Free-form surface parts are widely used in industries, and they consist of intricate 3D surfaces such as molds, impellers, and turbine blades that possess complex geometrical contours and demand high precision. Proper tool orientation is crucial for ensuring the efficiency and accuracy of five-axis computer numerical control (CNC) machining. Multi-scale methods have received much attention and have been widely used in various fields. They have been proven to be instrumental and can obtain fruitful outcomes. Ongoing research on multi-scale tool orientation generation methods, which aim to acquire tool orientations that satisfy both macro- and micro-scale requirements, is significantly important for improving the machining quality of workpiece surfaces. This paper proposes a multi-scale tool orientation generation method that considers both the machining strip width and roughness scales. This method also ensures a smooth tool orientation and avoids interference in the machining process. First, the correlation between the tool orientation and rotational axis is analyzed, and feasible area calculation and tool orientation adjustment methods are introduced. Then, the paper introduces the calculation method for machining strip widths on the macro-scale and the roughness calculation method on the micro-scale. Besides, tool orientation adjustment methods for both scales are proposed. Next, a multi-scale tool orientation generation method is developed to generate tool orientations that meet the macro- and micro-scale requirements. Finally, to verify the effectiveness of the proposed multi-scale tool orientation generation method, it is applied to the machining of a free-form surface. Experimental verification results have shown that the tool orientation generated by the proposed method can obtain the expected machining strip width and roughness, meeting both macro- and micro-scale requirements. Therefore, this method has significant potential for engineering applications. Free-form surface parts are widely used in the industry, and they usually consist of complex three-dimensional surfaces, such as turbine blades, impellers, and molds . These pThe bull-nose tool, characterized by its variable diameter, circumvents the issue of zero cutting speed. In recent years, numerous researchers have conducted mechanistic modeling studies on the machining process involving bull-nose tools. During the machining process, cutting forces can induce tool deflection, which may ultimately result in unacceptable dimensional errors . Budak aMulti-scale methods have been widely used in various fields. For example, they have been used in metal materials to study the surface behavior of martensitic tool steels  and in gThe objectives of conventional tool orientation planning mainly include avoiding interference , controlThe tool orientation significantly affects the machining strip widths, so many scholars have conducted related research. Frad et al.  investigThe roughness significantly affects the workpiece’s performance. Therefore, the effect of the tool orientation on the roughness of the workpiece has always been a research focus, and many related studies have been conducted. Duan et al.  investigIn five-axis tool path planning, achieving interference-free and smooth tool orientations is also a key issue. He et al.  analyzedPrevious research on the impact of tool orientations on machining strip width and roughness has obtained significant results. However, there has been limited investigation of tool orientation generation methods from a multi-scale perspective, and how to simultaneously satisfy both machining strip width and surface roughness at these scales through tool orientation planning is less studied. In response, this paper proposes a multi-scale tool orientation generation method that considers both machining strip width and roughness scales. The proposed method can also ensure no interference in the machining and guarantee the smoothness of the tool orientation.The rest of this paper is organized below. In This paper introduces the tool orientation generation method using a 5-axis CNC machine tool with a BC double turntable structure. The machine contains three translational axes  and two rotational axes (B and C), as shown in The spatial position of the tool is determined by the cutter location data (CL Data), which contains the cutting tool location  local inclination angle  angle ω . Based oIn When the workpiece is fixed on the machine table, the Combining Equations (2) and (3), the relationship between the tool orientation and the rotational angle of the machine rotational axis can be represented as:CC point, the rotational angle of the machine rotational axis can be obtained by Equation (4), as shown in Thus, based on the local inclination and local tilt angles at any CC point and guarantee that the tool orientation meets the basic requirements of tool path planning [In multi-axis CNC machining, the linkages between the axes are flexible, making interference problems easier to occur between the tool and the workpiece. Interference problems can affect the machining quality of the workpiece, scrap the part, seriously damage the machine spindle, or even cause problems such as machine scrapping. Thus, in five-axis CNC machining, it is necessary to avoid interference between the tool and the machined surface . To obtaplanning .CC point and parallel to CC point; when the condition CC point.As shown in Analyzing Since CC point, if local interference occurs, it is necessary to adjust the tool orientation to eliminate the interference and make it fall within the feasible area. The feasible area of tool orientation contains numerous options, and the process of adjusting the tool orientation is described below.When machining the CC point. For the convenience of calculation, take CC point, which is referred to as the potential interference-free tool orientation and denoted as The initial tool orientation The potential tool orientation with the shortest distance CC point. As illustrated in CC point, and the normal distance corresponding to each sampling point can be calculated. The sampling points corresponding to The machining strip width can be obtained by intersecting the scallop surface with the tool in the plane CC point is denoted as Observing in the negative direction of The tool orientation affects the machining strip width. With the above machining strip width calculation method, the effect of tool orientation on it can be easily calculated. As illustrated in CC point differs. Therefore, even if the tool orientation remains unchanged, it still leads to changes in From a geometric perspective, a larger machining strip width corresponds to a higher material removal rate. However, when the machined surface is a freeform surface, the curvature of each  quality . TherefoCC point. By changing the tool orientation, it is expected that the machining strip width at any CC point will converge to the expected machining strip width CC point on the plane CC point during processing, it is preferable to select the tool orientation of To maintain a uniform machining strip width, it is necessary to adjust the tool orientation at each CC point, principal direction, and principal curvature. The expression of the approximate surface of the scallop in the local coordinate system After using a bull-nose tool for five-axis CNC machining, a specific surface topography will be exhibited on the surface of the workpiece. From a geometric perspective, the surface topography is related to the step distance The profile method is an important method for evaluating surface topography and has been widely used. As an essential characteristic of surface topography, roughness irection . The evaRoughness The line Input the workpiece surface, tool parameters, and CL data.Calculate the discrete point Calculate the intersection point Calculate the intersection point between Repeat steps (c) and (d) for each scallop to obtain the minimum distance Repeat steps (b) to (e), for each discrete point The steps to calculate the 2D real profile are as follows:After the real and nominal profiles are obtained, the roughness of the workpiece can be calculated based on the difference between the two. The tool orientation significantly affects the roughness CC point is smaller than the design requirements. As illustrated in In the machining process, the roughness The multi-scale tool orientation generation method aims to generate tool orientations that satisfy both the macro-scale machining strip width constraint and the micro-scale roughness constraint.The tool orientation is nonlinear during the conversion between the workpiece coordinate system  machine . Poor toCC path is a continuous curve on the surface of the workpiece, as denoted as CC point on the CC path is denoted as The CC points. That is, the rotational axis is considered smooth if the sum of the squares of the angular velocities at all CC points is minimized, i.e.,The angular velocity of the rotational axis is an important parameter. To constrain the angular velocity to achieve a smooth rotational axis and to facilitate the calculation, the angular velocity is approximated by using the numerical differentiation method as follows:The least-square (LS) objective function shown in (20) can be obtained by substituting Equations (17) and (18) into Equation (19), which minimizes the angular velocity of the rotation axis by adjusting the control coefficient The necessary condition for the minimum of the LS objective function is At the start and end of each tool path, the tool orientation is given. Meanwhile, the first and last control coefficient CC points are found to have local interference or the machining strip width does not meet the expectation, their corresponding tool orientations should be corrected according to the adjustment method in the previous section and set to fixed values. Suppose there are CC points and their fixed tool orientations are Bredies, other constraints need to be added to the above set of equations. For instance, if some Substituting Combining Equations (22) and (24), a set of linear equations can be obtained with the control coefficient CC path, and roughness requirements, and the output is the NC program (including CL and tool orientation) that meets the roughness requirements on the micro-scale and has uniform machining strip widths on the macro-scale.The implementation of the multi-scale tool orientation generation method proposed in this paper is shown in Specifically, the generation method requires iterative calculation, which mainly includes the following four steps:CC paths to be planned CC paths can be conducted.Before planning the tool orientation, some preparation work needs to be performed: first, find the evaluation length Step 1: Specify the constraints for the tool orientation.Step 2: According to Equation (26), calculate the smooth angle of the rotational axis CC point in CC points to the constraints, and then execute steps 2 and 3 again until the tool orientations that satisfy the expectation of no local