CN106001928A - Selection method of laser parameters of laser paint removal - Google Patents

Abstract

The invention relates to a laser technology and provides a selection method of laser parameters of laser paint removal. The selection method solves the problems that existing selection of the laser parameters of laser paint removal is mainly based on experiments and experience. According to the technical scheme, first, a thermal stress removal threshold and erosion removal thresholds are obtained, and a paint ionization puncture threshold is obtained, wherein the erosion removal thresholds comprise the first erosion removal threshold and the second erosion removal threshold, the first erosion removal threshold regards that the paint rising temperature is equal to the melting point as the removal standard, and the second erosion removal threshold regards that the substrate rising temperature is equal to the paint melting point as the removal standard; and then whether the total thickness of a paint layer is smaller than the paint thickness corresponding to the paint ionization puncture threshold or not is judged, if yes, single-pulse removal or multi-pulse removal is selected according to the situations, and otherwise, multi-pulse removal is adopted. The selection method of the laser parameters of laser paint removal has the beneficial effects of being convenient to implement, practical and suitable for laser paint removal.

Description

The laser parameter system of selection of Investigation of Laser Delacquer-ing

Technical field

The present invention relates to laser technology, particularly to the technology of Investigation of Laser Delacquer-ing.

Background technology

Research to Investigation of Laser Delacquer-ing is a lot of both at home and abroad, and laser instrument kind has CO2, Nd:YAG, ultraviolet (excimer laser) And Er:YAG laser etc., pulsewidth can be divided into millisecond, microsecond, nanosecond, psec and femtosecond etc., and its research contents substantially concentrates three Aspect: the research of Investigation of Laser Delacquer-ing principle, the design of Investigation of Laser Delacquer-ing device and exploitation, the environmental factors research to paint removal influential effect (such as water environment, ambient pressure etc.) etc..

The reasonable selection of laser ablation painting process laser parameter, be related to removal efficiency and effect key factor it One.But existing selection mode is mainly based upon experiment to be groped and experience, make to remove variety classes and thickness in this way Paint time, need the experiment that repeats in a large number and grope, the most not only wasting time and energy, and can not be physically to paint removal Process recognizes clearly.So, the demand laser parameter system of selection removed for paint simple, practical, exercisable Become the most urgent.

Paint removal mechanisms at work is extremely complex, relates to heat effect, thermal stress effects, also has the gas under superlaser irradiation The effects such as change, ionization.The only physical mechanism of these effects of quantitative study, really could understand the removal process of paint, and Determine corresponding laser pulse parameter.And studied in the past and be mainly based upon simple paint removal model, as with paint temperature, oil Paint gasification temperatures etc. are as threshold value, the impact of the paint removal effects etc. such as Study of Laser repetition rate, pulsewidth.But in actual paint removal During, the thermodynamic process that under different parameter laser pulsed irradiations, paint is experienced has the biggest difference.Especially work as laser When irradiation is the most powerful, paint can occur ionization to produce laser plasma, and its blast effect, radiation effect etc. can significantly Increase the removal amount to paint, but also easily cause the damage of substrate simultaneously.So, only systematic study laser is to different qualities The ablation removal behavior of paint, just can reasonably be removed laser operation parameters.

Summary of the invention

The laser parameter that the invention aims to solve current laser ablation paint selects to be mainly based upon experiment and warp The problem tested, it is provided that the laser parameter system of selection of a kind of Investigation of Laser Delacquer-ing.

The present invention solves its technical problem, employed technical scheme comprise that, the laser parameter system of selection of Investigation of Laser Delacquer-ing, and it is special Levy and be, comprise the following steps:

Step 1, determine paint and the thermodynamic parameter of substrate, determine skin of paint adhesive stress and paint melting temperature, enter And obtain thermal stress and remove threshold value and ablation removal threshold value, and drawing paint ionization puncture threshold value, threshold value bag is removed in described ablation Including the first ablation and remove threshold value and the second ablation removal threshold value, the temperature etc. after threshold value raises is removed in described first ablation with paint Being removal standard in its fusing point, the second ablation removes the temperature after threshold value raises with substrate equal to paint fusing point for removing standard；

