Correlation Between Residual Stress and Acoustic Emission Signals in the Turning Operation of Hardened Aisi 4340 Steel

Correlation Between Residual Stress and Acoustic Emission Signals in the Turning Operation of Hardened Aisi 4340 Steel | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article Correlation Between Residual Stress and Acoustic Emission Signals in the Turning Operation of Hardened Aisi 4340 Steel Anderson Edson da Silva, Jorge Wanderson Barbosa, Ismael Nogueira Rabelo de Melo, and 3 more This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-5323003/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 04 Mar, 2025 Read the published version in The International Journal of Advanced Manufacturing Technology → Version 1 posted 5 You are reading this latest preprint version Abstract Residual stress is a critical factor that influences the lifespan of mechanical components subjected to fatigue. Compressive stress tends to extend the life of a component, whereas tensile stress can shorten it. Acoustic emission (AE) signals have been linked to phenomena occurring during manufacturing processes; however, only a few studies have been conduct to correlate AE signals with the surface integrity of machined parts. In this study, an approach for correlating residual stress with AE signals is introduced. AISI 4340 steel specimens are machined by using ceramic tools, with varied cutting speeds, feed rates, and depths of cut, and AE signals are recorded during the process. The signals are processed and analyzed by using the spectral entropy technique, also known as Shannon entropy or information entropy. The results reveal that the appropriate application of frequency filters uncovers regions of strong correlation between the spectral entropy of the AE signals and the residual stress. The observed correlation can contribute to the optimization and control of machining processes and help to achieve the desired residual stress levels. AISI 4340 Steel Residual Stress Acoustic Emission Spectral Entropy Machining Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 Figure 7 Figure 8 1. Introduction Machining hardened steels has become a routine industrial process, and ceramic tools are commonly used for this [ 1 ]. Turning operations performed by using ceramic tools not only reduce costs but also improve product quality; thus, these are a viable alternative to grinding in finishing processes [ 2 ], [ 3 ]. Studying surface integrity can help in understanding the changes occurring on the surface and subsurface of a part during manufacturing, as the performance and final quality of a product are directly linked to its surface integrity [ 4 ]. The key characteristics of surface integrity in machined parts include residual stress, hardening, microstructural changes, and surface roughness, all of which result from plastic deformation [ 5 ]. Residual stress has a significant impact on the lifespan of mechanical components used in engineering applications [ 6 ]. Tensile stress can promote crack propagation, whereas compressive stress can inhibit it. This relationship is crucial to the fatigue life of components subjected to cyclic loads that require high fatigue strength. The risk to the component’s lifespan increases when tensile residual stress combine with operational stress [ 7 ], [ 8 ], [ 9 ]. In machining processes, cutting parameters such as the speed, feed rate, and depth of cut influence the residual stress induced in the components [ 10 ]. The most common methods for measuring residual stress are X-ray diffraction (XRD) and the blind-hole technique. XRD enables the measurement of both micro and macro stresses but can be limited by the sample size; it is ideal for small samples. By contrast, the blind-hole technique is quick, easy to perform, and applicable to a wide range of materials; however, it has higher measurement uncertainty, is semi-destructive, and is restricted to simple geometries. For most materials, XRD remains the most accurate method [ 11 ]. Acoustic emission (AE) signals are defined as transient elastic energy released in the form of mechanical stress waves within materials. The detection and analysis of these stress waves can be monitored through AE signals [ 12 ]. AE signal analysis is a non-destructive testing technique with numerous industrial applications, such as in structural analysis [ 13 ], corrosion detection [ 14 ], pressure vessel testing [ 15 ], and machining [ 16 ]. Several methods are available for analyzing and processing captured AE signals [ 17 ]; however, regardless of the approach, detection systems must exhibit sensitivity that is appropriate for the phenomena being monitored. In machining, AE sensors are well-suited for monitoring cutting parameters, even at low material removal rates, and are sensitive to subsurface damage [ 18 ]. The use of AE monitoring in machining processes has been widely studied in recent years; the primary focus has been cutting parameters and tool life analysis. However, studies in which the correlation between AE signals and the surface integrity of machined parts—such as surface finish and residual stress—is investigated are still scarce. Traditional techniques for signal processing, such as hit counting and fast Fourier transform, are prone to errors during machining because AE signals often change over very short periods of time [ 19 ]. The study of AE signals by utilizing spectral entropy is particularly promising because spectral entropy, which originates from the uncertainty in amplitude distribution, is independent of thresholds and other time-based parameters; thus, spectral entropy is a useful tool for characterizing microstructural deformations [ 20 ]. Spectral entropy, also known as Shannon entropy, can be mathematically expressed in Eq. 1 [ 21 ]. $$\:SE=\:-\sum\:_{i=1}^{N}{p}_{i}{\text{log}}_{2}\left({p}_{i}\right),$$ 1 where \(\:{p}_{i}\) is determined by applying Equations 2 and 3 : $$\:{p}_{i}=\:\frac{X\left(i\right)}{\sum\:_{j=1}^{N}X\left(j\right)};$$ 2 $$\:\sum\:_{i=1}^{N}{p}_{i}=1.$$ 3 The events during an experiment determine the number of frequency components, and as the signal is analyzed, the probabilities are updated; \(\:{p}_{i}\) represents the percentage of each frequency \(\:i\) in the spectrum and denoted as \(\:\:{p}_{i}=\:\left\{p1,p2,p3,\dots\:,pN\right\},\:\) where these probabilities depend solely on the frequency distribution, X. Once the frequency distribution is obtained, spectral entropy is calculated by using Eq. 1 at each moment in time corresponding to the performed test [ 17 ], [ 22 ]. Spectral entropy values range between 0 and 1, with higher values indicating greater randomness. The closer the value is to 0, the less random the condition is [ 23 ]. Therefore, entropy is maximized for equiprobable events, whereas entropy equals zero for single events and is entirely dependent on the probability distribution of the event. Chai et al. [ 20 ] captured AE signals during a fatigue-crack-growth test in CrMoV steel and found that spectral entropy was more sensitive to small differences in AE signals than to signal amplitude. They observed that sudden changes in spectral entropy usually indicate critical damage, such as the initiation and growth of cracks. Thus, spectral entropy is valuable for monitoring mechanical systems. Karimian et al. [ 24 ] used spectral entropy to identify the nucleation and coalescence of microcracks in aeronautical structures. They found that minimal spectral entropy can be combined with increasing cumulative spectral entropy to reliably identify fatigue cracks. Different frequency ranges in AE signals correspond to specific phenomena, and the use of filters improves the understanding on these phenomena. Maia et al. [ 19 ] noted that the frequency range sensitive to the machining process is 90–110 kHz, whereas Marinescu and Axinte [ 26 ] suggested that this range could be extended slightly to 70–115 kHz. However, the frequency range displaying the strongest correlation between spectral entropy and residual stress is not necessarily restricted to the typical machining phenomena, and the signal may show greater sensitivity in bands outside these common frequencies. The aim of this study is to explore the correlation between AE signals and residual stress by identifying the frequency region in the spectrum that is most sensitive