interference and machining strip width are generated.Step 3: According to the formula in CC path is completed, the calculation of the next CC path is conducted until the tool orientations of CC paths are all planned.When the planning of the tool orientation of one CC paths is calculated to determine whether the roughness meets the design requirements. If the roughness does not meet the requirement, adjust the tool orientation according to CC points to the tool orientation constraint of the CC paths, and then execute steps (1) to (3) again until the tool orientations that meet the roughness requirements are generated.Step 4: According to the roughness calculation method in CC point. Meanwhile, it can ensure that the cutting bandwidth at the machining strip widths on the macro-scale is uniform and the roughness requirements on the micro-scale are met. Additionally, this method can ensure the smoothness of the rotational axis. During the machining process, kinematic singularities occur when the tool orientation passes through singular points, causing the rotation axis to move over a large range in a short period of time [The multi-scale tool orientation generation method proposed in this paper can ensure that no local interference occurs at any  of time . ConsequCC paths with CC points is, CC points are planned. The workpiece roughness requirement is To verify the effectiveness of the proposed multi-scale tool orientation generation method, it was applied to the machining of a free-form surface. The iso-parametric method is employed to generate In this experiment, a 5-axis CNC machine tool with a BC double turntable structure  was employed to machine the workpiece. The material used in the experiment was 2Cr13. Meanwhile, a 4-tooth bull-nose tool with a radius © 5-axis measurement system. The experimental equipment comprised a Renishaw Agility 5-axis measurement system outfitted with an SFM-C3 surface finish module, as depicted in After machining, the roughness of the workpiece was measured at 90 different locations evenly distributed on the surface with the Renishaw REVOIn the machining process, the minimum and maximum machining strip widths of the tool orientation generated by the Sturz method are, respectively In contrast, the minimum and maximum machining strip widths of the tool orientation generated by the multi-scale method are, respectively Therefore, it can be concluded that the proposed multi-scale method can obtain the tool orientation that meets the requirements of the macro-scale and micro-scale.(1)The method is proposed to calculate the machining strip width of a free-form surface machined by a bull-nose tool, and the influence of the tool orientation on the machining strip width is analyzed. Meanwhile, to solve the problem that frequent changes in machining strip width reduce machining quality, a tool orientation adjustment method is proposed to maintain the machining strip width uniform in the machining process.(2)The simulation model of the real profile of a free-form surface machined by a bull-nose tool is established, and the roughness is calculated based on this. Additionally, the influence of tool orientation on roughness is analyzed, and a tool orientation adjustment method is proposed to ensure that the roughness meets the design requirements.(3)Based on the above models, a multi-scale tool orientation generation method is proposed that can ensure no local interference at any CC point and meet the requirements for machining strip width on a macro-scale and roughness on a micro-scale. Additionally, the proposed method can ensure the minimum angular velocity of the rotational axis.(4)The experimental results indicate that the multi-scale method proposed in this paper is effective. It is experimentally verified that the tool orientation generated by the method can not only meet the requirement for machining strip widths but also ensure roughness, i.e., satisfy both macro-scale and micro-scale requirements.In five-axis CNC machining, the machining quality of the workpiece is closely related to tool orientation. An appropriate tool orientation can help to avoid interference, keep the machining strip width uniform, control the roughness, etc. In this paper, by considering the influence of both machining strip width in the macro-scale and roughness in the micro-scale, a multi-scale tool orientation generation method is proposed for 5-axis CNC machining of bull-nose tools, which can ensure no interference and smoothness of the rotational axis during machining. Based on the conducted analyses and the obtained findings, the following conclusions can be drawn:This demonstrates that the method proposed in this paper has a wide prospect and potential for practical applications and can provide an effective solution for the industry.


Cohesive and adhesive bindings degrade during operation and maintenance even if contacting materials in a manufactured laminated structure are perfectly matched at the interfaces. Two modelling approaches for describing partially closed delaminations or imperfect contact zones, which often occurs at the interfaces, are examined and considered. To confirm the adequateness of the applicability of the effective spring boundary conditions for guided wave scattering by a finite length delamination, guided wave propagation through a damaged zone with a distribution of micro-cracks is compared with an equivalent cohesive zone model, where the spring stiffnesses for the effective boundary conditions are calculated using the properties of the considered crack distribution. Two kinds of local interfacial decohesion zones with an imperfect contact at the interfaces are considered: uniform partially closed delaminations and bridged cracks. The possibility of the employment of the effective spring boundary conditions to substitute a distribution of micro-cracks is analysed and discussed. Two algorithms of generation of a distribution of open micro-cracks providing characteristics equivalent to the effective boundary conditions are presented and examined. The influence of the characteristics of a delamination on wave characteristics  is investigated for several kinds of partially closed delaminations. Multi-layered laminate composite materials are now widely employed in automobiles, marine vehicles, aircraft and other manufacturing industries since they have superior strength, toughness, ductility and fatigue lifetime, which improve the reliability and the durability of structures ,2. Even Simulation of elastic wave propagation through a fractured zone is a time-consuming and challenging procedure since it must take into account the influence of all the inhomogeneities. This problem can be solved by developing efficient improved numerical methods  ,54, the This section consists of three parts. First, two approaches applied here to model partially delaminated zones are discussed in detail: distribution of open micro-cracks and the EBSCs. The latter includes mathematical formulation of the corresponding boundary conditions and terms used. Next, the aspects of the simulation of two classes of delamination  for the two approaches are explained. Finally, two algorithms of generation of a distribution of open micro-cracks providing characteristics equivalent to the ESBCs are described. The introduced models are examined and compared in Following Perelmuter , two kinThe two approaches to model two kinds of delaminations (bridged cracks and imperfect interfaces) are examined here, see H. Materials of the elastic layers of thicknesses In this study, a plain-strain problem for a laminate with a finite length part of an interface being damaged is considered. For simplicity, let us consider wave motion in a two-layered elastic waveguide arts see : two briFor the first kind of delamination, which is partially closed delamination, an imperfect interface is assumed in all domain tiffness .M intervals of lengths C for the damaged area The first approach for modelling a damaged zone evaluates the damage as a distribution of cracks. In this case, the damaged area The EBSCs in the form  can be ure equal , i.e., κStiffness value C is also assumed to be a constant value. By constant density, we also mean the condition that in any chosen finite domain at the interface, the ratio of the cumulative damaged zone to the domain considered is independent of the particular domain chosen. As a result, the stiffness value C, material properties  in  is a conC depends on the spatial coordinate If some presuppositions for the crack distribution are used, then it makes sense to assume that the crack density fness in  depends tigation :(4)κ(x1)Employing representation , the stiHere, we consider two functional relationships relmuter , Perelmurelmuter , who protiffness  near craHere, An example of the variation of the spring stiffness C is assumed. In other words, the appearance of a micro-crack is equiprobable at any point in M sample points C is constant, the lengths of micro-cracks To simulate a partially closed delamination using crack distribution, an algorithm for the generation of the parameters of open micro-cracks Then the coordinates for crack tips of the cracks C. For all cases, 81 micro-cracks have been generated in the damaged area The Kolmogorov–Smirnov test shows that the crack widths An example illustrating how crack lengths are distributed is shown in Here, The routine Further, the damaged zone rding to . To veriThe bridged crack considered in the present study includes a single central macro-crack dominating over micro-cracks, which are defined using an algorithm analogous to the one described in milar to , but witfunctionC(x1)=f acting as an actuator and as a sensor. Rectangular PWATs mounted at the upper surface of the waveguide occupy, respectively, domains ther see . The PWAFor time-harmonic motion with the angular frequency ntial ϕ^ :(13)C^ijAt the side boundaries At the lower surfaces of the PWATs A given voltage The unknown electric potential The aim of this study is to compare the wave propagation characteristics estimated using two different approaches for modelling the interface damaged zone. Therefore, the results of the numerical analysis of the wave motion of a damaged multi-layered laminate, the geometry of which is depicted in the SAHA  and the For the numerics below, the damaged zone of total length C was first chosen to generate a crack distribution. Then, values C. The value denoted Since two approaches to modelling a partially closed delamination are employed, some parameters for boundary conditions  or 4) m m4) mustM open micro-cracks of length At first, let us consider wave scattering by a uniform partially closed delamination modelled using the ESBCs with a constant crack density in the damaged part of the interface rding to .f for a uniform partially closed delamination of length C are compared with eigenforms for damage modelled via the ESBCs. The eigenfrequencies and eigenforms calculated for a random distribution and for the ESBCs are in better agreement with each other compared to a periodic array. It should