicating extremely uniform mass distribution. Even at high rotational speeds, the rotor’s unbalance must remain within extremely tight limits to ensure system stability and precision performance [17].

3.2. Dynamics Analysis of a Transonic Rotor System

3.2.1. Rotor Dynamics Analysis

In high-speed rotor systems, it is essential to avoid resonance by ensuring that the critical speeds do not coincide with the operating speed range. A critical speed analysis of the designed rotor system was conducted using the rotor dynamics software Samcef Rotor [18], taking into account the gyroscopic effects on natural frequencies. Since the stiffness of the rotor system’s bearings varies with rotational speed, Figure 4 illustrates the variation in critical speeds with respect to bearing stiffness. The horizontal line in the figure indicates the maximum operating speed of the rotor, while the three curves represent the first, second, and third critical speeds as functions of bearing stiffness.

It can be observed that the critical speeds increase nonlinearly with bearing stiffness. In the stiffness range between 10⁷ N/m and 10⁹ N/m, the variation is more pronounced; beyond 10⁹ N/m, the critical speeds begin to stabilize. When the bearing stiffness reaches 10⁹ N/m, the first critical speed is approximately 24,140 rpm, which is significantly higher than the rotor’s maximum operating speed of 12,500 rpm. At the design bearing stiffness corresponding to the maximum operating speed (2.59 × 10⁸ N/m), the first critical speed of the rotor is above 24,000 rpm, ensuring that the rotor operates safely below its critical speed range.

Several typical operating conditions for rotor–stator rubbing tests are selected, and the corresponding critical speeds and modal shapes of the rotor at maximum and partial speeds are summarized in

Table 1. Critical speeds and mode shapes at different speeds.

Rotation Speed (rpm)	Bearing Stiffness (N/m)	Critical Speeds and Modal Shapes
12,500	2.59 × 108	1st: 17,230 rpm	2nd: 21,433 rpm
10,294	2.18 × 108	1st: 16,272 rpm	2nd: 20,796 rpm
4411	1.16 × 108	1st: 12,293 rpm	2nd: 17,534 rpm
882	2.88 × 108	1st: 18,239 rpm	2nd: 22,069 rpm

. Since the bearing stiffness of the rotor system varies with rotational speed, significant differences exist in bearing stiffness values at the four selected speeds, including 2.59 × 10⁸, 2.18 × 10⁸, 1.16 × 10⁸, and 2.88 × 10⁸ N/m. Consequently, the calculated critical speeds also differ considerably. However, from the first and second critical speeds, it can be observed that the operating speeds of the rotor system remain below the first critical speed, maintaining a sufficient safety margin. Therefore, although the critical speeds vary with changes in bearing stiffness at different speeds, this does not affect the normal operation of the rotor system, and resonance will not occur during regular operation.

The operating condition of this rotor system is rotor–stator rubbing. Consequently, the requirement for balancing accuracy is high, and it is established as G1 balancing accuracy [19,20]. The calculation results of the rotor response under G1 unbalance are presented in Figure 5. The results indicate that with the increase in the rotational speed, the response at the bearing in the unbalanced condition increases. The resonance occurs in the interval of 23,770~25,232 r/min. It can be concluded that the rotor system can operate normally in the designed operating speed interval (0–12,500 rpm) at an unbalance level of G1, which exceeds 90% of the maximum design speed. Therefore, the magnitude of unbalance does not affect the rotor stability.

3.2.2. Modal Analysis

The modal analysis of the rotor system is conducted to identify its resonance frequencies at various modal orders in order to avoid overlap with the critical speeds and operating speeds and to reveal the deformation patterns of the rotor system at specific frequencies. The boundary conditions of the entire rotor system are defined by the coupling constraints applied at the bearing locations via reference points. At the thrust bearing near the drive system, five degrees of freedom of the journal are constrained: three translational directions and two rotational directions around the radial axes, while rotational motion around the axial direction remains unconstrained. At the other end, the journal bearing constrains four degrees of freedom: two translational directions and two rotations around the radial axes, leaving both axial translation and rotation unconstrained.

