Dynamic Deformation Testing and Analysis of Wet Cylinder Liners Using the Eddy Current Method

Abstract

Improving the thermal efficiency of internal combustion engines plays a crucial role in reducing fuel consumption and engine emissions. Studies have shown that the friction loss caused by the piston ring–cylinder liner pair accounts for approximately 30–40% of the engine’s total mechanical friction. The key to improving mechanical and thermal efficiency lies in reducing frictional losses through advanced solutions. However, as engine intensification increases, the growing thermal and mechanical loads lead to out-of-round deformation of the cylinder liner. This deformation reduces the sealing conformity of the piston rings, leading to increased blow-by and elevated particulate matter (PM) emissions. To address this, a dynamic–static deformation testing system for cylinder liners, combined with a multi-physics simulation for data validation, has been developed to achieve energy conservation and emission reduction in engines. Based on established strain gauge and eddy current displacement sensors, this study developed a dynamic deformation testing system, modified for a specific type of diesel engine, and analyzed the cylinder liner deformation under fired conditions. Test results show that under engine speeds ranging from 700 rpm to 1100 rpm, the overall radial out-of-roundness of the cylinder liner increased, with a maximum deformation of 49.2 μm. The second-order component of out-of-roundness also increases with speed, showing a maximum rise of 28.9 μm, while the third-order and fourth-order components exhibit relatively minor changes. These findings suggest that the overall radial deformation under fired conditions is mainly dominated by second-order out-of-roundness, with third-order and fourth-order components contributing marginally.

1. Introduction

In recent years, overwhelming greenhouse gas emissions have led to unprecedented climate change. As a major contributor to these emissions, the automotive sector has prioritized improving the thermal efficiency of combustion engines to reduce environmental impact and conserve energy [1]. Efforts to overcome the friction reduction bottleneck between the piston ring and cylinder liner pair play a crucial role in improving mechanical efficiency in internal combustion engines. This friction loss accounts for approximately 20% to 50% [2,3] of the total friction loss. Nonlinear out-of-roundness may occur during the installation or operation of the cylinder liner. Various factors cause liner distortion, which can be grouped into manufacturing deformation, installation deformation, and operational deformation.

• Manufacturing deformation results from mechanical and thermal loads. During the manufacture of the liner, factors such as tool misalignment, rotational imbalance, radial vibration of the workpiece, material strain, and residual stresses generated during machining can lead to out-of-round deformation. These can be mitigated by improving the liner material and using bore surface strengthening [4] processes. Crosshatch honing [5] is also considered an optimization process, but it primarily improves the lubrication and friction performance of the mating surfaces and has little influence on liner deformation.
• Installation deformation is caused by mechanical load. Mohammed U et al. [6,7,8] investigated the effects of the installation process on liner deformation, including different gasket and liner thicknesses, varying numbers of cylinder head bolts, and changes in cylinder head bolt tightening torque. The results showed that liner thickness is inversely proportional to deformation, while cylinder head bolt preload is directly proportional to deformation. Under the condition of maintaining the required cylinder head bolt tightening torque, installation deformation can be reduced by increasing liner stiffness, rearranging the bolt tightening sequence, and improving the gasket structure.
• Operational deformation results from mechanical and thermal loads during engine operation. H. Fujimoto et al. [9] proposed a study focusing on the influence of dynamic cylinder deformation caused by the combination of different materials, adopting two material combinations: a cast-iron wet liner with an aluminum-alloy cylinder head and a cast-iron cylinder head with an aluminum-alloy cylinder block. Their study shows several conclusions: First, the magnitude of liner deformation under operating conditions is primarily determined by thermal deformation. Second, the liner deformation shows a gradual increase from the bottom dead center to the top dead center due to the combined effects of cylinder pressure, gas temperature, and mismatched thermal expansion and stiffness between various kinds of materials. Third, asymmetric deformation between the front-end and rear-end liners of the block occurs during the operating condition, which is attributed to the elevated temperature of the cylinder wall between adjacent cylinders, causing greater expansion of the liner in the direction perpendicular to the crankshaft axis. To address these problems, Flores G et al. [10,11] found that using conical and elliptical liners for pre-compensation design can significantly reduce the out-of-roundness of the liner in the fire condition and improve the overall performance of the tribological pair.

