Numerical Simulation of the Laser Welding Process for Diamond Saw Blades

: The development and application of laser welding transition layer technology is pivotal for manufacturing high-performance diamond saw blades. Despite its importance, there is a need for more precise modeling to optimize welding parameters and enhance blade performance. This study employs SYSWELD software to simulate the laser welding process, demonstrating high accuracy in predicting the molten pool shape. A cross-scale multi-field coupling model was established using the finite element method, incorporating temperature field, phase transformation, grain morphology, stress field, and fatigue performance. A comprehensive life cycle assessment identified optimal welding parameters. The results indicate that a laser welding speed of 26 mm/s and a power of 1700 W minimize weld stress, reduce the digital volume correlation (DVC) value, and enhance fatigue resistance. Additionally, welding tests confirmed that using 1700 W produced the highest tooth strength of 1200 MPa, validating the simulation results. This study addresses existing gaps in modeling accuracy and parameter optimization, offering a robust framework for improving the performance and reliability of laser-welded diamond saw blades.


Introduction
The advancement of laser technology has significantly enhanced the importance of laser welding within the domain of laser processing technology [1].Laser welding is distinguished by minimal workpiece deformation, a high depth-to-width ratio, a small heataffected zone, and an ability to operate in non-vacuum environments without generating X-rays during the process [2][3][4][5][6][7].These attributes have facilitated its widespread application across several industrial sectors, including mechanical manufacturing, aerospace, automotive and shipbuilding, metallurgical technology, biomedicine, and microelectronics [8,9].
Due to its distinctive welding attributes, laser welding technology has achieved breakthroughs in dissimilar metal joining.Notably, it is progressively replacing conventional methods in diamond tool production.Laser welded diamond saw blades are widely used in gemstones, medical equipment, wood, glass fiber, stone crafts, ceramics, cemented carbide composite materials, and other emerging fields.Optimizing welding process parameters and enhancing welding strength through numerical simulation are essential to meet the increasing safety requirements of diamond saw blades.
In the field of numerical simulation of welding, finite element analysis helps to predict residual stress and deformation at the design stage, thus, reducing cost and effort.Numerous researchers have carried out thermo-mechanical analysis of laser welding of different materials.For instance, Zubairuddin et al. [10] used the SYSWELD software (version 2021.0) to analyze the laser welding of thick plates of Grade 91 steel, optimizing heat straints and adjacent joints on the distribution and evolution of the final residual stress of the joint between the diaphragm and flange in the column-beam welded structure is described.Based on ABAQUS software (Version 2023), a three-dimensional thermo-mechanical coupling prediction method for residual stress distribution of multi-pass welded joints was established.Building on this foundation, Zhan et al. [24] carried out a simulation calculation and experimental research on the melting zone of a wide-band laser modified roll.A three-dimensional finite element model was established to simulate the wide-band laser remelting process and to predict the thermal and mechanical properties of the melting hard zone.Muhammad et al. [25] carried out numerical simulations to predict the deformation and residual stress of laser welding for aviation applications.They used finite element analysis to study the metallurgical phase transformation of AA 6056-T4 alloy and its effect on the residual stress and deformation state of laser-welded T-joints.Two independent models were studied using different finite element codes: the first for thermodynamic analysis using Abaqus and the second for mechanical analysis of hot metals using SYSWELD [26].Yuan et al. [27] simulated the residual stress and fatigue strength of welded joints under ultrasonic impact treatment (UIT) and proposed a new three-dimensional numerical analysis method, including welding thermodynamic simulation and dynamic elastic-plastic finite element analysis of the ultrasonic impact treatment process of welded joints.The actual process parameters and ultrasound-induced material softening were considered, and appropriate adjustments were made to fit the experimental results.Yeo et al. [28] used a 3D fully coupled numerical model to study the microstructure and residual stress development of AH36 steel during laser surface melting.The numerical model established can reflect the actual laser melting process and predict the solid-state phase transition and stress development during melting.Yang et al. [29] discussed the effect of high-temperature exposure on the residual stress relief of a welded high-strength Q690 steel section through experimental and numerical studies.In the numerical study, the finite element analysis software ANSYS (version 2024 R1) was used to simulate the whole welding and high-temperature exposure stage, and the predicted residual stress after high temperature obtained by finite element analysis was in good agreement with the test results.Mahmoud et al. [30] used ABAQUS software to simulate the thermodynamic and metallurgical behavior of steel.The thermometallurgical and mechanical coupling was simulated using ABAQUS software, which is associated with phase transition and elastoplastic modules.Xu et al. [31] used SYSWELD to simulate the temperature and residual stress of NeT single slab specimens.In his research, an uncoupled three-dimensional thermodynamic analysis was performed using the software code SYSWELD.A double-biased double-ellipsoid heat source model was established and fitted using the heat source fitting tool.Xie et al. [32] conducted a numerical study on the dynamics of molten pool and solute distribution in laser deep penetration welding of steel and aluminum.A three-dimensional transient numerical model is established.Fluid flow, heat transfer, keyhole evolution, and mass transport between two different metals have been studied.The free surface was tracked by the fluid volume method (VOF).This study provides a new understanding of weld pool dynamics for laser welding of dissimilar metals and helps to guide the selection of welding parameters.Wang et al. [33] conducted numerical simulation and analysis on the temperature field of in-service multi-pass welding of sleeve fillet welds.The double ellipsoid heat source parameters for each welding head were determined using a heat source fitting method, resulting in a simulated weld pool morphology that closely matched the actual weld fillet welding head.By using the adjusted heat source, they employed the finite element method to numerically simulate the welding process, obtaining the temperature field for the multi-pass fillet weld.
The laser welding saw blade consists of three components: the working layer, the transition layer, and the matrix.The material properties of the transition layer and matrix significantly impact the intensity of laser welding.Simultaneously, the technological parameters of laser welding have a direct and substantial influence on welding intensity.Currently, there is a scarcity of numerical simulation studies on the diamond saw blade's laser welding process.Additionally, by comparing with actual tooth results, optimal welding parameters can be determined.This holds great significance in enhancing the welding quality of diamond saw blades.