also be noted that the second eigenfrequency for The analysis of eigenfrequency values given in Eriksson  for partng EBSCs , real paC. Moreover, voltage measured in a laminate without damage is exhibited as a thick solid line. At low frequencies below 100 kHz, the measured voltage is almost the same for all kinds of damage. In the frequency range C and the frequency f.The stiffness influence is investigated considering Lamb wave transmission sensed by the PWAT behind the damaged zone, i.e., voltage To analyse the influence of adhesion or bridged zones near the crack tips for bridged cracks, eigenfrequencies of delamination modelled via relations  and 11)11) were Sensor voltage The cohesive and adhesive bindings degrade during operation and maintenance, even if contacting materials in a manufactured laminated structure are perfectly matched at the interfaces. Therefore, the analysis of the dynamic behavior of partially damaged interfaces between elastic materials is of significant importance, especially for damage identification in composite materials and bonded joints using ultrasonic waves . The conIn this paper, it is demonstrated that the effective spring boundary conditions proposed by Baik and Thompson  and specThe authors suppose further extension of the techniques and approaches developed in this investigation. To reduce the computational costs, an effective model is proposed and validated here for in-plane problems, but the approaches can be applied and developed for the three-dimensional problems employing relations for spring stiffnesses derived by Lekesiz et al. , Golub aIn addition, the EBSCs and can be employed for modelling partially closed delaminations in carbon fibre reinforced polymer composites made of anisotropic/orthotropic layers, which have increasingly become the material of choice for design of the main load carrying components in advanced structures over recent decades. An experimental validation of the theoretical results presented in this study could be provided using the fabrication techniques employed in ,69 to ma


Additive manufacturing technology overcomes the limitations imposed by traditional manufacturing techniques, such as fixtures, tools, and molds, thereby enabling a high degree of design freedom for parts and attracting significant attention. Combined with subtractive manufacturing technology, additive and subtractive hybrid manufacturing (ASHM) has the potential to enhance surface quality and machining accuracy. This paper proposes a method for simulating the additive and subtractive manufacturing process, enabling accurate deformation prediction during processing. The relationship between stress distribution and thermal stress deformation of thin-walled 316L stainless steel parts prepared by Laser Metal Deposition (LMD) was investigated using linear scanning with a laser displacement sensor and finite element simulation. The changes in stress and deformation of these thin-walled parts after milling were also examined. Firstly, 316L stainless steel box-shaped thin-walled parts were fabricated using additive manufacturing, and the profile information was measured using a Micro Laser Displacement Sensor. Then, finite element software was employed to simulate the stress and deformation of the box-shaped thin-walled part during the additive manufacturing process. The experiments mentioned were conducted to validate the finite element model. Finally, based on the simulation of the box-shaped part, a simulation prediction was made for the box-shaped thin-walled parts produced by two-stage additive and subtractive manufacturing. The results show that the deformation tendency of outward twisting and expanding occurs in the additive process to the box-shaped thin-walled part, and the deformation increases gradually with the increase of the height. Meanwhile, the milling process is significant for improving the surface quality and dimensional accuracy of the additive parts. The research process and results of the thesis have laid the foundation for further research on the influence of subtractive process parameters on the surface quality of 316L stainless steel additive parts and subsequent additive and subtractive hybrid manufacturing of complex parts. It is widely used to manufacture precision equipment, such as aviation engine parts, and transportation and electronic communication parts . Thin-waDue to its advantages in manufacturing complex geometries and reducing material waste, AM has been applied in many fields . HoweverAdditive/Subtractive Hybrid Manufacturing (ASHM) is an emerging manufacturing technology that combines the advantages of Additive Manufacturing (AM) and traditional Subtractive Manufacturing (SM) ,15. ThisHybrid-layered manufacturing refers to the alternating use of additive manufacturing and subtractive machining without changing the workpiece’s position, fixture, or reference surface, thereby reducing machining errors caused by repeated positioning. Its advantages are particularly evident in processing thin-walled parts with complex curved surfaces, internal structures, and enclosed cavities. Processing thin-walled parts with complex curved surfaces and internal structures poses significant challenges for traditional machining methods. However, hybrid-layered manufacturing technology optimizes the benefits of additive and subtractive manufacturing by initially milling the inner cavity of the part, followed by a second additive manufacturing step. This approach circumvents tool–workpiece interference and addresses the issue of inaccessible cavity regions during machining; therefore, hybrid-layered manufacturing technology is considered an efficient and precise machining method that can greatly improve production efficiency and reduce costs.p), scanning speeds (v), and laser scanning paths were used in the experiments. The results showed that the depth and width of the additive melt pool were significantly affected by Yang et al.  conducteg et al.  also useg et al.  systematg et al.  conducteg et al.  conducteIn 2018, Lockheed Martin used electron beam additive and subtractive manufacturing technology to produce the largest 3D-printed space component to date—a satellite fuel tank. Utilizing this process, the component achieved over 80% reduction in material waste and reduced the overall delivery time from two years to three months. The part underwent rigorous quality testing, enabling it to withstand the harsh demands of launch and perform reliably in the vacuum of space for several decades. Currently, this component is being utilized as a standard part of the LM 2100 satellite platform.DMG MORI’s unique hybrid  machining solution is a remarkable technology that integrates milling techniques with laser metal deposition processes. It is applied on a laser deposition machine tool that possesses complete milling capabilities. In May 2019, Virgin Orbit, a satellite launch company, utilized DMG MORI’s additive and subtractive integrated equipment to 3D print engine combustion chambers for NASA. The interior lining of the chambers was made of GRCop-84 copper alloy, while the exterior was composed of nickel-based high-temperature alloy. The structure and materials were identical to traditional designs, but the manufacturing time was reduced by several months.The study of the additive and subtractive hybrid manufacturing process with alternating increments and reductions is difficult and complex. Currently, most research focuses on the post-additive/subtractive manufacturing process, where the material is first added and then subtracted. In alternating between additive and subtractive manufacturing, it is essential to consider not only the impact of these processes on part quality but also factors such as thermal cutting, the timing of additive and subtractive steps, and temperature distribution across additively manufactured parts during cutting. Currently, there is a relative lack of research in this area, thus necessitating an investigation into the process of alternating additive and subtractive manufacturing.In this study, we investigate the utilization of additive and subtractive manufacturing tools to evaluate the additive and subtractive processes for thin-walled box components along two distinct paths. The experimental process and resulting data were acquired through a laser displacement sensor, which effectively characterized the deformation patterns exhibited by the box-shaped thin-walled part during additive/subtractive processing with different paths, thereby elucidating the underlying causes for deformation patterns.In this article, the deposition manufacturing of a thin-walled part is carried out on a rectangular substrate. First, the laser beam generates a melt pool on the substrate surface, and then the metal powder is sprayed into the melt pool through a powder feeder, forming the first layer. As the laser beam scans layer by layer, the melt pool gradually moves upward. The powder is sprayed into the melt pool and gradually melts, forming a new melt pool. In this new melt pool, the laser beam continues to scan and melt the powder, thus adding material layer by layer. After depositing 20 layers, the surface of the additive manufacturing part is milled to improve the surface quality. The above operations are repeated until the box-shaped thin-walled part is completed. The schematic diagram of the part-forming process is shown in During the laser additive manufacturing process, the melted metal powder is layered and deposited on the substrate as the high-energy laser beam moves back and forth. This process involves melting and solidifying the metal material, transforming the metallographic structure, etc. For isotropic materials, the heat transfer behaviors, such as conduction, convection, and thermal radiation among the melt pool, cladding layer, substrate, and the surrounding air, can be described by the heat transfer differential equations.The thermal boundary conditions in the additive process include the laser heat source, the convection of the cladding layer in contact with the air, and the thermal radiation boundary. A two-dimensional Gaussian heat source is used to describe the laser energy distribution heat source, and the maximum heat flow density at the center of the laser spot is:The convective heat transfer between a flowing fluid and a solid is proportional to its temperature difference and can be expressed by the following equation:The LMD stress and deformation simulation is based on the numerical simulation results of the temperature field. By applying boundary conditions in static analysis, the software can read the temperature history of all nodes and calculate the resulting stress and deformation of the model.Currently, the stress distribution in laser additive manufacturing is usually analyzed based on the theory of thermo-elasto-plasticity. In the stress–strain relationship of thermo-elasto-plastic mechanics, a term of strain caused by temperature change is added while considering the effect of temperature on yield stress, etc. Given that the stress