Investigation on digital twin of the ultraprecision machining system for manufacturing freeform surfaced components

Investigation on digital twin of the ultraprecision machining system for manufacturing freeform surfaced components | 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 Investigation on digital twin of the ultraprecision machining system for manufacturing freeform surfaced components Qiao Xuetao, Wang Yibo, Ning Gou, Kai Cheng, Dehong Huo, Zhao Zengxiao This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-6283975/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract Digital Twin (DT) is widely regarded as the future for advanced engineering manufacture, addresses the critical challenge for continuous improvement and optimization of manufacturing systems through real-time machining process monitoring, in-process diagnosis and dynamic process optimization, and digital and physical data fusion for higher manufacturing precision. Therefore, developing a DT for the ultraprecision manufacturing (UPM) system is inevitably essential for future generation UPM systems and machines. In this paper, an investigation on digital twin of the ultraprecision machining system and its implementation perspectives are presented particularly against the ever-increasing demand for higher precision machining accuracy, e.g. the increasingly more stringent requirement in manufacturing freeform surfaced components and devices. The investigation is focused on the kinematics and dynamics modelling of the machining system (as the foundation of the DT development), the DT implementation, and the application case study, which reflects the innovative attempt on seamless integration of ultraprecision machining fundamentals, innovative development of applied DT technology, and high value ultraprecision applications. Design, manufacturing and control, combined with computationally efficient DT design and optimization algorithms will lead to the higher form/dimensional accuracy and finer surface roughness of the ultraprecision components/parts, in a competitive and promising industrial manner. Ultraprecision machining system Ultraprecision diamond turning Digital twin Modelling of machining system dynamics Freeform surface machining Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 1. Introduction Ultraprecision Manufacturing (UMP) is an important indicator in precision engineering capability and applications, and the associated research and development for a nation and/or region[ 1 , 2 ]. To date, UPM technology has evolved as a high precision machining related technology developed to meet the manufacturing requirements of high-end cutting-edge and/or high throughput products including nuclear energy producers, ultra-large-scale integrated circuits, freeform optics[ 3 ], etc. With the latest development in power electronics, direct drives, sensors, and control technologies, the UPM machines and machining systems aim to continually achieve the higher machining accuracy in an industrial competitive manner[ 4 , 5 ]. However, the constraints and bottlenecks for the further development of the UPM machines and systems are also becoming obvious: Integration of multi-axis motion system, real-time machining quality monitoring and control, and time consuming for processing[ 6 ]. It is thus essential and much needed to develop an innovative approach to overcoming the nanometric level hurdle in the context of industrial scale ultraprecision manufacturing. The approach has to address the multiple factors in multiscale and multiphysics[ 7 ], at the same time, real-time data monitoring and processing has always been challenging while addressing the need for nanometric-level motion accuracy and higher control resolution at the ultra-precision machining system[ 8 ]. Currently, the next paradigm shift in UPM is upon, i.e., continuously improving product quality and precision through Digital Twin (DT) technology, with the capability of real-time sensing, stable processing control and improvement of dynamic performance[ 9 ]. DT as an industrial solution, can observe and reflect the physical behaviour of UPM equipment and utilize it to guide optimization decisions during the design and analysis phase[ 10 ]. The studies on DT approach in UPM field is limited but many researchers are keep exploring active exploratory studies, for instance, Guerra et.al. proposed a optimization method for ultraprecision motion system based on DT from the backlash and friction perspective in year 2019[ 11 ], later in 2021, Wu, et al [ 12 ] provided a comprehensive review of the application of digital twins in UPM from the perspectives of voxel modelling, process planning, process monitoring, vibration control, and quality control. Gou et al.[ 13 ] in their article proposed the application of COMSOL Multiphysics based DT in aerostatic bearing slideway design and analysis, which is the key component for UPM motion system. In terms of spindle system design, Liu et al. [ 14 ]presented a semi-physical simulation-based digital twin model of the spindle drive system, which aims to calculate cost/scrap in digital world, instead of destructive testing. This paper presents the feasibility and innovative application of using a DT for an ultra-precision single point diamond turning (SPDT) machine system. The study and application described in the paper will demonstrate the significance of developing and applying DT technology to UPM of optical components, and in particular those with freeform surfaces. The effect of how contact forces affecting the toolpath will be investigated as well, whilst it also showing the limitation of using automated dynamic analysis of mechanical systems (ADAMS) only for this application. This paper will also be concluded with a further discussion on the potential and application of a DT-integrated UPM machine system, and how in-process data and information being acquired in real time both virtually and physically, and used to continuously optimise the machine system against the stringent ultraprecision machining requirements. 2. Ultraprecision diamond turning system and its digital twin Diamond turning is defined as a process of ultraprecision mechanical turning of precision elements using natural or synthetic diamond-tipped tools. When turning, the workpiece is rotated and diamond tool is traversed along X, Z, and/or C axes of motion to produce precise diameters and depths, as shown in Fig. 1 . It is widely used for machining high-quality aspheric optical components. With the assistance of computer numerical control (CNC) technology, workpieces can be turned directly with complicated structure and surface quality. In order to achieve ultraprecision patterns (2D) and shapes (3D), it is essential that the causes of apparent random errors in processing machines be analysed, upgraded, refined or replaced, i.e., virtually eliminated and that the systematic errors be minimized. It is thus inevitably needing DT technology, very relevant and meaningful, which enables real-time monitoring and in-process processing and optimizing the complex data from multiple sources and aspects. Therefore, the objective of developing DT for ultraprecision diamond turning system can be summarized as follows: Real-time monitoring of the machining process, and in-process data transfer and the process optimization; Prevention for possible failures and machining errors; Prediction of the machined freeform surface and the in-process decision makings. 3. Kinematics and dynamics modelling and analysis of the ultraprecision turning system The modelling of ultraprecision diamond turning system is carried out by using multi-body dynamics analysis method and tool (ADAMS), while considering the mechanical structure of the system as multibody mass-spring-damping. Newton’s second law is thus considered on the system, the modelling process for the ultraprecision diamond turning system is illustrated in Fig. 2 . Due to the system being multibody whilst also having multi-degrees of freedom, the matrix Eq. ( 1 ) is proposed below to represent the system, with [M] mass, [K] stiffness & [C] damping being matrices of the system representing multi-bodies of multi-axis at the system[ 15 ]. $$\:\left[\text{M}\right]\ddot{\text{u}}\left(\text{t}\right)+\left[\text{C}\right]\stackrel{.