and correlates with residual stress values. The correlation between two conditions can be analyzed by using Pearson's correlation coefficient (r), a statistical metric that measures the strength of the linear relationship between two variables. This coefficient is widely applied in various fields [ 27 ], such as data analysis [ 28 ], financial analysis [ 29 ], and biological research [ 30 ]. Pearson’s correlation coefficient is dimensionless, indicating that it does not have units or a reference proportion. The coefficient ranges from − 1 to 1, with values closer to 1 or − 1 indicating a stronger correlation. Values near 0 suggest no correlation, positive values indicate a direct relationship, and negative values imply an inverse relationship [ 31 ]. "r" values between 0.1 and 0.3 represent a weak correlation, between 0.4 and 0.6 are considered moderate, and above 0.6 indicate a strong correlation [ 32 ], [ 33 ]. The aim of this study is to deepen the understanding on surface integrity control in the machining of AISI 4340 steel by analyzing AE signals emitted during the process. AE signals were captured when turning AISI 4340 steel with ceramic tools. An artificial intelligence (AI) tool was employed to identify the spectral region most sensitive to residual stress, and the signals were filtered in the frequency band having the highest correlation, as determined by the AI tool. The filtered signals were analyzed by using the spectral entropy technique, which revealed a strong correlation between residual stress and AE signals across varied cutting speeds, feed rates, and cutting depths. This correlation highlights the potential for improving machining process control, optimizing cutting techniques, and refining machining parameters. 2. Experimental procedure Figure 1 presents the schematic flowchart of the experimental procedure implemented in this study. The specimens were fabricated from AISI 4340 steel; the chemical composition is presented in Table 1 . Table 1 Chemical composition (%) of AISI 4340 steel used in the tests. C Mn P max Si S max Cr Ni Mo 0.40 0.70 0.007 0.35 0.001 0.78 1.74 0.24 The samples were heat-treated (quenched and tempered) to achieve a hardness of 52 ± 2 HRC. The specimens had a useful area of Ø32 × 42 mm, with a Ø24 mm section used for fixtures. Figure 2 shows a schematic of specimens used in the study. The samples were machined on a Romi computerized numerical control lathe (model Centur 30D) having a power output of 10 kW and equipped with a Spartan 2000 AE-signal-collection system (Physical Acoustics). The AE signals were acquired by using a National Instruments PCI-6251 data acquisition board at a sampling rate of 1.2 MHz. The AE sensor was positioned 150 mm from the tool tip, and the captured signals were processed by using the MATLAB software with the spectral entropy signal-processing technique. Raw AE signals were recorded during the tests and analyzed by using Python, an AI tool, to identify the frequency range most sensitive to residual stress. Python was used to scan the entire spectrum, and the frequency range having the highest correlation was found to be 400–403 kHz. Based on these results, a low-pass filter at 403 kHz and a high-pass filter at 400 kHz were applied to isolate this frequency range for further analysis. The cutting tool used in this study was a Sandvik mixed ceramic insert with SNGA 120408 T01020 geometry of the CC650 H05 class without any coating. The tool holder was a DSBNL 2525M12 system, which resulted in a cutting edge angle of 75° relative to the workpiece, with rake and inclination angles of − 6°. The tests were conducted under dry conditions, and a new cutting edge was used for each test. Each cutting condition was replicated twice. To analyze the influence of the cutting speed, tests were performed at 50, 100, 150, and 200 m/min with a constant feed rate of 0.1 mm/rev and cutting depth of 0.5 mm. To analyze the effects of the feed rate and cutting depth, the cutting speed was set at 150 m/min and the feed rates were 0.05, 0.1, and 0.15 mm/rev and the cutting depths were 0.25, 0.5, and 1 mm, respectively. The cutting conditions are summarized in Table 2 . Table 2 Cutting parameters Parameter analyzed Condition Cutting speed Vc (m/min) Feed rate f (mm/rev) Cutting depth Ap (mm) Cutting speed 1 50 0.1 0.5 2 100 0.1 0.5 3 150 0.1 0.5 4 200 0.1 0.5 Feed rate 5 150 0.05 0.5 6 150 0.1 0.5 7 150 0.15 0.5 Cutting depth 8 150 0.1 0.25 9 150 0.1 0.5 10 150 0.1 1 The residual stress measurements were performed using a SHIMADZU RDX-7000 X-ray diffractometer. For the measurements, Crκα radiation (λ = 2.289Å) was used, targeting the (211) crystallographic plane of the ferrite-martensite phase, which exhibits its peak at a 2θ angle of 156.2°. The 2θ diffraction angles ranged from 150° to 160°, whereas the Ψ angles were set at 7°, 14°, 21°, 28°, 35°, 42°, and 49°, with a pitch of 0.1°. The scanning speed was 2°/min. For the correlation analysis, Pearson's correlation coefficient, with a statistical significance threshold of p < 0.05, was used. 3. Results and discussion Figure 3 shows the mean residual stress and spectral entropy as functions of the cutting speed. The data indicate that the cutting speed influences residual stress; however, the relationship exhibits non-linear behavior. The maximum compressive residual stress values are observed at the lowest and highest cutting speeds tested (50 and 200 m/min), whereas the least compressive residual stress is observed at 100 m/min. The correlation between the mean residual stress and spectral entropy as a function of the cutting speed is analyzed by using Pearson's correlation coefficient (r), yielding a value of 0.97, as shown in Table 3 , indicating a strong correlation between the two properties analyzed. Table 3 Pearson's correlation coefficient (r) between the mean residual stress and spectral entropy as a function of the mean cutting speed. Analysis r Correlation Cutting Speed 0.97 Strong Figure 4 illustrates the variation in the residual stress and spectral entropy intensity with the cutting speed in each test; the residual stress is found to be compressive in all cases. Under the analyzed conditions, even with the same cutting parameters, the values of residual stress and spectral entropy fluctuate. Generally, spectral entropy increases as the residual stress becomes less compressive. Pearson's correlation coefficient between residual stress and spectral entropy as a function of the cutting speed is 0.69, as shown in Table 4 , indicating a strong correlation between the analyzed properties. This suggests sensitivity between residual stress and AE signals, consistent with the findings of Chai et al. [ 20 ]. Table 4 – Pearson's correlation coefficient (r) between residual stress and spectral entropy as a function of cutting speed. Analysis r Correlation Cutting Speed 0.69 Strong Figure 5 shows the mean residual stress and spectral entropy as functions of the cutting depth. Only compressive residual stress is observed under these cutting conditions. Pearson's correlation coefficient between the mean residual stresses and spectral entropy as a function of the cutting depth is − 0.97, as presented in Table 5 . Table 5 Pearson's correlation coefficient (r) between mean residual stress and spectral entropy as a function of cutting depth. Analysis r Correlation Cutting depth −0.97 Strong Figure 6 depicts the residual stress and spectral entropy values obtained in each test; compressive residual stress is observed in all cases. Pearson's correlation coefficient between the residual stress and spectral entropy as a function of the cutting depth is presented in Table 6 . Table 6 – Pearson's correlation coefficient (r) between residual stress and spectral entropy as a function of cutting depth. Analysis r Correlation Cutting depth −0.60 Strong Pearson's correlation coefficient is positive for the cutting speed and negative for the cutting depth. The negative value indicates an inverse correlation: as the residual stress increases (i.e., becomes less compressive), spectral entropy decreases. Nevertheless, the correlation remains strong, reaching − 0.97 for the mean and − 0.6 for individual tests. Figure 7 shows the residual stress and spectral entropy values as functions of the feed rate. Pearson's correlation coefficient between the mean residual stresses and