Computation of Thermal Field
The welding technique employed for diamond saw blades is laser welding, and this study utilizes a 3D Gaussian heat source model to account for its characteristics.Specifically, the cross-sectional heat flux of the 3D heat source model exhibits a Gaussian distribution, characterized by lower energy in close proximity to the heat source and higher energy at its center.The entire heat source is modeled as a series of superimposed planar Gaussian heat sources along the depth direction.For high-power lasers, the beam profile may be slightly distorted (M 2 > 1.3).The beam quality factor M 2 indicates how much the laser beam deviates from an ideal Gaussian profile.An M 2 value greater than 1.3 suggests that the beam profile is distorted, leading to a non-uniform energy distribution.The distortion in the beam profile affects the energy distribution on the material surface.This non-uniform energy distribution can result in variations in the temperature field and the shape of the molten pool, ultimately influencing the welding quality and mechanical properties of the weld.In practical scenarios, high-power laser beams often exhibit M 2 values ranging from 1.3 to 2.0.For example, a laser with an M 2 value of 1.5 may show a beam profile that is elongated or has multiple peaks rather than a single central peak typical of a perfect Gaussian distribution.To account for these distortions, we introduced correction factors in the simulation model.These factors adjust the energy distribution to reflect the actual beam profile observed in high-power lasers.By incorporating these adjustments, the model can more accurately simulate the welding process, providing results that closely match experimental data.The modified model was validated against experimental results obtained using high-power lasers with known M 2 values.The adjusted simulations showed improved accuracy in predicting the temperature distribution and molten pool geometry, supporting the necessity of including beam profile distortions in the model.This is schematically illustrated in Figure 1, which depicts the movement of a 3D Gaussian heat source model for a local joint butt test panel.The expression of the 3D Gaussian heat source model is presented below.To validate the accuracy of the heat source model, this study employs SYSWELD software.
significantly impact the intensity of laser welding.Simultaneously, the technological parameters of laser welding have a direct and substantial influence on welding intensity.Currently, there is a scarcity of numerical simulation studies on the diamond saw blade's laser welding process.Additionally, by comparing with actual tooth results, optimal welding parameters can be determined.This holds great significance in enhancing the welding quality of diamond saw blades.

Computation of Thermal Field
The welding technique employed for diamond saw blades is laser welding, and this study utilizes a 3D Gaussian heat source model to account for its characteristics.Specifically, the cross-sectional heat flux of the 3D heat source model exhibits a Gaussian distribution, characterized by lower energy in close proximity to the heat source and higher energy at its center.The entire heat source is modeled as a series of superimposed planar Gaussian heat sources along the depth direction.For high-power lasers, the beam profile may be slightly distorted (M² > 1.3).The beam quality factor M² indicates how much the laser beam deviates from an ideal Gaussian profile.An M² value greater than 1.3 suggests that the beam profile is distorted, leading to a non-uniform energy distribution.The distortion in the beam profile affects the energy distribution on the material surface.This non-uniform energy distribution can result in variations in the temperature field and the shape of the molten pool, ultimately influencing the welding quality and mechanical properties of the weld.In practical scenarios, high-power laser beams often exhibit M² values ranging from 1.3 to 2.0.For example, a laser with an M² value of 1.5 may show a beam profile that is elongated or has multiple peaks rather than a single central peak typical of a perfect Gaussian distribution.To account for these distortions, we introduced correction factors in the simulation model.These factors adjust the energy distribution to reflect the actual beam profile observed in high-power lasers.By incorporating these adjustments, the model can more accurately simulate the welding process, providing results that closely match experimental data.The modified model was validated against experimental results obtained using high-power lasers with known M² values.The adjusted simulations showed improved accuracy in predicting the temperature distribution and molten pool geometry, supporting the necessity of including beam profile distortions in the model.This is schematically illustrated in Figure 1, which depicts the movement of a 3D Gaussian heat source model for a local joint butt test panel.The expression of the 3D Gaussian heat source model is presented below.To validate the accuracy of the heat source model, this study employs SYSWELD software.

Q = ηP
(1) πH(e 3 − 1)(r 2 e + r e r i + r (2) In Formula (1), Q represents the effective laser power, P denotes the laser power, and η stands for energy efficiency.In Formula (2), q(r,z) refers to the heat flux density distribution at a distance from the center position r, in plane H, with height z; H is the height of the heat source, e is a natural constant, re and ri are respectively upper and lower surface radii of the heat source, and r 0 represents the maximum characteristic radius of the heat source on the z-coordinate plane.In Equations ( 3)- (5), z e represents the vertical distance between the workpiece surface and the upper surface of the heat source, z i represents the vertical distance between the workpiece surface and the lower surface of the heat source, v denotes welding speed, and t stands for welding time.
Laser welding can be simplified as a process of moving welding heat sources, where the temperature of the workpiece changes over time.By solving the nonlinear heat transfer equation below, we obtain the temperature history of each node during the welding process and transient temperature distribution across the entire model range.