}{\text{u}}\left(\text{t}\right)+\left[\text{K}\right]\text{u}\left(\text{t}\right)=\text{F}\left(\text{t}\right)$$ 1 Where: u(t), \(\:\stackrel{.}{\text{u}}\) (t), ü (t) represent the vector for displacement, velocity, and acceleration at (t) time respectively. In the realms of multibody dynamic systems, the bodies’ orientation and positions can be found by the absolute coordinates. Within the context of ADAMS solver, it uses the three Cartesian coordinates X, Y and Z for the position, and α, β, and γ for three Euler angles of rigid bodies. As seen below: $$\:\text{p}=\left[\begin{array}{c}x\\\:y\\\:z\end{array}\right],\:\epsilon\:=\left[\begin{array}{c}\alpha\:\\\:\beta\:\\\:\gamma\:\end{array}\right]$$ 2 Then, in turn, the generalised coordinate which is associated to the rigid body i within ADAMS is denoted: $$\:{q}_{i}=\left[\begin{array}{c}{p}_{i}\\\:{\epsilon\:}_{i}\end{array}\right]$$ Then the multibody’ s motion can be demonstrated as: $$\:{q}_{n}\times\:1={\left[{q}_{1}{q}_{2}\dots\:{q}_{n}\right]}^{T}={\left[{q}_{1}^{T}{q}_{2}^{T}t\dots\:{q}_{N}^{T}\right]}^{T}$$ Which contains the following: $$\:{q}_{i}={\left[{\text{x}}_{i}{\text{y}}_{i}{\text{z}}_{i}{\alpha\:}_{i},{\beta\:}_{i},{\gamma\:}_{i}\right]}^{T}$$ 3 n: at any point in time the orientation and position of the given body in the system. N: the number of bodies in the system Then the motion equation for Jacobian matrix can be written as: $$\:\begin{array}{c}{{\Phi\:}}_{q\left(m\times\:n\right)}=\\\:\end{array}{\left[\begin{array}{c}\frac{\partial\:{{\Phi\:}}_{1}}{\partial\:{q}_{1}}\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}\frac{\partial\:{{\Phi\:}}_{1}}{\partial\:{q}_{2}}\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}\cdots\:\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}\frac{\partial\:{{\Phi\:}}_{1}}{\partial\:{q}_{n}}\\\:\frac{\partial\:{\varphi\:}_{2}}{\partial\:{q}_{1}}\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}\frac{\partial\:{{\Phi\:}}_{2}}{\partial\:{q}_{2}}\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}\cdots\:\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}\frac{\partial\:{{\Phi\:}}_{2}}{\partial\:{q}_{n}}\\\:\because\::\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}\\\:\frac{\partial\:{{\Phi\:}}_{m}}{\partial\:{q}_{1}}\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}\frac{\partial\:{{\Phi\:}}_{m}}{\partial\:{q}_{2}}\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}\cdots\:\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}\frac{\partial\:{{\Phi\:}}_{m}}{\partial\:{q}_{n}}\end{array}\right]}_{\text{m}\times\:\text{n}}$$ 4 Where: \(\:{{\Phi\:}}_{q}\): the Jacobian matrix constraint equations The Jacobian matrix can be used for understanding and representing the force, position, acceleration and any reaction forces. The systems nature is of non-linear constraint, and the Newton-Raphson iterative method is used within ADAMS to calculate the q 1 at time t 1 . Therefore, the Taylor-expansion-based linearization with regards to non-linear constraint equation can be achieved by using the following: $$\:{\Phi\:}\left({\text{q}}_{1},{\text{t}}_{1}\right)={\Phi\:}\left({\text{q}}_{0},{\text{t}}_{1}\right)+{\Phi\:}\left({\text{q}}_{0},{\text{t}}_{1}\right)\left({\text{q}}_{1}-{\text{q}}_{0}\right)$$ 5 By utilising this method at any given time, the unknown constraints, acceleration and Lagrange Multiplier can be found at any given step. 4. Digital twin for the ultraprecision machining system and its implementation The degradation of surface quality during UPM processes is often attributed to dynamic instabilities. However, the existing methods for predicting instabilities in UPM processes are still in their infancy. In order to applicate the DT from this aspect, the relationship between different parameters and surface characteristics should be investigated using a combination of analytical modelling and real-time monitoring means. Therefore, by combining suitable virtual models and sensing data, it is possible to help select suitable and "stable" process conditions, observe variations in surface roughness while obtaining it at the nanoscale, and predict machining errors that are barely visible, thus reducing post-processing difficulties. 4.1 Cutting forces modelling and the associated algorithms As demonstrated in Fig. 3 , the multi-body dynamics-based approach and the associated modelling and simulation (implemented with ADAMS) allow simulated data to be taken in real time from the virtual system. Through developing a multibody dynamics-based system (in ADAMS), cutting forces and machining error prediction can be realized by the created virtual digital simulation system, thus to provide measurement and insights during the entirety of the cutting process. The main parameters that have a profound effect on the surface finish, are the cutting forces and tool wear. For cutting forces, this is down to the interfacial actions between the diamond tool and workpiece surface. In this scale, there are numerous influence factors being involved, those being feed rate and depth of cut etc. By understanding the cutting forces in a digital twin manner, it can provide better understanding of its behaviour and the consequent effect on the machining system dynamics and consequently the machining errors of the system. Therefore, it is able to further in process monitor these cutting forces in the physical system and optimize the machining process dynamically and the surface finishing, which is particularly beneficial for ultraprecision diamond turning of freeform surfaces. 4.2 'In-process' Data retrieval from the machining system Data retrieval will be done through the metrology systems which are already in use and have had vast amounts of research undertaken into them. Those being such systems as scanning probing method, optical detection method and microsensors etc. These sensors in real-time feedback the totality of what is happening in the physical system to the digital system as seen above. The feasible methods for data transmission and collecting of DT system can be summarised as: Using the encoder outputs (position, velocity, acceleration) within the machine system: Optical encoders are high-precision positioning sensors based on the interference patterns produced by the relative movement between two gratings, the nanometric resolution and MHz-level data response led it to be an ideal real-time monitor for DT. According to the operating principle, the displacement, velocity and even acceleration for the motion parts of UPM system can be directly obtained during machining in real time based on the approach of encoders. These data provide a very visual representation of the relative movement between cutting tool and workpiece, which directly influences the machining quality. By integrating the collected data into the virtual model of DT, it is possible to observe the state of the motion system in real time throughout the machining process, thus to detect and predict machining defects in advance and to reduce repetitive post-processing works. Using cutting forces data from the machining process: Cutting force calculation, modelling and analysis has been always an important process indicator in UPM, which can collectively reflect the various cutting process phenomena and dynamics such as size effect, chip formation, energy consumption and cutting heat partition, and the machining instability and chatter. It can also be correlated with the tool cutting performance particularly with the tool wear and tool life. Therefore, cutting force is seen as a key factor to optimize the cutting process variables and tool geometries in