spectral entropy as a function of the feed rate reaches − 0.95, as shown in Table 7 , signifying a strong but inverse relationship. Table 7 Pearson's correlation coefficient (r) between mean residual stress and spectral entropy as a function of feed rate. Analysis r Correlation Feed rate −0.95 Strong Figure 8 presents the residual stress and spectral entropy intensity in each test as functions of the feed rate. Increasing the feed rate transforms tensile residual stress into compressive stress. Shaw [ 34 ] explained that increased hardness in AISI 4340 steel tends to promote the development of compressive residual stress. Therefore, in this study, the heat treatment, combined with the machining parameters, likely contributes to the generation of compressive residual stress in most of the tests. The feed rate exhibits an inverse correlation with spectral entropy. The maximum compressive residual stress corresponds with the highest spectral entropy intensity, and the maximum tensile residual stress corresponds with the lowest spectral entropy intensity. Pearson's correlation coefficient of − 0.72 confirms this inverse relationship, as shown in Table 8 , thereby aligning with the correlations found for the mean values across tests. This suggests a strong correlation between the spectral entropy and residual stress under the analyzed conditions. The negative correlation coefficient indicates that as one variable increases, the other decreases. Table 8 – Pearson's correlation coefficient (r) between residual stress and spectral entropy as a function of feed rate. Analysis r Correlation Feed rate −0.72 Strong The condition with a feed rate of 0.05 mm/rev was the only scenario in which tensile residual stress is observed. Figure 8 reveals that spectral entropy is sensitive to the variations in residual stress. Additionally, residual stress values of the same magnitude but applied in opposite directions result in different spectral entropy values. This suggests that spectral entropy can be correlated with both the magnitude and direction of residual stress; this can help distinguish between compressive and tensile residual stresses. 4. Conclusion Residual stress is sensitive to variations in cutting parameters. The stress was found to be predominantly compressive under the conditions analyzed; the only exception was the machining condition with the lowest feed rate exhibiting tensile residual stress. Increasing the feed rate shifted the residual stress from tensile to compressive, whereas increasing the cutting depth suppressed the compressive nature of the residual stress. The lowest and highest cutting speeds (50 and 200 m/min, respectively) produced the maximum compressive residual stress. In contrast, the cutting speeds of 100 and 150 m/min yielded reduced compressive residual stress. Spectral entropy exhibited sensitivity to residual stress signals, indicating that a correlation can be established between them. Identifying the exact frequency at which AE signals are most sensitive to residual stress values and appropriately applying filters are essential for this. The analysis conducted by using Pearson's correlation coefficient revealed a strong correlation between residual stress and spectral entropy in response to the cutting speed, cutting depth, and feed rate. Positive correlation values were observed for the cutting speed, whereas negative values were noted for the cutting depth and feed rate. Furthermore, spectral entropy was sensitive to variations in both the magnitude and direction of residual stress, thereby indicating a correlation between its intensity and the corresponding tensile and compressive residual stresses. Declarations Funding This work was supported by the Coordination for the Improvement of Higher Education Personnel – Brazil (CAPES) – under Financing Code 001. Competing Interests The authors declare that they have no relevant financial or non-financial interests to disclose. Author Contributions All authors contributed to the conception and design of the study. Material preparation, data collection, and analysis were performed by Anderson Edson da Silva, André Leon Ferreira Pottie, Mariana de Paula Souza, and Luís Henrique Andrade Maia. The first draft of the manuscript was written by Anderson Edson da Silva, and all authors provided feedback on previous versions of the manuscript. All authors have read and approved the final manuscript. References S. Y. Luo, Y. S. Liao, and Y. Y. 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Cite Share Download PDF Status: Published Journal Publication published 04 Mar, 2025 Read the published version in The International Journal of Advanced Manufacturing Technology → Version 1 posted Editorial decision: Major Revisions Needed 09 Jan, 2025 Reviewers agreed at journal 08 Nov, 2024 Reviewers invited by journal 25 Oct, 2024 Editor assigned by journal 25 Oct, 2024 First submitted to journal 24 Oct, 2024 You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. 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Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-5323003","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":370455507,"identity":"b4a5b473-f648-4b15-b4d2-45c5ea24db0f","order_by":0,"name":"Anderson Edson da Silva","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAABD0lEQVRIiWNgGAWjYHACAwjFzNzAwFDBwMDeAOYeIEYLI1DtGQYGngPMxGphAGphbCNCC//s5o2PK/7Y5Mm3M7ZJ/JxnJ8fD3n904xeGO/m4tEjcOVZseLYtrdjgMGObZO+2ZGMensNst2UYnlk24NJzI8dMsrHhcOIGZsZmA95tBxL3SySz3ZZgOGyAS4f8jRzznw1/DifOb2ZsNvw750B9j/xj/FoMgLYwNrAdTmw4zNj4mLfhQAKPBDPbzQ94tBjeSCuWbGxLS9wA0iJzLNmwhyfZ7DaDwTOcWuRuJG/82PDHJnF+/+EDB9/U2MnzsB98dvNHxR2cWrADZh4SNQBj9QepOkbBKBgFo2A4AwCsqF46OVChPQAAAABJRU5ErkJggg==","orcid":"https://orcid.org/0000-0001-9982-0110","institution":"CEFET-MG: Centro Federal de Educacao Tecnologica de Minas Gerais","correspondingAuthor":true,"prefix":"","firstName":"Anderson","middleName":"Edson da","lastName":"Silva","suffix":""},{"id":370455508,"identity":"7a9bde41-90d3-4455-841b-4745aad35498","order_by":1,"name":"Jorge Wanderson Barbosa","email":"","orcid":"","institution":"","correspondingAuthor":false,"prefix":"","firstName":"Jorge","middleName":"Wanderson","lastName":"Barbosa","suffix":""},{"id":370455509,"identity":"80252d91-b750-4cdf-a723-2a75813172af","order_by":2,"name":"Ismael Nogueira Rabelo de Melo","email":"","orcid":"","institution":"","correspondingAuthor":false,"prefix":"","firstName":"Ismael","middleName":"Nogueira Rabelo","lastName":"de Melo","suffix":""},{"id":370455510,"identity":"fb74a360-3df7-4740-8f7f-ab3d37780633","order_by":3,"name":"André Leon Ferreira Pottie","email":"","orcid":"","institution":"","correspondingAuthor":false,"prefix":"","firstName":"André","middleName":"Leon Ferreira","lastName":"Pottie","suffix":""},{"id":370455511,"identity":"8bc3c743-3af0-4992-8ea1-5d752c35739a","order_by":4,"name":"Mariana de Paula Souza","email":"","orcid":"","institution":"","correspondingAuthor":false,"prefix":"","firstName":"Mariana","middleName":"de Paula","lastName":"Souza","suffix":""},{"id":370455512,"identity":"103d2f7b-1124-4215-8bb5-e1f6a1217058","order_by":5,"name":"Luís Henrique Andrade Maia","email":"","orcid":"","institution":"","correspondingAuthor":false,"prefix":"","firstName":"Luís","middleName":"Henrique Andrade","lastName":"Maia","suffix":""}],"badges":[],"createdAt":"2024-10-24 06:07:48","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-5323003/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-5323003/v1","draftVersion":[],"editorialEvents":[{"content":"https://doi.org/10.1007/s00170-025-15315-2","type":"published","date":"2025-03-04T15:58:43+00:00"}],"editorialNote":"","failedWorkflow":false,"files":[{"id":67776242,"identity":"a03648a5-b5e2-4833-b8c5-7c0bbd753f72","added_by":"auto","created_at":"2024-10-29 15:01:50","extension":"png","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":793216,"visible":true,"origin":"","legend":"\u003cp\u003eSchematic flowchart of the experimental procedure\u003c/p\u003e","description":"","filename":"1.png","url":"https://assets-eu.researchsquare.com/files/rs-5323003/v1/61f52580f7ae04c22bf3811e.png"},{"id":67776237,"identity":"7a6e1ce7-b06e-43da-9a43-44733e0190c3","added_by":"auto","created_at":"2024-10-29 15:01:49","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":31226,"visible":true,"origin":"","legend":"\u003cp\u003eSpecimen\u003c/p\u003e","description":"","filename":"2.png","url":"https://assets-eu.researchsquare.com/files/rs-5323003/v1/a7fc2f1d64c3abd422418cfa.png"},{"id":67776244,"identity":"ba977bc0-3775-4902-b436-b76cdf5e2c21","added_by":"auto","created_at":"2024-10-29 15:01:50","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":123701,"visible":true,"origin":"","legend":"\u003cp\u003eMean residual stress and spectral entropy as functions of cutting speed.