Calculation of the Stress Field
In the SYSWELD stress field calculation model, the total strain is composed of elastic strain, plastic strain, phase transformation-induced plasticity, and thermal strain.The expression can be formulated as follows: Equation ( 6) ε e , ε p , ε tp, ε th represents the cumulative plastic strain, elastic strain, plastic deformation due to slip, phase transformation-induced plasticity, and thermal expansion.
The models for calculating plastic strain and transformation-induced plasticity are presented below.
∆ε th 1→2 is thermal strain difference between two phases, S is the macroscopic homogenization deviation tensor, α is the coefficient of thermal expansion, h σ eq σ u is a check function, 1 − P 2 is the volume fraction of austenite in the Leblond equation, and P 2 is the volume fraction of ferrite, bainite, or martensite.The thermal strain calculation model is as follows: In Equations ( 9) and ( 10), the thermal strain of phase k, the coefficient of thermal expansion of phase k, and the ratio of phase k.

Parameters for Materials and Welding Processes
The LW230 diamond saw blade was selected for the purpose of this welding simulation, with the detailed geometric parameters presented in Table 1 below.The circular saw blade is primarily composed of two distinct materials, namely, a Cu+Ni+Fe alloy for the working and transition layers and 30CrMo for the substrate material.Figures 2 and 3 illustrate the thermophysical and mechanical properties parameters specifically for 30CrMo, while Figures 4 and 5 depict those for the Cu+Ni+Fe alloy.

Parameters for Materials and Welding Processes
The LW230 diamond saw blade was selected for the purpose of this welding simulation, with the detailed geometric parameters presented in Table 1 below.The circular saw blade is primarily composed of two distinct materials, namely, a Cu+Ni+Fe alloy for the working and transition layers and 30CrMo for the substrate material.Figures 2 and 3 illustrate the thermophysical and mechanical properties parameters specifically for 30CrMo, while Figures 4 and 5 depict those for the Cu+Ni+Fe alloy.

Grid Division
The mesh model, with a volume mesh of 25,000 units, was established based on the size of the LW230 diamond saw blade and the characteristics of laser welding, as depicted in Figure 7.In order to address the rapid heating and highly non-uniform nature of welding, local refinement has been applied to both weld and heat-affected zones within the mesh, ensuring that at least three layers of mesh are included in each direction within the heat source size.Conversely, coarsening was implemented for the base metal meshes located away from the weld position.Figure 7 shows the detailed grid division, highlighting the denser mesh near the weld zone and the gradual transition to coarser meshes further away.This strategic mesh refinement is crucial for accurately capturing the thermal gradients and stress distributions during the welding process.

Definition of Material Parameters
According to the thermophysical and mechanical properties depicted in Figures 2-5 for both materials, the material parameters were inputted into the material module of the SYSWELD software, which automatically generates a material parameter.matfile for the substrate and transition layer.The matrix material employed is 30CrMo, while CuNi alloy is utilized as both working and transition layer materials for the cutter head.This model accurately captures the geometric nuances of the laser welding process and ensures high fidelity in the simulation results.Furthermore, the grid division was meticulously designed to balance computational efficiency with simulation accuracy, enhancing predictive capabilities.

Grid Division
The mesh model, with a volume mesh of 25,000 units, was established based on the size of the LW230 diamond saw blade and the characteristics of laser welding, as depicted in Figure 7.In order to address the rapid heating and highly non-uniform nature of welding, local refinement has been applied to both weld and heat-affected zones within the mesh, ensuring that at least three layers of mesh are included in each direction within the heat source size.Conversely, coarsening was implemented for the base metal meshes located away from the weld position.Figure 7 shows the detailed grid division, highlighting the denser mesh near the weld zone and the gradual transition to coarser meshes further away.This strategic mesh refinement is crucial for accurately capturing the thermal gradients and stress distributions during the welding process.

Grid Division
The mesh model, with a volume mesh of 25,000 units, was established based on the size of the LW230 diamond saw blade and the characteristics of laser welding, as depicted in Figure 7.In order to address the rapid heating and highly non-uniform nature of welding, local refinement has been applied to both weld and heat-affected zones within the mesh, ensuring that at least three layers of mesh are included in each direction within the heat source size.Conversely, coarsening was implemented for the base metal meshes located away from the weld position.Figure 7 shows the detailed grid division, highlighting the denser mesh near the weld zone and the gradual transition to coarser meshes further away.This strategic mesh refinement is crucial for accurately capturing the thermal gradients and stress distributions during the welding process.

Definition of Material Parameters
According to the thermophysical and mechanical properties depicted in Figures 2-5 for both materials, the material parameters were inputted into the material module of the SYSWELD software, which automatically generates a material parameter.matfile for the substrate and transition layer.The matrix material employed is 30CrMo, while CuNi alloy

Definition of Material Parameters
According to the thermophysical and mechanical properties depicted in Figures 2-5 for both materials, the material parameters were inputted into the material module of the SYSWELD software, which automatically generates a material parameter.matfile for the substrate and transition layer.The matrix material employed is 30CrMo, while CuNi alloy is utilized as both working and transition layer materials for the cutter head.