micro-cutting processes, and thus make it meaningful to use cutting forces data as an in-process monitoring aspect for the DT. The use of cutting forces as a data resource of DT enables in-process detection of the variation such as energy input, environmental disturbances during machining and prediction of tool wear. From another aspect, with the integration of pre-established cutting force models in DT enables the observation of unexpected changes of cutting force and thus the prediction of possible defects before post-processing and surface inspection work. Using the surface ‘signature’ data from the component ultraprecision machined. Direct inspection of the 3D surface texturing and characteristics of the machined workpiece surface during processing is a relatively more intuitive method. The real-time monitoring and control of surface morphology variations in their incipient stages are vital for assuring nanometric range finish in SPDT process. To date, the method for surface monitoring of UPM are various, for instance, by the analytical approach of non-parametric Bayesian to capture the inherently complex, non-Gaussian, and non-stationary sensor signal patterns observed in process[ 16 ] or use acoustic emission (AE) to collect the signals of the transient elastic waves generated from the rapid release of energy from one or more sources within the material[ 17 ], etc. With these data, DT can thus directly intervene the cutting process and compensate surface errors based on the pre-implemented algorithms. 5. Application case studies on ultraprecision machining of freeform surfaces Ultraprecision machining of freeform surfaced component requires more degrees of freedom than conventional methods, which brings in numerous challenges. The experimental setup and partial results are shown in Fig. 4 , based on an ultraprecision diamond turning machine (Moore Nanotech UPL 250), computer aided manufacturing (CAM) + non-uniform rational B-splines (NURBS) generated tool paths, and synchronized multi-axis actuation in a digital twin manner. Although the in-process data collection facility is limited, the cross-validation with the created digital twin is still realizable. The generation of freeform surface and the related calculation are shown in Fig. 4 . With the help of NURBS, freeform surface can be obtained in 3D model, then detailed surface contour is differentiated into finite elements and calculated by the pre-set mathematic models regarding cutting force and tool path in ADAMS. Figure 5 illustrates the Z-axis displacement data and cutting force data calculated based on the pre-established mathematic model in DT, both with a processing time of 60 seconds. As found from Fig. 5 , the cutting force and tool path simulated by DT can be used to predict the machining process in advance, and by comparing with the in-process data fed back from the encoder and the dynamometer, it is possible to realize the prediction and prevention of machining defects during the turning process directly. If the corresponding CAM algorithms is integrated, it is possible to achieve the remote monitoring of the machining process and online defects compensation through the operating of G-Codes. The scientific understanding of the corresponding micro cutting mechanics in freeform surface machining is thus essentially important, while constantly achieving the nanometric level optical surface finishing, multiscale modelling and analysis is likely a useful technique on this combined with advanced algorithms spanned out from NURBS[ 18 , 19 ]. Ultraprecision diamond turning of freeform surfaced components and devices are increasingly demanded in particular in industrial scale ultraprecision manufacturing of head-up display (HUD) and light detection and ranging (LiDAR) devices, ophthalmic lenses, off-axis laser mirrors, and space optics[ 20 , 21 ].The experimental and application case studies above have indicated the potential and applications of the Ultraprecision diamond turning system working with its digital twin. 6. Conclusion This paper presents an innovative approach to developing digital twin for the ultraprecision diamond turning system and its implementation and application perspectives. It will likely provide new insights into the development of next generation ultraprecision machining systems in the era of Industry 4.0. The advanced modelling, design and analysis methods are used in the development, including multi-body dynamics modelling and analysis, machining system dynamics, in-process cutting forces monitoring, and digital twin integration, etc. The ultraprecision machining system digital twin has shown the capability map organically and can coordinate the functional, structural, behavioural, control, intelligence and performance of a machine system represented both virtually and physically. However, there is still the systematic gap in building multi-dimensional and high-fidelity DT in particular effectively integrated with an ultraprecision manufacturing. This should be the future research and development direction for applying DT in ultraprecision diamond turning systems, albeit the work presented here has made the attempt and efforts along the line. Abbreviations ADAMS Automated Dynamic Analysis of Mechanical Systems AE Acoustic Emission CAM Computer Aided Manufacturing CNC Computer Numerical Control DT Digital Twin HUD Head-Up Display LiDAR Light Detection and Ranging NURBS Non-Uniform Rational B-Splines SPDT Single Point Diamond Turning UPM Ultra-Precision Manufacturing Declarations Conflicts of interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. Funding This work was supported by Henan Province science and Technology Research Project [grant numbers 21202210318]; Henan Province Graduate Education Reform and Quality Improvement Project(YJS2023AL041); Zhongyuan University of Technology Advantage Discipline Strength Improvement Plan Funding (GG202407); National Key Laboratory of Intelligent Manufacturing Equipment and Technology Open Project [grant numbers IMETKF2025019]. Authors' contributions Ning Gou contributed to this work by conceiving, conducting experiments, and writing the original draft. Qiao Xuetao and Wang Yibo contributed to this work by providing necessary concepts and comparisons, organizing information, technical writing, and presentation. Cheng Kai and Dehong Huo contributed by formatting, results, and discussion. Zhao Zengxiao contributed by numerical investigation, fabrication. References Yuan J et al (2017) Review on the progress of ultra-precision machining technologies. Front Mech Eng 12:158–180 Li D et al (2019) On-machine surface measurement and applications for ultra-precision machining: a state-of-the-art review. Int J Adv Manuf Technol 104:831–847 Corbett J, McKeown PA, Peggs GN et al (2000) Nanotechnology: international developments and emerging products. CIRP Ann 49(2):523–545 Lucca DA, Matthew J, Klopfstein, Riemer O (2020) Ultra-precision machining: cutting with diamond tools. 