Step 2, judge skin of paint gross thickness whether less than paint paint thickness corresponding to ionization puncture threshold value, if then Enter step 3, otherwise enter step 4；

Step 3, according to circumstances selection use pulse to remove or multiple-pulse is removed, and when using pulse removal, this swashs Light pulse removes threshold value according to the thermal stress corresponding to this skin of paint gross thickness and the second ablation is removed value minimum in threshold value and entered Row laser parameter selects, and removes according to multiple-pulse, then enter step 4；

Step 4, employing multiple-pulse are removed, and it is total equal to skin of paint that skin of paint is removed thickness sum by the most all laser pulses Thickness, then each laser pulse before last laser pulse is right according to the skin of paint removal thickness of required removal The first ablation answered is removed threshold value and is carried out laser parameter selection, and it is right less than paint ionization puncture threshold value institute that this skin of paint removes thickness The paint thickness answered, last laser pulse is removed the thermal stress corresponding to thickness according to last skin of paint and is removed threshold value And second ablation remove value minimum in threshold value and carry out laser parameter selection.

Concrete, in step 4, when last laser pulse removes the heat corresponding to thickness according to last skin of paint When stress removal threshold value carries out laser parameter selection, each laser pulse is identical, when finally to skin of paint removal thickness before One laser pulse is removed threshold value according to the second ablation corresponding to last skin of paint removal thickness and is carried out laser parameter choosing When selecting, it is identical that skin of paint is removed thickness by the most all laser pulses.

Further, the thermal stress removed corresponding to thickness according to last skin of paint when last laser pulse is gone Except, when in threshold value and the second ablation removal threshold value, minimum value carries out laser parameter selection, it is big that last skin of paint removes thickness Thickness is removed in the skin of paint corresponding to each laser pulse before.

Concrete, method that described laser parameter selects by: according to the skin of paint thickness of required removal and going of being used Except threshold value selects corresponding laser parameter, described removal threshold value includes that thermal stress removes threshold value, threshold value and the is removed in the first ablation Threshold value is removed in two ablations, and described laser parameter includes laser single-pulse energy density, laser pulse hot spot radius and laser pulse Width, selected laser parameter is laser single-pulse energy density, is embodied as:

When using the first ablation to remove threshold value as removal threshold value,

$Y=\frac{E}{{\mathrm{\π\ω}}^2}=\frac{(M-J)\·\mathrm{\τ}}{\[\underset{n=1}{\overset{\mathrm{\∞}}{\Σ}}\frac{C_n{\mathrm{\ρ}}_1{c}_1}{k_1}{\left(\frac{l}{n\mathrm{\π}}\right)}^{2}cos\left(n\mathrm{\π}\right)\×\[1-e^{-\left(\frac{k_1}{{\mathrm{\ρ}}_1{c}_1}\right){\left(\frac{n\mathrm{\π}}{l}\right)}^2\·\mathrm{\τ}}\]+C_0\mathrm{\τ}\]}$

Wherein,

$C_n=\frac{2(1-R)}{{\mathrm{\ρ}}_1{c}_{1}l}\·\frac{(1-e^{-\mathrm{\α}l}\·\cos n\mathrm{\π})}{1+{\left(\frac{n\mathrm{\π}}{\mathrm{\α}l}\right)}^2},(n=1,2,3...)$

$C_0=\frac{(1-R)}{{\mathrm{\ρ}}_1{c}_{1}l}(1-e^{-\mathrm{\α}l})$

k₁For paint heat conductivity, ρ₁For paint density, c₁For paint specific heat capacity, α is paint absorptance, and R is anti-for paint Penetrating rate, A represents room temperature for paint absorbance, J, and M represents the melting temperature of paint, and E is laser single-pulse energy, and Y is laser energy Metric density, ω laser pulse hot spot radius, τ laser pulse width, l represents that skin of paint removes thickness；

When using the second ablation to remove threshold value as removal threshold value,

$Y=\frac{E}{{\mathrm{\π\ω}}^2}=\frac{(M-J)\·\mathrm{\τ}\·e^{\mathrm{\α}l}}{\left(\frac{2\mathrm{\τ}}{k_2}\sqrt{\frac{k_2\mathrm{\τ}}{{\mathrm{\ρ}}_2{c}_2}}\right)\·ierfc\left(\frac{l}{2\sqrt{\frac{k_2\mathrm{\τ}}{{\mathrm{\ρ}}_2{c}_2}}}\right)}$

