Gear steel surface treatment method based on electron beam pre-scanning

By adopting electron beam prescanning treatment method on the surface of gear steel and optimizing process parameters through finite element simulation, the problems of low efficiency and poor tissue performance of traditional atmosphere carburizing technology are solved, and the carburizing treatment effect with high efficiency and low energy consumption is achieved .

CN119475842APending Publication Date: 2025-02-18GUILIN FUDA +2
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Patent Information

Application Number
CN202411260678.3
Authority / Receiving Office
CN · China
Patent Type
Applications(China)
Current Assignee / Owner
Filing Date
2024-09-10
Publication Date
2025-02-18

AI Technical Summary

Technical Problem

Traditional atmosphere carburizing technology has low efficiency, high energy consumption, and poor permeability in gear surface treatment.

Method used

The gear steel surface treatment method based on electron beam prescanning is adopted to optimize the electron beam scanning process parameters through finite element simulation to improve carburizing efficiency and improve tissue performance.

Benefits of technology

The efficiency and tissue performance of carburizing treatment are improved, energy consumption is reduced, and the microstructure and mechanical properties of the seepage layer are optimized.

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Abstract

The invention relates to a gear steel surface treatment method based on electron beam pre-scanning. The method comprises the steps that a moving heat source model is established; setting at least two electron beams, planning a moving path for each electron beam, and setting scanning process parameters (beam size, acceleration voltage, moving speed and the like); simulating the action of the scanning electron beam and the gear / gear steel matrix under the parameters, and obtaining a simulation result set; the electron beam actually acts on the gear / gear steel surface according to the set parameters based on the simulation result, and an actual result set is obtained; and the gear / gear steel obtained after electron beam scanning pretreatment is subjected to carburizing treatment, a plurality of first treatment results are obtained, meanwhile, gear steel which is not pretreated is subjected to carburizing treatment, a second treatment result is obtained, and the first treatment results and the second treatment result are analyzed and compared. A plurality of electron beams are arranged, the scanning beams of the electron beams are different, other conditions are not changed, and then the target (optimal) beam intensity of the electron beams is obtained.
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Description

Technical Field

[0001] The invention relates to the technical field of engineering application simulation and test verification methods, and in particular to a gear steel surface treatment method based on electron beam pre-scanning. Background Art

[0002] Atmosphere carburizing is one of the main technical means of gear surface strengthening at present. It has the advantages of low total cost and controllable hardened layer thickness and microstructure properties. However, the traditional atmosphere carburizing technology has low carburizing efficiency. Gears and other parts need to be kept at high temperature for a long time to obtain the target thickness of the carburized layer, which will extend the production cycle and increase production energy consumption. At the same time, it will cause problems such as gear structure deformation and microstructure deterioration. Therefore, it is necessary to develop appropriate catalytic carburizing technology or pre-treat it before carburizing to improve the carburizing efficiency and improve the microstructure and properties of the carburized layer.

[0003] The carburizing of low-carbon steel gears mainly consists of three processes: "formation of active carbon atoms → adsorption of carbon atoms on the gear surface → diffusion and reaction of carbon atoms in the metal part". Among them, the diffusion of carbon atoms in the metal surface obeys Fick's law. Therefore, by increasing the number of carbon atoms in the system, the concentration of carbon atoms on the metal surface, increasing the high-temperature activity of carbon elements, and increasing the diffusion channels of carbon elements in the substrate such as grain boundaries and dislocations, the diffusion of carbon elements can be promoted and the carburizing efficiency can be improved. Therefore, appropriately increasing the surface roughness of the gear to be carburized and refining the grain structure of the steel surface will help to enrich and diffuse carbon elements on the surface of the gear / gear steel during the carburizing process, thereby improving the carburizing efficiency. At the same time, the microstructure and mechanical properties of the carburized layer can be improved through tissue heredity, so as to achieve high-efficiency carburizing and simultaneous regulation of tissue properties.