\u003c/p\u003e","description":"","filename":"3.png","url":"https://assets-eu.researchsquare.com/files/rs-5323003/v1/cb84f7f00b6add4b243816cb.png"},{"id":67776238,"identity":"450ae964-ba0b-43dc-bbae-c8ac094a3d06","added_by":"auto","created_at":"2024-10-29 15:01:49","extension":"png","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":145857,"visible":true,"origin":"","legend":"\u003cp\u003eResidual stress and spectral entropy as functions of cutting speed.\u003c/p\u003e","description":"","filename":"4.png","url":"https://assets-eu.researchsquare.com/files/rs-5323003/v1/cb87bb423a62dab1c4d4e98e.png"},{"id":67777215,"identity":"88e2ed03-29d2-4f65-8431-54be82b6543a","added_by":"auto","created_at":"2024-10-29 15:09:50","extension":"png","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":126212,"visible":true,"origin":"","legend":"\u003cp\u003eMean residual stress and spectral entropy as functions of cutting depth.\u003c/p\u003e","description":"","filename":"5.png","url":"https://assets-eu.researchsquare.com/files/rs-5323003/v1/165d3ac0ca1d867a71ff4f3c.png"},{"id":67777216,"identity":"d92d633b-e319-493f-bd59-16e07727d465","added_by":"auto","created_at":"2024-10-29 15:09:50","extension":"png","order_by":6,"title":"Figure 6","display":"","copyAsset":false,"role":"figure","size":151844,"visible":true,"origin":"","legend":"\u003cp\u003eResidual stress and spectral entropy as functions of cutting depth.\u003c/p\u003e","description":"","filename":"6.png","url":"https://assets-eu.researchsquare.com/files/rs-5323003/v1/e447db73d2abd4b3f40a0244.png"},{"id":67776240,"identity":"8e8c1f86-b2b4-41ee-9ab8-69d1864c6815","added_by":"auto","created_at":"2024-10-29 15:01:49","extension":"png","order_by":7,"title":"Figure 7","display":"","copyAsset":false,"role":"figure","size":113665,"visible":true,"origin":"","legend":"\u003cp\u003eMean residual stress and spectral entropy as functions of feed rate.\u003c/p\u003e","description":"","filename":"7.png","url":"https://assets-eu.researchsquare.com/files/rs-5323003/v1/8812e9429d80c35ec9b7b3f5.png"},{"id":67777214,"identity":"bfa04d26-7d3f-4b28-a447-4dca8eb233ef","added_by":"auto","created_at":"2024-10-29 15:09:49","extension":"png","order_by":8,"title":"Figure 8","display":"","copyAsset":false,"role":"figure","size":125516,"visible":true,"origin":"","legend":"\u003cp\u003eResidual stresses and spectral entropy as a function of feed rate.\u003c/p\u003e","description":"","filename":"8.png","url":"https://assets-eu.researchsquare.com/files/rs-5323003/v1/138152df306c52286c2b4694.png"},{"id":78190836,"identity":"992deadc-7b13-42de-93bb-2b3dddbd9692","added_by":"auto","created_at":"2025-03-10 19:51:11","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":2650872,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-5323003/v1/3bce3951-62ab-401b-a3a2-e7fc520d23ee.pdf"}],"financialInterests":"","formattedTitle":"\u003cp\u003eCorrelation Between Residual Stress and Acoustic Emission Signals in the Turning Operation of Hardened Aisi 4340 Steel\u003c/p\u003e","fulltext":[{"header":"1. Introduction","content":"\u003cp\u003eMachining hardened steels has become a routine industrial process, and ceramic tools are commonly used for this [\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e]. Turning operations performed by using ceramic tools not only reduce costs but also improve product quality; thus, these are a viable alternative to grinding in finishing processes [\u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e], [\u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e3\u003c/span\u003e]. Studying surface integrity can help in understanding the changes occurring on the surface and subsurface of a part during manufacturing, as the performance and final quality of a product are directly linked to its surface integrity [\u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e4\u003c/span\u003e]. The key characteristics of surface integrity in machined parts include residual stress, hardening, microstructural changes, and surface roughness, all of which result from plastic deformation [\u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e5\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eResidual stress has a significant impact on the lifespan of mechanical components used in engineering applications [\u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e]. Tensile stress can promote crack propagation, whereas compressive stress can inhibit it. This relationship is crucial to the fatigue life of components subjected to cyclic loads that require high fatigue strength. The risk to the component\u0026rsquo;s lifespan increases when tensile residual stress combine with operational stress [\u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e7\u003c/span\u003e], [\u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e8\u003c/span\u003e], [\u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e9\u003c/span\u003e]. In machining processes, cutting parameters such as the speed, feed rate, and depth of cut influence the residual stress induced in the components [\u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e10\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eThe most common methods for measuring residual stress are X-ray diffraction (XRD) and the blind-hole technique. XRD enables the measurement of both micro and macro stresses but can be limited by the sample size; it is ideal for small samples. By contrast, the blind-hole technique is quick, easy to perform, and applicable to a wide range of materials; however, it has higher measurement uncertainty, is semi-destructive, and is restricted to simple geometries. For most materials, XRD remains the most accurate method [\u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e11\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eAcoustic emission (AE) signals are defined as transient elastic energy released in the form of mechanical stress waves within materials. The detection and analysis of these stress waves can be monitored through AE signals [\u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e12\u003c/span\u003e]. AE signal analysis is a non-destructive testing technique with numerous industrial applications, such as in structural analysis [\u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e13\u003c/span\u003e], corrosion detection [\u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e14\u003c/span\u003e], pressure vessel testing [\u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e15\u003c/span\u003e], and machining [\u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e16\u003c/span\u003e]. Several methods are available for analyzing and processing captured AE signals [\u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e17\u003c/span\u003e]; however, regardless of the approach, detection systems must exhibit sensitivity that is appropriate for the phenomena being monitored. In machining, AE sensors are well-suited for monitoring cutting parameters, even at low material removal rates, and are sensitive to subsurface damage [\u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e18\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eThe use of AE monitoring in machining processes has been widely studied in recent years; the primary focus has been cutting parameters and tool life analysis. However, studies in which the correlation between AE signals and the surface integrity of machined parts\u0026mdash;such as surface finish and residual stress\u0026mdash;is investigated are still scarce.\u003c/p\u003e \u003cp\u003eTraditional techniques for signal processing, such as hit counting and fast Fourier transform, are prone to errors during machining because AE signals often change over very short periods of time [\u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e19\u003c/span\u003e]. The study of AE signals by utilizing spectral entropy is particularly promising because spectral entropy, which originates from the uncertainty in amplitude distribution, is independent of thresholds and other time-based parameters; thus, spectral entropy is a useful tool for characterizing microstructural deformations [\u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e20\u003c/span\u003e]. Spectral entropy, also known as Shannon entropy, can be mathematically expressed in Eq.