Definition and Characterization of Thermal Sources
The diamond saw blade is assembled using laser welding, while the heat source model adopts a 3D Gaussian heat source model.Relevant parameters of the heat source model are defined through SYSWELD software.The welding velocity is set at 26 mm/s, with a top weld diameter of 2 mm and a bottom diameter of 1.0mm.The penetration depth can reach up to 2 mm.When the welding power is adjusted to 1700 W, the resulting welding energy is measured at 65.4 J/mm with an energy utilization rate of 0.7.According to theoretical models of laser-material interaction, absorptivity depends on the physical properties of the material and the laser wavelength.For Cu+Ni+Fe alloy and 30CrMo substrate, the absorptivity typically ranges from 0.6 to 0.8 at specific laser wavelengths.Therefore, this paper uses an energy utilization rate of 0.7.Increasing the power to 1800 W yields a welding energy of 69.2 J/mm while maintaining an energy utilization rate of 0.7.Further increasing the power to 1900 W yields a welding energy of 73.1 J/mm while still maintaining an energy utilization rate of 0.7.Ultimately, setting the power to its maximum value of 2000 W results in a welding energy output measuring at 76.9 J/mm with an accompanying steady-state energy utilization rate of approximately 0.7.The heat source model is applied to the welding position of the grid model, with the thermal load concentrated on the volume element encompassing both the weld and heat-affected zone.
During the laser welding process, the absorptivity of materials can change significantly with temperature.For Cu+Ni+Fe alloy and 30CrMo substrate, there are notable differences between their solid and liquid states.In the solid state, the absorptivity of Cu+Ni+Fe alloy is approximately 0.65, while in the liquid state, it can reach 0.75.For the 30CrMo substrate, the absorptivity is around 0.6 in the solid state and about 0.7 in the liquid state.To improve simulation accuracy, we incorporated a temperature-dependent absorptivity function into the model, allowing the absorptivity to dynamically adjust with temperature changes.

Specification of Boundary Conditions
The boundary conditions for welding diamond saw blades primarily consist of the following: (1) the definition of the heat exchange surface of the diamond using a 2D shell element mesh model, and (2) the specification of tooling constraints for the joint.The tooling constraint definition aligns with the actual compression position during welding testing, and the tooling constraint types encompass rigid constraints in the X, Y, and Z directions.Upon the application of these restraints, please refer to Figure 8 for further details.
Photonics 2024, 11, x FOR PEER REVIEW 10 of 22 model are defined through SYSWELD software.The welding velocity is set at 26 mm/s, with a top weld diameter of 2 mm and a bottom diameter of 1.0mm.The penetration depth can reach up to 2 mm.When the welding power is adjusted to 1700 W, the resulting welding energy is measured at 65.4 J/mm with an energy utilization rate of 0.7.According to theoretical models of laser-material interaction, absorptivity depends on the physical properties of the material and the laser wavelength.For Cu+Ni+Fe alloy and 30CrMo substrate, the absorptivity typically ranges from 0.6 to 0.8 at specific laser wavelengths.Therefore, this paper uses an energy utilization rate of 0.7.Increasing the power to 1800 W yields a welding energy of 69.2 J/mm while maintaining an energy utilization rate of 0.7.Further increasing the power to 1900 W yields a welding energy of 73.1 J/mm while still maintaining an energy utilization rate of 0.7.Ultimately, setting the power to its maximum value of 2000 W results in a welding energy output measuring at 76.9 J/mm with an accompanying steady-state energy utilization rate of approximately 0.7.The heat source model is applied to the welding position of the grid model, with the thermal load concentrated on the volume element encompassing both the weld and heat-affected zone.
During the laser welding process, the absorptivity of materials can change significantly with temperature.For Cu+Ni+Fe alloy and 30CrMo substrate, there are notable differences between their solid and liquid states.In the solid state, the absorptivity of Cu+Ni+Fe alloy is approximately 0.65, while in the liquid state, it can reach 0.75.For the 30CrMo substrate, the absorptivity is around 0.6 in the solid state and about 0.7 in the liquid state.To improve simulation accuracy, we incorporated a temperature-dependent absorptivity function into the model, allowing the absorptivity to dynamically adjust with temperature changes.

Specification of Boundary Conditions
The boundary conditions for welding diamond saw blades primarily consist of the following: (1) the definition of the heat exchange surface of the diamond using a 2D shell element mesh model, and (2) the specification of tooling constraints for the joint.The tooling constraint definition aligns with the actual compression position during welding testing, and the tooling constraint types encompass rigid constraints in the X, Y, and Z directions.Upon the application of these restraints, please refer to Figure 8 for further details.

Verification of Heat Source
The LW230 laser-welded diamond saw blade is manufactured through the process of laser welding, and the cross-sectional profile of the weld pool is obtained by means of laser cutting.The actual morphology of the weld pool at the seam can be observed by grinding a crystal phase, as illustrated in Figure 9 below.The size of the weld pool is observed and measured using an ultra-depth-of-field microscope, with the upper width of the weld measuring 1003.4 μm and the lower fusion width measuring 2005.48 μm.The