[0004] Electron beam scanning, as an emerging surface modification technology, has been studied and applied in the field of high-end manufacturing. When the electron beam acts on the metal, its surface temperature rises sharply and causes the metal surface to melt and volatilize. After the scanning, the molten metal will solidify rapidly and cool rapidly. The grains and structure of the metal surface can be significantly refined, and there are a large number of crystal defects such as vacancies, dislocations and grain boundaries. Based on this, the present invention proposes to improve the carburizing efficiency and improve the structure and mechanical properties of gears / gear steel by electron beam scanning pretreatment, and at the same time use finite element simulation to guide the electron beam scanning process (mainly beam current) and obtain better process parameters. Summary of the invention

[0005] The purpose of the present invention is to provide a gear steel surface treatment method based on electron beam pre-scanning, which provides a new method and idea to solve the problems of low efficiency, high energy consumption and poor performance of carburized layer in traditional atmosphere carburizing of gears. This project also proposes to optimize and obtain better electron beam scanning process parameters based on numerical simulation to improve the process optimization rate and provide guidance for the selection of scanning process parameters. Based on the above technical problems, the experimental method includes:

[0006] S1: Establish a mobile heat source model;

[0007] S2: setting at least two electron beams, and setting a scanning path, a moving speed, a beam current parameter, and a distance between an electron beam emission port and a surface of a gear steel substrate for each electron beam;

[0008] S3: Simulate the interaction process between the electron beam and the gear steel matrix under the parameters set in step S2, and obtain a set of simulation results;

[0009] S4: Based on the simulation results of S3, the electron beam under the parameters set in step S2 is actually applied to the gear steel, and an actual result set is obtained;

[0010] S5: Carburizing the gear steel pre-treated in step S4 and obtaining a plurality of first processing results, carburizing the gear steel not pre-treated in step S4 and obtaining a second processing result, and analyzing and comparing the first processing result and the second processing result;

[0011] Wherein, establishing the mobile heat source model comprises:

[0012] S1-1: Select Gaussian surface heat source as the finite element numerical model;

[0013] S1-2: Mesh construction and division of the gear steel matrix;

[0014] S1-3: Set the thermophysical parameters of the gear steel matrix;

[0015] S1-4: Set boundary conditions and temperature field parameters.

[0016] Furthermore, the gear steel matrix includes A, B, C and D regions, the A region, C region and D region are divided with a first grid density, the B region is divided with a second grid density, the A region, B region and C region are arranged in sequence and located on one side of the D region, and the orthographic projection of the moving path is located in the B region.

[0017] Further, the B area is provided with a first detection group, a second detection group and a third detection group, the first detection group includes a plurality of first detection points distributed at intervals along the first direction, and the plurality of the first detection points are located at a first horizontal depth; the second detection group includes a plurality of second detection points distributed at intervals along the first direction, and the plurality of the second detection points are located at a second horizontal depth; the third detection group includes a plurality of third detection points distributed at intervals along the first direction, and the plurality of the third detection points are located at a third horizontal depth; wherein the first horizontal depth, the second horizontal depth and the third horizontal depth increase sequentially, and the data information acquired from the first detection point, the second detection point and the third detection point constitute the simulation result set.

[0018] Furthermore, the process parameters include acceleration voltage, scanning beam current and beam spot diameter. There are three electron beams, namely the first electron beam, the second electron beam and the third electron beam, and the moving path, moving speed, acceleration voltage, beam spot diameter, and the distance between the electron beam emission port and the surface of the gear steel matrix of each electron beam are the same. The scanning beam current of the first electron beam is 3mA, the scanning beam current of the second electron beam is 4mA, and the scanning beam current of the third electron beam is 5mA.

[0019] Furthermore, the total power P1 of the electron beam on the gear steel matrix is:

[0020]

[0021] Where Q(r) is the surface heat flux density at point r, the radius of the heat source (W / m 2 );Q max is the maximum heat density of the Gaussian heat source (W / m 2 ), C is the heat flux coefficient, and r is the distance between any point b and the center point on the horizontal plane (m).

[0022] Furthermore, the effective power P2 of the electron beam scanning is:

[0023] P2=ηUI

[0024] Among them, U is the acceleration voltage (KV) during the electron beam scanning process, I is the acceleration current (mA), and according to the heat conduction effect, the heat transfer efficiency η of the electron beam scanning on the material surface is 0.95.

[0025] Furthermore, the heat flow coefficient C is:

[0026]

[0027] Where r0 is the distance between any point b and the center point on the horizontal plane (m).