\u0026nbsp;\u003cspan refid=\"Equ1\" class=\"InternalRef\"\u003e1\u003c/span\u003e [\u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e21\u003c/span\u003e].\u003cdiv id=\"Equ1\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ1\" name=\"EquationSource\"\u003e\n$$\\:SE=\\:-\\sum\\:_{i=1}^{N}{p}_{i}{\\text{log}}_{2}\\left({p}_{i}\\right),$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e1\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003ewhere \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{p}_{i}\\)\u003c/span\u003e\u003c/span\u003e is determined by applying Equations \u003cspan refid=\"Equ2\" class=\"InternalRef\"\u003e2\u003c/span\u003e and \u003cspan refid=\"Equ3\" class=\"InternalRef\"\u003e3\u003c/span\u003e:\u003cdiv id=\"Equ2\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ2\" name=\"EquationSource\"\u003e\n$$\\:{p}_{i}=\\:\\frac{X\\left(i\\right)}{\\sum\\:_{j=1}^{N}X\\left(j\\right)};$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e2\u003c/div\u003e\u003c/div\u003e\u003cdiv id=\"Equ3\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ3\" name=\"EquationSource\"\u003e\n$$\\:\\sum\\:_{i=1}^{N}{p}_{i}=1.$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e3\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eThe events during an experiment determine the number of frequency components, and as the signal is analyzed, the probabilities are updated; \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{p}_{i}\\)\u003c/span\u003e\u003c/span\u003e represents the percentage of each frequency \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:i\\)\u003c/span\u003e\u003c/span\u003e in the spectrum and denoted as\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\:{p}_{i}=\\:\\left\\{p1,p2,p3,\\dots\\:,pN\\right\\},\\:\\)\u003c/span\u003e\u003c/span\u003ewhere these probabilities depend solely on the frequency distribution, X. Once the frequency distribution is obtained, spectral entropy is calculated by using Eq.\u0026nbsp;\u003cspan refid=\"Equ1\" class=\"InternalRef\"\u003e1\u003c/span\u003e at each moment in time corresponding to the performed test [\u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e17\u003c/span\u003e], [\u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e22\u003c/span\u003e]. Spectral entropy values range between 0 and 1, with higher values indicating greater randomness. The closer the value is to 0, the less random the condition is [\u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e23\u003c/span\u003e]. Therefore, entropy is maximized for equiprobable events, whereas entropy equals zero for single events and is entirely dependent on the probability distribution of the event.\u003c/p\u003e \u003cp\u003eChai et al. [\u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e20\u003c/span\u003e] captured AE signals during a fatigue-crack-growth test in CrMoV steel and found that spectral entropy was more sensitive to small differences in AE signals than to signal amplitude. They observed that sudden changes in spectral entropy usually indicate critical damage, such as the initiation and growth of cracks. Thus, spectral entropy is valuable for monitoring mechanical systems. Karimian et al. [\u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e24\u003c/span\u003e] used spectral entropy to identify the nucleation and coalescence of microcracks in aeronautical structures. They found that minimal spectral entropy can be combined with increasing cumulative spectral entropy to reliably identify fatigue cracks.\u003c/p\u003e \u003cp\u003eDifferent frequency ranges in AE signals correspond to specific phenomena, and the use of filters improves the understanding on these phenomena. Maia et al. [\u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e19\u003c/span\u003e] noted that the frequency range sensitive to the machining process is 90\u0026ndash;110 kHz, whereas Marinescu and Axinte [\u003cspan citationid=\"CR26\" class=\"CitationRef\"\u003e26\u003c/span\u003e] suggested that this range could be extended slightly to 70\u0026ndash;115 kHz. However, the frequency range displaying the strongest correlation between spectral entropy and residual stress is not necessarily restricted to the typical machining phenomena, and the signal may show greater sensitivity in bands outside these common frequencies. The aim of this study is to explore the correlation between AE signals and residual stress by identifying the frequency region in the spectrum that is most sensitive and correlates with residual stress values.\u003c/p\u003e \u003cp\u003eThe correlation between two conditions can be analyzed by using Pearson's correlation coefficient (r), a statistical metric that measures the strength of the linear relationship between two variables. This coefficient is widely applied in various fields [\u003cspan citationid=\"CR27\" class=\"CitationRef\"\u003e27\u003c/span\u003e], such as data analysis [\u003cspan citationid=\"CR28\" class=\"CitationRef\"\u003e28\u003c/span\u003e], financial analysis [\u003cspan citationid=\"CR29\" class=\"CitationRef\"\u003e29\u003c/span\u003e], and biological research [\u003cspan citationid=\"CR30\" class=\"CitationRef\"\u003e30\u003c/span\u003e]. Pearson\u0026rsquo;s correlation coefficient is dimensionless, indicating that it does not have units or a reference proportion. The coefficient ranges from \u0026minus;\u0026thinsp;1 to 1, with values closer to 1 or \u0026minus;\u0026thinsp;1 indicating a stronger correlation. Values near 0 suggest no correlation, positive values indicate a direct relationship, and negative values imply an inverse relationship [\u003cspan citationid=\"CR31\" class=\"CitationRef\"\u003e31\u003c/span\u003e]. \"r\" values between 0.1 and 0.3 represent a weak correlation, between 0.4 and 0.6 are considered moderate, and above 0.6 indicate a strong correlation [\u003cspan citationid=\"CR32\" class=\"CitationRef\"\u003e32\u003c/span\u003e], [\u003cspan citationid=\"CR33\" class=\"CitationRef\"\u003e33\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eThe aim of this study is to deepen the understanding on surface integrity control in the machining of AISI 4340 steel by analyzing AE signals emitted during the process. AE signals were captured when turning AISI 4340 steel with ceramic tools. An artificial intelligence (AI) tool was employed to identify the spectral region most sensitive to residual stress, and the signals were filtered in the frequency band having the highest correlation, as determined by the AI tool. The filtered signals were analyzed by using the spectral entropy technique, which revealed a strong correlation between residual stress and AE signals across varied cutting speeds, feed rates, and cutting depths. This correlation highlights the potential for improving machining process control, optimizing cutting techniques, and refining machining parameters.\u003c/p\u003e"},{"header":"2. Experimental procedure","content":"\u003cp\u003eFigure \u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e presents the schematic flowchart of the experimental procedure implemented in this study.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eThe specimens were fabricated from AISI 4340 steel; the chemical composition is presented in Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab1\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 1\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eChemical composition (%) of AISI 4340 steel used in the tests.