The oil consumption and the blow-by increase due to the out-of-roundness of the liner. The byproducts, originating from the combustion of engine oil that enters the combustion chamber, constitute a significant source of soluble organic fraction (SOF) of diesel particulate matter (PM) [12]. The improvement of sealing performance can be achieved by increasing the conformity between the piston rings and distorted cylinder bores. This approach will increase frictional losses, leading to higher fuel consumption and greenhouse gas emissions. Hence, optimizing the roundness characteristic of the liner bore plays a key role in improving the performance of internal combustion engines; other improvements can be found in the reduction in greenhouse gas emissions, PM emissions, and fuel consumption [11].

The accuracy of simulation studies on cylinder liner deformation relies on validation using experimental data. Two types of measurements are listed below:

• Static measurement:

• After the assembly of the cylinder block, head gasket, and cylinder head, with bolt preload applied, deformation is measured using a high-precision 3D metrology system.

• Dynamic measurement:

• This measurement is performed under engine operating conditions with varying loads. Several non-contact measurement sensors or strain gauges are installed inside the cylinder bore. The data is obtained through direct or indirect measurement methods, followed by signal processing to extract the actual linear deformation.

Existing studies have conducted thorough investigations in the field of cylinder liner out-of-roundness by integrating dynamic liner measurement systems with numerical simulation methods. Fujimoto et al. [13] studied the influence of load and speed on cylinder liner deformation. They achieved a real-time measurement system by mounting a gap sensor capable of high-temperature measurement on the second piston ring land and devised a rotating piston mechanism. By installing eddy current measurement sensors on the piston ring land, Koch et al. [14] developed a method to measure cylinder liner deformation under operating conditions. Other approaches based on optical measurement methods have been employed for deformation measurement in controlled environments [15,16]. Methods mentioned above have also been adopted in subsequent studies [17,18,19]. Taiga Hibi et al. [20] proposed a cylinder bore pre-compensation scheme and investigated the effects of non-uniform cylinder liner deformation on the tribological performance of the piston skirt and blow-by characteristics. Research showed that this method can effectively reduce engine friction loss, noise, and oil consumption. In addition, several other studies have been conducted to measure the deformation of the cylinder bore at specific cross-sections [21,22,23,24].

Due to the structural characteristics of the cylinder liner, that is, acting as the moving support in the piston–liner friction pair and being deeply embedded within the engine, it is challenging to integrate sophisticated sensors and cables into the measurement system. Moreover, the high-speed operating environment is also unsuitable for embedded systems, as oscillations may disrupt their normal function.

In response to these challenges, a dynamic deformation measurement system for liners under fired conditions was proposed. This system enables the acquisition of dynamic liner deformation data under various conditions. The results can serve as validation data for multi-physics coupling simulation studies, while also providing an analytical basis for liner deformation control and for optimizing the trade-off between oil consumption and friction loss.

This study examines two types of high-pressure, common-rail diesel engines designed for off-road applications. A measurement was developed using sets of eddy current measurement sensors combined with a hardware–software integrated system and a data processing system for cylinder liner deformation. Bench tests were performed to measure the liner deformation in its key characteristic directions. The results offer valuable insights for managing liner deformation and enhancing the performance of the piston–liner friction pair. The overall research workflow is illustrated in Figure 1.

2. Experimental Theoretical Background

During operation, the cylinder liner in diesel engines experiences out-of-roundness, resulting in variations in piston–liner clearance. The clearance between the ring land and the liner wall during the piston’s reciprocating motion can be tracked by using a gap sensor mounted on the piston ring land. The out-of-roundness profile along a specific characteristic line of the cylinder liner can be obtained by fitting a curve to the gap data.

