Substance removal thickness estimation method

Abstract

This substance removal thickness estimation method involves: estimating, by using a solid heat conduction equation, a rising temperature in the vicinity of a laser irradiation point when a coating, rust, a deposit, or the like on the surface of a material such as a metal is irradiated with a laser beam; introducing a virtual substance which is a solid in the whole temperature range; and assuming that energy per unit area absorbed by the substance from the laser is equal to the energy per unit area required for vaporizing the substance having a prescribed depth from the surface, thereby estimating the thickness at which the substance on the surface is removed.

Description

Material removal thickness estimation method

[0001] The present invention relates to a method for estimating a material removal thickness, which estimates the thickness of a material formed on a surface of a metal or the like when the material is irradiated with a laser.

[0002] Laser cleaning technology, which removes rust, paint, and other deposits formed on the surface of materials such as metals by irradiating them with laser light, has been attracting attention. Patent Document 1 proposes a method for removing paint films from the surface of structures by rotating and scanning light in a circular pattern. Also, Non-Patent Document 1 reports that rust and salt can be removed by irradiating corroded steel plates with a laser.

[0003] Patent No. 5574354

[0004] Koji Onoue et al., "Applicability of a new laser-based surface preparation method to steel structures," Journal of Structural Engineering, Japan Society of Civil Engineers, Vol. 63 A, pp. 476-482, 2017.

[0005] The laser to be irradiated can be a continuous wave (CW laser) as in Patent Document 1, or a pulsed laser as in Non-Patent Document 1. In order to remove surface paint, rust, deposits, etc., it is important to set the irradiation conditions of these lasers appropriate for the object to be removed. Laser irradiation conditions (parameters) include laser power, laser beam diameter at the irradiation point, beam scanning speed, beam movement distance in the direction perpendicular to the scan, and number of irradiations when irradiation is repeated. In addition, in the case of a pulsed laser, parameters such as the pulse period and the length of one pulse are also used.

[0006] As described above, because there are many parameters related to laser irradiation, when trying to experimentally determine the appropriate parameter values ​​for removing surface paint, rust, deposits, etc., it is necessary to experimentally change many parameters and repeat trial and error, which is a time-consuming process.

[0007] The present invention has been made to solve the above problems, and aims to enable the determination of laser irradiation conditions in a shorter time by estimating the thickness of material that will be removed depending on the laser irradiation conditions, without experimental trial and error.

[0008] The material removal thickness estimation method according to the present invention is a method for estimating the thickness of material removed when a laser is irradiated onto a material formed on the surface of a metal or the like. The method estimates the temperature due to laser irradiation near the laser irradiation point using the heat conduction equation for a solid shown in the following equations (1), (2), and (3), and calculates the initial temperature T before laser irradiation. ini The temperature rise calculated by dividing the energy per unit mass required to vaporize the substance by the heat capacity per unit mass of the substance in a solid state is called the hypothetical boiling point T b When the laser is a pulsed laser, the temperature at the surface of the material is equal to the virtual boiling point T b The energy per unit area absorbed by the material from the laser between the time it reaches the target and the time the pulse ends is E absorption and the energy E required to vaporize the material from surface z = 0 to z = L per unit area. required By assuming that the thickness L of the material removed is equal to the temperature at the surface of the material, the temperature at the surface of the material is equal to the hypothetical boiling point T ｂ The energy E per unit area absorbed by the material from the laser between the time when the temperature reaches its maximum and the time when the temperature reaches its maximum. absorption and the energy E required to vaporize the material from surface z = 0 to z = L per unit area. required By equating , the thickness L of material removed is estimated.

[0009] r (r is a vector): Position near the laser irradiation point t: Time (point in time) J (J is a vector): Thermal energy passing through unit time / unit area ρ: Density of the substance c: Heat capacity per unit mass of the substance T: Temperature rise of the substance A: Energy generated in the substance by laser irradiation per unit time / unit volume K: Thermal conductivity of the substance f(r): Spatial dependence of the intensity of the irradiated laser (0≦f(r)≦1) q(t): Time dependence of the intensity of the irradiated laser (0≦q(t)≦1) A p : Peak power density of the laser incident on the surface of the material R: Reflectance of the laser irradiated on the material α: Laser absorption coefficient of the material z: Depth position from the surface of the material

[0010] As explained above, according to the present invention, the laser irradiation conditions can be determined in a shorter time by estimating the thickness of material that will be removed depending on the laser irradiation conditions, without experimental trial and error.