\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"8\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c7\" colnum=\"7\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c8\" colnum=\"8\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eC\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eMn\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eP\u003csub\u003emax\u003c/sub\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eSi\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003eS\u003csub\u003emax\u003c/sub\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c6\"\u003e \u003cp\u003eCr\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c7\"\u003e \u003cp\u003eNi\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c8\"\u003e \u003cp\u003eMo\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e0.40\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.70\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.007\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.35\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.001\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0.78\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e1.74\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e0.24\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003eThe samples were heat-treated (quenched and tempered) to achieve a hardness of 52\u0026thinsp;\u0026plusmn;\u0026thinsp;2 HRC. The specimens had a useful area of \u0026Oslash;32 \u0026times; 42 mm, with a \u0026Oslash;24 mm section used for fixtures. Figure\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e shows a schematic of specimens used in the study.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eThe samples were machined on a Romi computerized numerical control lathe (model Centur 30D) having a power output of 10 kW and equipped with a Spartan 2000 AE-signal-collection system (Physical Acoustics). The AE signals were acquired by using a National Instruments PCI-6251 data acquisition board at a sampling rate of 1.2 MHz. The AE sensor was positioned 150 mm from the tool tip, and the captured signals were processed by using the MATLAB software with the spectral entropy signal-processing technique.\u003c/p\u003e \u003cp\u003eRaw AE signals were recorded during the tests and analyzed by using Python, an AI tool, to identify the frequency range most sensitive to residual stress. Python was used to scan the entire spectrum, and the frequency range having the highest correlation was found to be 400\u0026ndash;403 kHz. Based on these results, a low-pass filter at 403 kHz and a high-pass filter at 400 kHz were applied to isolate this frequency range for further analysis. The cutting tool used in this study was a Sandvik mixed ceramic insert with SNGA 120408 T01020 geometry of the CC650 H05 class without any coating. The tool holder was a DSBNL 2525M12 system, which resulted in a cutting edge angle of 75\u0026deg; relative to the workpiece, with rake and inclination angles of \u0026minus;\u0026thinsp;6\u0026deg;. The tests were conducted under dry conditions, and a new cutting edge was used for each test. Each cutting condition was replicated twice. To analyze the influence of the cutting speed, tests were performed at 50, 100, 150, and 200 m/min with a constant feed rate of 0.1 mm/rev and cutting depth of 0.5 mm. To analyze the effects of the feed rate and cutting depth, the cutting speed was set at 150 m/min and the feed rates were 0.05, 0.1, and 0.15 mm/rev and the cutting depths were 0.25, 0.5, and 1 mm, respectively. The cutting conditions are summarized in Table\u0026nbsp;\u003cspan refid=\"Tab2\" class=\"InternalRef\"\u003e2\u003c/span\u003e.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab2\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 2\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eCutting parameters\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"5\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eParameter analyzed\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eCondition\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eCutting speed Vc (m/min)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eFeed rate f (mm/rev)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003eCutting depth Ap (mm)\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\" morerows=\"3\" rowspan=\"4\"\u003e \u003cp\u003eCutting speed\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e50\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.5\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e100\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.5\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e150\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.5\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e4\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e200\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.5\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\" morerows=\"2\" rowspan=\"3\"\u003e \u003cp\u003eFeed rate\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e5\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e150\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.05\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.5\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e6\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e150\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.5\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e7\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e150\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.15\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.5\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\" morerows=\"2\" rowspan=\"3\"\u003e \u003cp\u003eCutting depth\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e8\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e150\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.25\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e9\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e150\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.5\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e10\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e150\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003eThe residual stress measurements were performed using a SHIMADZU RDX-7000 X-ray diffractometer. For the measurements, Crκα radiation (λ\u0026thinsp;=\u0026thinsp;2.289\u0026Aring;) was used, targeting the (211) crystallographic plane of the ferrite-martensite phase, which exhibits its peak at a 2θ angle of 156.2\u0026deg;. The 2θ diffraction angles ranged from 150\u0026deg; to 160\u0026deg;, whereas the Ψ angles were set at 7\u0026deg;, 14\u0026deg;, 21\u0026deg;, 28\u0026deg;, 35\u0026deg;, 42\u0026deg;, and 49\u0026deg;, with a pitch of 0.1\u0026deg;. The scanning speed was 2\u0026deg;/min. For the correlation analysis, Pearson's correlation coefficient, with a statistical significance threshold of p\u0026thinsp;\u0026lt;\u0026thinsp;0.05, was used.\u003c/p\u003e"},{"header":"3. Results and discussion","content":"\u003cp\u003eFigure \u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e shows the mean residual stress and spectral entropy as functions of the cutting speed.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eThe data indicate that the cutting speed influences residual stress; however, the relationship exhibits non-linear behavior. The maximum compressive residual stress values are observed at the lowest and highest cutting speeds tested (50 and 200 m/min), whereas the least compressive residual stress is observed at 100 m/min. The correlation between the mean residual stress and spectral entropy as a function of the cutting speed is analyzed by using Pearson's correlation coefficient (r), yielding a value of 0.97, as shown in Table\u0026nbsp;\u003cspan refid=\"Tab3\" class=\"InternalRef\"\u003e3\u003c/span\u003e, indicating a strong correlation between the two properties analyzed.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab3\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 3\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003ePearson's correlation coefficient (r) between the mean residual stress and spectral entropy as a function of the mean cutting speed.\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"3\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eAnalysis\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003er\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eCorrelation\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eCutting Speed\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.97\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eStrong\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003eFigure \u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e illustrates the variation in the residual stress and spectral entropy intensity with the cutting speed in each test; the residual stress is found to be compressive in all cases.