The experiment requires compact, heat-resistant sensors due to the high thermal load at the ring land region of the piston crown, where temperatures can reach approximately 200 °C. Based on previous research [14,19,25], the eddy current sensor is capable of dynamic cylinder liner deformation measurement.

3. Integrated System Design

According to the functional division, the system can be divided into two parts: a DAQ system for data collection and a data processing system for analysis. Details of each are provided in the following sections.

3.1. DAQ System

3.1.1. Measurement Principle

• Clearance measurement principle

The eddy current sensor operates based on Faraday’s law of electromagnetic induction. It can transform the distance between its tip and a metallic surface into a voltage signal within a defined range. Mechanical interference is avoided since the eddy current sensor does not require physical contact, making it particularly suitable for high-speed and high-precision measurement scenarios. Faraday’s Law of Induction is mathematically expressed as the following:

$$\epsilon =-d\Phi /dt$$

(1)

where ε is the induced electromotive force (EMF), and Φ is the magnetic flux through the loop.

However, as a wired sensor, the eddy current sensor required cable routing and an installation-supported structure. To perform a bench test, a specialized data acquisition system designed for gap measurement has been implemented. The following section outlines the design and details of this measurement system.

• Synchronization of the top dead center

The structural features of the combustion engine make it impossible to establish a direct correlation between the eddy current sensor signal and the piston position. Therefore, a photoelectric encoder was implemented to provide a crankshaft angle reference signal, enabling calibration between the time-domain sensor data and the mechanical position of the piston.

The incremental photoelectric encoder outputs three sets of square-wave pulses: A, B, and Z (Figure 2). The rotation direction is determined from the 90° phase shift between signals A and B, while the missing-tooth characteristic of the Z-phase pulse is used to locate TDC (top dead center).

3.1.2. Hardware Selection

The hardware component of the system includes a multi-channel synchronous data acquisition card, various sensors (such as eddy current sensors and photoelectric encoders), a computer for data storage and processing, and a regulated power supply. The necessary hardware components are listed below:

• Eddy current sensors

The DT3060/LC-M-ES1/200 eddy current displacement sensor is manufactured by Micro-Epsilon (Germany Ortenburg). The main parameters are as follows: probe diameter of 5 mm, length of 6 mm, measurement range of 0.1–1.1 mm, accuracy of 0.02 μm, operating temperature from −20 °C to 200 °C, and temperature drift ≤0.15 μm/°C. The sensor system consists of a controller, a heat-resistant cable, and a probe. Accurate measurements under fluctuating in-cylinder conditions are ensured by pre-calibrated temperature compensation in the probe and controller.

• Photoelectric encoders

The LF-72BM-C05B photoelectric encoder (with an angular resolution of ±0.5°) is used to synchronize the gap signals with the crankshaft angular position. The encoder supports rotational speeds of up to 6000 rpm.

• Data acquisition card

The Advantech PCIE-1812 high-speed data acquisition (DAQ) card is capable of a 16-bit high-precision ADC sample, eight-channel differential synchronous sampling at up to 250 Ks/s, and an anti-aliasing filter design. To meet the requirement of simultaneously acquiring multi-channel gap signals (with a resolution of 0.02 μm) and crankshaft angle signals (with an accuracy of ±0.5°), two PCIE-1812 cards are installed, and the software is synchronized within the LabVIEW platform.

• Industrial computer

The Advantech IPC-940 high-reliability industrial computer, equipped with the Windows 10 operating system, is used in the test system. Its AIMB-785G2 industrial motherboard supports up to four DAQ cards via the PCIe interface. To ensure data integrity and acquisition continuity under vibration-intensive conditions, the hardware configuration also integrates a RAID 1 vibration-resistant disk array and an industrial-grade solid-state drive (SSD).