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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-6283975","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":436208857,"identity":"85858f97-f0cb-4a6c-b1dc-c826b1bc88c7","order_by":0,"name":"Qiao Xuetao","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAtUlEQVRIiWNgGAWjYJCCAwwMNjz87A3EqmcDa0mTkew5QIIWIDhsY3DDgUgdBvebNx74UXGeh+EGA+OHjzlEaJFsYys42HPmNg/j7AZmyZnbiNDCz8ZjcIC37TYPs8wBNmZeYrSwAbUc/Nt2jodNIoFILSBbDvO2HeDhIVqLZFtawWGZM8k8EjwHm4nzi8Hhw5s/vqmws7c/3nzww0ditIB0QWnGBuLUI2kZBaNgFIyCUYADAAArMDOuI/vYWQAAAABJRU5ErkJggg==","orcid":"","institution":"Zhongyuan University of Technology","correspondingAuthor":true,"prefix":"","firstName":"Qiao","middleName":"","lastName":"Xuetao","suffix":""},{"id":436208858,"identity":"283581bf-84b0-4eda-9aa3-306941920ec9","order_by":1,"name":"Wang Yibo","email":"","orcid":"","institution":"","correspondingAuthor":false,"prefix":"","firstName":"Wang","middleName":"","lastName":"Yibo","suffix":""},{"id":436208859,"identity":"dbceaaf9-f285-46c3-8aa3-1e6edaf89841","order_by":2,"name":"Ning Gou","email":"","orcid":"","institution":"","correspondingAuthor":false,"prefix":"","firstName":"Ning","middleName":"","lastName":"Gou","suffix":""},{"id":436208860,"identity":"7c33238a-dce9-446e-9833-bb100a2e48b7","order_by":3,"name":"Kai Cheng","email":"","orcid":"","institution":"","correspondingAuthor":false,"prefix":"","firstName":"Kai","middleName":"","lastName":"Cheng","suffix":""},{"id":436208861,"identity":"d93c1a51-e9ee-44ce-a270-c0185ad1edc6","order_by":4,"name":"Dehong Huo","email":"","orcid":"","institution":"","correspondingAuthor":false,"prefix":"","firstName":"Dehong","middleName":"","lastName":"Huo","suffix":""},{"id":436208862,"identity":"c44ddcfa-5dbd-450f-b0bc-915742859d76","order_by":5,"name":"Zhao Zengxiao","email":"","orcid":"","institution":"","correspondingAuthor":false,"prefix":"","firstName":"Zhao","middleName":"","lastName":"Zengxiao","suffix":""}],"badges":[],"createdAt":"2025-03-22 13:51:05","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-6283975/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-6283975/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":81693675,"identity":"ea5b2167-94c6-4bb1-a9fa-8ac3e79b0695","added_by":"auto","created_at":"2025-04-30 11:48:45","extension":"png","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":119348,"visible":true,"origin":"","legend":"\u003cp\u003eIllustration of the ultraprecision diamond turning system and its digital twin (DT)\u003c/p\u003e","description":"","filename":"1.png","url":"https://assets-eu.researchsquare.com/files/rs-6283975/v1/c0e5daae31e5467a615c2103.png"},{"id":81695792,"identity":"a8364a79-9e99-4220-88fb-227f2667a4fd","added_by":"auto","created_at":"2025-04-30 12:04:46","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":27711,"visible":true,"origin":"","legend":"\u003cp\u003eModelling of the simplified ultraprecision diamond turning system\u003c/p\u003e","description":"","filename":"2.png","url":"https://assets-eu.researchsquare.com/files/rs-6283975/v1/4270d5c0839630a916b184a9.png"},{"id":81695348,"identity":"5714a8a1-15ca-4d40-9e2f-f79b10d2aff5","added_by":"auto","created_at":"2025-04-30 11:56:46","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":182031,"visible":true,"origin":"","legend":"\u003cp\u003eCutting forces prediction by using ADAMS based simulations, (a): Flat surface machining; \u003cbr\u003e\n(b): Freeform surface machining.\u003c/p\u003e","description":"","filename":"3.png","url":"https://assets-eu.researchsquare.com/files/rs-6283975/v1/00f82b223baf26c512386657.png"},{"id":81693682,"identity":"dc8b2a1a-075e-4be1-b2c6-7f672cc5f64f","added_by":"auto","created_at":"2025-04-30 11:48:46","extension":"png","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":384715,"visible":true,"origin":"","legend":"\u003cp\u003eFreeform surface DT model generation\u003c/p\u003e","description":"","filename":"4.png","url":"https://assets-eu.researchsquare.com/files/rs-6283975/v1/7adf8b42083ab13ec9f9bdbb.png"},{"id":81693680,"identity":"03e6107e-c120-4d2c-8431-1a1cb68f2b2f","added_by":"auto","created_at":"2025-04-30 11:48:46","extension":"png","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":77038,"visible":true,"origin":"","legend":"\u003cp\u003eDisplacement and cutting force data generated by DT\u003c/p\u003e","description":"","filename":"5.png","url":"https://assets-eu.researchsquare.com/files/rs-6283975/v1/98e7cbfded62bb4ec0fae344.png"},{"id":81693697,"identity":"c441c209-e27e-4fe9-b0b6-50b19db96455","added_by":"auto","created_at":"2025-04-30 11:48:46","extension":"png","order_by":6,"title":"Figure 6","display":"","copyAsset":false,"role":"figure","size":1027046,"visible":true,"origin":"","legend":"\u003cp\u003eFreeform surfaced components ultraprecision machined at the diamond turning machine with further support of digital twin approach.\u003c/p\u003e","description":"","filename":"6.png","url":"https://assets-eu.researchsquare.com/files/rs-6283975/v1/2e1285337e8104cd3041cde7.png"},{"id":92547843,"identity":"930957af-2fc0-4135-8c70-42d6f54fb7a7","added_by":"auto","created_at":"2025-09-30 21:33:20","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":2752320,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-6283975/v1/03b1c83b-38b9-4ed8-80c1-6a36b0d0f0eb.pdf"}],"financialInterests":"","formattedTitle":"Investigation on digital twin of the ultraprecision machining system for manufacturing freeform surfaced components","fulltext":[{"header":"1. Introduction","content":"\u003cp\u003eUltraprecision Manufacturing (UMP) is an important indicator in precision engineering capability and applications, and the associated research and development for a nation and/or region[\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e, \u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e]. To date, UPM technology has evolved as a high precision machining related technology developed to meet the manufacturing requirements of high-end cutting-edge and/or high throughput products including nuclear energy producers, ultra-large-scale integrated circuits, freeform optics[\u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e3\u003c/span\u003e], etc. With the latest development in power electronics, direct drives, sensors, and control technologies, the UPM machines and machining systems aim to continually achieve the higher machining accuracy in an industrial competitive manner[\u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e4\u003c/span\u003e, \u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e5\u003c/span\u003e]. However, the constraints and bottlenecks for the further development of the UPM machines and systems are also becoming obvious: Integration of multi-axis motion system, real-time machining quality monitoring and control, and time consuming for processing[\u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e]. It is thus essential and much needed to develop an innovative approach to overcoming the nanometric level hurdle in the context of industrial scale ultraprecision manufacturing. The approach has to address the multiple factors in multiscale and multiphysics[\u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e7\u003c/span\u003e], at the same time, real-time data monitoring and processing has always been challenging while addressing the need for nanometric-level motion accuracy and higher control resolution at the ultra-precision machining system[\u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e8\u003c/span\u003e]. Currently, the next paradigm shift in UPM is upon, i.e., continuously improving product quality and precision through Digital Twin (DT) technology, with the capability of real-time sensing, stable processing control and improvement of dynamic performance[\u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e9\u003c/span\u003e]. DT as an industrial solution, can observe and reflect the physical behaviour of UPM equipment and utilize it to guide optimization decisions during the design and analysis phase[\u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e10\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eThe studies on DT approach in UPM field is limited but many researchers are keep exploring active exploratory studies, for instance, Guerra et.al. proposed a optimization method for ultraprecision motion system based on DT from the backlash and friction perspective in year 2019[\u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e11\u003c/span\u003e], later in 2021, Wu, et al [\u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e12\u003c/span\u003e] provided a comprehensive review of the application of digital twins in UPM from the perspectives of voxel modelling, process planning, process monitoring, vibration control, and quality control. Gou et al.