Considering the influence of gyroscopic moments and centrifugal stiffening effects, the modal analysis is carried out in two steps. Firstly, a rotational speed of 12,500 rpm is applied to the entire rotor system. The centrifugal stress in the rotating state is obtained through static analysis. Then, the centrifugal stress field is used as the pre-stress, and the modal analysis is carried out to obtain the natural frequency and vibration mode considering the centrifugal stiffening effects. The first, second, and third natural frequencies are 486 Hz, 537 Hz, and 6125 Hz, respectively. The mode shapes are shown in Figure 6. The first natural frequency exceeds 130% of the maximum design speed. Therefore, the whole rotor system has no resonance risk within the operating speed range.

When rotor–stator rubbing occurs, the resulting radial contact forces may induce an axial compressive load on the rotor, potentially leading to a reduction in system stiffness, a corresponding decrease in critical speeds, and the emergence of coupled vibration modes [21]. However, based on the preceding analysis, the present rotor system behaves close to a rigid rotor, with a sufficient margin between the operating and critical speeds. Moreover, experimental data suggest that typical radial rubbing forces are on the order of several hundred newtons. As shown in the strength verification in Section 3.2.3, the force transmitted to the shaft produces only a minor response. Therefore, the influence of rubbing-induced axial loads on critical speed and modal characteristics is not discussed in this paper and will be further investigated in future experimental studies.

3.2.3. Strength Assessment

The rotor disk, blades, and locking plates are fabricated from GH4169, a nickel-based high-temperature alloy widely employed in aero-engine applications due to its excellent mechanical strength and thermal stability. The shaft material is 42CrMo, a chromium–molybdenum alloy steel known for its high toughness and fatigue resistance. Grade 10.9 high-strength bolts are used for fastening.

To more accurately simulate the blade boundary, the entire disk and blade assembly are selected as the subject of investigation. A fixed displacement constraint is applied to the center of the disk. The system in its entirety is subjected to a centrifugal load at 12,500 r/min. The blade and the disk are configured for surface-to-surface contact. The simplified model of the blade and disk, along with the results of the stress calculation, are presented in Figure 7. It is evident that the maximum stress of 342 MPa in the blade occurs on both sides of the tenon, which is below the yield limit of 1000 MPa. Thus, it satisfies the strength requirements.

In the assessment of disk strength, the disk and shaft are analyzed as an integrated system. Fixed displacement constraints are applied to both sides of the shaft as boundary conditions. A centrifugal load at 12,500 r/min is applied to the entire system, and the shaft and disk are set in contact. According to the simulation results, the maximum stress in the disk is 433 MPa, as shown in Figure 8, located at the midsection of the web. This value is below the yield strength of GH4169 (1240 MPa), corresponding to a safety factor of 2.3. The maximum deformation is 0.325 mm, as shown in Figure 9, which is within the 10% elongation limit of GH4169. Based on the S-N curve of GH4169, the low-cycle fatigue life exceeds 10,000 start–stop cycles, thus meeting the strength and service life requirements of the disk.

In the assessment of the shaft strength, constraints are established at the bearing support and the shaft–disk connection flange. The axial displacement is constrained in the translation direction, while only axial rotation is permitted in the rotational direction. The rotational speed is set at 12,500 rpm. The calculated maximum stress in the shaft is 176.92 MPa, occurring at the connection between the coupling-end shaft and the disk. This corresponds to a safety factor of 5.3. Therefore, based on the strength analysis results, the structural strength of the rotor components meets the design requirements.

3.2.4. Analysis of Working Conditions

The operating condition of the transonic rotor system involves the high-speed rotation of the blades rubbing against a stator rubbing plate fed by a micro-positioning stage. Based on previous experimental data, under the maximum rotational speed and maximum feed rate, the rotor–stator rubbing interaction imposes an estimated radial force of 4500 N and a tangential force of 1500 N on the blade, with a safety margin factor of three [22]. Accordingly, for the strength verification under this critical condition, a centrifugal load corresponding to 12,500 r/min is applied along with a radial rubbing force of 4500 N and a tangential rubbing force of 1500 N at the blade tip. Under these loads, the maximum stress occurs at the blade root and reaches 736 MPa, which is below the yield strength of GH4169 (1000 MPa). Therefore, no plastic deformation is expected, and the blade meets the structural strength requirements.

Under this condition, the variation trend of the radial force at the bearing locations during rubbing is calculated, as shown in Figure 10. The maximum radial forces on the journal bearing and the thrust bearing are 563.1 N and 817.3 N, respectively. Both values are well within the allowable radial load limits of the bearings (9800 N and 16,000 N), indicating that the bearings will not be damaged under the rubbing conditions.