• Regulated power supply

An external, regulated power supply that provides 5 V and 24 V stabilized AC power is required to ensure the proper operation of the incremental photoelectric encoder and the eddy current sensor controller.

3.1.3. Data Acquistion Software System Design

The software system shown in Figure 3 is based on the LabVIEW platform. It consists of four modules: data acquisition, data processing, data storage, and data display.

• Data acquisition

The data acquisition module imports DLL files and utilizes virtual instruments (VIs) to initialize and configure the DAQ card. Once a configuration is loaded, a DAQ task can be created. Then the program can invoke relevant VIs to manage the task status, such as starting, pausing, or stopping the acquisition process.

• Data processing

The data processing module converts the input signals from the eddy current sensors into displacement values using a pre-defined calibration formula. The output format can be switched between the voltage and the displacement values. To mitigate the influence of noise on the acquired data, a filtering module is also integrated. Different filter parameters can be configured according to the noise characteristics, ensuring the accuracy of the processed data.

• Data storage

The collected data is stored in the Technical Data Management System (TDMS) file format. The customized TDMS file consists of three levels: file, group, and channel. One can define the attributes at each level. This format provides a structured and manageable data storage solution by pre-defining descriptive information within the file, avoiding the need for a header structure specification.

• Data display

The data display module accommodates a variety of display requirements during data acquisition.

3.2. Data Processing System

3.2.1. Data Processing Principle

• Processing bias from secondary motion

Secondary motion refers to the lateral displacement of the piston within the cylinder liner and its rocking motion around the piston pin during engine operation. This phenomenon is primarily caused by the clearance between the piston and the liner and the non-vertical thrust force induced by the inclination of the connecting rod (demonstrated in Figure 4a).

Secondary motion causes piston tilt and radial displacement, affecting the measurement accuracy of the sensor in directions other than the thrust and anti-thrust sides. The actual deformation S can be obtained using the following equation:

$$S=S^{\prime }-S_0+D$$

(2)

where $S^{\prime }$ is the measured clearance under bolt preload or engine operation, $S_0$ is the original clearance measured before the cylinder head was installed, and $D$, which is from the calculation of piston multi-body dynamics, represents the radial displacement caused by secondary motion.

A multi-body dynamics model is established using AVL Piston & Ring software. By simulating the piston’s motion during a working cycle under specific operating conditions, the impact of secondary motion on the measured clearance can be determined [26].

Taking the calculation of piston secondary motion under the idling condition of the test engine as an example [27], the simulation results for piston radial displacement and piston angle are illustrated in Figure 4b and Figure 4c, respectively, where 0° CA to 180° CA represents a power stroke. During a complete working cycle, the piston undergoes six reversals in radial movement direction, each accompanied by a significant piston swing. The largest radial displacement can be found at 42° CA, reaching 0.037 mm. The piston exhibits an oscillation when it reaches the TDC or BDC. Therefore, under the effect of the explosion pressure, it can reach a maximum tilt angle of 0.156° near the TDC.

• Cubic spline interpolation of the Liner deformation

The original clearance data obtained from the eddy current sensor is limited to eight axial sampling lines due to spatial constraints during sensor installation. The remaining angular data can be acquired using interpolation algorithms that estimate the most appropriate values at other points based on the provided data. This process transforms discrete data points into a continuous function, resulting in a smooth curve that passes through all the required points. Since the conventional interpolation algorithms become unreliable as the number of points increases, a cubic spline interpolation algorithm is adopted.

Suppose the interval $[a,b]$ is divided into $\left[\right(x_0,x_1),(x_1,x_2),\dots ,(x_{n-1},x_n\left)\right]$, resulting in a total of $n + 1$ points, where the two endpoints are $x_0=a, x_n=b$. The resulting function satisfies the following conditions [27]:

• Interpolation Condition

The spline must pass through all the given data points:

$$S\left(x_i\right)=y_i\left(i=\mathrm{0,1},\dots n,\right)$$

(3)

where Si(x) is a cubic equation defined on the subinterval $[x_i,x_{i+1}]$.

