The editorial, authored by Chitaranjan Pany of the Vikram Sarabhai Space Centre in India, Dawood Desai of Tshwane University of Technology in South Africa, and Wagner de Rossi of the Institute of Energy and Nuclear Research in Brazil, frames manufacturing as a domain dominated by brutal physical phenomena: burr creation, plastic deformation, frictional contact, and thermo-mechanical coupling. Since at least the 1980s, FEM has been the most prevalent method for simulating these processes, and its continuous development has allowed it to replicate experimental techniques even when intricate characteristics are involved, such as complex process parameters, non-linearity, composite and multi-layered materials, shape memory alloys, and varied tool geometries. The appeal is straightforward: experiments near the cutting tool are laborious and costly, yet quantities like strain, strain rate, cutting force, and temperature are precisely the ones engineers need to understand metal cutting mechanisms. Simulation fills that measurement gap.

But FEM is only as good as its inputs, and the editorial is candid about which inputs matter most. The material constitutive law describing flow stresses, the type of friction at the tool-chip interface, and fracture control are all highly significant to the finite element analysis of machining problems. When these constitutive models are paired with experimental data to calibrate a simulation, researchers can predict characteristics that determine surface integrity: surface roughness, residual stresses, micro-hardness, plastic deformation, phase transitions, elastic recovery, and thermal behavior. Both academia and industry are paying increasing attention to this coupling of models and measurements, because surface integrity ultimately dictates the fatigue life and reliability of manufactured components, from orthopedic implants to jet engine parts.

One of the standout contributions highlighted in the editorial tackles a biomedical challenge head-on. Titanium alloy Ti6Al4V is a favorite of the biomedical field thanks to its remarkable biocompatibility, corrosion resistance, and mechanical properties, and the design of surface textures for dental implants has evolved over time to address oral rehabilitation in both healthy and compromised bone. A research team led by Lebea and colleagues explored laser shock peening, or LSP, as a surface modification technique to enhance the mechanical characteristics of implants, examining how material orientation, loading angle, and single-shot repetition of the peening process affect surface roughness. Because implant durability depends considerably on surface roughness, and because no prior computational studies had established roughness parameters for this process, the team built a numerical model in the commercial finite element software ABAQUS/Explicit to replicate the dynamic conditions of LSP, effectively using simulation to predict what experiments had not yet measured.

A second study, by Baloyi and colleagues, dives into the powder that feeds the additive manufacturing revolution. Spherical particles are essential in powder-based additive manufacturing because their enhanced flowability, packing density, and mechanical properties improve printing accuracy and the quality of final products. Traditional routes to spherical powder, such as gas atomization and plasma spheroidization, have been thoroughly examined, but laser spheroidization remains inadequately investigated. To close that gap, the researchers performed comprehensive numerical analyses using models built in Abaqus and OpenFOAM, simulating heat transfer from the laser to titanium Ti-6Al-4V powder particles with a transient uncoupled heat transfer approach that accounts for latent heat, while particle deformation was modeled with a phase-fraction-based interface-capturing technique combined with the Navier-Stokes equations. The payoff is striking: laser spheroidization of Ti-6Al-4V powder may enhance powder yield by 10 percent compared with plasma processing, delivering greater power density and reduced melting durations, and offering a more effective route to spherical particles of specific dimensions.

The third highlighted study shifts from the factory floor to the power generation sector, where steam turbine blades endure one of the harshest mechanical environments in engineering. Mashiachidi and Desai examined the complex factors impacting the fatigue life of these blades, including steam flow-induced bending, centrifugal forces, vibration response, structural mistuning, and temperature-dependent influences. The concept of mistuning is critical: manufacturing tolerances mean that nominally identical blades in a bladed disk actually vary slightly in shape, and those small deviations can dramatically alter vibration behavior and fatigue life. Using finite element analysis software, the researchers created a basic, mistuned, scaled-down model of a steam turbine bladed disk that accounts for temperature-dependent material characteristics, providing the power generation industry with a computational window into failure modes that are nearly impossible to probe directly in a running turbine.

Not every application of FEM is glamorous, and the editorial makes a point of celebrating that. A study by Gobi and Guo focused on the modeling, internal structure examination, and automation of a cassava grinding machine used in starch production. The researchers selected a single-cylinder grinder for its simplicity and versatility, then implemented automation using a GRAFCET model, a graphical sequential function chart standard in industrial control, together with an advanced human-machine interface. The HMI added an extra safety feature and allowed operators to oversee the operation through an easy graphical interface, enabling continuous operation with minimal human involvement. The result is a modest but meaningful demonstration that finite element analysis and control automation can enhance the efficiency and safety of food processing equipment in agricultural economies.