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eUnder the analyzed conditions, even with the same cutting parameters, the values of residual stress and spectral entropy fluctuate. Generally, spectral entropy increases as the residual stress becomes less compressive. Pearson's correlation coefficient between residual stress and spectral entropy as a function of the cutting speed is 0.69, as shown in Table\u0026nbsp;\u003cspan refid=\"Tab4\" class=\"InternalRef\"\u003e4\u003c/span\u003e, indicating a strong correlation between the analyzed properties. This suggests sensitivity between residual stress and AE signals, consistent with the findings of Chai et al. [\u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e20\u003c/span\u003e].\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab4\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 4\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003e\u0026ndash; Pearson's correlation coefficient (r) between residual stress and spectral entropy as a function of cutting speed.\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"3\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eAnalysis\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003er\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eCorrelation\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eCutting Speed\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.69\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eStrong\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003eFigure \u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003e shows the mean residual stress and spectral entropy as functions of the cutting depth. Only compressive residual stress is observed under these cutting conditions.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003ePearson's correlation coefficient between the mean residual stresses and spectral entropy as a function of the cutting depth is \u0026minus;\u0026thinsp;0.97, as presented in Table\u0026nbsp;\u003cspan refid=\"Tab5\" class=\"InternalRef\"\u003e5\u003c/span\u003e.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab5\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 5\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003ePearson's correlation coefficient (r) between mean residual stress and spectral entropy as a function of cutting depth.\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"3\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eAnalysis\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003er\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eCorrelation\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eCutting depth\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u0026minus;0.97\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eStrong\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003eFigure \u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003e depicts the residual stress and spectral entropy values obtained in each test; compressive residual stress is observed in all cases.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003ePearson's correlation coefficient between the residual stress and spectral entropy as a function of the cutting depth is presented in Table\u0026nbsp;\u003cspan refid=\"Tab6\" class=\"InternalRef\"\u003e6\u003c/span\u003e.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab6\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 6\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003e\u0026ndash; Pearson's correlation coefficient (r) between residual stress and spectral entropy as a function of cutting depth.\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"3\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eAnalysis\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003er\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eCorrelation\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eCutting depth\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u0026minus;0.60\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eStrong\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003ePearson's correlation coefficient is positive for the cutting speed and negative for the cutting depth. The negative value indicates an inverse correlation: as the residual stress increases (i.e., becomes less compressive), spectral entropy decreases. Nevertheless, the correlation remains strong, reaching \u0026minus;\u0026thinsp;0.97 for the mean and \u0026minus;\u0026thinsp;0.6 for individual tests. Figure\u0026nbsp;\u003cspan refid=\"Fig7\" class=\"InternalRef\"\u003e7\u003c/span\u003e shows the residual stress and spectral entropy values as functions of the feed rate.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003ePearson's correlation coefficient between the mean residual stresses and spectral entropy as a function of the feed rate reaches \u0026minus;\u0026thinsp;0.95, as shown in Table\u0026nbsp;\u003cspan refid=\"Tab7\" class=\"InternalRef\"\u003e7\u003c/span\u003e, signifying a strong but inverse relationship.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab7\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 7\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003ePearson's correlation coefficient (r) between mean residual stress and spectral entropy as a function of feed rate.\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"3\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eAnalysis\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003er\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eCorrelation\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eFeed rate\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u0026minus;0.95\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eStrong\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003eFigure \u003cspan refid=\"Fig8\" class=\"InternalRef\"\u003e8\u003c/span\u003e presents the residual stress and spectral entropy intensity in each test as functions of the feed rate.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eIncreasing the feed rate transforms tensile residual stress into compressive stress. Shaw [\u003cspan citationid=\"CR34\" class=\"CitationRef\"\u003e34\u003c/span\u003e] explained that increased hardness in AISI 4340 steel tends to promote the development of compressive residual stress. Therefore, in this study, the heat treatment, combined with the machining parameters, likely contributes to the generation of compressive residual stress in most of the tests. The feed rate exhibits an inverse correlation with spectral entropy. The maximum compressive residual stress corresponds with the highest spectral entropy intensity, and the maximum tensile residual stress corresponds with the lowest spectral entropy intensity. Pearson's correlation coefficient of \u0026minus;\u0026thinsp;0.72 confirms this inverse relationship, as shown in Table\u0026nbsp;\u003cspan refid=\"Tab8\" class=\"InternalRef\"\u003e8\u003c/span\u003e, thereby aligning with the correlations found for the mean values across tests. This suggests a strong correlation between the spectral entropy and residual stress under the analyzed conditions. The negative correlation coefficient indicates that as one variable increases, the other decreases.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab8\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 8\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003e\u0026ndash; Pearson's correlation coefficient (r) between residual stress and spectral entropy as a function of feed rate.\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"3\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eAnalysis\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003er\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eCorrelation\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eFeed rate\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u0026minus;0.72\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eStrong\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003eThe condition with a feed rate of 0.05 mm/rev was the only scenario in which tensile residual stress is observed. Figure\u0026nbsp;\u003cspan refid=\"Fig8\" class=\"InternalRef\"\u003e8\u003c/span\u003e reveals that spectral entropy is sensitive to the variations in residual stress. Additionally, residual stress values of the same magnitude but applied in opposite directions result in different spectral entropy values. This suggests that spectral entropy can be correlated with both the magnitude and direction of residual stress; this can help distinguish between compressive and tensile residual stresses.