• Interpolation piecewise cubic form

On each subinterval $[x_i,x_{i+1}]$, the function $Si\left(x\right)$ is a cubic polynomial:

$$S\left(x_i\right)=a_i+b_{i}x+c_i{x}^2+d_i{x}^3$$

(4)

• Continuity conditions

To ensure the smoothness of the curve, the adjacent cubic polynomials must satisfy the following continuity constraints at the knots:

• Function continuity:

$$S_i\left(x_i\right)=y_i$$

(5)

$$S_i\left(x_i+1\right)=y_i+1$$

(6)

2.

First derivative continuity:

$${S_i}^{\prime }\left(x_{i+1}\right)={S_{i+1}}^{\prime }\left(x_{i+1}\right)$$

(7)

3.

Second derivative continuity:

$$S_i″\left(x_{i+1}\right)=S_{i+1}″\left(x_{i+1}\right)$$

(8)

• Boundary Conditions

There are three common types of boundary conditions in cubic spline interpolation:

Natural spline: The second derivatives at both endpoints are zero.

Clamped spline: The first derivatives at both endpoints are specified.

Not-a-knot spline (used in this software module): Enforces that the third derivative at the first point equals that at the second point, and likewise at the last two points:

$$S_0‴\left(x_0\right)=S_1‴\left(x_1\right), S_{n-2}‴\left(x_{n-1}\right)=S_{n-1}‴\left(x_n\right)$$

(9)

• Approach for calculating cylinder liner out-of-roundness

According to different computational approaches, the calculation of cylinder liner out-of-roundness can be classified into four methods: minimum zone circle (MZC), least squares circle (LSC), maximum inscribed circle (MIC), and minimum circumscribed circle (MCC). In this study, the out-of-roundness $\Delta r\left(\theta \right)$ is defined as the difference between the measured radial position and the radius of the least squares circle, i.e., $\Delta r\left(\theta \right) = r\left(\theta \right) - R_{avg}$. This approach yields both positive and negative deviation values.

• Fourier transform of cylinder liner deformation

Assessment of cylinder liner deformation tolerance is a critical aspect of engine engineering. One commonly used method is to represent the actual deformation of the liner as a combination obtained through Fourier series expansion (Figure 5). By applying the Fourier series, the inner cross-section of the liner can be expressed as a set of Fourier coefficients and phase angles. The reconstruction of the original deformation profile of the liner can be achieved by extracting the spectral coefficients of each harmonic order through a finite number of measured or calculated radial values $\Delta r$ [28].

The Fourier Transform equation is shown below:

$$\begin{gathered} \Delta r=A_0+A_1\mathit{cos}(\theta )+A_2\mathit{cos}(2\theta )+\cdots +A_i\mathit{cos}(i\theta )+ \\ {B}_1\mathit{sin}(\theta )+B_2\mathit{sin}(2\theta )+\cdots +B_i\mathit{sin}(i\theta ) \end{gathered}$$

(10)

Two tables of the calculated Fourier coefficients are provided in Appendix A.

After transformation, the following occurs:

$$\Delta r=A_0+{\displaystyle \frac{U_1}{2}}\mathit{cos}(\theta -{\theta }_1)+{\displaystyle \frac{U_2}{2}}\mathit{cos}(\theta -{\theta }_2)+\cdots +{\displaystyle \frac{U_i}{2}}\mathit{cos}(\theta -{\theta }_i)$$

(11)

where $\Delta r$ represents the radial deformation, $A_i$ and $B_i$ are the Fourier series coefficients, the deformation amplitude is defined as $U_i=2\sqrt{A_i^2+B_i^2}$, and the phase angle is given by ${\theta }_i={\displaystyle \frac{1}{i}}\mathit{arctan}{\displaystyle \frac{B_i}{A_i}}$.