Assuming a blade fracture and separation due to fatigue or other causes, the rotor would experience an unbalance of 4.541 gm at a rotational speed of 12,500 rpm. If the blade loss occurs within 15 s and no braking is applied to the rotor system, the resulting bearing unbalanced forces are shown in Figure 11. The maximum radial forces on the thrust bearing and journal bearing can reach 11,468 N and 9207 N, respectively, which remain within their allowable load limits (16,000 N and 9800 N).

The corresponding unbalance-induced displacements of the thrust and journal bearings are 34.2 μm and 24.8 μm, respectively, as shown in Figure 12. Both displacements are within the allowable oil film thickness. Therefore, even under such an extreme off-design failure scenario, the bearings would not be damaged, and the high-speed rotor test rig remains in a safe operating condition.

In addition, a safety containment system is designed to capture any blade fragments in the event of fracture and separation, thereby preventing secondary damage to the test rig. Vibration monitoring lands are incorporated at both ends of the main shaft, where eddy current sensors, integrated with a condition monitoring system, continuously track the vibration amplitude during operation. If excessive vibration is detected, the motor is triggered to initiate braking, rapidly reducing the rotor system’s unbalance response and ensuring the safety of the test apparatus.

4. The Design and Analysis of the Rubbing Feeding System

The primary function of the rubbing feed-in system is to achieve precise control of the rotor–stator clearance and intrusion depth. Rubbing occurs when the relative radial displacement between the rotor and stator exceeds the predefined clearance. A key characteristic of this mechanism is the occurrence of high-speed rotor–stator rubbing accompanied by a controlled radial feed-in motion at a certain rate. This feed rate can be regarded as the radial vibration velocity of the rotor shaft. In rubbing wear tests, to simulate the actual material removal behavior in aero-engines, the single-pass wear depth produced by a blade scraping the coating is used as a modeling variable. The single-pass wear depth can be determined based on the blade count, blade tip diameter, rotational speed, and radial vibration amplitude. Subsequently, the feed rate under simulated wear conditions can be calculated using the single-pass wear depth, simulated blade pitch circle diameter, blade tangential speed, and the number of simulated blades.

To achieve micron-level precision and stable feed rates, three primary types of precision mechanical feed drive systems are commonly used: (1) stepper motor + ball screw + precision linear guideway; (2) servo motor + ball screw + precision linear guideway; and (3) linear motor + precision linear guideway [23]. The first two configurations are widely applied in high-precision machine tools and have reached a high level of technical maturity. The third option, while offering high precision, is less common due to its complex control system and significantly higher cost. To meet the uniform wear depth requirement for each blade pass, the system must maintain ultra-low feed rates with high stability—specifically, a stable feed rate of 2 μm/s. As stepper motors exhibit limitations in speed control stability at such low velocities, a “servo motor + ball screw + precision linear guideway” architecture was selected. In this configuration, a servo motor serves as the power source, driving a precision ball screw stage to achieve highly stable, micron-level low-speed feed motion. The complete feed-in system consists of a servo motor, linear guideways, a ball screw, a working platform, a lubrication tank, and an oil chiller, as shown in Figure 13.

Table 2. Feeding rate debugging results.

Screw Backlash (mm)	Motor Speed (r/min)		Feeding Rate (μm/s)
	Low	High	Low	High
1	10	1000	25	2500
1	15	1500	6.5	645
1	25	2500	1.8	178.3

summarizes the feed system test results. By employing a high gear-ratio precision planetary gearbox, the servo motor generates stable ultra-low-speed rotational motion, which is converted into linear motion by the ball screw mechanism. Experimental validation confirmed that the feed system can reliably achieve a feed rate of 2 μm/s with high stability, fully meeting the requirements of rubbing wear simulation.

5. Design and Analysis of the Rubbing Test System

5.1. Design of the Rubbing Test System

The overall layout of the rubbing test platform is shown in Figure 14. The platform integrates multiple components, including the coating specimen, substrate, thermal insulation plate, cooling plate, force sensor, and base, to form a comprehensive rubbing force measurement system. Driven by the feed-in mechanism, the specimen is mounted on the substrate. A thermal insulation layer and a cooling plate are arranged between the substrate and the force sensor to ensure that the sensor operates within its allowable temperature range. During the rubbing process, the force sensor provides real-time measurements of the contact forces between the rotating blade and the specimen, enabling the accurate monitoring of rubbing dynamics.