Wherein, k₂Substrate heat conductivity, ρ₂Substrate paint density, c₂Substrate paint specific heat capacity；

When using thermal stress to remove threshold value as removal threshold value,

$Y=\frac{E}{{\mathrm{\π\ω}}^2}=\frac{F\·\mathrm{\τ}}{Y_2{\mathrm{\γ}}_2\[\frac{2{\mathrm{\πe}}^{(-\mathrm{\α}l)}}{k_2}\sqrt{\frac{k_2\mathrm{\τ}}{{\mathrm{\ρ}}_2{c}_2}}\·ierfc\[\frac{l}{2\sqrt{\frac{k_2\mathrm{\τ}}{{\mathrm{\ρ}}_2{c}_2}}}\]\]-Y_1{\mathrm{\γ}}_1\[\underset{n=1}{\overset{\mathrm{\∞}}{\Σ}}\frac{C_n{\mathrm{\ρ}}_1{c}_1}{k_1}{\left(\frac{l}{n\mathrm{\π}}\right)}^{2}cos\left(n\mathrm{\π}\right)\×\[1-e^{-\left(\frac{k_1}{{\mathrm{\ρ}}_1{c}_1}\right){\left(\frac{n\mathrm{\π}}{l}\right)}^2\·\mathrm{\τ}}\]+C_0\mathrm{\τ}\]}$

Wherein, Y₁For paint elastic modelling quantity, γ₁For paint thermal linear expansion coefficient, F represents the adhesive force of paint and substrate, Y₂Based elastic modulus, γ₂Substrate thermal linear expansion coefficient.

The invention has the beneficial effects as follows, in the present invention program, by the laser parameter system of selection of above-mentioned Investigation of Laser Delacquer-ing, Can quickly determine the laser parameter required for Investigation of Laser Delacquer-ing, the most each laser pulse is required select laser energy Density, convenient and practical.

Figure of description

Fig. 1 is the schematic diagram that in the embodiment of the present invention, the relation curve between thickness and laser parameter removed by paint.

Detailed description of the invention

Below in conjunction with the accompanying drawings and embodiment, technical scheme is described in detail.

The laser parameter system of selection of the Investigation of Laser Delacquer-ing of the present invention, it is first determined paint and the thermodynamic parameter of substrate, really Stand oil enamelled coating adhesive stress and paint melting temperature, and then obtain thermal stress removal threshold value and ablation removal threshold value, and obtain fuel-displaced Paint ionization puncture threshold value, described ablation removes threshold value and includes that the first ablation is removed threshold value and the second ablation and removed threshold value, and described the Temperature after single firing etching off raises with paint except threshold value is removal standard equal to its fusing point, and the second ablation removes threshold value with substrate liter Temperature after height is removal standard equal to paint fusing point, then judges that whether skin of paint gross thickness is less than paint ionization puncture threshold value institute Corresponding paint thickness, if the most according to circumstances selecting to use pulse to remove or multiple-pulse removal, otherwise uses multiple-pulse to go Removing, when using pulse to remove, this laser pulse removes threshold value and the according to the thermal stress corresponding to this skin of paint gross thickness Two ablations are removed value minimum in threshold value and are carried out laser parameter selection, when using multiple-pulse to remove, and the most all laser pulses Skin of paint is removed thickness sum equal to skin of paint gross thickness, then each the laser pulse root before last laser pulse The the first ablation removal threshold value removed corresponding to thickness according to the skin of paint of required removal carries out laser parameter selection, this skin of paint Remove thickness to paint according to last less than the paint thickness painted corresponding to ionization puncture threshold value, last laser pulse Layer removes the thermal stress removal threshold value corresponding to thickness and the second ablation is removed value minimum in threshold value and carried out laser parameter selection.