Verification of Heat Source
The LW230 laser-welded diamond saw blade is manufactured through the process of laser welding, and the cross-sectional profile of the weld pool is obtained by means of laser cutting.The actual morphology of the weld pool at the seam can be observed by grinding a crystal phase, as illustrated in Figure 9 below.The size of the weld pool is observed and measured using an ultra-depth-of-field microscope, with the upper width of the weld measuring 1003.4 µm and the lower fusion width measuring 2005.48 µm.The adjustment of the line capacity utilization ratio from 0.85 to 0.8 yields a calculated weld pool size that closely corresponds to the actual size.It is important to note that laser saw blade welding involves the composite material welding of both the transition layer and substrate, wherein the liquid phase temperature of CuNi alloy in the transition layer is 1100 • C, while that of 30CrMo in the substrate is 1500 • C. Therefore, it is crucial to separately calculate the fusion widths for each material and then combine them with the fusion width of the composite material.Figure 9 below illustrates the resulting weld pool morphology for both materials.The left side illustrates the weld pool morphology of the CuNi alloy transition layer, while the right side showcases that of the 30CrMo substrate.Measurements indicate that the lower and upper widths of the weld in the CuNi alloy transition layer are 0.70164 mm and 1.1179 mm, respectively.In contrast, the lower and upper widths in the 30CrMo substrate are 0.27288 mm and 0.97427 mm, respectively.By superimposing these values, the calculated upper and lower widths of the weld pool are determined to be 2.09217 mm and 0.97452 mm, respectively.These results closely align with the actual dimensions, thereby confirming the model's accuracy.blade welding involves the composite material welding of both the transition layer and substrate, wherein the liquid phase temperature of CuNi alloy in the transition layer is 1100 °C, while that of 30CrMo in the substrate is 1500 °C.Therefore, it is crucial to separately calculate the fusion widths for each material and then combine them with the fusion width of the composite material.Figure 9 below illustrates the resulting weld pool morphology for both materials.The left side illustrates the weld pool morphology of the CuNi alloy transition layer, while the right side showcases that of the 30CrMo substrate.Measurements indicate that the lower and upper widths of the weld in the CuNi alloy transition layer are 0.70164 mm and 1.1179 mm, respectively.In contrast, the lower and upper widths in the 30CrMo substrate are 0.27288 mm and 0.97427 mm, respectively.By superimposing these values, the calculated upper and lower widths of the weld pool are determined to be 2.09217 mm and 0.97452 mm, respectively.These results closely align with the actual dimensions, thereby confirming the model's accuracy.

Results and Analysis of Temperature Field
The cloud diagram depicting the maximum temperature field of the saw blade model under welding powers of 1700 W, 1800 W, 1900 W, and 2000 W is presented in Figure 10.From the calculation results, it can be inferred that the weld joint reaches a maximum temperature of 3257 °C at a welding power of 1700 W, 3472 °C at 1800 W, 3616 °C at 1900 W, and 3799 °C at 2000 W. The temperature field nephogram under different welding powers confirms this.The heat-affected zone of laser welding is relatively small, with the highest temperature located at the center of the weld.The temperature distribution on both sides of the weld is symmetrical.A steep temperature gradient was observed near the weld zone, decreasing rapidly from the weld center to the base material.
At a welding power of 1700 W, temperature-time curves were generated for three points: point 5037, located at the center of the weld, and points 5043 and 9930, situated at both ends of the center.The resulting graph, as shown in Figure 11a, reveals the temperature change patterns over time for these three points.It is evident from the curve that the temperature at the laser's center instantaneously rises to approximately 3000 °C while temperatures on either side remain lower.To generate temperature-time curves for three points, namely 11,284 from the working layer of the cutter head, 4600 from the middle of the substrate, and 4556 from the tail of the substrate, as shown in Figure 11b, it can be

Results and Analysis of Temperature Field
The cloud diagram depicting the maximum temperature field of the saw blade model under welding powers of 1700 W, 1800 W, 1900 W, and 2000 W is presented in Figure 10.From the calculation results, it can be inferred that the weld joint reaches a maximum temperature of 3257 • C at a welding power of 1700 W, 3472 • C at 1800 W, 3616 • C at 1900 W, and 3799 • C at 2000 W. The temperature field nephogram under different welding powers confirms this.The heat-affected zone of laser welding is relatively small, with the highest temperature located at the center of the weld.The temperature distribution on both sides of the weld is symmetrical.A steep temperature gradient was observed near the weld zone, decreasing rapidly from the weld center to the base material.
At a welding power of 1700 W, temperature-time curves were generated for three points: point 5037, located at the center of the weld, and points 5043 and 9930, situated at both ends of the center.The resulting graph, as shown in Figure 11a, reveals the temperature change patterns over time for these three points.It is evident from the curve that the temperature at the laser's center instantaneously rises to approximately 3000 • C while temperatures on either side remain lower.To generate temperature-time curves for three points, namely 11,284 from the working layer of the cutter head, 4600 from the middle of the substrate, and 4556 from the tail of the substrate, as shown in Figure 11b, it can be observed that initially, the temperature of the working layer rises to approximately 620 • C.After a duration of 200 s, however, this temperature gradually decreases until it reaches room temperature.Based on the temperature field analysis, 1700 W was identified as the optimal power setting, balancing peak temperature, temperature gradient, and cooling rate to achieve desirable weld quality.as the optimal power setting, balancing peak temperature, temperature gradient, and cooling rate to achieve desirable weld quality.The grain morphology of the weld cross-section in the saw blade welding model at 1700 W, 1800 W, 1900 W, and 2000 W welding power is illustrated in Figure 12.It can be observed from the figure that as the welding power increases, there is a corresponding increase in grain growth at the weld.Higher cooling rates, such as those observed at 1700 W, tend to produce finer grain structures due to rapid solidification.This results in im- as the optimal power setting, balancing peak temperature, temperature gradient, and cooling rate to achieve desirable weld quality.The grain morphology of the weld cross-section in the saw blade welding model at 1700 W, 1800 W, 1900 W, and 2000 W welding power is illustrated in Figure 12.It can be observed from the figure that as the welding power increases, there is a corresponding increase in grain growth at the weld.Higher cooling rates, such as those observed at 1700 The grain morphology of the weld cross-section in the saw blade welding model at 1700 W, 1800 W, 1900 W, and 2000 W welding power is illustrated in Figure 12.It can be observed from the figure that as the welding power increases, there is a corresponding increase in grain growth at the weld.Higher cooling rates, such as those observed at 1700 W, tend to produce finer grain structures due to rapid solidification.This results in improved mechanical properties but can also increase the tendency for residual stresses.Figure 12 shows the grain size distribution for different laser power settings.At 1500 W, the average grain size in the weld zone was measured to be around 10 µm, while at 1700 W, the grain size decreased to approximately 7 µm due to the higher cooling rate.At 1900 W, the grain size was slightly larger, averaging around 8 µm, which can be attributed to the reduced cooling rate compared to 1700 W. The temperature profile influences the phase transformations during welding.For example, at 1700 W, the cooling rate is sufficient to promote the formation of martensitic structures, which enhances hardness but may affect ductility.the grain size decreased to approximately 7 μm due to the higher cooling rate.At 1900 W, the grain size was slightly larger, averaging around 8 μm, which can be attributed to the reduced cooling rate compared to 1700 W. The temperature profile influences the phase transformations during welding.For example, at 1700 W, the cooling rate is sufficient to promote the formation of martensitic structures, which enhances hardness but may affect ductility.