According to the maximum rotor speed n_max = 12,500 r/min, it can be obtained that, when the single blade rubbing, the highest rubbing force fundamental frequency is

$$f_{r\max }={\displaystyle \frac{n_{\max }}{60}}=208.33 \mathrm{Hz}$$

Due to the integration of the sensor and its mounting structures, the natural frequency of the assembled rubbing force measurement platform is significantly lower than that of the sensor alone. To minimize the risk of base resonance, the first-order natural frequency of the platform is required to be at least four times higher than the fundamental frequency of the rubbing force. Accordingly, the platform’s first natural frequency must not be lower than 832 Hz. Given the impulsive nature of rubbing forces and their broad frequency content, the measurement bandwidth must cover at least ten times the fundamental frequency of the rubbing force—i.e., at least 2083.3 Hz—to ensure accurate and reliable force acquisition. Although high-frequency components may exceed the platform’s first natural frequency, their energy is relatively low, and thus they are not expected to induce significant vibrations in the structure.

The natural frequency of the force measurement platform is designed to be 1.5 times greater than the required measurement bandwidth, with consideration given to the influence of specimen fixtures and other structural components on the platform’s dynamic characteristics. Based on this, the rubbing force sensor was required to have a natural frequency exceeding 4 kHz, with a minimum longitudinal measurement range of 10 kN and a transverse range of no less than 5 kN. According to these specifications, the triaxial force sensor model 9397C from Kistler which is made in Winterthur Switzerland was selected to meet the demands of the rubbing test system.

Upon completion of the mechanical construction and sensor integration of the test platform, an industrial PC was employed as the host computer to run both the data acquisition and signal analysis software. The data acquisition module performs fundamental functions such as sampling control, real-time data display, and storage. To investigate the rubbing mechanism and rotor dynamic characteristics, the rubbing force signals must undergo in-depth processing. Therefore, a dedicated data analysis module is utilized to perform filtering, statistical analysis, frequency-domain analysis, and time–frequency analysis of the acquired rubbing force signals. Furthermore, the measured rubbing force data are fed back into the control system in real time. Based on this feedback, the micro-feed mechanism is regulated accordingly, enabling the precise control of the rubbing process and ensuring the accurate simulation of rubbing behavior during testing.

5.2. Dynamic Characteristics Analysis of the Rubbing Test System

Since the force sensor is an assembly with unknown material properties, it is initially modeled as a single equivalent component based on its natural frequency. A rigid constraint is applied to the sensor’s bottom surface. During finite element modal analysis, the material properties of the equivalent model are iteratively adjusted until its natural frequency closely matches the actual measured value. The modal analysis results of the sensor are shown in Figure 15, with the first-mode natural frequency calculated as 10,259 Hz. The corresponding first-mode shape is presented in Figure 16, which is in good agreement with the actual natural frequency of approximately 10.3 kHz.

Subsequently, a dynamic characteristic analysis is conducted on the force measurement platform. The modal analysis results are shown in Figure 17, indicating that the first-order natural frequency is 981.89 Hz. The corresponding mode shape is illustrated in Figure 18. Since the first natural frequency exceeds four times the fundamental frequency of the rubbing force, the platform meets the dynamic performance requirements for the rubbing force testing system.

5.3. Analysis of the Force Transmission Characteristics of the Rubbing Test System

Since the first-order natural frequency of the force measurement platform is lower than the bandwidth of the rubbing force, the high-frequency components of the rubbing force exceed the effective measurement range. Consequently, the rubbing force measured by the sensor will deviate from the actual force exerted by the blade on the specimen. This discrepancy is analyzed through transient dynamic simulation.