[\u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e13\u003c/span\u003e] in their article proposed the application of COMSOL Multiphysics based DT in aerostatic bearing slideway design and analysis, which is the key component for UPM motion system. In terms of spindle system design, Liu et al. [\u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e14\u003c/span\u003e]presented a semi-physical simulation-based digital twin model of the spindle drive system, which aims to calculate cost/scrap in digital world, instead of destructive testing.\u003c/p\u003e \u003cp\u003eThis paper presents the feasibility and innovative application of using a DT for an ultra-precision single point diamond turning (SPDT) machine system. The study and application described in the paper will demonstrate the significance of developing and applying DT technology to UPM of optical components, and in particular those with freeform surfaces. The effect of how contact forces affecting the toolpath will be investigated as well, whilst it also showing the limitation of using automated dynamic analysis of mechanical systems (ADAMS) only for this application. This paper will also be concluded with a further discussion on the potential and application of a DT-integrated UPM machine system, and how in-process data and information being acquired in real time both virtually and physically, and used to continuously optimise the machine system against the stringent ultraprecision machining requirements.\u003c/p\u003e"},{"header":"2. Ultraprecision diamond turning system and its digital twin","content":"\u003cp\u003eDiamond turning is defined as a process of ultraprecision mechanical turning of precision elements using natural or synthetic diamond-tipped tools. When turning, the workpiece is rotated and diamond tool is traversed along X, Z, and/or C axes of motion to produce precise diameters and depths, as shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e. It is widely used for machining high-quality aspheric optical components. With the assistance of computer numerical control (CNC) technology, workpieces can be turned directly with complicated structure and surface quality.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eIn order to achieve ultraprecision patterns (2D) and shapes (3D), it is essential that the causes of apparent random errors in processing machines be analysed, upgraded, refined or replaced, i.e., virtually eliminated and that the systematic errors be minimized. It is thus inevitably needing DT technology, very relevant and meaningful, which enables real-time monitoring and in-process processing and optimizing the complex data from multiple sources and aspects. Therefore, the objective of developing DT for ultraprecision diamond turning system can be summarized as follows:\u003c/p\u003e \u003cp\u003e \u003cul\u003e \u003cli\u003e \u003cp\u003eReal-time monitoring of the machining process, and in-process data transfer and the process optimization;\u003c/p\u003e \u003c/li\u003e \u003cli\u003e \u003cp\u003ePrevention for possible failures and machining errors;\u003c/p\u003e \u003c/li\u003e \u003cli\u003e \u003cp\u003ePrediction of the machined freeform surface and the in-process decision makings.\u003c/p\u003e \u003c/li\u003e \u003c/ul\u003e \u003c/p\u003e"},{"header":"3. Kinematics and dynamics modelling and analysis of the ultraprecision turning system","content":"\u003cp\u003eThe modelling of ultraprecision diamond turning system is carried out by using multi-body dynamics analysis method and tool (ADAMS), while considering the mechanical structure of the system as multibody mass-spring-damping. Newton\u0026rsquo;s second law is thus considered on the system, the modelling process for the ultraprecision diamond turning system is illustrated in Fig.\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e2\u003c/span\u003e.\u003c/p\u003e\n\u003cp\u003e\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eDue to the system being multibody whilst also having multi-degrees of freedom, the matrix Eq.\u0026nbsp;(\u003cspan class=\"InternalRef\"\u003e1\u003c/span\u003e) is proposed below to represent the system, with [M] mass, [K] stiffness \u0026amp; [C] damping being matrices of the system representing multi-bodies of multi-axis at the system[\u003cspan class=\"CitationRef\"\u003e15\u003c/span\u003e].\u003c/p\u003e\n\u003cdiv id=\"Equ1\" class=\"Equation\"\u003e\n\u003cdiv id=\"FileID_Equ1\" class=\"mathdisplay\"\u003e$$\\:\\left[\\text{M}\\right]\\ddot{\\text{u}}\\left(\\text{t}\\right)+\\left[\\text{C}\\right]\\stackrel{.}{\\text{u}}\\left(\\text{t}\\right)+\\left[\\text{K}\\right]\\text{u}\\left(\\text{t}\\right)=\\text{F}\\left(\\text{t}\\right)$$\u003c/div\u003e\n\u003cdiv class=\"EquationNumber\"\u003e1\u003c/div\u003e\n\u003c/div\u003e\n\u003cp\u003eWhere:\u003c/p\u003e\n\u003cp\u003eu(t), \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\stackrel{.}{\\text{u}}\\)\u003c/span\u003e\u003c/span\u003e (t), \u0026uuml; (t) represent the vector for displacement, velocity, and acceleration at (t) time respectively.\u003c/p\u003e\n\u003cp\u003eIn the realms of multibody dynamic systems, the bodies\u0026rsquo; orientation and positions can be found by the absolute coordinates. Within the context of ADAMS solver, it uses the three Cartesian coordinates X, Y and Z for the position, and \u0026alpha;, \u0026beta;, and \u0026gamma; for three Euler angles of rigid bodies. As seen below:\u003c/p\u003e\n\u003cdiv id=\"Equ2\" class=\"Equation\"\u003e\n\u003cdiv id=\"FileID_Equ2\" class=\"mathdisplay\"\u003e$$\\:\\text{p}=\\left[\\begin{array}{c}x\\\\\\:y\\\\\\:z\\end{array}\\right],\\:\\epsilon\\:=\\left[\\begin{array}{c}\\alpha\\:\\\\\\:\\beta\\:\\\\\\:\\gamma\\:\\end{array}\\right]$$\u003c/div\u003e\n\u003cdiv class=\"EquationNumber\"\u003e2\u003c/div\u003e\n\u003c/div\u003e\n\u003cp\u003eThen, in turn, the generalised coordinate which is associated to the rigid body i within ADAMS is denoted:\u003c/p\u003e\n\u003cdiv id=\"Equa\" class=\"Equation\"\u003e\n\u003cdiv id=\"FileID_Equa\" class=\"mathdisplay\"\u003e$$\\:{q}_{i}=\\left[\\begin{array}{c}{p}_{i}\\\\\\:{\\epsilon\\:}_{i}\\end{array}\\right]$$\u003c/div\u003e\n\u003c/div\u003e\n\u003cp\u003eThen the multibody\u0026rsquo; s motion can be demonstrated as:\u003c/p\u003e\n\u003cdiv id=\"Equb\" class=\"Equation\"\u003e\n\u003cdiv id=\"FileID_Equb\" class=\"mathdisplay\"\u003e$$\\:{q}_{n}\\times\\:1={\\left[{q}_{1}{q}_{2}\\dots\\:{q}_{n}\\right]}^{T}={\\left[{q}_{1}^{T}{q}_{2}^{T}t\\dots\\:{q}_{N}^{T}\\right]}^{T}$$\u003c/div\u003e\n\u003c/div\u003e\n\u003cp\u003eWhich contains the following:\u003c/p\u003e\n\u003cdiv id=\"Equ3\" class=\"Equation\"\u003e\n\u003cdiv id=\"FileID_Equ3\" class=\"mathdisplay\"\u003e$$\\:{q}_{i}={\\left[{\\text{x}}_{i}{\\text{y}}_{i}{\\text{z}}_{i}{\\alpha\\:}_{i},{\\beta\\:}_{i},{\\gamma\\:}_{i}\\right]}^{T}$$\u003c/div\u003e\n\u003cdiv class=\"EquationNumber\"\u003e3\u003c/div\u003e\n\u003c/div\u003e\n\u003cp\u003e\u003cstrong\u003en:\u0026nbsp;\u003c/strong\u003eat any point in time the orientation and position of the given body in the system.