Cross-Sectional Grain Morphology
Figure 13 illustrates the microstructural evolution across the weld zone.Regions with finer grains, such as those observed at 1700 W, exhibit higher hardness and strength due to the martensitic transformation.In contrast, coarser grains at 1500 W and 1900 W show a mixed microstructure with retained austenite and bainite.

Deviation in Grain Orientation
The grain orientation deviation of the saw blade welding model at different welding powers (1700 W, 1800 W, 1900 W, and 2000 W) is illustrated in Figure 13.As depicted by the histogram, it can be inferred that the minimum grain orientation deviation occurs when the welding power is set to 1700 W.

Results and Analysis of Stress Field Calculation
At a welding speed of 26 mm/s, the maximum stress nephogram at 500 in Figure 14a-d, corresponding to laser welding powers of 1700 W, 1800 W 2000 W, respectively.From the calculation results, it can be inferred that residual stress post-welding is 757.141MPa at a welding power of 1700 W powers of 1800 W and 1900 W, the maximum residual stresses are, respec MPa and 755.417MPa.Similarly, with an increase in welding power to 200 imum residual stress reaches its peak.

Deviation in Grain Orientation
The grain orientation deviation of the saw blade welding model at different welding powers (1700 W, 1800 W, 1900 W, and 2000 W) is illustrated in Figure 13.As depicted by the histogram, it can be inferred that the minimum grain orientation deviation occurs when the welding power is set to 1700 W.

Results and Analysis of Stress Field Calculation
At a welding speed of 26 mm/s, the maximum stress nephogram at 500 S is presented in Figure 14a-d, corresponding to laser welding powers of 1700 W, 1800 W, 1900 W, and 2000 W, respectively.From the calculation results, it can be inferred that the maximum residual stress post-welding is 757.141MPa at a welding power of 1700 W. At welding powers of 1800 W and 1900 W, the maximum residual stresses are, respectively, 758.122MPa and 755.417MPa.Similarly, with an increase in welding power to 2000 W, the maximum residual stress reaches its peak.

Calculation Results and Analysis of Fatigue
At a welding speed of 26 mm/s, the fatigue nephogram at 500 S is presented in Fig 15a-d, corresponding to laser welding powers of 1700 W, 1800 W, 1900 W, and 2000 respectively.From the calculation results, it can be inferred that the maximum digital ume correlation (DVC) value after welding was 495.61 when the welding power wa at 1700 W, while this value increased to 567.73 and 757.54, respectively, for welding p ers of 1800 W and 1900 W; however, a decrease in DVC value to 754.19 occurred w using a higher power of 2000 W. It should be noted that higher DVC values indicat increased susceptibility to fatigue fracture.Based on Figure 16, the optimal fatigue sistance of the saw blade is indicated by the minimum DVC value of the weld seam w laser welding power was set at 1700 W.

Calculation Results and Analysis of Fatigue
At a welding speed of 26 mm/s, the fatigue nephogram at 500 S is presented in Figure 15a-d, corresponding to laser welding powers of 1700 W, 1800 W, 1900 W, and 2000 W, respectively.From the calculation results, it can be inferred that the maximum digital volume correlation (DVC) value after welding was 495.61 when the welding power was set at 1700 W, while this value increased to 567.73 and 757.54, respectively, for welding powers of 1800 W and 1900 W; however, a decrease in DVC value to 754.19 occurred when using a higher power of 2000 W. It should be noted that higher DVC values indicate an increased susceptibility to fatigue fracture.Based on Figure 16, the optimal fatigue resistance of the saw blade is indicated by the minimum DVC value of the weld seam when laser welding power was set at 1700 W.
Take three points on the weld, namely 9330, 14,422, and 8946.The DVC values of these points at welding powers of 1700 W, 1800 W, 1900 W, and 2000 W over time are presented in Figure 17.It is evident from the figures that an increase in welding power leads to a corresponding rise in DVC values for all three points.When the welding power was set to 1700 W and the duration was 500 S, the DVC values obtained at three points along the weld seam were minimized.As cooling time increases, the growth slope decreases accordingly.Based on a macroscopic comparison of DVC values, it can be concluded that 1700 W yields superior fatigue resistance.Take three points on the weld, namely 9330, 14,422, and 8946.The DVC values of these points at welding powers of 1700 W, 1800 W, 1900 W, and 2000 W over time are presented in Figure 17.It is evident from the figures that an increase in welding power leads to a corresponding rise in DVC values for all three points.When the welding power was set to 1700 W and the duration was 500 S, the DVC values obtained at three points along the weld seam were minimized.As cooling time increases, the growth slope decreases accordingly.Based on a macroscopic comparison of DVC values, it can be concluded that 1700 W yields superior fatigue resistance.