At the maximum rotational speed, the rubbing period is 4.8 ms, with the maximum rubbing length approximately 50 mm. The rubbing action duration accounts for about 3% of the rubbing period, approximately 0.15 ms. Transient impact dynamic simulations show the force on the sensor’s upper surface as depicted in Figure 19, with a peak value of 7544 N. This corresponds to a rubbing force amplification factor of 7544/4500 = 1.68. When the rubbing depth decreases, the rubbing duration shortens, leading to a further reduction in the amplification factor. Thus, although the rubbing force is amplified, it remains within an acceptable range. In subsequent experiments, more accurate rubbing forces can be obtained through sensor sensitivity calibration and error compensation algorithms. The main approach involves correcting the force sensor response using the system’s transfer function between the excitation force and sensor output. This transfer function depends solely on the structural characteristics of the system and is independent of external factors such as the excitation or response signals. Excitation can be applied via a force hammer or shaker. During experimental calibration, the sampling frequency and number of sampling points for the rubbing force must be consistent with those used when determining the transfer function, ensuring the force sensor response and transfer function share the same bandwidth and frequency resolution. The sensor signal is first transformed into the frequency domain, then multiplied by the transfer function, and finally transformed back to the time domain to obtain the time-domain excitation force signal.

6. Rubbing Heating System Design

Based on the structure of the blade disk and the rubbing feed device in the experimental setup, two symmetrically arranged heating units are employed to apply thermal loads. Positioned between the two heating units is a turbine disk simulator. The heating units are mounted on specially designed support plates and are secured to the rubbing feed platform using bolts.

Each heating unit comprises quartz lamps, water-cooled electrodes, water-cooled reflectors, fixed support plates, and water-cooled thermal insulation plates, as illustrated in Figure 20. The water-cooled reflector, thermal insulation plate, and fixed support plate form the main structural framework of the heating unit are also shown. The quartz lamps, serving as the heating elements, are fixed in a curved heating array by the water-cooled electrodes, which are insulated from the main framework by ceramic insulators. Each heating unit is equipped with five quartz lamps, each 220 mm in length, arranged with a spacing of 16 mm between adjacent lamps. Each lamp has a rated power of 2 kW and an effective heating length of 160 mm, sufficiently covering the heated surface of the specimen. The power density of the quartz lamp heating array is 801 kW/m². Assuming a thermal conversion efficiency of 50%, the heating array can deliver an effective heating capacity of 400 kW/m², meeting the requirement to achieve a maximum temperature of 1200 °C.

The heating system is powered by silicon-controlled rectifiers (IGBTs) and operates under closed-loop control. The control system adjusts the IGBT output voltage based on the temperature feedback from the heated surface and the setpoint command to achieve precise temperature regulation. Each heating unit has a total power of 10 kW, with two units providing a combined power of 20 kW. Considering the potential overvoltage conditions of the quartz lamps, two 25 kW IGBT power modules are employed to supply the heating system. All components’ water-cooling circuits use tap water without requiring dedicated piping or booster pumps.

Thermal insulation for the test specimen fixtures and the portion of the rubbing feed device exposed within the heating zone is provided by insulating needle mats. The turbine disk simulator is thermally insulated by water-cooled insulation plates integrated with the heating units. The heating elements are quartz lamps, each 310 mm in length and rated at 3.6 kW, with a total of 12 quartz lamps in the system. The flow guiding elements consist of four 90° brass circular rings featuring internal cooling channels, through which coolant is circulated via hollow threaded pipes. The fixing elements are made of high-temperature-resistant ceramics, with eight pairs used to secure the flow guiding elements. Additionally, two 90° cylindrical metal reflectors with polished mirror-finish inner surfaces are employed; these reflectors feature 22 mm diameter holes for mounting the fixing elements.

7. Debugging and Test Verification of Rotor Static Rubbing Experimental Device

The purpose of the integrated commissioning of the high-speed rotating experimental rig is to verify whether the various subsystems work collaboratively to meet the required specifications, with a particular focus on assessing the key parameters of the transmission system. According to the rotor vibration level requirements, the vibration velocity alarm threshold for the rotor system is set at 7.1 mm/s, and the shutdown threshold at 11.2 mm/s. During commissioning, the rotor system was gradually accelerated, and no critical speed resonance points were detected throughout the speed range. When the rotational speed reached 12,500 rpm, the rotor vibration velocity response was 4.7 mm/s, as shown in Figure 21, indicating stable system operation. After the test system was shut down, inspections were carried out on the installation condition and damage status of each component. All components were found to be securely installed without any looseness. Non-destructive inspections performed after disassembly revealed no damage.

Figure 22 shows the temperature measurements of the coating specimen during heating experiments using both an infrared thermometer and thermocouples. The temperature readings from the infrared thermometer are slightly higher than those from the thermocouples because the former measures the temperature at the heated surface of the coating specimen, whereas the latter measures the temperature of the underlying metal substrate. Due to thermal attenuation within the material, the temperature difference decreases gradually as the heating duration increases. The temperature curves indicate that the maximum temperature can reach up to 1200 °C and that stable heating is maintained throughout the test.