\u003c/p\u003e\n\u003cp\u003eN: the number of bodies in the system\u003c/p\u003e\n\u003cp\u003eThen the motion equation for Jacobian matrix can be written as:\u003c/p\u003e\n\u003cdiv id=\"Equ4\" class=\"Equation\"\u003e\n\u003cdiv id=\"FileID_Equ4\" class=\"mathdisplay\"\u003e$$\\:\\begin{array}{c}{{\\Phi\\:}}_{q\\left(m\\times\\:n\\right)}=\\\\\\:\\end{array}{\\left[\\begin{array}{c}\\frac{\\partial\\:{{\\Phi\\:}}_{1}}{\\partial\\:{q}_{1}}\\hspace{0.25em}\\hspace{0.25em}\\hspace{0.25em}\\hspace{0.25em}\\frac{\\partial\\:{{\\Phi\\:}}_{1}}{\\partial\\:{q}_{2}}\\hspace{0.25em}\\hspace{0.25em}\\hspace{0.25em}\\hspace{0.25em}\\cdots\\:\\hspace{0.25em}\\hspace{0.25em}\\hspace{0.25em}\\hspace{0.25em}\\frac{\\partial\\:{{\\Phi\\:}}_{1}}{\\partial\\:{q}_{n}}\\\\\\:\\frac{\\partial\\:{\\varphi\\:}_{2}}{\\partial\\:{q}_{1}}\\hspace{0.25em}\\hspace{0.25em}\\hspace{0.25em}\\hspace{0.25em}\\frac{\\partial\\:{{\\Phi\\:}}_{2}}{\\partial\\:{q}_{2}}\\hspace{0.25em}\\hspace{0.25em}\\hspace{0.25em}\\hspace{0.25em}\\cdots\\:\\hspace{0.25em}\\hspace{0.25em}\\hspace{0.25em}\\hspace{0.25em}\\frac{\\partial\\:{{\\Phi\\:}}_{2}}{\\partial\\:{q}_{n}}\\\\\\:\\because\\::\\hspace{0.25em}\\hspace{0.25em}\\hspace{0.25em}\\hspace{0.25em}\\hspace{0.25em}\\hspace{0.25em}\\hspace{0.25em}\\hspace{0.25em}\\\\\\:\\frac{\\partial\\:{{\\Phi\\:}}_{m}}{\\partial\\:{q}_{1}}\\hspace{0.25em}\\hspace{0.25em}\\hspace{0.25em}\\hspace{0.25em}\\frac{\\partial\\:{{\\Phi\\:}}_{m}}{\\partial\\:{q}_{2}}\\hspace{0.25em}\\hspace{0.25em}\\hspace{0.25em}\\hspace{0.25em}\\cdots\\:\\hspace{0.25em}\\hspace{0.25em}\\hspace{0.25em}\\hspace{0.25em}\\frac{\\partial\\:{{\\Phi\\:}}_{m}}{\\partial\\:{q}_{n}}\\end{array}\\right]}_{\\text{m}\\times\\:\\text{n}}$$\u003c/div\u003e\n\u003cdiv class=\"EquationNumber\"\u003e4\u003c/div\u003e\n\u003c/div\u003e\n\u003cp\u003eWhere:\u003c/p\u003e\n\u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{{\\Phi\\:}}_{q}\\):\u003c/span\u003e\u003c/span\u003e\u003cstrong\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\u0026nbsp;\u003c/span\u003e\u003c/span\u003e\u003c/strong\u003ethe Jacobian matrix constraint equations\u003c/p\u003e\n\u003cp\u003eThe Jacobian matrix can be used for understanding and representing the force, position, acceleration and any reaction forces. The systems nature is of non-linear constraint, and the Newton-Raphson iterative method is used within ADAMS to calculate the q\u003csub\u003e1\u003c/sub\u003e at time t\u003csub\u003e1\u003c/sub\u003e. Therefore, the Taylor-expansion-based linearization with regards to non-linear constraint equation can be achieved by using the following:\u003c/p\u003e\n\u003cdiv id=\"Equ5\" class=\"Equation\"\u003e\n\u003cdiv id=\"FileID_Equ5\" class=\"mathdisplay\"\u003e$$\\:{\\Phi\\:}\\left({\\text{q}}_{1},{\\text{t}}_{1}\\right)={\\Phi\\:}\\left({\\text{q}}_{0},{\\text{t}}_{1}\\right)+{\\Phi\\:}\\left({\\text{q}}_{0},{\\text{t}}_{1}\\right)\\left({\\text{q}}_{1}-{\\text{q}}_{0}\\right)$$\u003c/div\u003e\n\u003cdiv class=\"EquationNumber\"\u003e5\u003c/div\u003e\n\u003c/div\u003e\n\u003cp\u003eBy utilising this method at any given time, the unknown constraints, acceleration and Lagrange Multiplier can be found at any given step.\u003c/p\u003e"},{"header":"4. Digital twin for the ultraprecision machining system and its implementation","content":"\u003cp\u003eThe degradation of surface quality during UPM processes is often attributed to dynamic instabilities. However, the existing methods for predicting instabilities in UPM processes are still in their infancy. In order to applicate the DT from this aspect, the relationship between different parameters and surface characteristics should be investigated using a combination of analytical modelling and real-time monitoring means. Therefore, by combining suitable virtual models and sensing data, it is possible to help select suitable and \"stable\" process conditions, observe variations in surface roughness while obtaining it at the nanoscale, and predict machining errors that are barely visible, thus reducing post-processing difficulties.\u003c/p\u003e\n\u003cdiv id=\"Sec5\" class=\"Section2\"\u003e\n\u003ch2\u003e4.1 Cutting forces modelling and the associated algorithms\u003c/h2\u003e\n\u003cp\u003eAs demonstrated in \u003cstrong\u003eFig.\u0026nbsp;3\u003c/strong\u003e, the multi-body dynamics-based approach and the associated modelling and simulation (implemented with ADAMS) allow simulated data to be taken in real time from the virtual system.\u003c/p\u003e\n\u003cp\u003e\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eThrough developing a multibody dynamics-based system (in ADAMS), cutting forces and machining error prediction can be realized by the created virtual digital simulation system, thus to provide measurement and insights during the entirety of the cutting process. The main parameters that have a profound effect on the surface finish, are the cutting forces and tool wear. For cutting forces, this is down to the interfacial actions between the diamond tool and workpiece surface. In this scale, there are numerous influence factors being involved, those being feed rate and depth of cut etc. By understanding the cutting forces in a digital twin manner, it can provide better understanding of its behaviour and the consequent effect on the machining system dynamics and consequently the machining errors of the system. Therefore, it is able to further in process monitor these cutting forces in the physical system and optimize the machining process dynamically and the surface finishing, which is particularly beneficial for ultraprecision diamond turning of freeform surfaces.\u003c/p\u003e\n\u003c/div\u003e\n\u003cdiv id=\"Sec6\" class=\"Section2\"\u003e\n\u003ch2\u003e4.2 'In-process' Data retrieval from the machining system\u003c/h2\u003e\n\u003cp\u003eData retrieval will be done through the metrology systems which are already in use and have had vast amounts of research undertaken into them. Those being such systems as scanning probing method, optical detection method and microsensors etc. These sensors in real-time feedback the totality of what is happening in the physical system to the digital system as seen above. The feasible methods for data transmission and collecting of DT system can be summarised as:\u003c/p\u003e\n\u003cul\u003e\n\u003cli\u003e\n\u003cp\u003eUsing the encoder outputs (position, velocity, acceleration) within the machine system:\u003c/p\u003e\n\u003c/li\u003e\n\u003c/ul\u003e\n\u003cp\u003eOptical encoders are high-precision positioning sensors based on the interference patterns produced by the relative movement between two gratings, the nanometric resolution and MHz-level data response led it to be an ideal real-time monitor for DT. According to the operating principle, the displacement, velocity and even acceleration for the motion parts of UPM system can be directly obtained during machining in real time based on the approach of encoders. These data provide a very visual representation of the relative movement between cutting tool and workpiece, which directly influences the machining quality. By integrating the collected data into the virtual model of DT, it is possible to observe the state of the motion system in real time throughout the machining process, thus to detect and predict machining defects in advance and to reduce repetitive post-processing works.\u003c/p\u003e\n\u003cul\u003e\n\u003cli\u003e\n\u003cp\u003eUsing cutting forces data from the machining process:\u003c/p\u003e\n\u003c/li\u003e\n\u003c/ul\u003e\n\u003cp\u003eCutting force calculation, modelling and analysis has been always an important process indicator in UPM, which can collectively reflect the various cutting process phenomena and dynamics such as size effect, chip formation, energy consumption and cutting heat partition, and the machining instability and chatter. It can also be correlated with the tool cutting performance particularly with the tool wear and tool life. Therefore, cutting force is seen as a key factor to optimize the cutting process variables and tool geometries in micro-cutting processes, and thus make it meaningful to use cutting forces data as an in-process monitoring aspect for the DT. The use of cutting forces as a data resource of DT enables in-process detection of the variation such as energy input, environmental disturbances during machining and prediction of tool wear. From another aspect, with the integration of pre-established cutting force models in DT enables the observation of unexpected changes of cutting force and thus the prediction of possible defects before post-processing and surface inspection work.\u003c/p\u003e\n\u003cul\u003e\n\u003cli\u003e\n\u003cp\u003eUsing the surface \u0026lsquo;signature\u0026rsquo; data from the component ultraprecision machined.