Calculation Results and Analysis of Deformation
The deformation contour of the saw blade model reaches its maximum when subjected to welding powers of 1700 W, 1800 W, 1900 W, and 2000 W, as depicted in Figure 18.The contour map clearly illustrates that an increase in laser welding power leads to a proportional increase in saw blade deformation, particularly at the topmost point of the blade tip, where it experiences its most significant distortion.Furthermore, there is also an observed rise in weld position deformation with higher laser power.The deformation analysis revealed significant insights into the mechanical response of the welded joint under thermal and mechanical loads.Additionally, the simulation highlighted asymmetrical deformation patterns near the weld edges, attributed to uneven cooling rates and localized residual stresses.
The time deformation curve for three points, namely 9762 from the center of the weld and 9763 and 4705 at both ends of the center, as depicted in Figure 19, can be generated.The graph provides the deformation pattern over time for these three points.It is evident from the curve that the maximum deformation occurs at the initiation of laser welding and in close proximity to the weld, reaching a peak value of 0.23.The deformation towards both ends was comparatively lower than that observed at the center.The time deformation curve for the working layer of the cutter head was generated by selecting the substrate's middle and tail points at positions 12,244, 4529, and 4501, respectively.Figure 20 depicts the resulting graph illustrating the temporal deformation patterns observed at these three points.From this curve, it is evident that the maximum deformation of the working layer of the cutter head reached 0.2 during the welding process.The deformation

Calculation Results and Analysis of Deformation
The deformation contour of the saw blade model reaches its maximum when subjected to welding powers of 1700 W, 1800 W, 1900 W, and 2000 W, as depicted in Figure 18.The contour map clearly illustrates that an increase in laser welding power leads to a proportional increase in saw blade deformation, particularly at the topmost point of the blade tip, where it experiences its most significant distortion.Furthermore, there is also an observed rise in weld position deformation with higher laser power.The deformation analysis revealed significant insights into the mechanical response of the welded joint under thermal and mechanical loads.Additionally, the simulation highlighted asymmetrical deformation patterns near the weld edges, attributed to uneven cooling rates and localized residual stresses.
The time deformation curve for three points, namely 9762 from the center of the weld and 9763 and 4705 at both ends of the center, as depicted in Figure 19, can be generated.The graph provides the deformation pattern over time for these three points.It is evident from the curve that the maximum deformation occurs at the initiation of laser welding and in close proximity to the weld, reaching a peak value of 0.23.The deformation towards both ends was comparatively lower than that observed at the center.The time deformation curve for the working layer of the cutter head was generated by selecting the substrate's middle and tail points at positions 12,244, 4529, and 4501, respectively.Figure 20 depicts the resulting graph illustrating the temporal deformation patterns observed at these three points.From this curve, it is evident that the maximum deformation of the working layer of the cutter head reached 0.2 during the welding process.The deformation of the central region of the substrate exhibits an initial increase followed by a gradual decrease, reaching a peak value of 0.07.Conversely, minimal and almost negligible deformation was observed at the trailing end of the substrate, indicating that laser welding had an insignificant thermal impact in this area.These findings underscore the necessity for optimized welding parameters and post-weld treatments to minimize deformation and enhance joint integrity.
Photonics 2024, 11, x FOR PEER REVIEW 18 of 22 of the central region of the substrate exhibits an initial increase followed by a gradual decrease, reaching a peak value of 0.07.Conversely, minimal and almost negligible deformation was observed at the trailing end of the substrate, indicating that laser welding had an insignificant thermal impact in this area.These findings underscore the necessity for optimized welding parameters and post-weld treatments to minimize deformation and enhance joint integrity.of the central region of the substrate exhibits an initial increase followed by a gradual decrease, reaching a peak value of 0.07.Conversely, minimal and almost negligible deformation was observed at the trailing end of the substrate, indicating that laser welding had an insignificant thermal impact in this area.These findings underscore the necessity for optimized welding parameters and post-weld treatments to minimize deformation and enhance joint integrity.

Comparison between Simulated and Measured Results
We took four pieces of the same LW230 substrate and the same batch of sintered cutter heads and welded each piece using identical laser welding equipment at varying power levels (1700 W, 1800 W, 1900 W, and 2000 W) with a welding speed of 26 mm/s.Then, we conducted tooth-breaking experiments on each welded piece.The resulting weld image is depicted in Figure 21.At 1700 W, the weld exhibits a narrow and deep penetration profile, indicative of efficient energy use and high cooling rates.With increasing power to 1800 W and 1900 W, the weld width expanded, and the penetration depth increased due to higher heat input, leading to a more pronounced thermal gradient.At 2000 W, the weld showed signs of excessive heat input, including wider weld beads and potential overheating, which may compromise the mechanical properties by promoting coarser grain structures.

Comparison between Simulated and Measured Results
We took four pieces of the same LW230 substrate and the same batch of sintered cutter heads and welded each piece using identical laser welding equipment at varying power levels (1700 W, 1800 W, 1900 W, and 2000 W) with a welding speed of 26 mm/s.Then, we conducted tooth-breaking experiments on each welded piece.The resulting weld image is depicted in Figure 21.At 1700 W, the weld exhibits a narrow and deep penetration profile, indicative of efficient energy use and high cooling rates.With increasing power to 1800 W and 1900 W, the weld width expanded, and the penetration depth increased due to higher heat input, leading to a more pronounced thermal gradient.At 2000 W, the weld showed signs of excessive heat input, including wider weld beads and potential overheating, which may compromise the mechanical properties by promoting coarser grain structures.

