<p>This paper presents a study on the laser surface hardening of a low alloy AISI 4340 steel workpiece with finite width, such as a gear. A three-dimensional (3D) model implemented using commercial software is employed to solve the heat transfer equation, determine the temperature distribution under the surface, and predict the optimal process parameters. The laser beam is modeled as a moving disc heat flux applied to the surface, with a Gaussian distribution of heat intensity. By determining the temperature distribution at any given time during the process, the width and depth of the hardened zone beneath the surface can be calculated using the Ashby and Easterling metallurgical equations. The primary process parameters considered include laser power (<i>P</i>), laser beam focus diameter<InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="170_2025_15292_Article_IEq1.gif" Format="GIF" Height="20" Rendition="HTML" Resolution="72" Type="Linedraw" Width="46" /> </InlineMediaObject> <EquationSource Format="TEX">$({ D}_{foc })$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mo stretchy="false">(</mo> <msub> <mi>D</mi> <mrow> <mi mathvariant="italic">foc</mi> </mrow> </msub> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation>, and the transverse scanning velocity <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="170_2025_15292_Article_IEq2.gif" Format="GIF" Height="20" Rendition="HTML" Resolution="72" Type="Linedraw" Width="39" /> </InlineMediaObject> <EquationSource Format="TEX">${(V}_{sc})$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msub> <mrow> <mo stretchy="false">(</mo> <mi>V</mi> </mrow> <mrow> <mi mathvariant="italic">sc</mi> </mrow> </msub> <mrow> <mo stretchy="false">)</mo> </mrow> </mrow> </math></EquationSource> </InlineEquation>. In this setup, the gears are mounted on a lathe, and the laser beam is stationary and positioned above the rotating gear which operates at a rotation speed of <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="170_2025_15292_Article_IEq3.gif" Format="GIF" Height="12" Rendition="HTML" Resolution="72" Type="Linedraw" Width="20" /> </InlineMediaObject> <EquationSource Format="TEX">${w}_{r}$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>w</mi> <mi>r</mi> </msub> </math></EquationSource> </InlineEquation>. A commercial Nd:Yag laser beam is used to validate the simulation results experimentally. The simulation results closely matched the experimental findings, with a maximum relative error of approximately less than 10%. The optimal preheating temperature (873 K) allowed for a case depth exceeding 1 mm at the top of the gear teeth while preventing undesirable melting. At 1500 W laser power, 750 rpm rotation speed, and 0.75 mm/s scanning velocity, the hardened zone was comparable to induction hardening but with significantly lower power consumption. These results demonstrate the feasibility of predictive modeling in optimizing laser surface hardening for industrial applications.</p>

Thermal analysis of laser surface hardening of gears—3D simulation and experimental validation

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发表日期：

2025年3月3日

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Guillaume Billaud,
Abderrazak El Ouafi,
Noureddine Barka,
Narges Omidi

摘要

This paper presents a study on the laser surface hardening of a low alloy AISI 4340 steel workpiece with finite width, such as a gear. A three-dimensional (3D) model implemented using commercial software is employed to solve the heat transfer equation, determine the temperature distribution under the surface, and predict the optimal process parameters. The laser beam is modeled as a moving disc heat flux applied to the surface, with a Gaussian distribution of heat intensity. By determining the temperature distribution at any given time during the process, the width and depth of the hardened zone beneath the surface can be calculated using the Ashby and Easterling metallurgical equations. The primary process parameters considered include laser power (P), laser beam focus diameter $({ D}_{foc })$ $(D_{foc})$ , and the transverse scanning velocity ${(V}_{sc})$ ${(V}_{sc})$ . In this setup, the gears are mounted on a lathe, and the laser beam is stationary and positioned above the rotating gear which operates at a rotation speed of ${w}_{r}$ $w_{r}$ . A commercial Nd:Yag laser beam is used to validate the simulation results experimentally. The simulation results closely matched the experimental findings, with a maximum relative error of approximately less than 10%. The optimal preheating temperature (873 K) allowed for a case depth exceeding 1 mm at the top of the gear teeth while preventing undesirable melting. At 1500 W laser power, 750 rpm rotation speed, and 0.75 mm/s scanning velocity, the hardened zone was comparable to induction hardening but with significantly lower power consumption. These results demonstrate the feasibility of predictive modeling in optimizing laser surface hardening for industrial applications.