\u003c/p\u003e\n\u003c/li\u003e\n\u003c/ul\u003e\n\u003cp\u003eDirect inspection of the 3D surface texturing and characteristics of the machined workpiece surface during processing is a relatively more intuitive method. The real-time monitoring and control of surface morphology variations in their incipient stages are vital for assuring nanometric range finish in SPDT process. To date, the method for surface monitoring of UPM are various, for instance, by the analytical approach of non-parametric Bayesian to capture the inherently complex, non-Gaussian, and non-stationary sensor signal patterns observed in process[\u003cspan class=\"CitationRef\"\u003e16\u003c/span\u003e] or use acoustic emission (AE) to collect the signals of the transient elastic waves generated from the rapid release of energy from one or more sources within the material[\u003cspan class=\"CitationRef\"\u003e17\u003c/span\u003e], etc. With these data, DT can thus directly intervene the cutting process and compensate surface errors based on the pre-implemented algorithms.\u003c/p\u003e\n\u003c/div\u003e"},{"header":"5. Application case studies on ultraprecision machining of freeform surfaces","content":"\u003cp\u003eUltraprecision machining of freeform surfaced component requires more degrees of freedom than conventional methods, which brings in numerous challenges. The experimental setup and partial results are shown in \u003cstrong\u003eFig.\u0026nbsp;4\u003c/strong\u003e, based on an ultraprecision diamond turning machine (Moore Nanotech UPL 250), computer aided manufacturing (CAM)\u0026thinsp;+\u0026thinsp;non-uniform rational B-splines (NURBS) generated tool paths, and synchronized multi-axis actuation in a digital twin manner. Although the in-process data collection facility is limited, the cross-validation with the created digital twin is still realizable.\u003c/p\u003e\n\u003cp\u003eThe generation of freeform surface and the related calculation are shown in \u003cstrong\u003eFig.\u0026nbsp;4\u003c/strong\u003e. With the help of NURBS, freeform surface can be obtained in 3D model, then detailed surface contour is differentiated into finite elements and calculated by the pre-set mathematic models regarding cutting force and tool path in ADAMS.\u003c/p\u003e\n\u003cp\u003e\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eFigure \u003cspan class=\"InternalRef\"\u003e5\u003c/span\u003e illustrates the Z-axis displacement data and cutting force data calculated based on the pre-established mathematic model in DT, both with a processing time of 60 seconds.\u003c/p\u003e\n\u003cp\u003eAs found from Fig.\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e5\u003c/span\u003e, the cutting force and tool path simulated by DT can be used to predict the machining process in advance, and by comparing with the in-process data fed back from the encoder and the dynamometer, it is possible to realize the prediction and prevention of machining defects during the turning process directly. If the corresponding CAM algorithms is integrated, it is possible to achieve the remote monitoring of the machining process and online defects compensation through the operating of G-Codes.\u003c/p\u003e\n\u003cp\u003e\u0026nbsp;The scientific understanding of the corresponding micro cutting mechanics in freeform surface machining is thus essentially important, while constantly achieving the nanometric level optical surface finishing, multiscale modelling and analysis is likely a useful technique on this combined with advanced algorithms spanned out from NURBS[\u003cspan class=\"CitationRef\"\u003e18\u003c/span\u003e, \u003cspan class=\"CitationRef\"\u003e19\u003c/span\u003e]. Ultraprecision diamond turning of freeform surfaced components and devices are increasingly demanded in particular in industrial scale ultraprecision manufacturing of head-up display (HUD) and light detection and ranging (LiDAR) devices, ophthalmic lenses, off-axis laser mirrors, and space optics[\u003cspan class=\"CitationRef\"\u003e20\u003c/span\u003e, \u003cspan class=\"CitationRef\"\u003e21\u003c/span\u003e].The experimental and application case studies above have indicated the potential and applications of the Ultraprecision diamond turning system working with its digital twin.\u003c/p\u003e"},{"header":"6. Conclusion","content":"\u003cp\u003eThis paper presents an innovative approach to developing digital twin for the ultraprecision diamond turning system and its implementation and application perspectives. It will likely provide new insights into the development of next generation ultraprecision machining systems in the era of Industry 4.0. The advanced modelling, design and analysis methods are used in the development, including multi-body dynamics modelling and analysis, machining system dynamics, in-process cutting forces monitoring, and digital twin integration, etc. The ultraprecision machining system digital twin has shown the capability map organically and can coordinate the functional, structural, behavioural, control, intelligence and performance of a machine system represented both virtually and physically. However, there is still the systematic gap in building multi-dimensional and high-fidelity DT in particular effectively integrated with an ultraprecision manufacturing. This should be the future research and development direction for applying DT in ultraprecision diamond turning systems, albeit the work presented here has made the attempt and efforts along the line.\u003c/p\u003e"},{"header":"Abbreviations","content":"\u003cdiv class=\"DefinitionList\"\u003e \u003cdiv class=\"DefinitionListEntry\"\u003e \u003cdiv class=\"Term\"\u003eADAMS\u003c/div\u003e \u003cdiv class=\"Description\"\u003e \u003cp\u003eAutomated Dynamic Analysis of Mechanical Systems\u003c/p\u003e \u003c/div\u003e \u003c/div\u003e \u003cdiv class=\"DefinitionListEntry\"\u003e \u003cdiv class=\"Term\"\u003eAE\u003c/div\u003e \u003cdiv class=\"Description\"\u003e \u003cp\u003eAcoustic Emission\u003c/p\u003e \u003c/div\u003e \u003c/div\u003e \u003cdiv class=\"DefinitionListEntry\"\u003e \u003cdiv class=\"Term\"\u003eCAM\u003c/div\u003e \u003cdiv class=\"Description\"\u003e \u003cp\u003eComputer Aided Manufacturing\u003c/p\u003e \u003c/div\u003e \u003c/div\u003e \u003cdiv class=\"DefinitionListEntry\"\u003e \u003cdiv class=\"Term\"\u003eCNC\u003c/div\u003e \u003cdiv class=\"Description\"\u003e \u003cp\u003eComputer Numerical Control\u003c/p\u003e \u003c/div\u003e \u003c/div\u003e \u003cdiv class=\"DefinitionListEntry\"\u003e \u003cdiv class=\"Term\"\u003eDT\u003c/div\u003e \u003cdiv class=\"Description\"\u003e \u003cp\u003eDigital Twin\u003c/p\u003e \u003c/div\u003e \u003c/div\u003e \u003cdiv class=\"DefinitionListEntry\"\u003e \u003cdiv class=\"Term\"\u003eHUD\u003c/div\u003e \u003cdiv class=\"Description\"\u003e \u003cp\u003eHead-Up Display\u003c/p\u003e \u003c/div\u003e \u003c/div\u003e \u003cdiv class=\"DefinitionListEntry\"\u003e \u003cdiv class=\"Term\"\u003eLiDAR\u003c/div\u003e \u003cdiv class=\"Description\"\u003e \u003cp\u003eLight Detection and Ranging\u003c/p\u003e \u003c/div\u003e \u003c/div\u003e \u003cdiv class=\"DefinitionListEntry\"\u003e \u003cdiv class=\"Term\"\u003eNURBS\u003c/div\u003e \u003cdiv class=\"Description\"\u003e \u003cp\u003eNon-Uniform Rational B-Splines\u003c/p\u003e \u003c/div\u003e \u003c/div\u003e \u003cdiv class=\"DefinitionListEntry\"\u003e \u003cdiv class=\"Term\"\u003eSPDT\u003c/div\u003e \u003cdiv class=\"Description\"\u003e \u003cp\u003eSingle Point Diamond Turning\u003c/p\u003e \u003c/div\u003e \u003c/div\u003e \u003cdiv class=\"DefinitionListEntry\"\u003e \u003cdiv class=\"Term\"\u003eUPM\u003c/div\u003e \u003cdiv class=\"Description\"\u003e \u003cp\u003eUltra-Precision Manufacturing\u003c/p\u003e \u003c/div\u003e \u003c/div\u003e \u003c/div\u003e"},{"header":"Declarations","content":"\u003cp\u003e \u003ch2\u003eConflicts of interest\u003c/h2\u003e \u003cp\u003eThe authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.