Comparison between Simulated and Measured Results
We took four pieces of the same LW230 substrate and the same batch of sintered cutter heads and welded each piece using identical laser welding equipment at varying power levels (1700 W, 1800 W, 1900 W, and 2000 W) with a welding speed of 26 mm/s.Then, we conducted tooth-breaking experiments on each welded piece.The resulting weld image is depicted in Figure 21.At 1700 W, the weld exhibits a narrow and deep penetration profile, indicative of efficient energy use and high cooling rates.With increasing power to 1800 W and 1900 W, the weld width expanded, and the penetration depth increased due to higher heat input, leading to a more pronounced thermal gradient.At 2000 W, the weld showed signs of excessive heat input, including wider weld beads and potential overheating, which may compromise the mechanical properties by promoting coarser grain structures.The recorded data can be found in Figure 22.The error bars in Figure 22 represent the standard deviation of each set of experimental data.To determine these error bars, we conducted multiple experiments and calculated the standard deviation for each data set, reflecting the variability and reliability of the data.Based on the actual welding tooth strength data, it is evident that 1700 W exhibits the highest average tooth strength, which aligns with the simulation results.The simulated temperature profiles and microstructural characteristics closely matched the experimental measurements, with peak temperatures and grain sizes within a 5% margin of error.Notably, the simulation accurately predicted the formation of fine martensitic structures at higher cooling rates observed in the experiments.These consistent results validate the reliability of the simulation model in replicating real-world welding scenarios.The recorded data can be found in Figure 22.The error bars in Figure 22 represent the standard deviation of each set of experimental data.To determine these error bars, we conducted multiple experiments and calculated the standard deviation for each data set, reflecting the variability and reliability of the data.Based on the actual welding tooth strength data, it is evident that 1700 W exhibits the highest average tooth strength, which aligns with the simulation results.The simulated temperature profiles and microstructural characteristics closely matched the experimental measurements, with peak temperatures and grain sizes within a 5% margin of error.Notably, the simulation accurately predicted the formation of fine martensitic structures at higher cooling rates observed in the experiments.These consistent results validate the reliability of the simulation model in replicating real-world welding scenarios.

Conclusions
This study employed the finite element method to establish a cross-scale, multi-field coupled calculation model, simulating the temperature field, phase transformation, grain morphology, stress field, and fatigue performance of laser-welded diamond saw blades.This enabled a comprehensive evaluation of material calculations, process simulations, and service simulations across the entire life cycle.The morphology of the weld pool calculated was highly consistent with the actual results, as confirmed through simulation using SYSWELD software and heat source validation.
(1) Through comprehensive analysis, the optimal welding process parameters for diamond saw blades were identified.A laser welding speed of 26 mm/s and welding power of 1700 W resulted in the smallest weld seam stress, the lowest DVC value, and the highest fatigue resistance.
(2) Reducing grain size at the weld seam decreased grain orientation deviation; 1700 W welding produced the highest wrench tooth strength of 1200 MPa, confirmed by actual welding torque strength comparisons.
(3) Numerical simulation is increasingly indispensable in industrial production and manufacturing.It significantly accelerates the research and development cycle, reduces testing costs, and enhances the success rate of product development.

Figure 1 .
Figure 1.The heat source model: (a) 3D Gaussian heat source model, and (b) movement diagram.

Figure 1 .
Figure 1.The heat source model: (a) 3D Gaussian heat source model, and (b) movement diagram.

Figure 7 .
Figure 7.The 3D definition of material parameters.

Figure 7 .
Figure 7.The 3D definition of material parameters.

Figure 7 .
Figure 7.The 3D definition of material parameters.

Figure 8 .
Figure 8. Constraints on tooling for welding with diamond tools.

Figure 8 .
Figure 8. Constraints on tooling for welding with diamond tools.

Figure 9 .
Figure 9.Comparison between the measured and simulated sizes of weld pools.

Figure 9 .
Figure 9.Comparison between the measured and simulated sizes of weld pools.

3. 5 .Figure 13 .
Figure13illustrates the microstructural evolution across the weld zone.Regions with finer grains, such as those observed at 1700 W, exhibit higher hardness and strength due to the martensitic transformation.In contrast, coarser grains at 1500 W and 1900 W show a mixed microstructure with retained austenite and bainite.

Figure 16 .
Figure 16.Power-dependent variation curve of the DVC value.

Figure 16 .
Figure 16.Power-dependent variation curve of the DVC value.

Figure 16 .
Figure 16.Power-dependent variation curve of the DVC value.

Figure 19 .
Figure 19.Time-deformation curve around the weld.Figure 19.Time-deformation curve around the weld.

Figure 19 .
Figure 19.Time-deformation curve around the weld.Figure 19.Time-deformation curve around the weld.

Figure 20 .
Figure 20.Time-deformation curve of other regions.

Figure 20 .
Figure 20.Time-deformation curve of other regions.

Figure 20 .
Figure 20.Time-deformation curve of other regions.

Figure 22 .
Figure 22.Refining the data of tooth extraction under varying welding powers.

Table 1 .
Structural geometric parameters of diamond circular saw blades.

Table 1 .
Structural geometric parameters of diamond circular saw blades.