changes in the LMD process are very complex, it is necessary to perform reasonable and moderate simplification when conducting thermo-elasto-plastic analysis. It is usually based on the assumptions that (1) the yield criterion for metallic materials is based on the Von–Mises criterion, and (2) the flow criterion and the hardening criterion are satisfied when the metallic material is in the plastic region.According to the Von–Mises criterion, the component undergoes yielding when the equivalent stress exceeds the yield stress.The flow criterion defines the magnitude and direction of the plastic strain components when the material undergoes plastic deformation. Its differential equation is as follows:The hardening criterion is used to describe the variations in the yield surface. In this model, known as the kinematic hardening model, the center of the yield surface moves along the yielding direction in stress space, while the size and shape of the yield surface remain unchanged, as shown in The thermo-elasto-plastic equation is as follows:(1)Stress–strain relationshipThe equation for the stress–strain relationship when the material is in a thermo-elasto-plastic state is as follows:In the elastic region:In the plastic region, it is assumed that the yield condition of the material is:According to the plastic flow rule, the plastic strain increment The loading or unloading of the plastic region is judged by (2)Equilibrium equationFor a numerical model unit of laser cladding, the following equilibrium equation holds:Based on the unit being in an elastic or plastic state, Considering that there is generally no external force in the laser additive remanufacturing process, the corresponding nodal forces of the unit around each node are self-equalizing force systems, i.e., In CNC milling, most energy expended during chip deformation is transformed into thermal energy. With an increased cutting speed, there is a corresponding increase in heat generation, thereby significantly affecting machining deformations . The temThe deformation model of a workpiece includes two parts: deformation caused by thermal stress and deformation caused by the interaction between the cutting tool and the workpiece. During the additive manufacturing process, due to the high temperature gradient and rapid heating–cooling process, thermal expansion and contraction cause materials to undergo uneven plastic deformation under constraints, generating high residual stress. During the subtractive manufacturing process, on the one hand, the residual stress generated during the additive manufacturing stage will redistribute as materials are removed, resulting in the deformation of the material; on the other hand, due to the thin wall thickness and poor stiffness of the part, deformation occurs under the cutting force of the cutting tool and the workpiece, causing the material removal amount to not reach the theoretical value and resulting in machining errors due to material rebound after processing. These two effects interact with each other, ultimately leading to part deformation.−6 (can be defined as needed). The mass, specific heat, and strain of the “dead” elements are all set to zero, and their mass and energy will not be included in the solution results.The “birth–death element” technique is a commonly used numerical simulation method in additive manufacturing, which simulates the molted and to-be-molted parts of the additive process through the “birth” and “death” of the elements. In ANSYS, “dead” elements are not simply removed elements but rather have their stiffness matrix multiplied by a very small factor, which the program defaults to 1 × 10In the simulation process, the “birth–death element” technique is first used to simulate the additive process, and the material’s morphology after processing is obtained through thermal stress simulation. In the subtractive stage, three-dimensional cutting forces are applied to the mesh positions, causing deformation of the thin-walled part. Material is removed by selecting the coordinate values in the y direction and killing the corresponding elements. After killing, the solution is obtained, and the stress is redistributed, resulting in the final deformation result of the workpiece. The schematic diagram of the milling of thin-walled parts is shown in The laser deposition path design is crucial in the additive and subtractive manufacturing of box-shaped thin-walled parts. It impacts the surface deformation of the formed part and its processing efficiency. Consequently, minimizing surface deformation while reducing the laser head’s empty walking time is essential to ensure optimal processing efficiency. The deposition path for box-shaped thin-walled parts has multiple right-angle turning points that the laser head must traverse multiple times during the same layer’s deposition process.This can lead to deformation accumulation at the intersection position, resulting in a higher forming height at the right-angle turning point than other positions when the additive height reaches a certain level. Therefore, it is necessary to avoid redundant deposition of the box-shaped deposition path on the same layer as much as possible. However, not producing repeated deposition will increase the laser deposition head’s empty walking time, which can negatively affect the part’s processing efficiency. Additionally, discontinuous processing requires multiple repeated positioning, which can cause unnecessary processing errors. Therefore, VERICUT 9.0.1 software is used to simulate the deposition path of additive manufacturing to seek a deposition path with high forming accuracy and processing efficiency.Several different processing paths have been designed to address the processing issues of thin-walled box-shaped parts, as illustrated in VERICUT simulation was performed on the G-codes of Path 1 and 2, respectively, and the processing efficiency was compared. From the simulation results of VERICUT, it is clear that the same shape of the workpiece can be obtained after the subtractive processing regardless of the deposition method of the path, but there is a big difference in the time required for the processing. Since the machining process is slow, the machining time of different paths was counted using the same process and the same resultant animation playback factor (50× speed), as shown in The metal powder used in the LMD manufacturing process in this paper is 316L stainless steel (GB standard name: 022Cr17Ni12Mo2). The geometry of the powder particles is a spherical shape, and the main chemical components are C, Si, Mn, Cr, Ni, Mo, and Fe. The particle size ranges from 75 to 150 μm, and the powder has good flowability and thermal processing properties. The chemical composition of the powder is shown in The thermal physical parameters of 316L stainless steel at different temperatures are shown in The additive and subtractive hybrid equipment is a modified additive and subtractive processing machine formed by adding an additive manufacturing system and related auxiliary systems to an existing machine tool.In the experimental system, the laser emitter is a YLS-2000 fiber laser produced by IPG, with a maximum output power of 2000 W. The laser has advantages, such as high beam quality and high energy utilization, making it suitable for laser-cladding-forming experiments. The powder feeder is an RC-PG-FD dual-barrel powder feeder produced by Nanjing Zhongke Yuchen, which delivers a stable powder flow, precise powder delivery, low noise and vibration, and a size range of 45–149 µm for conveying metal powder. The powder delivery rate can be controlled by setting the rotation speed of the powder delivery disk during processing operations, and metal powder can be continuously and stably delivered to the laser cladding head under reasonable carrier gas flow rate parameters. The YC52 coaxial powder feeding laser cladding head produced by German company PRECITEC has a compact and sturdy structure suitable for fiber lasers with high output power. The laser cladding head is equipped with a ring-shaped nozzle, which can accurately converge the metal powder flow within the focal point of the laser beam to achieve negative defocusing and improve the quality and efficiency of laser additive manufacturing.In the additive and subtractive hybrid manufacturing detection process, a high-precision HG-C1030 laser displacement sensor produced by Panasonic Corporation of Japan was used to detect the surface deformation of the formed parts during the hybrid manufacturing process. The measurement range is ±5 mm, with a measurement center distance of 30 mm and an accuracy of 10 μm.An additive and subtractive manufacturing process experiment was conducted on the box-shaped thin-walled part with the process parameters shown in To address the box deposition problem, a box additive manufacturing experiment was conducted with a side length of 50 mm and 20 layers deposited. A laser displacement sensor was used to measure the surface deformation of the box-shaped thin-walled part produced using Path 1. The lateral deformation data at heights of 2 mm, 5 mm, and 8 mm on one side of the part were extracted, as shown in The indirect coupling field analysis method is utilized to conduct nonlinear transient thermal analysis, followed by stress analysis based on the thermal analysis results. Sequential coupling can be alternately performed between different physical fields until convergence to a desired level of accuracy is achieved. Solid70 and Solid185 elements are used in the study. Solid70 is a low-order element consisting of eight nodes with heat transfer capability in all three directions and is utilized for thermal analysis. Solid185 is a relatively high-order solid element, with eight nodes in each element with three degrees of freedom each. It possesses the ability of hyperelasticity, stress hardening, and large deformation and can be used as a stress analysis element after temperature analysis.As additive manufacturing involves a process of continuous deposition, the birth–death element technique commonly used in simulations currently has discontinuities. To achieve better simulation results for this process, it is necessary to use a small enough mesh size and time step. However, a small element size and a large number of time steps can result in a huge computational cost. Therefore, the mesh size of this study’s additive manufacturing simulation elements is set to be less than 1 mm. Additionally, an interpolation method is utilized to read the result files to ensure the effectiveness of the simulation without exceeding the expected computational scale.ANSYS provides a command to read the temperature field as a load, dividing the temperature field simulation into multiple segments. Only the area near the processing zone is refined for meshing during each segment simulation, while the mesh size in other areas can be adjusted appropriately. The temperature distribution at the end of the last simulation is read and used as the initial temperature field for the next simulation, ensuring