T

∂
t

=

2
⁢
π
⁢
λϑ

Bq

⁢

(

T
-

T
0

)

;

E_{utilized} = \int_{T_{0}}^{T_{f}} ρ {VC}_{p} dT + ρ {VL}_{p} = ρ {AvC}_{p} (A_{3} - T_{0}) + ρ {AvL}_{p};

H = \frac{Δ H * A}{E_{in}};

According to the Rosenthal equation (which is for analyzing a temperature distribution of a moving point heat source on a plate), in Equation [Image Omitted] , λ is a thermal conductivity of a material to be processed, v is a feed speed of the material, B is an absorption rate, q is a laser source power, and T₀is an ambient temperature; whether the hardening treatment of the material is complete is confirmed based on a conversion time from a phase change temperature to a cooling temperature on the surface of the material, and if a cooling rate on the surface of the material and a cooling rate of the material at a certain depth are both higher than a critical cooling rate of the material, it is known that the laser heat treatment is complete.

In Equation [Image Omitted] , E_utilizedis a lowest energy rate, ρ is a density of a material to be processed, C_pis a specific heat capacity of the material, V is a volume of the material in a processed hardened zone, L_pis heat energy required for a phase change transformation of the material, T₀is an ambient temperature, T_fis a highest temperature of the surface of the material, for materials with an austenitic structure, A₃is an upper limit temperature for material hardening, v is a scanning speed of the laser beam, and A is a cross-sectional area of the material; the energy for performing heat treatment on the surface of the material includes two parts, one is the energy required to raise the temperature to reach a phase transition state of the material, and the other is the energy required for a phase change, for example, temperature energy required for a phase change in iron quenching and energy to obtain the martensitic metallurgical organization, i.e., E_utilizedis calculated in Equation [Image Omitted] .

In Equation [Image Omitted] , H is a hardening efficiency index, ΔH is an average adding value of material hardness, A is a cross-sectional area of a material quenching surface, E_incorresponds to an overall energy density provided, and E_utilizedis an actually utilized energy density.

Further, a spot profile of the laser beam is first modulated by the binary grating 31 and the mask 4 in the spatial light modulator 3 to reduce a diffraction effect around the shaped laser beam, and a rectangular spot profile with an arbitrary shape can be trimmed, so that ±1st order beam is blocked by a slit by adjusting a diffraction period of the binary grating 31, and higher-order beams are completely removed. The diffraction angle and the diffraction efficiency of the laser beam are affected by the binary grating 31, and successive orders of diffracted beams will partially overlap, which leads to a less uniform energy density distribution of the laser beam and the reduced quality of the surface of the workpiece subjected to heat treatment.

The equation for local energy ratios under different grating densities of the mask 4 is as follows:

$ζ = \frac{\int I_{shaped} {ds}_{mask}}{\int \int I_{0} ds}$

- ζ corresponds to a local energy ratio, I_shapedis an energy intensity after shaping, s_maskis a mask area, and ∫∫I₀ds corresponds to an original spot curved surface integral, where a reference grating period is changed from 120 lm to 500 lm, and a local energy ratio is changed from 65% to 72%.

The diffraction angle of the laser beam can be calculated according to the following equations:

$T (\sin α + \sin β) = m λ;$