\u003c/p\u003e \u003c/p\u003e\u003ch2\u003eFunding\u003c/h2\u003e \u003cp\u003eThis work was supported by Henan Province science and Technology Research Project [grant numbers 21202210318]; Henan Province Graduate Education Reform and Quality Improvement Project(YJS2023AL041); Zhongyuan University of Technology Advantage Discipline Strength Improvement Plan Funding (GG202407); National Key Laboratory of Intelligent Manufacturing Equipment and Technology Open Project [grant numbers IMETKF2025019].\u003c/p\u003e\u003ch2\u003eAuthors' contributions\u003c/h2\u003e \u003cp\u003eNing Gou contributed to this work by conceiving, conducting experiments, and writing the original draft. Qiao Xuetao and Wang Yibo contributed to this work by providing necessary concepts and comparisons, organizing information, technical writing, and presentation. Cheng Kai and Dehong Huo contributed by formatting, results, and discussion. Zhao Zengxiao contributed by numerical investigation, fabrication.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\u003cli\u003e\u003cspan\u003eYuan J et al (2017) Review on the progress of ultra-precision machining technologies. Front Mech Eng 12:158\u0026ndash;180\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eLi D et al (2019) On-machine surface measurement and applications for ultra-precision machining: a state-of-the-art review. Int J Adv Manuf Technol 104:831\u0026ndash;847\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eCorbett J, McKeown PA, Peggs GN et al (2000) Nanotechnology: international developments and emerging products. CIRP Ann 49(2):523\u0026ndash;545\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eLucca DA, Matthew J, Klopfstein, Riemer O (2020) Ultra-precision machining: cutting with diamond tools. J Manuf Sci Eng 142(11):110817\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eZhang SJ et al (2015) A review of machine-tool vibration and its influence upon surface generation in ultra-precision machining. Int J Mach Tools Manuf 91:34\u0026ndash;42\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eGao W et al (2023) Machine tool calibration: Measurement, modeling, and compensation of machine tool errors. Int J Mach Tools Manuf 187:104017\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eGeng Z, Tong Z et al (2021) Review of geometric error measurement and compensation techniques of ultra-precision machine tools. Light: Adv Manuf 2(2):211\u0026ndash;227\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eLi D et al (2019) On-machine surface measurement and applications for ultra-precision machining: a state-of-the-art review. Int J Adv Manuf Technol 104:831\u0026ndash;847\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eWu L, Leng J, Ju B (2021) Digital twins-based smart design and control of ultra-precision machining: A review. Symmetry 13(9):1717\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eXu Z et al (2024) A review: Insight into smart and sustainable ultra-precision machining augmented by intelligent IoT. J Manuf Syst 74:233\u0026ndash;251\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eGuerra R, Haber et al (2019) Digital twin-based optimization for ultraprecision motion systems with backlash and friction. IEEE Access 7:93462\u0026ndash;93472\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eWu L, Leng J, Ju B (2021) Digital twins-based smart design and control of ultra-precision machining: A review. Symmetry 13(9):1717\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eGou N, Cheng K, Huo D (2021) Multiscale modelling and analysis for design and development of a high-precision aerostatic bearing slideway and its digital twin. Machines 9(5):85\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eLiu J et al (2020) Current Hysteresis Control Design of Motorized Spindle Driven System Based on Semi-Physical Simulation Model. Chinese Control And Decision Conference (CCDC). IEEE, 2020\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eKhaghani A, Cheng K (2020) Investigation on multi-body dynamics based approach to the toolpath generation for ultraprecision machining of freeform surfaces. Proceedings of the Institution of Mechanical Engineers, Part B: Journal of Engineering Manufacture 234.3 : 571\u0026ndash;583\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eRao P et al (2014) Real-time identification of incipient surface morphology variations in ultraprecision machining process. J Manuf Sci Eng 136(2):021008\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eChen X (1998) Monitoring and analysis of ultra-precision machining processes using acoustic emission. University of California, Berkeley\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eSun X, Cheng K (2010) Multi-scale simulation of the nano-metric cutting process. Int J Adv Manuf Technol 47:891\u0026ndash;901\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eHuo D (2013) Micro-cutting: fundamentals and applications. Wiley\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eLiu S, Cheng K, Zhao L (2023) Development of the personalised manufacturing system framework for freeform vari-focal lenses and its implementation and application perspectives. Int J Mechatronics Manuf Syst 16(1):1\u0026ndash;21\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eJiang X, Jane (2020) and Paul J. Scott. Advanced metrology: freeform surfaces. Academic\u003c/span\u003e\u003c/li\u003e\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":true,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"Ultraprecision machining system, Ultraprecision diamond turning, Digital twin, Modelling of machining system dynamics, Freeform surface machining","lastPublishedDoi":"10.21203/rs.3.rs-6283975/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-6283975/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eDigital Twin (DT) is widely regarded as the future for advanced engineering manufacture, addresses the critical challenge for continuous improvement and optimization of manufacturing systems through real-time machining process monitoring, in-process diagnosis and dynamic process optimization, and digital and physical data fusion for higher manufacturing precision. Therefore, developing a DT for the ultraprecision manufacturing (UPM) system is inevitably essential for future generation UPM systems and machines. In this paper, an investigation on digital twin of the ultraprecision machining system and its implementation perspectives are presented particularly against the ever-increasing demand for higher precision machining accuracy, e.g. the increasingly more stringent requirement in manufacturing freeform surfaced components and devices. The investigation is focused on the kinematics and dynamics modelling of the machining system (as the foundation of the DT development), the DT implementation, and the application case study, which reflects the innovative attempt on seamless integration of ultraprecision machining fundamentals, innovative development of applied DT technology, and high value ultraprecision applications. Design, manufacturing and control, combined with computationally efficient DT design and optimization algorithms will lead to the higher form/dimensional accuracy and finer surface roughness of the ultraprecision components/parts, in a competitive and promising industrial manner.\u003c/p\u003e","manuscriptTitle":"Investigation on digital twin of the ultraprecision machining system for manufacturing freeform surfaced components","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2025-04-30 11:48:41","doi":"10.21203/rs.3.rs-6283975/v1","editorialEvents":[{"type":"communityComments","content":0}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"4574c0b8-4cda-4043-9ea9-b3ea69d7b525","owner":[],"postedDate":"April 30th, 2025","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[],"tags":[],"updatedAt":"2025-09-30T21:25:11+00:00","versionOfRecord":[],"versionCreatedAt":"2025-04-30 11:48:41","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-6283975","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-6283975","identity":"rs-6283975","version":["v1"]},"buildId":"8U1c8b4HqxoKbykW_rLl7","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}