Here, $i$ is a non-negative integer indicating the harmonic order of the Fourier series, and different values of $i$ correspond to various modes of out-of-roundness of the cylinder liner.

Higher-order deformation modes are often disregarded, with the first four harmonics accounting for the majority of the total deformation.

3.2.2. Data Processing Software System Design

A MATLAB-based data processing system was developed for analyzing the dynamic deformation of the liner. The system generates radial cross-sectional plots and unwrapped circumferential diagrams of the cylinder liner, corresponding to various harmonic orders extracted via Fourier transformation. This enables effective correction for deviations and the analytical evaluation of experimental data. The software framework is shown in Figure 6.

• Data deviation processing module

The data bias processing module is responsible for calibrating the eddy current sensor measurements. First, it applies the least-squares circle method to determine the center of each cylinder liner cross-section and calculates the out-of-roundness at various circumferential angles for each section. Then, a data deviation correction strategy is employed to eliminate the influence of piston secondary motion (the effects of radial piston displacement and piston tilt) on the measurements. Finally, this process returns the real dynamic liner deformation data.

• Radial data interpolation module

The primary task of the radial data interpolation module is to transform the discrete measurement sensor data points into a continuous function. The module can estimate the approximate values at other positions based on the known values. Once the eddy current sensor data are obtained, the module applies interpolation methods to calculate the data for uncovered angular positions within the liner cross-section, thereby meeting the requirements of subsequent analysis.

• Fourier transform module

The Fourier transform module is used to perform the Fourier transformation on the raw data. By calculating the out-of-roundness of different harmonic orders, the second-, third-, and fourth-order components at each cross-section are extracted. These components correspond to the effects of different operating conditions and provide a basis for further control.

• Circumferential unwrapping and plotting module

The circumferential unwrapping and plotting module produces graphs of the circumferential liner deformation data to give a clear view of the out-of-roundness for later analysis. It uses MATLAB (R2022b) 3D plotting and polar coordinate functions to create circumferential unwrapping diagrams and radial cross-section views for both the raw dynamic liner deformation data and the processed Fourier data.

4. Setup and Analysis

4.1. Implementation Details

The angular positions on the cylinder liner are defined as follows: viewed from the top of the engine block, the sub-thrust side is set as the reference point at 0°, with the angle increasing in the counterclockwise direction. Accordingly, the flywheel side is defined as 90°, the main thrust side as 180°, and the pulley side as 270°.

4.1.1. Sensor Installation

As shown in Figure 7, stepped holes were machined along the circumferential direction of the second piston ring land, with the ring land corresponding to the thrust side of the cylinder liner defined as the 0° reference point. Two engine types were used in the experiment. Engine Type 1 is a single-cylinder engine with eight evenly distributed threaded holes, while Engine Type 2 is a compact four-cylinder engine with four evenly distributed threaded holes.

4.1.2. Thermal Deformation Compensation

The tested piston is cast from an Invar alloy, which exhibits significant thermal expansion. The Invar alloy used is grade 4J36, with a composition of 36% Ni, 63.8% Fe, and 0.2% C. Its coefficient of thermal expansion, measured in the range of −20 °C to 200 °C, is 1.82 × 10⁻⁶ °C⁻¹. Under operating conditions, the temperature at the second piston ring groove can exceed 200 °C, which severely affects the measurement accuracy of the sensors mounted on the ring land. Therefore, Invar steel, known for its low coefficient of thermal expansion, was selected as the material for fabricating the sensor mount (Figure 7). The Invar steel sleeve was centrally installed on the inner surface of the piston using hex socket bolts. It was radially threaded onto the mount, with the high-temperature cable routed through the internal bores of both components. A slotted head was designed to allow installation and removal using a custom tool (Figure 7).

The partial interference between three components—the Invar steel mount, the small end of the connecting rod, and the inner cavity of the piston—compromised the accuracy of the measurement. The structural strength of the connecting rod and piston was re-evaluated before testing. Simulation results confirmed that both components had safety factors greater than 1.5.