Beyond these four research articles, contributed by ten authors, the editorial sketches a sweeping landscape of where FEM is being applied across precision manufacturing. Ideal cutting parameters in machining, rolling, turning, milling, and high-speed machining are being mapped numerically. Laser applications in sheet metal forming, tube end-forming processes, micro-manufacturing, and ball-burnishing processes are being examined through combined numerical and experimental simulations. Welding and electron beam welding of high-strength steels, aluminum, titanium, and nickel-base alloys for aerospace applications are being modeled to predict joining quality. Additive manufacturing, particularly metallic powder bed processes, is being optimized with the help of artificial intelligence and machine learning algorithms trained on simulation and experimental data. Even the fabrication of blazed grating structures, which are essential for optical communication, structural coloration, precision measurement, and digital display, is being advanced through techniques such as ultrasonic-assisted ultraprecision planing, with FEM providing the predictive backbone.

The editorial’s authors, who have themselves published extensively on periodic structure theory and wave propagation in curved panels using finite element approaches, see a future where robust and reliable FE techniques for diverse manufacturing processes are integrated into AI and machine learning algorithms and digital production chains. Acoustic metamaterials and phononic crystals aimed at vibration reduction, spacecraft and antenna structures produced via 3D printing, and composite multi-layered products all feature in their vision of new potential applications. Laser processes receive special attention as a particularly intriguing and challenging domain for FEM: the intricacy and temporal sequence of phenomena that occur when a laser beam interacts with matter, combined with the speed of the processes, the complex parameter interactions, and the small regions affected, render experimental measurements incredibly difficult. In these situations, simulation is not merely a convenience but the primary means of comprehending the physics and improving outcomes.

What emerges from this collection is a portrait of a field at an inflection point. The finite element method, once a specialist tool for structural analysts, has become the connective tissue linking machining, additive manufacturing, laser processing, biomedical engineering, and industrial automation. As experimental data increasingly feeds the calibration of numerical models, and as those models in turn feed machine learning systems that optimize entire production chains, the boundary between virtual and physical manufacturing continues to blur. For researchers and engineers, the message of this Research Topic is clear: the reported advances may help the community study and better understand precision manufacturing processes, and the rapid development of manufacturing approaches and methods suggests that the most interesting applications of FEM are still ahead.

Subject of Research: Applications of finite element methods in precision manufacturing processes including machining, laser processing, additive manufacturing, and industrial automation

Article Title: Editorial: Advances of finite element methods in the precision manufacturing processes

Article References: Editorial: Advances of finite element methods in the precision manufacturing processes. (n.d.). https://doi.org/10.3389/fmtec.2025.1608699

Image Credits: AI Generated

DOI: 10.3389/fmtec.2025.1608699

Keywords: finite element method, precision manufacturing, laser shock peening, additive manufacturing, titanium alloy Ti6Al4V, powder spheroidization, steam turbine blades, fatigue life prediction, surface integrity, machine learning, machining simulation, cassava grinding automation

The study, published in Results in Engineering by Kazuki Kaneko and Zongze Li, addresses a fundamental blind spot in digital manufacturing. Computer-aided manufacturing (CAM) software can simulate geometry and generate tool paths from a CAD model, but it cannot simulate what happens inside the machine’s controller. The G-code is filtered by the CNC interpolator, feedforward controllers and feedback control loops before it ever reaches the servomotors, and these proprietary algorithms are closely guarded black boxes maintained by machine tool builders. Physical modeling of this chain is extraordinarily difficult precisely because the control algorithms are secret and the dynamics are deeply nonlinear. The result is that manufacturers often discover machining errors only after cutting — or resort to time-consuming air runs in which the machine executes the program without a workpiece just to observe its behavior.

The authors reframed the problem as one of sequence translation. From a data-processing perspective, G-code execution is a stream of discrete commands fed row by row into a black-box system that emits corresponding sequences of tool-path and cycle time errors. Predicting those errors for a given program is therefore fundamentally a sequence-to-sequence problem — exactly the kind of task at which Transformers excel. Unlike recurrent networks or long short-term memory (LSTM) models, which process sequences step by step, a Transformer uses multi-head self-attention to derive global relational weights across all positions simultaneously. This allows it to capture long-range temporal dependencies, such as how a sharp corner several blocks ahead causes the servo system to decelerate and how a large acceleration from a previous segment continues to influence subsequent commands as the transient response gradually decays.

The researchers drew a striking analogy between the Transformer’s internal machinery and the physics of a CNC controller. In their framing, the query represents the motion state of the current G-code command, while the keys and values carry error features of the surrounding tool path; scaled dot-product attention then assigns weights to nearby and distant blocks, mirroring the feedforward and feedback structure of a real servo loop. Position-wise feedforward networks introduce the nonlinear modeling capacity needed to emulate local servo behaviors such as PID control and friction, while residual connections — which pass inputs directly forward — resemble a closed-loop feedback system that focuses on predicting small dynamic deviations rather than reconstructing the entire tool path. Layer normalization, meanwhile, stabilizes the wildly different physical scales of position increments and feed rates, functioning much like a gain stabilizer in a servo drive.