[0028] Furthermore, when the electron beam scans the surface of the gear steel substrate, the electron beam moves along the first direction, and its arbitrary time coordinate is assumed to be x0=vt, y0 is a fixed value, and the distance r from any point in the scanning area to the center of the electron beam spot is:

[0029]

[0030] Among them, v is the scanning speed and t is the action time.

[0031] Furthermore, the numerical model of the Gaussian heat source of the electron beam scanning is:

[0032]

[0033] Where Q is the maximum heat density of the Gaussian heat source (W / m 2 ).

[0034] Furthermore, the temperature field control equation is:

[0035]

[0036] Where ρ is the density of 22CrMoH steel kg / m3, c is the specific heat capacity of 22CrMoH steel, and K is the thermal conductivity.

[0037] Implementing the embodiments of the present invention will have the following beneficial effects:

[0038] The gear steel surface treatment method based on electron beam pre-scanning in this embodiment uses finite element simulation software to simulate the surface state of the gear steel substrate after electron beam scanning, and then verifies it through actual experiments. First, the actual result set is obtained by pre-processing with an electron beam, and then the gear steel after electron beam scanning and the gear steel without electron beam scanning are carburized respectively, thereby obtaining the first treatment result and the second treatment result. It can be seen from the first treatment result and the second treatment result that after electron beam scanning pre-treatment, the carburizing treatment effect is better. At the same time, multiple electron beams are set, and the scanning beam current of each electron beam is different, and other conditions remain unchanged, thereby verifying the influence of different scanning beam currents on the microstructure characteristics of the gear steel surface and the carburizing treatment effect, and then obtaining the target (optimal) beam current intensity of the electron beam. BRIEF DESCRIPTION OF THE DRAWINGS

[0039] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative work.

[0040] Figure 1This is a flow chart of a gear steel surface treatment method based on electron beam pre-scanning according to an embodiment of the present invention;

[0041] Figure 2 Establishing processes for mobile heat source models;

[0042] Figure 3 It is a schematic diagram of Gaussian surface heat source model;

[0043] Figure 4 Model diagram for meshing the gear steel matrix;

[0044] Figure 5 This is a schematic diagram of the surface morphology of the sample after electron beam scanning treatment;

[0045] Figure 6 This is a schematic diagram of the cross-sectional metallographic structure after electron beam scanning;

[0046] Figure 7 Schematic diagram of carburized layer thickness of gear steel after carburizing treatment: (a) unscanned sample, (b) sample pretreated by electron beam scanning (5mA);

[0047] Figure 8 Schematic diagram of the metallographic structure of the carburized layer of gear steel after carburizing treatment: (a) unscanned sample, (b) electron beam scanning pre-treated sample (5mA);

[0048] Fig. 9 Schematic diagram of EDS composition analysis results of the surface layer of gear steel after carburizing treatment: (a) unscanned sample, (b) electron beam scanning pre-treated sample (5mA);

[0049] Fig.10 This is a schematic diagram of the hardness gradient of gear steel after carburizing treatment;

[0050] Fig.11 Schematic diagram of the friction coefficient test results of gear steel after carburizing treatment. DETAILED DESCRIPTION

[0051] In order to facilitate the understanding of the present invention, the present invention will be described more fully below with reference to the relevant drawings. The preferred embodiments of the present invention are given in the drawings. However, the present invention can be implemented in many different forms and is not limited to the embodiments described herein. On the contrary, the purpose of providing these embodiments is to make the understanding of the disclosure of the present invention more thorough and comprehensive.

[0052] It should be noted that when an element is referred to as being "fixed to" another element, it may be directly on the other element or there may be a central element. When an element is considered to be "connected to" another element, it may be directly connected to the other element or there may be a central element at the same time. The terms "vertical", "horizontal", "left", "right" and similar expressions used herein are for illustrative purposes only.

[0053] Unless otherwise defined, all technical and scientific terms used herein have the same meaning as those commonly understood by those skilled in the art of the present invention. The terms used herein in the specification of the present invention are only for the purpose of describing specific embodiments and are not intended to limit the present invention. The term "and / or" used herein includes any and all combinations of one or more related listed items.