the continuity of the temperature simulation. In additive manufacturing simulations, the 2D Gaussian heat source is a heat source model that closely approximates the actual laser energy distribution. In this study, the maximum heat flux density at the center of the laser spot is given by Equation (2).Therefore, the maximum volumetric heat generation rate is given by:Combined with the Gaussian function, the volumetric heat generation rate is distributed in a Gaussian shape within the element, so the Gaussian heat source used in the numerical simulation is defined as Equation (3) above.A universal fixture on a CNC machine is used to fix the substrate during the deposition process to prevent the workpiece’s high-temperature oxidation from affecting the performance of the formed parts. The laser head has a protective gas to spray onto the deposition area. For ANSYS numerical simulation, different heat dissipation boundary conditions are set for each part. To simplify the model, the fixture is not included. The area near the laser head experiences high temperatures due to the forced convection of gas and heat radiation exchange. Therefore, the heat radiation coefficient is relatively large in this region. Additionally, the gas convection intensity is highest near the laser melting head. Parts farther away from the laser head experience lower temperatures as gas convection intensity decreases with increasing distance, resulting in lower heat radiation intensity. Finally, the substrate’s bottom and two ends are furthest from the laser head, resulting in natural convection dominating these areas with a convective coefficient typically around 20.For the part, the internal thermal conductivity coefficient is determined by the material properties, while the heat radiation and forced convection are based on the convective function related to the number of additive layers, as shown in Equation (18):Due to the simplicity of the geometry model, the geometric modeling of the box-shaped thin-walled part and the deposition substrate was directly carried out in the ANSYS 19.2 classic interface Mechanical APDL, as shown in The closer the box is to the laser head, the greater the heat dissipation coefficient, which is mainly from thermal radiation and convection. On the other hand, the heat dissipation of the part farther away from the laser head and closer to the substrate is mainly through thermal conduction and convection. Therefore, the heat dissipation coefficient in different areas is also different. It should be noted that because the surface inside the box is in a relatively closed space, the heat dissipation effect of the outer surface of the box is better than that of the inner surface during the deposition process of the box. Numerical simulations of additive manufacturing with different deposition paths are conducted to find the temperature and deformation distribution law, select the optimal path, and predict the stress and deformation.(1)Path 1As shown in When the laser scans the arc area at a constant speed, it can be seen that the temperature is 2004 °C. When the next layer is deposited, the laser continuously scans at the other end adjacent to the arc; the temperature of the molten pool is 2014 °C. Although the temperature has increased slightly compared to the arc area, the difference is relatively small. This is because the laser continuously scans and there is no deceleration, so the temperature is relatively stable.(2)Path 2As illustrated in Based on the above analysis, it is apparent that for Path 1, the heat deposition effect caused by the laser start–stop is almost non-existent due to continuous processing. Therefore, further simulation of 20 deposition layers was carried out for Path 1. To better illustrate the temperature changes during the entire processing process, the highest temperature at each moment was extracted from the simulation to draw a temperature–time curve, as shown in In addition, the curve illustrates that there is a certain temperature rise during interlayer processing. This is due to the absence of cooling time after the previous layer, resulting in heat accumulation and temperature rise during the next layer processing. However, this temperature accumulation is much smaller than the temperature accumulation at the starting point of other paths. These phenomena are consistent with the temperature field described above. Overall, the additive molten pool temperature of the box-shaped thin-walled part is relatively regular, and the highest temperature at most moments is stable at around 2000 °C. The periodic temperature changes can also predict the distribution of stress and deformation to a certain extent.The stress distribution of Path 2 is shown in In the above study, path planning of the box-shaped thin-walled part, machine tool motion simulation, and additive manufacturing simulation of the box-shaped thin-walled part were conducted. It was found that the first path planning had the best effect on the box-shaped additive forming, and the finite element model of the box-shaped part was validated through a first-stage additive and subtractive hybrid manufacturing experiment, demonstrating the effectiveness of the box-shaped finite element model. Therefore, based on the above box-shaped simulation, a simulation prediction of the two-stage additive and subtractive hybrid manufacturing of the box-shaped thin-walled part was carried out. The residual stress and deformation distribution (enlarged by 10 times) of the second box-shaped thin-walled part is presented in The maximum residual stress after the second stage of additive manufacturing is 431 MPa, which is slightly higher than the first stage. In addition, from the stress distribution, the second stage of additive manufacturing heated the first stage part and changed its stress state, reducing the maximum residual stress of the first stage. Regarding deformation, the box-shaped thin-walled part collapses downward in the arc additive manufacturing area in the second stage, with some concave deformations on the four sides. The deformation is more pronounced near the arc, with a maximum deformation of 0.63 mm.To provide a more intuitive representation of the deformation of the four sides of the box-shaped thin-walled part, a schematic diagram of data extraction for the box-shaped thin-walled part is presented in Based on the deformation data of the four sides, it can be seen that the four sides of the box-shaped thin-walled part show a trend of increasing deformation with the increase of deposition height. This indicates that the second section of the additive part also exhibits a similar pattern to the first section, where the higher the deposition height, the more the box-shaped part bends outward. This may be due to the fact that the higher the deposition height, the greater the cumulative temperature and the corresponding increase in thermal stress. This occurs in the inner surface, wherein the higher the deposition height, the more the box-shaped part bends outward. Thin-walled parts are in a relatively closed space, so the higher the deposition height of the outer surface, the more outward bending of the box shape; it has better heat dissipation than the inner surface. This causes the outer surface to contract faster, causing the thin-walled part to twist outward as the deposition height increases.In addition, the surface deformation data after milling was extracted from four faces at a height of 5 mm. The box line diagram plotted in This paper used the additive and subtractive hybrid manufacturing machine tool to carry out the additive and subtractive hybrid manufacturing process experiment of the box-shaped thin-walled parts of 316L stainless steel, collected the relevant experimental data, and used ANSYS 19.2 software to establish the thermal–mechanical finite element model of additive and subtractive manufacturing; the temperature change of the additive process and the deformation of the formed parts were numerically simulated, finishing the summary of the experiment and simulation results of this paper. The following conclusions were obtained:(1) According to the LMD process simulation theory, a simulation model for additive manufacturing of box-shaped thin-walled structures was established, predicting the temperature field, stress, and deformation of box-shaped thin-walled structures after laser additive manufacturing. The experimental results were generally consistent with the simulation prediction trend, with a difference of 0.025 mm in the predicted maximum deformation.(2) Using this model, simulation predictions were conducted for a box-shaped thin-walled structure with two segments of additive and subtractive manufacturing. For the temperature field, a point on the outer surface of the thin-walled part was selected, and the time–temperature profile of the point was obtained. The temperature increase process had a gradually increasing peak before the arrival of the laser heat source. After the arrival of the heat source, the temperature peak decreases, and the temperature fluctuation gradually stabilizes. The temperature drop curve approximates one of the inverse proportional function curves.(3) For stress and deformation, the second segment’s processing caused the first segment’s workpiece to be heated and change its stress state, reducing the maximum residual stress of the first segment. The closer the second segment’s thin-walled structure is to the arc, the greater the deformation, with a maximum deformation of 0.63 mm. At a height of 5 mm, the surface deformation was extracted after milling on all four sides, with a maximum deformation of less than 0.06 mm, which was reduced by more than 90%, indicating that milling improved the surface quality after additive manufacturing.In this paper, a series of experiments were carried out for the alternating hybrid manufacturing of additive and subtractive materials to study the additive and subtractive hybrid manufacturing process of the thin-walled parts of the box, as well as the deformation of the various stages of the law, to obtain some of the important defects affecting the distribution of the residual stress, deformation of the size of the important defects, and to predict the deformation of the thin-walled parts of the box; however, there is still a part of the problem that needs to be solved.Although a finite element model was established for numerical simulation in the study, there are still certain limitations. The model only considers the starting position and low scanning speed during the deposition process without accounting for excessive powder feeding, leading to inadequate control over deformation. Additionally, thermal conditions play a significant role in the simulation, affecting temperature distribution, stress field results, and deformation. While a linear thermal condition was established in this paper, in reality, the thermal conditions at different nodes vary with time. Therefore, a more accurate thermal model can be developed in future research to improve the simulation accuracy.