4.1.3. Dual-Link Lead-Out Mechanism

Since the sensor is installed inside the engine and the eddy current sensor requires an external power supply, both data and power cables must be routed outside. The inevitable damage to sensor data cables caused by the high-speed rotation of the crank-connecting rod mechanism is also a major issue in data transmission. Therefore, an interference-free dual-link lead-out mechanism was designed based on kinematic simulations. It consists of two links: The first link connects to the large end of the connecting rod, while the other link is attached to the observation port bracket on the engine block (see Figure 7). This mechanism protects the routed data and power cables from mechanical damage even in extreme operating conditions.

The dual-link mechanism is a statically indeterminate structure influenced by multiple variables, resulting in complex loading conditions. To verify the mechanical reliability, a transient dynamic simulation and strength evaluation were performed using ANSYS, a leading simulation software provider. The results indicate that both links satisfy the safety factor requirement of being greater than 1.5.

4.2. System Setup

4.2.1. System Installation

The schematic of the test system is illustrated in Figure 8. The installation was carried out in three main steps.

First, each eddy current sensor was encapsulated in an Invar steel sleeve, which was then embedded into the corresponding pre-machined groove inside the piston to ensure thermal compatibility and mechanical stability.

Next, the sensor lead was routed through a pre-cut groove along the connecting rod shank and firmly secured using a modified acrylate adhesive to prevent displacement during high-speed operation.

Finally, the dual-linkage mechanism was employed to guide the lead out of the engine. The lead was then connected to the external data acquisition system.

4.2.2. System Verification

Several support subsystems were also implemented to help engine evaluation, including:

• Eddy current dynamometer
• Measurement and control system
• Coolant temperature control unit
• Fuel consumption meter
• Fuel temperature control system
• Cylinder pressure and heat release rate acquisition system
• ECU calibration system

An initial functional verification was performed to ensure signal transmission, power supply, and data synchronization. Results show that the system is capable of operating in a high-temperature environment.

4.3. Test Case

Three test conditions were selected, as listed in

Table 1. Test cases.

State	Description
Free state	The liner is installed in the engine block without the cylinder head.
Bolt load state	The cylinder head is assembled; the engine is manually rotated.
Fired (hot) state	The cylinder head is assembled; the engine is running at 700 rpm and 1100 rpm.

. The clearance between the piston and liner for each condition was measured using the dynamic deformation data acquisition system, as shown in Figure 9. The first two channels are receiving input data from the photoelectric encoder. Subsequently, the data was processed with the processing system to obtain real-time linear deformation.

4.4. Test Results and Analysis

Previous studies have investigated the cylinder bore out-of-roundness under different operating loads. Yang Z.H., Bird, and Gartside [29,30] conducted experimental and simulation-based analyses to examine the effects of thermal and mechanical loads on the deformation behavior of cylinder bores. From their results, thermal loading primarily induces second-order deformation, with a peak deformation of 86 μm observed at 6000 rpm, while the influence of bolt preload around the bore mainly contributes to fourth-order deformation. Higher-order modes tend to result in poorer conformity between the liner and piston ring under equal amplitude deformation conditions.

Building on these insights, two different conditions were set for the experiment: one at 700 rpm and the other at 1100 rpm to evaluate the cylinder liner’s radial out-of-roundness under varying engine speeds. The results show the following trends in the deformation of the cylinder liner under different conditions:

• 700 rpm operating condition

Under the 700 rpm operating condition, the overall radial out-of-roundness of the cylinder liner and its harmonic components obtained through Fourier decomposition are shown in Figure 10a–d. Overall, significant deformation is observed at both 90° and 270°, with the maximum occurring at 270°. The middle cross-sections of the liner exhibit greater deformation, while the variation in deformation angle across different sections is relatively small. The top section of the liner shows less deformation.