[0054] The present invention provides a gear steel surface treatment method based on electron beam pre-scanning, and firstly uses numerical simulation to simulate the phase change state of the gear / gear steel surface after electron beam scanning to guide the setting of scanning process parameters (especially beam size). Please refer to the method flow of the implementation case of this invention Figure 1 , mainly including:

[0055] S1: Establish a mobile heat source model;

[0056] S2: setting at least two electron beams, and setting a moving path, moving speed, process parameters, and a distance between the electron beam emission port and the surface of the gear steel substrate for each electron beam;

[0057] S3: using an electron beam to act on the gear steel matrix according to the setting parameters of step S2, and obtaining a set of simulation results;

[0058] S4: using the electron beam to act on the gear steel according to the setting parameters of step S2, and obtaining an actual result set;

[0059] S5: Carburizing the gear steel pre-treated in step S4 and obtaining a plurality of first processing results, carburizing the gear steel not pre-treated in step S4 and obtaining a second processing result, and analyzing and comparing the first processing result and the second processing result;

[0060] The steps for establishing the mobile heat source model are as follows: Figure 2 As shown, it mainly includes:

[0061] S1-1: Select Gaussian surface heat source as the finite element numerical model;

[0062] S1-2: Mesh construction and division of the gear steel matrix;

[0063] S1-3: Set the thermal physical parameters of the gear steel matrix;

[0064] S1-4: Set boundary conditions and temperature field parameters.

[0065] Figure 3 is a Gaussian surface heat source model, and its establishment process in step S1-1 is as follows. In a possible implementation, the total power P1 of the electron beam on the gear steel matrix is:

[0066]

[0067] Where Q(r) is the surface heat flux density at point r, the radius of the heat source (W / m 2 );Q max is the maximum heat density of the Gaussian heat source (W / m 2 ), C is the heat flux coefficient, and r is the distance between any point b and the center point on the horizontal plane (m).

[0068] like Figure 3 As shown, in a possible implementation manner, the effective power P2 of the electron beam scanning is:

[0069] P2=ηUI

[0070] Among them, U is the acceleration voltage (KV) during the electron beam scanning process, I is the acceleration current (mA), and according to the heat conduction effect, the heat transfer efficiency η of the electron beam scanning on the material surface is 0.95.

[0071] In one possible implementation, the heat flow coefficient C is:

[0072]

[0073] Where r0 is the distance between any point b and the center point on the horizontal plane (m).

[0074] In a possible implementation, when the electron beam scans the surface of the gear steel substrate, the electron beam moves along the first direction, and its arbitrary time coordinate is assumed to be x0=vt, y0 is a fixed value, and the distance r from any point in the scanning area to the center of the electron beam spot is:

[0075]

[0076] Among them, v is the scanning speed and t is the action time.

[0077] like Figure 3 As shown, in a possible implementation, the numerical model of the Gaussian heat source of electron beam scanning is:

[0078]

[0079] Where Q is the maximum heat density of the Gaussian heat source (W / m 2).

[0080] like Figure 3 As shown, in a possible implementation, the temperature field control equation is:

[0081]

[0082] Where ρ is the density of 22CrMoH steel kg / m3, c is the specific heat capacity of 22CrMoH steel, and K is the thermal conductivity.

[0083] In finite element simulation, setting appropriate boundaries has a very important impact on the accuracy of simulation. Among them, step S1-4 mainly includes three types of boundary conditions:

[0084] 1) Initial boundary conditions: The initial temperature before simulation (model temperature and scanning environment temperature), expressed as:

[0085] T0=298K

[0086] 2) Heat source boundary condition: This condition is mainly applicable to a fixed or constant heat flux density on the surface. In this study, the heat source is selected as a Gaussian surface heat source to meet this condition. As the electron beam scanning heat source, its expression is:

[0087]

[0088] 3) Radiative heat dissipation boundary conditions: The finite element simulation of electron beam scanning material surface is carried out in a vacuum environment. It is a non-convective heat dissipation transfer, but it is accompanied by thermal radiation transfer, so there is energy loss

[65] . The thermal radiation energy equation is:

[0089]

[0090] In the above formula, ε is the thermal emissivity; σ is the Stefan-Boltzmann constant; T c is the model temperature; T s Ambient temperature under vacuum scan.