Based on the stable and reliable operation of the rotor system, blade-to-coated casing rubbing tests were conducted. The specific procedure was as follows: First, the single-step preliminary feed depth was adjusted until the force sensor detected a rubbing force signal, which was set as the contact zero position. The feed was then retracted to the initial position, and the rotor system was started and accelerated to the test speed. Subsequently, the feed system was gradually advanced to the preset gap value to achieve controlled rubbing between the blade and the coated casing.

In the test, the blades are made of TC4 material, and the coating is an AC100 consumable coating with a thickness of 6 mm. Under the conditions of a blade tip speed of 425 m/s, a feed depth of 3 mm, and a feed rate of 50 μm/s, the morphology of the blade and coating after rubbing is shown in Figure 23. The figure reveals a relatively smooth cutting zone and a rougher rubbing zone on the worn coating surface. The rough zone extends prominently along the rubbing direction, indicating severe wear in the corresponding blade tip rubbing area, with evident localized cracking and plastic deformation. In contrast, the relatively smooth cutting zone corresponds to a more intact portion of the blade tip, where wear is comparatively light.

During the rubbing process, the rubbing force exhibits a periodic variation pattern, with a cycle consistent with the blade rotation period. At the moment of contact, the rubbing force experiences an instantaneous peak followed by a gradual decay. The rubbing force profile during the process is shown in Figure 24. The peak value of the rubbing force reflects the magnitude of the force applied during the rubbing event, and the collected data demonstrate stability and repeatability.

Therefore, through performance testing of the experimental system, it is verified that the designed rubbing test system can accurately control key test parameters such as blade tip speed and feed rate, achieving the required technical specifications and functionalities. Moreover, the rubbing tests demonstrated that high-frequency rubbing forces occurring during high-speed rubbing can be effectively captured, confirming that the system’s testing capabilities meet the requirements for evaluating the wear performance of coatings.

Considering that in real engine environments, rotor–stator rubbing often occurs at multiple points or even circumferentially, the current system can be modified by redesigning the stator casing into an arc-shaped structure to achieve multi-point rubbing. However, for component-level testing under full-circumferential rubbing conditions, the feed system would need to be redesigned accordingly. This system primarily targets material-level assessment and verification tests that closely simulate actual engine operating conditions. Additionally, since the duration of the test is relatively short—thermal exposure time being within 10 min—the influence of the thermal environment on material properties is neglected. Nonetheless, the rotor–stator rubbing test does evaluate the thermal effects induced by the rubbing process.

8. Conclusions

This paper presents the design of a typical dual-bearing, single-disk transonic rotor system, a feed system, and a high-frequency rubbing force measurement system from multidisciplinary perspectives, including structural dynamics and rotor dynamics. The system achieves a maximum blade tip speed of 425 m/s and a feed rate ranging from 2 to 2000 μm/s, enabling rotor–stator rubbing wear tests. The performance of the system is verified through experiments, demonstrating stable operation and reliable results. The main conclusions are as follows:

(1)

The designed transonic rotor system’s critical speeds and natural frequencies avoid the operational speed range, eliminating resonance risk.

(2)

For limited-life components such as the blade and disk, stress responses under working conditions remain below yield strength, and deformations are within material elongation limits with an adequate safety margin, meeting strength and safety requirements.

(3)

Under extreme abnormal conditions, such as blade loss causing bearing unbalance, the bearing response and deformation remain within safe limits, and protective measures prevent secondary damage to the rotor assembly.

(4)

As the force measurement platform is an integrated system, its natural frequency is significantly lower than that of the sensor alone. The first natural frequency is below the bandwidth of the rubbing force, causing the high-frequency components of the rubbing force to exceed the effective measurement range. Consequently, the measured rubbing force may differ from the actual force acting on the specimen. Sensor sensitivity calibration and error compensation algorithms are therefore necessary to obtain accurate rubbing force data.

(5)

The designed rubbing test rig meets the requirements of a blade tip speed of 425 m/s, a feed rate accuracy of 2 μm/s, and a heating temperature of up to 1200 °C. The rubbing force measurements are stable, enabling rotor–stator rubbing wear tests under transonic operating conditions.