Embodiment

In Investigation of Laser Delacquer-ing, according to analyze and related experiment, laser ablation paint main mechanism be chemical ablation, Thermal stress and laser plasma action effect, when paint is removed by these three effect, so to enter according to removal effect Row selects.From experimental result it is found that use single laser pulse to remove relatively thin skin of paint, to thicker skin of paint, If using single laser pulse to remove, required pulsed laser energy is big, and when pulsed laser energy is big to a certain extent, Paint can occur ablation to puncture, thus the laser plasma produced, it can carry out strong absorption, reduce and swash post laser Optically coupling to the energy of paint, the destruction that painted substrates is easily produced by laser plasma bulk effect simultaneously.And, along with pulse The increase of energy, the cost of laser instrument can be continuously increased, which increase operating cost, goes so being suitable for repeatedly laser pulse Remove.All paint are removed in effect, and thermal stress effects removal effect is best, and paint does not the most remain in substrate, removes the most dry Only, next to that chemical ablation effect is removed.According to above result of study, we can obtain laser ablation several principle: 1. Laser irradiation intensity is less than ionization threshold；2. thicker when skin of paint, the most handy multiple-pulse is removed, so can avoid laser etc. from The generation of daughter；3. paint is removed and is selected thermal stress to remove effect as far as possible.

According to above principle, to a specific paint, the heating power according to irradiating laser pulse parameter and paint to be carried out Learn parameter and determine four threshold values that laser ablation paints, then determine that the irradiation ginseng of laser pulse removed by corresponding optimal paint Amount: first, obtains ablation removal threshold value and thermal stress removal laser irradiance pulse energy density corresponding to threshold value is gone with paint Except the relation of the degree of depth, then contrasting under same laser radiation parameter, depth value removed by each paint.When paint gross thickness is less than When painting the thickness corresponding to ionization threshold, pulse can be used to remove, the principle of selection is the burning corresponding to paint thickness Etching off removes a corresponding laser parameter minimum in threshold value except threshold value and thermal stress；When paint gross thickness is more than paint electricity When thickness corresponding to threshold value, needing to use multi-pulse laser to remove, this situation is more complicated: at same laser pulse spoke Under the conditions of according to, front several pulses should be to paint the ablation removal that temperature rise causes to the removal of paint, last pulse Removing the paint being then to cause due to substrate temperature rise or thermal stress to remove, this depends on both size contrasts, it should take wherein The removal thickness as last pulse big to paint removal amount, its condition selected is strong at same laser pulse irradiation Under the conditions of degree, the thickness sum of removing removing thickness and last pulse of front several pulses is equal to total paint thickness.

Thus, the laser parameter system of selection of the Investigation of Laser Delacquer-ing in the embodiment of the present invention, including step in detail below:

Step 1, determine paint and the thermodynamic parameter of substrate, determine skin of paint adhesive stress and paint melting temperature, enter And obtain thermal stress and remove threshold value and ablation removal threshold value, and draw paint ionization puncture threshold value (can be obtained) by experiment, Described ablation is removed threshold value and is included that the first ablation is removed threshold value and the second ablation and removed threshold value, described first ablation remove threshold value with Temperature after paint raises is removal standard equal to its fusing point, and the second ablation removes the temperature after threshold value raises with substrate equal to oil Paint fusing point is removal standard.

In this step, employing the first ablation can be respectively obtained and remove threshold value, the second ablation removal threshold value and thermal stress During except threshold value, the relation curve between thickness and laser parameter removed by paint, is respectively defined as curve A, curve B and curve C, ginseng See Fig. 1, wherein, L_A、L_B、L_CRepresent paint corresponding to this removal threshold value respectively and remove thickness.

Step 2, judge skin of paint gross thickness whether less than paint paint thickness corresponding to ionization puncture threshold value, if then Enter step 3, otherwise enter step 4.

Step 3, according to circumstances selection use pulse to remove or multiple-pulse is removed, and when using pulse removal, this swashs Light pulse removes threshold value according to the thermal stress corresponding to this skin of paint gross thickness and the second ablation is removed value minimum in threshold value and entered Row laser parameter selects, and removes according to multiple-pulse, then enter step 4.

Step 4, employing multiple-pulse are removed, and it is total equal to skin of paint that skin of paint is removed thickness sum by the most all laser pulses Thickness, then each laser pulse before last laser pulse is right according to the skin of paint removal thickness of required removal The first ablation answered is removed threshold value and is carried out laser parameter selection, and it is right less than paint ionization puncture threshold value institute that this skin of paint removes thickness The paint thickness answered, last laser pulse is removed the thermal stress corresponding to thickness according to last skin of paint and is removed threshold value And second ablation remove value minimum in threshold value and carry out laser parameter selection.