[0091] like Figure 4As shown, in a possible embodiment, the gear steel matrix includes region A, region B, region C and region D, region A, region C and region D are divided with a first grid density, region B is divided with a second grid density, region A, region B and region C are sequentially arranged and located on one side of region D, and the positive projection of the moving path is located in region B. Exemplarily, the size of the gear steel matrix model is 50mm×50mm×20mm. In addition. The model is mainly divided into four parts, namely region A, region B, region C and region D. Among them, the region B is the electron beam scanning heat source moving area, with a size of 20mm×50mm×2mm; the size of the region A and region C is 15mm×50mm×2mm; the size of the region D is 50mm×50mm×18mm. The electron beam scanning process parameters mainly include acceleration voltage, beam current, beam spot diameter and scanning frequency. Three electron beams are set up in the embodiment, and except for the beam current size, the other scanning process parameters of the three electron beams are the same. Exemplarily, the acceleration voltage is set to 60 KV, the moving speed is 250 mm / min, the beam spot diameter is 10 mm, the scanning frequency is 700 Hz, and the scanning currents of the three electron beams are set to 3 mA, 4 mA, and 5 mA, respectively.

[0092] Figure 5 The surface morphology of the gear / gear steel under the above scanning process parameters shows that the electron beam scanning treatment can change the surface morphology of the gear steel, form molten pits and scanning marks, and improve the surface roughness of the sample.

[0093] Figure 6 Figure 2 is the metallographic structure after electron beam scanning at different scanning currents. It can be seen that a martensitic phase change layer is formed on the surface of the workpiece after electron beam scanning, and the thickness of the phase change layer increases with the scanning current.

[0094] Figure 7 The cross-sectional morphology of the carburized layer of the gear steel after carburizing and subsequent heat treatment before and after electron beam scanning treatment and after scanning at 5mA beam current parameters. It can be seen that the carburizing rate of the gear / gear steel can be effectively improved after electron beam scanning pretreatment with certain process parameters.

[0095] Figure 8The metallographic structure of the carburized layer of the gear steel without electron beam scanning pretreatment and after scanning at 5mA beam parameters. According to GB / T25744-2010, the martensite and retained austenite structures are graded. It can be seen that the length of the martensite structure in the carburized layer of the sample without electron beam pretreatment is between 13-15μm, which is a five-level needle-shaped martensite structure, and the volume fraction of retained austenite is between 5%-10%; while the length of the martensite in the sample pretreated by electron beam scanning after carburization is between 9-12μm, which is a four-level needle-shaped martensite structure, and the volume fraction of retained austenite is less than 5%. The electron beam scanning pretreatment has a certain improvement effect on the carburized layer structure.

[0096] Fig. 9 The EDS composition analysis results of the upper part of the carburized layer of gear steel after carburizing treatment show that the carbon content of the carburized layer surface of gear / gear steel can be effectively increased after electron beam scanning pretreatment with certain process parameters, which is beneficial to improve its surface hardness and wear resistance.

[0097] Fig.10 The hardness gradient of gear steel after carburizing treatment shows that the microhardness of the sample pretreated by electron beam scanning with certain process parameters is significantly improved compared with the untreated sample, the effective hardened layer depth is larger and the hardness gradient distribution is more reasonable.

[0098] Fig.11 The test results of the friction coefficient of gear steel after carburizing treatment show that under the same atmosphere carburizing process, electron beam scanning pretreatment with certain parameters can reduce the friction coefficient and wear of gears / gear steel, thereby improving the friction and wear performance of the carburized layer.

[0099] The above-mentioned embodiments only express the implementation method and process of the present invention, and the description thereof is relatively specific and detailed, but it cannot be understood as limiting the scope of the patent application. It should be pointed out that, for ordinary technicians in this field, several variations and improvements can be made without departing from the concept of the present invention, which all belong to the protection scope of the present invention. Therefore, the protection scope of the patent of the present invention shall be based on the attached claims.