The maximum radial expansion occurs at the 156 mm cross-section in the upper region along the 90° direction, with a deformation of 15.1 μm. In contrast, the maximum radial contraction is found at the 49 mm cross-section in the upper region along the 180° direction, measuring −52.7 μm.

The upper sections of the liner exhibit relatively large deformation; the angular locations of peak deformation remain consistent across other cross-sections. The maximum radial expansion of the liner occurs at 359° and the 44 mm cross-section, with a peak deformation of 43.7 μm—only 1 μm greater than the maximum expansion observed under the 1000 rpm condition. The maximum radial contraction occurs at 270° in the circumferential direction and at the 141 mm axial cross-section, with a peak deformation of 101.9 μm. Compared to the maximum expansion at 1100 rpm, this shows an increase of 20.7 μm.

• 1100 rpm operating condition

Under the 1100 rpm operating condition, the overall radial out-of-roundness of the cylinder liner can be obtained through Fourier decomposition, with the resulting harmonic components shown in Figure 11a–d. Unlike the result at 700 rpm, the second-order component contributes the most to the deformation, while the fourth-order component contributes the least. The second-order deformation is more pronounced in the middle-to-lower region of the cylinder liner, with the maximum value of 36.7 μm observed at the 203 mm cross-section. In contrast, the third-order deformation is more prominent in the upper region, with a peak of 14.5 μm at the 48 mm cross-section. Notably, this cross-section also exhibits the second-largest deformation at 48 mm, reaching 2.5 μm. Results show that at 1100 rpm, the peak positions of the second-, third-, and fourth-order deformation components remain consistent across all liner cross-sections.

With increasing engine speed, the liner’s thermal load also rises, resulting in greater maximum deformation. The maximum deformation reaches 49.2 μm between the two experimental conditions, highlighting a significant difference.

The second-order deformation increases significantly with the engine speed, with the maximum second-order deformation reaching 28.9 μm between the two conditions. The bolt preload primarily determines the third- and fourth-order deformations. Therefore, the calculation results show that no significant change occurs with increasing engine speed. The peak deformation phase of the liner remains largely consistent across different operating conditions.

5. Conclusions

This paper presents a method for building a practical system for liner dynamic deformation measurement. A deformation data testing system using an eddy current sensor was developed. A data acquisition system and a data processing system were built. Finally, a series of experiments was conducted using a specific type of diesel engine. The research results show the following:

• A dual-link lead-out mechanism was implemented to safely route the sensor cables outside the engine under high-speed operation.
• A multi-sensor synchronous acquisition system was designed for real-time recording of data and synchronized signals, and a deformation data analysis system was implemented for processing and filtering the acquired signals. The effect of secondary piston motion on measurement accuracy was modeled through multibody dynamics simulation and effectively corrected during post-processing.
• The overall radial out-of-roundness of the cylinder liner increases with engine speed from 700 to 1100 rpm, with the maximum deformation rising by 49.2 μm. Fourier analysis further reveals that the second-order component exhibits a significant increase across the speed range, with a maximum growth of 28.9 μm, while the third- and fourth-order components show only minor variations.
• Test results demonstrate that the system is capable of continuously measuring deformation inside the liner or cylinder bore while maintaining good thermal stability.
• The use of three-dimensional visualization provides a clear representation of dynamic liner deformation, while the Fourier transform enables targeted analysis of the influencing factors.

These indicate that, under hot operating conditions, the overall out-of-roundness is dominated by the second-order mode, with a marginal contribution from higher-order components. The results also demonstrate that the proposed system is capable of accurately capturing the dynamic deformation characteristics of the cylinder liner in real engine environments.

The cylinder block structure type determines the coolant flow characteristics, leading to significant differences in liner deformation among different cylinder block designs. Therefore, the results of this study are primarily applicable to the qualitative analysis of similar diesel engine types. Owing to the limited installation space for sensors, the proposed method has certain restrictions when applied to small-bore engines.