This paper presents an average treatment effect analysis of Spain’s furlough program during the onset of the COVID-19 pandemic. Using 2020 labour force quarterly microdata, we construct a counterfactual made of comparable nonfurloughed individuals who lost their jobs and apply propensity score matching based on their pretreatment characteristics. Our findings show that the probability of being re-employed in the next quarter significantly increased for the treated (furlough granted group). These results appear robust across models, after testing a wide range of matching specifications that reveal a reemployment probability premium of near 30 percentage points in the group of workers who had been furloughed for a single quarter. Nevertheless, a different time arrangement affected the magnitude of the effect, suggesting that it may decrease with the furlough duration. Thus, an analogous analysis for a longer (two quarter) scheme estimated a still positive but smaller effect, approximately 12 percentage points. Although this finding might alert against long lasting schemes under persistent recessions, this policy still stands as a useful strategy to face essentially transitory adverse shocks. We present a novel contribution that assesses the causal effects of furlough programs usingupdated microdata from the pandemic period in Spain.We found key evidence of a robust and positive average effect (approx. 30 percentage points) offurlough schemes on the probability of being re-employed in the short run.However, this positive effect was time-dependent and lessened when the furlough scheme was extended for two consecutive quarters (down to 12 percentage points). This result suggests effectiveness losses with time and advises against long-lasting schemes. The COVID-19 outbreak caused an unprecedented sanitary crisis worldwide, forcing governments to implement restrictive measures, such as mandatory lockdowns and social distancing. Concerned about a boost in unemployment digits, most countries devised portfolios of coronavirus job retention schemes as a way to temporarily protect employees’ positions while the labour market was adjusting to the shock. Although we can find differences in the eligibility requirements, the degree of coverage, and the duration, these national temporary workforce reduction programs share a considerable number of characteristics.In this paper, we assess the furlough program that was intensively used in Spain during the initial phase of the COVID-19 pandemic in 2020. Spanning our sample of individuals in furloughed and their layoff counterparts and applying propensity score matching to estimate the average effect of furlough schemes on subsequent reemployment probabilities, our findings suggest a significant and positive reemployment premium for the furloughed sample. The magnitude of the effect, however, turns out to be highly dependent on scheme duration.The debate about the introduction of some sort of furlough programs as an alternative to layoffs has been discussed from long ago  over the counterfactual. Nonetheless, this effect is attenuated to 12.2 p.p. for two quarters extended schemes. To complete the analysis, we included a battery of robustness checks to test the sensitivity of our benchmark results to model selection issues, proving the stability of these results.The rest of the paper is organized as follows: Sect. In this paper, we evaluate the impacts of the Spanish furlough program, the so-called temporary employment adjustment schemes (ERTEs). Spain is presented as a suitable case study due to the kind of labour adjustment suffered during the previous Great Recession. In this country, labour adjustment has predominantly been extensive, with collective layoffs being the usual. As a result, no euro country, with the exception of Greece, destroyed more jobs than Spain then, which reached an unemployment rate of 26.94% in the first quarter of 2013.art. 47, Estatuto de Trabajadores, 1980), it was only during the pandemic that such a policy tool saw wider application, covering approximately 3 million workers (more than 20% of the affiliated workers) in the second quarter of 2020 , encouraging the use of these schemes and imposing penalties on companies that after being granted, were dismissing employees within the next 6 months. This policy, essentially consists of a temporary suspension of the labour relationship between the employer and the employee, or alternatively, a reduction of working hours, justified by a major cause. This cause must be related to economic, technical, organizational or production issues, including COVID-related consequences from March 2020. During this period of suspension, the employee receives a social security allowance while the employer only has to assume a social contribution, which is a minor part of the employee’s wage that sometimes might be even relieved or discharged. As a result, it works as a transitory mechanism of flexibility to adjust the labour market, whose cost is essentially borne by the public administration.In mid-March 2020, convinced about the transitory nature of the sanitary crisis, the Spanish government quickly entrusted the labour adjustment to fast and wide-coverage COVID-19-related ERTEs  to perform our analysis. This survey is conducted by the National Statistical Institute and is a large household sample survey providing results on labour participation of people aged 16 and over as well as people outside the labour force in which each sampled individual remains in the survey for a period of six quarters at a time, with no resampling after individuals are rotated out of the sample. The survey is targeted at a rotating sample of approximately 60,000 households throughout the national territory. For every household member, both socioeconomic and labour information is collected to summarize the main characteristics of the Spanish workforce each quarter. As mentioned, individuals in the sample are interviewed for six consecutive quarters; thus, we have information on quarterly labour transitions for a maximum period of 18 months for each individual in the sample.As we look for a way to rearrange our data for our initial matching analysis we partly followed the intuition of Izquierdo et al. . First, This final sample I keeps a total number of 4,824 individuals, with 1,629 in the control group and 3,195 being furloughed for a single quarter. In addition, the proportion of furloughed individuals who were re-employed in the next quarter was 76.31%, compared with only 44.51% in the comparison group, as shown in Table We now ask what would happen if we were to aggregate those workers who have been furloughed during both the second and third quarters of 2020 to verify the causal consistency of the impact of the Spanish ERTE on employment in the last quarter of 2020. Hence, the point of this section is to compare the average treatment effect in the previous quarter-to-quarter analysis with an estimate coming from a treatment group that has spent relatively more time being furloughed. We are thus mainly interested in 1) estimating a medium-term effect and 2) establishing a relative comparison in terms of magnitude between the previous and the current exercise. This time, the filtering procedure for the data is analogous. However, now the individuals considered for both the control and treatment groups must necessarily stay in the same situation during the second and third quarters consecutively, as illustrated in Fig. Table Based on the standard potential outcomes framework for causal evaluation, our approach looks for an average treatment effect by using Propensity Score Matching techniques (PSM), developed in the seminal contribution of Rosenbaum and Rubin . PSM useX is our set of controls and D is the assignment to treatment (furlough).Our first assumption will be based on the concept of conditional independence: once a set of observable variables able to capture all possible forms of heterogeneity has been identified and fixed, this identifying assumption implies that the results of the two groups of units (treated and untreated) have the same potential outcome on average in the population, represented in Expression X) to solve the dimensionality problem when matching on a large set of controls. Thus, the propensity score represents the probability that an individual might be part of the furloughed group given the observables X controls selected for the propensity score calculation can be classified into two categories: social demographics and labour conditions. For the social-demographic dimension, we considered a set of standard controls as sex, age, age squared, region (Spanish Autonomous Community level), education (five levels from primary to higher education) and a foreign dummy. On the other hand, the labour economic dimension comprises the 1st quarter industry or economic activity where the individual was employed , combined with 1-digit occupation, type of contract (either temporary or permanent) and the type of working day (either part or full-time).3However, the PSM method uses a propensity score  as the average difference in potential outcomes for the furloughed individuals:z et al. ). AdditiIn this section, we offer an overview of our benchmark results, together with pre- and postestimation checks, illustrating how the average treatment effect on the treated stands out as being statistically significant, favouring the furlough scheme as a means of reemployment. Remember we evaluate the transition from a state of furlough to a state of employment on the quarterly basis of 2020, as explained in the data section, leading to an analogous propensity score matching analysis using both samples described. As previously mentioned, our first preliminary look at the data starts with a simple smoothing baseline approach, pairing each treated individual with the nearest neighbour  of 0.294 for single quarter furloughs and 