\u003c/p\u003e"},{"header":"4. Conclusion","content":"\u003cp\u003eResidual stress is sensitive to variations in cutting parameters. The stress was found to be predominantly compressive under the conditions analyzed; the only exception was the machining condition with the lowest feed rate exhibiting tensile residual stress. Increasing the feed rate shifted the residual stress from tensile to compressive, whereas increasing the cutting depth suppressed the compressive nature of the residual stress. The lowest and highest cutting speeds (50 and 200 m/min, respectively) produced the maximum compressive residual stress. In contrast, the cutting speeds of 100 and 150 m/min yielded reduced compressive residual stress.\u003c/p\u003e \u003cp\u003eSpectral entropy exhibited sensitivity to residual stress signals, indicating that a correlation can be established between them. Identifying the exact frequency at which AE signals are most sensitive to residual stress values and appropriately applying filters are essential for this.\u003c/p\u003e \u003cp\u003eThe analysis conducted by using Pearson's correlation coefficient revealed a strong correlation between residual stress and spectral entropy in response to the cutting speed, cutting depth, and feed rate. Positive correlation values were observed for the cutting speed, whereas negative values were noted for the cutting depth and feed rate.\u003c/p\u003e \u003cp\u003eFurthermore, spectral entropy was sensitive to variations in both the magnitude and direction of residual stress, thereby indicating a correlation between its intensity and the corresponding tensile and compressive residual stresses.\u003c/p\u003e"},{"header":"Declarations","content":"\u003cp\u003e\u003cstrong\u003eFunding\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThis work was supported by the Coordination for the Improvement of Higher Education Personnel \u0026ndash; Brazil (CAPES) \u0026ndash; under Financing Code 001.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eCompeting Interests\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe authors declare that they have no relevant financial or non-financial interests to disclose.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eAuthor Contributions\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eAll authors contributed to the conception and design of the study. Material preparation, data collection, and analysis were performed by Anderson Edson da Silva, Andr\u0026eacute; Leon Ferreira Pottie, Mariana de Paula Souza, and Lu\u0026iacute;s Henrique Andrade Maia. The first draft of the manuscript was written by Anderson Edson da Silva, and all authors provided feedback on previous versions of the manuscript. All authors have read and approved the final manuscript.\u003c/p\u003e\n\u003cp\u003e\u0026nbsp;\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\n\u003cli\u003eS. Y. Luo, Y. S. Liao, and Y. Y. Tsai, \u0026ldquo;Wear characteristics in turning high hardness alloy steel by ceramic and CBN tools\u0026rdquo;, \u003cem\u003eJournal of Materials Processing Technology\u003c/em\u003e, vol. 88, no. 1\u0026ndash;3, p. 114\u0026ndash;121, April 1999, doi: 10.1016/S0924-0136(98)00376-8.\u003c/li\u003e\n\u003cli\u003eA. Kumar and S. K. 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New York: Oxford University Press, 2005.\u003c/li\u003e\n\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":true,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"the-international-journal-of-advanced-manufacturing-technology","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"jamt","sideBox":"Learn more about [The International Journal of Advanced Manufacturing Technology](https://www.springer.com/journal/170)","snPcode":"170","submissionUrl":"https://submission.nature.com/new-submission/170/3","title":"The International Journal of Advanced Manufacturing Technology","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"em","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false},"keywords":"AISI 4340 Steel, Residual Stress, Acoustic Emission, Spectral Entropy, Machining","lastPublishedDoi":"10.21203/rs.3.rs-5323003/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-5323003/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eResidual stress is a critical factor that influences the lifespan of mechanical components subjected to fatigue. Compressive stress tends to extend the life of a component, whereas tensile stress can shorten it. Acoustic emission (AE) signals have been linked to phenomena occurring during manufacturing processes; however, only a few studies have been conduct to correlate AE signals with the surface integrity of machined parts. In this study, an approach for correlating residual stress with AE signals is introduced. AISI 4340 steel specimens are machined by using ceramic tools, with varied cutting speeds, feed rates, and depths of cut, and AE signals are recorded during the process. The signals are processed and analyzed by using the spectral entropy technique, also known as Shannon entropy or information entropy. The results reveal that the appropriate application of frequency filters uncovers regions of strong correlation between the spectral entropy of the AE signals and the residual stress. The observed correlation can contribute to the optimization and control of machining processes and help to achieve the desired residual stress levels.\u003c/p\u003e","manuscriptTitle":"Correlation Between Residual Stress and Acoustic Emission Signals in the Turning Operation of Hardened Aisi 4340 Steel","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2024-10-29 15:01:45","doi":"10.21203/rs.3.rs-5323003/v1","editorialEvents":[{"type":"communityComments","content":0},{"type":"decision","content":"Major Revisions Needed","date":"2025-01-09T11:26:02+00:00","index":"","fulltext":""},{"type":"reviewerAgreed","content":"","date":"2024-11-08T15:17:43+00:00","index":0,"fulltext":""},{"type":"reviewersInvited","content":"","date":"2024-10-25T14:46:51+00:00","index":"","fulltext":""},{"type":"editorAssigned","content":"","date":"2024-10-25T07:39:48+00:00","index":"","fulltext":""},{"type":"submitted","content":"The International Journal of Advanced Manufacturing Technology","date":"2024-10-24T10:45:52+00:00","index":"","fulltext":""}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"the-international-journal-of-advanced-manufacturing-technology","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"jamt","sideBox":"Learn more about [The International Journal of Advanced Manufacturing Technology](https://www.springer.com/journal/170)","snPcode":"170","submissionUrl":"https://submission.nature.com/new-submission/170/3","title":"The International Journal of Advanced Manufacturing Technology","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"em","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false}}],"origin":"","ownerIdentity":"bf815584-f2a4-4bf3-b81f-d5924c3e0a75","owner":[],"postedDate":"October 29th, 2024","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"published-in-journal","subjectAreas":[],"tags":[],"updatedAt":"2025-03-10T19:50:36+00:00","versionOfRecord":{"articleIdentity":"rs-5323003","link":"https://doi.org/10.1007/s00170-025-15315-2","journal":{"identity":"the-international-journal-of-advanced-manufacturing-technology","isVorOnly":false,"title":"The International Journal of Advanced Manufacturing Technology"},"publishedOn":"2025-03-04 15:58:43","publishedOnDateReadable":"March 4th, 2025"},"versionCreatedAt":"2024-10-29 15:01:45","video":"","vorDoi":"10.1007/s00170-025-15315-2","vorDoiUrl":"https://doi.org/10.1007/s00170-025-15315-2","workflowStages":[]},"version":"v1","identity":"rs-5323003","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-5323003","identity":"rs-5323003","version":["v1"]},"buildId":"qtupq5eGEP_6zYnWcrvyt","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}