Training such a model requires data that spans the machine’s full dynamic repertoire, so the team avoided reliance on specific workpiece geometries, which would limit generalization. Instead, they semi-randomly generated ten sets of training G-code combining local blending segments, where the path passes directly through control points, and global blending segments, where B-spline interpolation smooths the trajectory at constant feed rate. Displacements and feed rates were drawn randomly from defined ranges, producing tool paths with varied travel ranges and frequent direction changes. Each program was then executed on a real three-axis ROBODRILL machine equipped with a Fanuc Series 31i controller, and actual tool-path data were captured at a sampling frequency of 1 kHz using Fanuc’s SERVO Guide monitoring software. The training targets were thus experimentally measured servo responses rather than virtual simulations, grounding the digital twin in physical reality.

The model itself is an encoder-only Transformer with a model dimension of 512, eight layers and four attention heads, trained for 2000 epochs on a workstation with an RTX 4090 GPU. Input sequences consisted of nominal positional increments along the three feed axes plus the commanded feed rate, segmented into windows of 32 control points using a causal sliding window. The output comprised the three-dimensional tool-path error and the cumulative cycle time error at each point. Notably, the authors found that longer input sequences converged more slowly without improving final accuracy — a result that aligns neatly with servo physics, since the transient influence of any single command naturally fades over time. When compared against a Bi-LSTM model of equal dimensions trained on identical data, the Transformer converged in roughly 500 epochs, three times faster than its recurrent rival.

Validation was carried out on six G-code programs derived from two physical specimens: a 25-millimeter-radius hemispherical part machined along morphing spiral and bidirectional paths, and a complex artifact geometry, each run at nominal feed rates of 1000 and 3000 millimeters per minute. The results were decisive. Both models avoided large systematic bias, with mean prediction deviations generally within ±1 micrometer or millisecond, but the Transformer’s uncertainty bands were roughly 1.5 to 2 times tighter than the Bi-LSTM’s across all error components — and in some conditions nearly four times tighter. Its error distributions clustered markedly more sharply around zero, and while the Bi-LSTM’s cycle time root-mean-square error ballooned to about 8 milliseconds on the most demanding program against a mean error of 2.5 milliseconds, the Transformer suppressed such outliers, keeping RMSE close to MAE.

The comparison also revealed how differently the two architectures degrade under stress. Higher feed rates inherently reduce the accuracy of the controller’s feedforward and feedback loops, and the Bi-LSTM’s errors doubled or even tripled when the feed rate rose from 1000 to 3000 millimeters per minute. The Transformer, by contrast, showed far more graceful degradation, keeping mean errors below 2 micrometers or milliseconds even on the most challenging high-speed program. The authors attribute the residual errors that remain — small but nonzero — to highly random mechanical nonlinearities such as micro-friction variations and backlash during axis reversals, along with the quantization limits of encoder feedback at the 1 kHz sampling rate.

Perhaps the most industrially compelling result is speed. Predicting errors for an entire validation program took the Transformer less than 3.5 seconds, regardless of program complexity, whereas air-running the same programs on the machine took anywhere from roughly 38 to 202 seconds. Because prediction time depends only on G-code length, the trained model can instantly screen massive production programs offline, eliminating the need for preliminary air runs and sharpening both production scheduling and machining efficiency. The approach does not generalize across machines — each machine tool has unique controller and mechanical characteristics — but the authors emphasize that adapting to a new machine requires only executing the training G-codes, acquiring a fresh dataset and retraining, after which the model serves as a customized digital surrogate for that specific machine.

The work points toward a future in which every machine tool carries its own learned digital twin, capable of vetting programs before metal is ever cut. The team’s next steps include extending the model to account for cutting force-induced deflections of tool and workpiece, which superimpose on servo tracking errors in real machining; probing how specific G-code features such as control point density affect prediction performance; scaling the sequence-to-sequence methodology to five-axis simultaneous machining; and developing real-time servo signal acquisition for online error prediction during actual cutting. They also plan to build open-architecture experimental CNC systems, since proprietary commercial controllers block the integration of theoretical control equations needed for hybrid physical-digital modeling. If those ambitions pan out, the humble G-code file may one day arrive at the shop floor already annotated with a complete forecast of its own imperfections.

Subject of Research: Transformer-based deep learning prediction of tool-path and cycle time errors in CNC machining from G-code

Article Title: Prediction of tool-path and cycle time errors of CNC machining using a transformer-based deep learning model

Article References: Kaneko, K., & Li, Z. (2026). Prediction of tool-path and cycle time errors of CNC machining using a transformer-based deep learning model. Results in Engineering, 32, Article 112872. https://doi.org/10.1016/j.rineng.2026.112872

Image Credits: AI Generated

DOI: 10.1016/j.rineng.2026.112872

Keywords: CNC machining, Transformer model, deep learning, digital twin, tool-path error, cycle time prediction, G-code, servo dynamics, Bi-LSTM comparison, precision manufacturing, sequence-to-sequence learning, machine tools