In this step, the thermal stress removed corresponding to thickness according to last skin of paint when last laser pulse is gone When carrying out laser parameter selection except threshold value, each laser pulse can be identical to skin of paint removal thickness before, when finally One laser pulse is removed threshold value according to the second ablation corresponding to last skin of paint removal thickness and is carried out laser parameter choosing When selecting, skin of paint is removed thickness by the most all laser pulses can also be identical, when last laser pulse is according to last Skin of paint removes the thermal stress removal threshold value corresponding to thickness and the second ablation is removed value minimum in threshold value and carried out laser parameter During selection, last skin of paint removes thickness can remove thickness more than skin of paint corresponding to each laser pulse before Degree.

In this example, the method that laser parameter selects is specifically as follows: according to the skin of paint thickness of required removal and used Removal threshold value select corresponding laser parameter, remove threshold value and include that thermal stress removes threshold value, threshold value and the is removed in the first ablation Threshold value is removed in two ablations, and laser parameter includes laser single-pulse energy density, laser pulse hot spot radius and laser pulse width, Selected laser parameter is laser single-pulse energy density, is embodied as:

When using the first ablation to remove threshold value as removal threshold value,

$Y=\frac{E}{{\mathrm{\π\ω}}^2}=\frac{(M-J)\·\mathrm{\τ}}{\[\underset{n=1}{\overset{\mathrm{\∞}}{\Σ}}\frac{C_n{\mathrm{\ρ}}_1{c}_1}{k_1}{\left(\frac{l}{n\mathrm{\π}}\right)}^{2}cos\left(n\mathrm{\π}\right)\×\[1-e^{-\left(\frac{k_1}{{\mathrm{\ρ}}_1{c}_1}\right){\left(\frac{n\mathrm{\π}}{l}\right)}^2\·\mathrm{\τ}}\]+C_0\mathrm{\τ}\]}$

Wherein,

$C_n=\frac{2(1-R)}{{\mathrm{\ρ}}_1{c}_{1}l}\·\frac{(1-e^{-\mathrm{\α}l}\·\cos n\mathrm{\π})}{1+{\left(\frac{n\mathrm{\π}}{\mathrm{\α}l}\right)}^2},(n=1,2,3...)$

$C_0=\frac{(1-R)}{{\mathrm{\ρ}}_1{c}_{1}l}(1-e^{-\mathrm{\α}l})$

k₁For paint heat conductivity, ρ₁For paint density, c₁For paint specific heat capacity, α is paint absorptance, and R is anti-for paint Penetrating rate, A represents room temperature for paint absorbance, J, and M represents the melting temperature of paint, and E is laser single-pulse energy, and Y is laser energy Metric density, ω laser pulse hot spot radius, τ laser pulse width, l represents that skin of paint removes thickness；

When using the second ablation to remove threshold value as removal threshold value,

$Y=\frac{E}{{\mathrm{\π\ω}}^2}=\frac{(M-J)\·\mathrm{\τ}\·e^{\mathrm{\α}l}}{\left(\frac{2\mathrm{\τ}}{k_2}\sqrt{\frac{k_2\mathrm{\τ}}{{\mathrm{\ρ}}_2{c}_2}}\right)\·ierfc\left(\frac{l}{2\sqrt{\frac{k_2\mathrm{\τ}}{{\mathrm{\ρ}}_2{c}_2}}}\right)}$

Wherein, k₂Substrate heat conductivity, ρ₂Substrate paint density, c₂Substrate paint specific heat capacity；