0.122 for two quarters, which can be interpreted as a premium of 29.4 percentage points (hereafter p.p.) in the probability of being re-employed thanks to the single quarter furlough scheme, and 12.2 p.p. when the scheme lasts for two quarters. These coefficients have been tested significantly different from zero based on both methods considered for estimating the standard errors.These results suggest that the effect on reemployment for two quarter schemes is smaller in magnitude when compared to one quarter duration, which may favour the idea of effectiveness losses in the furloughs schemes when they are extended. Remember that a single quarter scheme had an ATT that was approximately 17 p.p. above the estimated effects for the two-consecutive quarter. Be that as it may, the positive causal effect of furloughs on employment appears to have helped workers in Spain across the whole year, regardless of the duration of the furlough policy.To infer the (joint) validity of the matching procedure, Fig. We used the 2020 quarterly waves of the Spanish Labour Force Survey to collect a sample of workers who were furloughed during the initial phase of the pandemic, together with comparable nonfurloughed individuals who lost their job at that time and joined any source of potential workforce, using the latter to construct the counterfactual. Then, performing propensity score matching techniques, we provide evidence on how the probability of being re-employed was significantly higher in the treated group (furlough granted group) than in the control group, indicating a positive net effect on after-furlough re-employability near 30 percentage points. This result seems consistent with previous findings of Giupponi and Landais (To conclude, intuition tells us that when many jobs were suspended due to lockdown and social distancing measures at the beginning of the pandemic, these short-time work schemes did a great job of preserving the workers’ position while favouring labour market adjustment at the lowest cost for economic agents. Conversely, jobs affected by more structural changes will probably be captured in a furlough program for a long time, wasting public resources and generating deadweight losses while hindering the workforce reallocation process. Therefore, as an implication for policy-making, STW public schemes appear to be once more a very relevant policy tool when labour market stability is the target as long as the shock is expected to be transitory. However, any public choice related to this kind of tool should be considered, keeping in mind that the duration and timing of the manoeuvre is essential for it to reduce social costs and achieve the highest possible effect on re-employability, given the conditions of the labour market in the COVID era. Future research may continue exploring this topic with new data, trying to overcome some of the limitations that we have faced, looking for long-term and dynamic effects, using other identification strategies and identifying some of the heterogeneity sources.


Autonomous driving is a complex task that requires high-level hierarchical reasoning. Various solutions based on hand-crafted rules, multi-modal systems, or end-to-end learning have been proposed over time but are not quite ready to deliver the accuracy and safety necessary for real-world urban autonomous driving. Those methods require expensive hardware for data collection or environmental perception and are sensitive to distribution shifts, making large-scale adoption impractical. We present an approach that solely uses monocular camera inputs to generate valuable data without any supervision. Our main contributions involve a mechanism that can provide steering data annotations starting from unlabeled data alongside a different pipeline that generates path labels in a completely self-supervised manner. Thus, our method represents a natural step towards leveraging the large amounts of available online data ensuring the complexity and the diversity required to learn a robust autonomous driving policy. Driving a vehicle is a difficult task that requires complex reasoning and visual perception. The high level of stochasticity in the environment structure and dynamics leads to an intractable state space for traditional robotics trajectory planning approaches; thus, developing a system that can drive safely and can generalize to a wide variety of environmental setups remains an open problem. In 1989, the proposal of  analyzedIn addition to extremely time-consuming human annotation processes for tasks such as semantic segmentation  or objecPrior work has been focused primarily on the supervised paradigm to learn a driving policy  or path We present two self-supervised methods to label an autonomous driving dataset for steering control and path segmentation. We combined existing work on path labeling, previously conducted in a weakly-supervised manner, using data from the camera, IMU, and LIDAR , with thPropose a heuristic method for estimating the scaling factor of the vehicle ego-motion;Generate steering labels starting from predicted ego-motion estimations made by a network trained in a self-supervised manner;Generate trajectory segmentation labels from the same ego-motion estimations;Train a steering neural network on the generated steering labels and ground truth steering labels and compare the results;Provide a method for improving the steering commands by using the predicted trajectory labels.The main contributions of our work are:Recent research for autonomous driving has been focused primarily on the end-to-end paradigm, after the proposal of and introduction of ALVINN , one of A common approach for learning an end-to-end driving policy is via imitation learning from human expert demonstrations. One of the first successful deployments of a self-driving policy into the real-world environment is presented by , showingRather than learning a single objective, some approaches include secondary tasks to enhance the main motion planning module ,12. SegmBy combining sensor fusion and end-to-end learning, the authors of  replacedIn addition to the supervised learning paradigm, reinforcement learning has been successfully applied in autonomous driving. The authors of  designedOne of the main challenges regarding the learning of steering commands, especially in end-to-end methods is the inability to correctly react to scenarios that are not previously met in the training data and the exponential amount of data needed to be added for every parameter of the environment.The authors of  proposedFollowing a similar principle, the work of  describeFurther work shows different improvements brought to the trajectory segmentation models, including the usage of Bayesian encoder-decoder networks  which caIn off-road environments, terrain segmentation methods can provide valuable input and similar approaches that can be adapted for the path generation task. It has been shown how using image and laser data can be used to generate datasets for the unsupervised learning of traversable area segmentation . AnotherDepth prediction from an RGB image has been a long-standing problem in computer vision. Although many approaches using stereo-vision ,24 existRef.  introducIn addition to providing a correct depth estimation up to scale, previous methods suffer from scale-inconsistent results. Ref.  proposedIn a survey regarding single image depth estimation, ref.  present We selected two publicly available datasets to train and test our models, which comply with the needed requirements for evaluating our methods. First, we must be able to assess the reliability of the steering labeling, therefore a dataset with the ground-truth labels for steering has to be used. Secondly, the evaluation of the path labeling method requires a dataset with available ground truth data for this path or data that can be used to generate the path, such as the ego-motion labels. In this section, we describe the datasets we used for training and evaluating the proposed methods.UPB campus dataset: the UPB campus dataset [ dataset  was collIt contains 408 videos of normal driving, covering a distance of KITTI odometry dataset: the KITTI odometry dataset [ dataset  providesThe frames from this dataset are sampled at 10 FPS and we scaled them to 256 × 832, before cropping 96 pixels from each side to reach a final size of 256 × 640 for the path labeling using the estimated poses and the training of the segmentation neural network.For this dataset, the split contains the sequences 3, 6, 9 and 10 for testing, 4, 11 and 19 for validation and the rest for training. We chose this dataset for training and evaluating our segmentation model against both the path labels generated using the ground truth ego-motion and the path labels obtained with the ego-motion network.In this section, we present the methods we employed for solving the steering labels generation, path labeling, path segmentation, followed by the implementation of the steering network and the improvements we proposed for enhancing the predictions of the network by leveraging the Ackermann steering geometry. We provided a detailed description of the mechanisms for each method, the models’ architecture, and the experimental setup we configured for both training and evaluation. The pipeline starts with the depth and ego-motion prediction network, which is trained on the UPB campus dataset and is followed by the scaling factor estimation, a step that is needed for recovering an accurate description of the motion. The obtained motion prediction is then utilized for two separate annotation tasks: the labeling of the steering and the labeling of the followed path, for each frame. At the end of the section, we also present a method of combining the path labeling into the steering prediction network for improved autonomy results.A conceptual chart of the entire pipeline can be visualized in One disadvantage of