Claims

1. A gear steel surface treatment method based on electron beam pre-scanning, which is used to improve the carburizing efficiency of gears / gear steel and improve its structure and mechanical properties. Its characteristics and experimental methods include: S1: Establish a mobile heat source model; S2: setting at least two electron beams, planning a moving path for each electron beam and setting process parameters (beam current, acceleration voltage, moving speed, etc.); S3: Simulate the interaction process between the electron beam and the gear steel matrix under the parameters set in step S2, and obtain a set of simulation results; S4: Based on the simulation results of S3, the electron beam under the parameters set in step S2 is actually applied to the gear steel, and an actual result set is obtained; S5: Carburizing the gear steel pre-treated in step S4 and obtaining a plurality of first processing results, carburizing the gear steel not pre-treated in step S4 and obtaining a second processing result, and analyzing and comparing the first processing result and the second processing result; Wherein, establishing the mobile heat source model comprises: S1-1: Select Gaussian surface heat source as the finite element numerical model; S1-2: Mesh construction and division of the gear steel matrix; S1-3: Set the thermophysical parameters of the gear steel matrix; S1-4: Set boundary conditions and temperature field parameters.

2. The gear steel surface treatment method based on electron beam pre-scanning according to claim 1 is characterized in that: The gear steel matrix includes region A, region B, region C and region D, wherein region A, region C and region D are divided with a first grid density, region B is divided with a second grid density, region A, region B and region C are sequentially arranged and located on one side of region D, and the orthographic projection of the moving path is located in region B.

3. The gear steel surface treatment method based on electron beam pre-scanning according to claim 2 is characterized in that: The B area is provided with a first detection group, a second detection group and a third detection group, the first detection group includes a plurality of first detection points distributed at intervals along a first direction, and the plurality of the first detection points are located at a first horizontal depth; the second detection group includes a plurality of second detection points distributed at intervals along the first direction, and the plurality of the second detection points are located at a second horizontal depth; the third detection group includes a plurality of third detection points distributed at intervals along the first direction, and the plurality of the third detection points are located at a third horizontal depth; wherein the first horizontal depth, the second horizontal depth and the third horizontal depth increase sequentially, and the data information acquired from the first detection point, the second detection point and the third detection point constitute the simulation result set.

4. The gear steel surface treatment method based on electron beam pre-scanning according to claim 3 is characterized in that: The process parameters include acceleration voltage, scanning beam current and beam spot diameter. There are three electron beams, namely the first electron beam, the second electron beam and the third electron beam, and the moving path, moving speed, acceleration voltage, beam spot diameter, and the distance between the electron beam emission port and the surface of the gear steel substrate of each electron beam are the same. The scanning beam current of the first electron beam is 3mA, the scanning beam current of the second electron beam is 4mA, and the scanning beam current of the third electron beam is 5mA.

5. The gear steel surface treatment method based on electron beam pre-scanning according to claim 1, characterized in that: The total power P1 of the electron beam on the gear steel matrix is: Where Q(r) is the surface heat flux density at point r, the radius of the heat source (W / m 2 );Q max is the maximum heat density of the Gaussian heat source (W / m 2 ), C is the heat flux coefficient, and r is the distance between any point b and the center point on the horizontal plane (m).

6. The gear steel surface treatment method based on electron beam pre-scanning according to claim 5 is characterized in that: The effective power P2 of the electron beam scanning is: P2=ηUI Among them, U is the acceleration voltage (KV) during the electron beam scanning process, I is the acceleration current (mA), and according to the heat conduction effect, the heat transfer efficiency η of the electron beam scanning on the material surface is 0.

95.

7. The gear steel surface treatment method based on electron beam pre-scanning according to claim 6 is characterized in that: The heat flow coefficient C is: Where r0 is the distance between any point b and the center point on the horizontal plane (m).

8. The gear steel surface treatment method based on electron beam pre-scanning according to claim 7, characterized in that: When the electron beam scans the surface of the gear steel substrate, the electron beam moves along the first direction. Assuming that its arbitrary time coordinate is x0=vt, y0 is a fixed value, the distance r from any point in the scanning area to the center of the electron beam spot is: Among them, v is the scanning speed and t is the action time.

9. The gear steel surface treatment method based on electron beam pre-scanning according to claim 8, characterized in that: The numerical model of the Gaussian heat source of the electron beam scanning is: Where Q is the maximum heat density of the Gaussian heat source (W / m 2 ).

10. The gear steel surface treatment method based on electron beam pre-scanning according to claim 1, characterized in that: The temperature field control equation is: Where ρ is the density of 22CrMoH steel (kg / m 3 ), c is the specific heat capacity of 22CrMoH steel, and K is the thermal conductivity.