When using thermal stress to remove threshold value as removal threshold value,

$Y=\frac{E}{{\mathrm{\π\ω}}^2}=\frac{F\·\mathrm{\τ}}{Y_2{\mathrm{\γ}}_2\[\frac{2{\mathrm{\πe}}^{(-\mathrm{\α}l)}}{k_2}\sqrt{\frac{k_2\mathrm{\τ}}{{\mathrm{\ρ}}_2{c}_2}}\·ierfc\[\frac{l}{2\sqrt{\frac{k_2\mathrm{\τ}}{{\mathrm{\ρ}}_2{c}_2}}}\]\]-Y_1{\mathrm{\γ}}_1\[\underset{n=1}{\overset{\mathrm{\∞}}{\Σ}}\frac{C_n{\mathrm{\ρ}}_1{c}_1}{k_1}{\left(\frac{l}{n\mathrm{\π}}\right)}^{2}cos\left(n\mathrm{\π}\right)\×\[1-e^{-\left(\frac{k_1}{{\mathrm{\ρ}}_1{c}_1}\right){\left(\frac{n\mathrm{\π}}{l}\right)}^2\·\mathrm{\τ}}\]+C_0\mathrm{\τ}\]}$

Wherein, Y₁For paint elastic modelling quantity, γ₁For paint thermal linear expansion coefficient, F represents the adhesive force of paint and substrate, Y₂Based elastic modulus, γ₂Substrate thermal linear expansion coefficient.

Wherein, the laser pulse hot spot radius in laser parameter can be adjusted by the way of lens, the most relatively For fixing value or artificial confirmable value, and laser pulse width is all the preset parameter of laser instrument self, thus not Needing to select it, after have selected laser instrument, selected laser parameter the most only remains laser single-pulse energy density, Note that the present invention is applicable to middle laser pulse width in nanosecond, musec order condition, be generally unsuitable for pulsewidth psec, Femtosecond magnitude condition.

Claims (4)

1. the laser parameter system of selection of Investigation of Laser Delacquer-ing, it is characterised in that comprise the following steps:

Step 1, determine paint and the thermodynamic parameter of substrate, determine skin of paint adhesive stress and paint melting temperature, and then Removing threshold value and ablation to thermal stress and remove threshold value, and draw paint ionization puncture threshold value, described ablation is removed threshold value and is included the Single firing etching off removes threshold value except threshold value and the second ablation, and described first ablation removes the temperature after threshold value raises with paint equal to it Fusing point is removal standard, and the second ablation removes the temperature after threshold value raises with substrate equal to paint fusing point for removing standard；

Step 2, judge skin of paint gross thickness whether less than paint paint thickness corresponding to ionization puncture threshold value, if then entering Step 3, otherwise enters step 4；

Step 3, according to circumstances selection use pulse to remove or multiple-pulse is removed, when using pulse removal, and this laser arteries and veins Rush and swash according to minimum value in the thermal stress removal threshold value corresponding to this skin of paint gross thickness and the second ablation removal threshold value Optical parameter selects, and removes according to multiple-pulse, then enter step 4；

Step 4, employing multiple-pulse are removed, and skin of paint is removed thickness sum equal to skin of paint total thickness by the most all laser pulses Degree, then each laser pulse before last laser pulse is removed corresponding to thickness according to the skin of paint of required removal First ablation remove threshold value carry out laser parameter selection, this skin of paint remove thickness less than paint ionization puncture threshold value corresponding to Paint thickness, last laser pulse according to last skin of paint remove the thermal stress corresponding to thickness remove threshold value and Second ablation is removed value minimum in threshold value and is carried out laser parameter selection.

2. the laser parameter system of selection of Investigation of Laser Delacquer-ing as claimed in claim 1, it is characterised in that in step 4, when last When individual laser pulse carries out laser parameter selection according to the thermal stress removal threshold value corresponding to last skin of paint removal thickness, Each laser pulse is identical, when last laser pulse goes according to last skin of paint to skin of paint removal thickness before When carrying out laser parameter selection except the second ablation removal threshold value corresponding to thickness, skin of paint is removed thickness by the most all laser pulses Spend identical.

3. the laser parameter system of selection of Investigation of Laser Delacquer-ing as claimed in claim 1, it is characterised in that when last laser arteries and veins Rush and remove minimum in the thermal stress removal threshold value corresponding to thickness and the second ablation removal threshold value according to last skin of paint Value carries out laser parameter when selecting, and last skin of paint removes thickness more than paint corresponding to each laser pulse before Layer removes thickness.