monocular depth estimation is that we can only recover the actual depth up to scale. To find the scaling factor automatically, we proposed a heuristic method that uses the position of the acquisition camera. We first transform the pixel coordinates to camera coordinates by the following sequence of operations:y coordinates in the pixel space from a rectangular box corresponding to the road patch in front of the vehicle. Let y coordinate Pt,tWe considered 60 future points which were projected into the current frame using the pose and the camera parameters.Generating hard labels. The hard labels use the initial generated labels and consists of two separate classes. The first class represents the path followed and the second class consists of all the pixels that belong to the rest of the scene. Generating soft labels. To obtain the soft labels cost map for the segmentation process, we started from the initial hard labels generated at the previous step as a two colors image and obtained a blurred version of them by applying a Gaussian filter with a kernel size of 31 × 31 and a standard deviation of 51. After applying the blurring filter, the obtained values are normalized between The intuition behind using a soft version of the labels lies in the possibility to train a segmentation network with these labels as a target and then apply a threshold over the segmentation map that results as an output. This threshold would suggest how strong the network’s belief in the prediction should be, to consider this prediction as part of the predicted path.We adapted the work of  to a sinR is the turning radius. As previously remarked in [We used imitation learning to predict the instantaneous road curvature recorded by the steering acquisition sensor or predicted by the pose-estimation module from two consecutive frames sampled at 0.1 s. The road curvature is defined as arked in , this reThe architecture of our model follows a ResNet18  structuri, N is the total number of samples in the dataset, i and To address the systematic bias from the dataset y=L(RS represents the segmentation network which is applied on the image input and (·) is a tensor multiplication operator.The process of obtaining the output distribution for the encoded ROI solution is shown in Equation :(6)y=L, and finally combining data balancing and shifts. During our training procedure, we monitored the open-loop performance on the validation dataset, but we did not find it to be informative and correlated with the closed-loop evaluation. Thus, we reported the evaluation results for the model that achieves the best closed-loop performance on the validation dataset. The results of our experiments are summarized in We applied the same training procedure by replacing the ground-truth road curvature with the one resulted from the pose estimation module to evaluate the feasibility of our proposed method. In One limitation of our pose estimation labeling pipeline is the recovery of the correct scaling factor. We analyzed the impact of the estimated scaling value on the steering network’s performance by training multiple models on different pose estimation labels obtained by varying the scaling factor between In terms of the open-loop evaluation against the ground-truth labels, as suggested by the downward-upward trend captured by our results, a better estimate of the scaling factor results in a lower error metric. On the other hand, the open-loop evaluation against pose estimation labels on the validation dataset does not offer any relevant information. As previously emphasized in Similarly to the open-loop evaluation against the ground-truth labels, we observe a downward-upward trend in the closed-loop performance. The average autonomy over the scaling factor sweep is 76.11% with a standard deviation of HL: the model trained with the targets defined by the hard labels.SL Logits: the model trained with the targets defined by the soft labels, where a threshold is applied directly of the output of the model.SL Sigmoid: as SL Logits, but a Sigmoid operation is applied on the output logits.SL Softmax: as SL Logits, but a Softmax operation is applied on the output logits.SL Tanh: as SL Logits, but a Tanh operation is applied on the output logits.After the path labels have been obtained, we trained the segmentation model on both the KITTI odometry and UPB datasets. We define five different model alternatives: one which is trained with the hard labels as targets and four which are trained with the soft labels and we will denote them as below:SL Logits: search interval SL Sigmoid: search interval SL Softmax: search interval SL Tanh: search interval To find the best threshold for the soft labels evaluation, we selected an interval and performed a search for each one of the four variants of the model. This search employs running the model on the testing split of the UPB campus dataset and then selecting the threshold that leads to the highest mIOU. The setup for this search follows the cases:For evaluating the path segmentation, we chose two popular metrics: accuracy (Acc) and mean intersection over union (mIOU). Accuracy represents the percentage of pixels that were correctly classified, and the formula for this metric can be seen in Equation . In thismIOU can be described as the ratio between the intersection of the target with the prediction and the union of the two, averaged over all classes. Since we only have one class, denoting the followed path, the intersection represents the pixels where the ground-truth label of the path and the predicted label are overlapped, while the union represents the pixels where either the ground truth or the prediction is present. Equation (mIOU metric for segmentation.The second metric, Equation  describeWe can see the models are able to generalize well for new driving sections that are not found in the training split of the dataset.One feature we desired for the segmentation model was the ability to generate multiple paths in cases of reaching an intersection. There are some cases where the segmentation network generates multiple path possibilities, as seen in The segmentation results show reliable path generation even for the cases of intersection, where the network is able to generate multiple paths, despite their absence from the ground truth ego-motion trajectories of the vehicle. However, there are also situations where the paths generated by the network show a lack of confidence in the trajectory followed by the vehicle, especially in turns where the road is not very well delimited.For the steering improvement evaluation, we use the steering network models trained on the dataset where the ground truth is generated by the steering labeling algorithm as described in Therefore, in this section, we introduce two new models: We compared these two additional models with the We have presented a fully self-supervised labeling pipeline for an autonomous driving dataset in the context of steering control and path labeling. We applied our method on two open-source driving datasets ,44, and We consider that our current proposal can address two of the main limitations of the end-to-end approach regarding the amount and the diversity of available training data. Our method is flexible and applicable to a minimalistic data acquisition setup consisting of a single camera, which makes it suitable for data generation in the case of videos in the wild, significantly broadening the data that can be used for learning driving policies without being limited by the labels from a dataset or additional equipment which might not be available to everyone. Therefore, one potential line of research that we intend to investigate is to leverage the vast amount of online driving video resources to learn a robust driving policy.In addition to providing two different self-supervised labeling techniques, one for steering labels and one for path masks, we have shown how the path segmentation network and steering geometry can be leveraged with the purpose of improving the decisions taken by the steering network, demonstrated by the fact that this setup surpassed the autonomy of the steering network when trained on ground truth steering data.a comprehensive performance evaluation of the unsupervised steering labeling procedure;a sensitivity analysis of the steering models performance relative to the estimated scaling factor;a pipeline that generates path labels for any given dataset, in a self-supervised manner;a performance evaluation of different variations of segmentation models trained on the generated paths;two different approaches used to improve the performance of the base models using the paths obtained through segmentation.In summary, our contributions are as follows:As for future work, we propose on pursuing a more robust way of generating the path labels, keeping the self-supervised approach, but also considering the obstacles that interfere in the trajectory followed by the vehicle. One approach involves the idea of discarding the path regions from the current frame that are not supposed to be visible due to occlusions and to achieve this, the disparity maps of all the frames alongside the trajectory can be used. Another possible research direction we want to follow through consists of eliminating the steering network from the decision making process and only provide steering outputs by leveraging the trajectory segmentation results and the Ackermann geometry. We are also commited to trying newer segmentation approaches, using state-of-the-art methods involving vision transformers and we plan on introducing a user-guided text embedding which represents the intention about the directions of the trajectories outputed by the segmentation model in intersection scenarios.We believe that leveraging the vast amount of driving video recordings available on the internet will be a natural next step towards improving the capability of an autonomous driving system.