4. the laser parameter system of selection of the Investigation of Laser Delacquer-ing as described in claim 1 or 2 or 3, it is characterised in that described laser is joined The method that amount selects by: select corresponding laser parameter according to the skin of paint thickness of required removal and the removal threshold value that used, Described removal threshold value includes that thermal stress removes threshold value, threshold value is removed in the first ablation and threshold value is removed in the second ablation, and described laser is joined Amount includes laser single-pulse energy density, laser pulse hot spot radius and laser pulse width, and selected laser parameter is sharp Light single pulse energy metric density, is embodied as:

When using the first ablation to remove threshold value as removal threshold value,

$Y=\frac{E}{{\mathrm{\π\ω}}^2}=\frac{(M-J)\·\mathrm{\τ}}{\[\underset{n=1}{\overset{\mathrm{\∞}}{\Σ}}\frac{C_n{\mathrm{\ρ}}_1{c}_1}{k_1}{\left(\frac{l}{n\mathrm{\π}}\right)}^{2}cos\left(n\mathrm{\π}\right)\×\[1-e^{-\left(\frac{k_1}{{\mathrm{\ρ}}_1{c}_1}\right){\left(\frac{n\mathrm{\π}}{l}\right)}^2\·\mathrm{\τ}}\]+C_0\mathrm{\τ}\]}$

Wherein,

$C_n=\frac{2(1-R)}{{\mathrm{\ρ}}_1{c}_{1}l}\·\frac{(1-e^{-\mathrm{\α}l}\·\cos n\mathrm{\π})}{1+{\left(\frac{n\mathrm{\π}}{\mathrm{\α}l}\right)}^2},(n=1,2,3...)$

$C_0=\frac{(1-R)}{{\mathrm{\ρ}}_1{c}_{1}l}(1-e^{-\mathrm{\α}l})$

k₁For paint heat conductivity, ρ₁For paint density, c₁For paint specific heat capacity, α is paint absorptance, and R is paint reflection Rate, A represents room temperature for paint absorbance, J, and M represents the melting temperature of paint, and E is laser single-pulse energy, and Y is laser energy Density, ω laser pulse hot spot radius, τ laser pulse width, l represents that skin of paint removes thickness；

When using the second ablation to remove threshold value as removal threshold value,

$Y=\frac{E}{{\mathrm{\π\ω}}^2}=\frac{(M-J)\·\mathrm{\τ}\·e^{\mathrm{\α}l}}{\left(\frac{2\mathrm{\τ}}{k_2}\sqrt{\frac{k_2\mathrm{\τ}}{{\mathrm{\ρ}}_2{c}_2}}\right)\·ierfc\left(\frac{l}{2\sqrt{\frac{k_2\mathrm{\τ}}{{\mathrm{\ρ}}_2{c}_2}}}\right)}$

Wherein, k₂Substrate heat conductivity, ρ₂Substrate paint density, c₂Substrate paint specific heat capacity；

When using thermal stress to remove threshold value as removal threshold value,

$Y=\frac{E}{{\mathrm{\π\ω}}^2}=\frac{F\·\mathrm{\τ}}{Y_2{\mathrm{\γ}}_2\[\frac{2{\mathrm{\πe}}^{(-\mathrm{\α}l)}}{k_2}\sqrt{\frac{k_2\mathrm{\τ}}{{\mathrm{\ρ}}_2{c}_2}}\·ierfc\[\frac{l}{2\sqrt{\frac{k_2\mathrm{\τ}}{{\mathrm{\ρ}}_2{c}_2}}}\]\]-Y_1{\mathrm{\γ}}_1\[\underset{n=1}{\overset{\mathrm{\∞}}{\Σ}}\frac{C_n{\mathrm{\ρ}}_1{c}_1}{k_1}{\left(\frac{l}{n\mathrm{\π}}\right)}^{2}cos\left(n\mathrm{\π}\right)\×\[1-e^{-\left(\frac{k_1}{{\mathrm{\ρ}}_1{c}_1}\right){\left(\frac{n\mathrm{\π}}{l}\right)}^2\·\mathrm{\τ}}\]+C_0\mathrm{\τ}\]}$

Wherein, Y₁For paint elastic modelling quantity, γ₁For paint thermal linear expansion coefficient, F represents the adhesive force of paint and substrate, Y₂Base End elastic modelling quantity, γ₂Substrate thermal linear expansion coefficient.