[0011] FIG. 1 is a characteristic diagram showing the temperature dependence of rust energy. FIG. 2 is a characteristic diagram showing the temperature dependence of rust energy (a) and the temperature dependence of hypothetical rust energy (b). FIG. 3A is an explanatory diagram showing the state of irradiating rust with a laser. FIG. 3B is an explanatory diagram explaining a pulsed laser (a) and a CW laser (b). FIG. 4A is a characteristic diagram showing the time dependence of the temperature on the surface of a material (rust) being irradiated with a pulse. FIG. 4B is a characteristic diagram showing the temperature of a material (rust) being irradiated with a pulse at time t １ 5A is a characteristic diagram showing the depth dependence of the laser power density at a peak power density of 1.73×10 12 W / m 2 5B is a graph showing the calculation results of the time dependence of the temperature rise on the rust surface when irradiating the rusted steel with pulsed laser light at a peak power density of 1.73 × 10 12 W / m 2 5C is a graph showing the calculation results of the depth dependency of the temperature rise at the time when the temperature rise at the surface of the rust reaches the boiling point when the pulsed laser beam is irradiated onto rusted steel under condition A. 12 W / m2 5D is a graph showing the calculation results of the time dependence of the temperature rise on the surface of the rust when irradiating the rusted steel with pulsed laser light at a peak power density of 3.21 × 10 12 W / m 2 FIG. 6 is a graph showing the calculation results of the depth dependence of the temperature rise at the time when the temperature rise at the surface of the rust reaches the boiling point when irradiated under condition B. FIG. 6 is a photograph showing the appearance of rusted steel after irradiating it with a pulsed laser under different conditions. FIG. 7A is a characteristic diagram showing the time dependence of the temperature at the surface of a material (rust) irradiated with CW laser light. FIG. 7B is a characteristic diagram showing the depth dependence of the temperature at time t2 of a material (rust) irradiated with CW laser light. FIG. 8A is a graph showing the calculation results of the time dependence of the temperature rise at the surface of the rust when irradiating rusted steel with a CW laser light by scanning at 1 m / s (condition C.). FIG. 8B is a graph showing the calculation results of the depth dependence of the temperature rise at the time when the temperature rise at the surface of the rust reaches the boiling point when irradiating rusted steel with a CW laser light by scanning at 1 m / s (condition C.). Figure 8C is a graph showing the calculation results of the time dependence of the temperature rise on the surface of the rust when rusted steel is irradiated by scanning with a CW laser beam at 2 m / s (condition D.). Figure 8D is a graph showing the calculation results of the depth dependence of the temperature rise at the time when the temperature rise on the surface of the rust reaches the boiling point when rusted steel is irradiated by scanning with a CW laser beam at 2 m / s (condition D.). Figure 9 is a photograph showing the appearance of rusted steel after irradiating with a CW laser under different conditions.

[0012] A method for estimating whether a substance can be removed according to an embodiment of the present invention will be described below. In the method for estimating whether a substance can be removed according to an embodiment of the present invention, when a laser beam is irradiated onto paint, rust, or deposits on the surface of a material such as metal, the temperature rise in the vicinity of the laser irradiated point is estimated using the heat conduction equation of a solid.

[0013] In general, when a solid material is irradiated with a laser, the temperature rise of the solid in the vicinity of the laser irradiated area can be estimated by solving the heat conduction equation (1) (Reference 1).

[0014]

[0015] In equation (1), r (r is a vector) is the position near the laser irradiation point, T is the temperature of the material to be estimated, and is a function of the position r near the laser irradiation point and time t. J (J is a vector) is the thermal energy passing through per unit time / unit area, and is a function of the position and time t. ρ is the density of the material. c is the heat capacity per unit mass of the material. Therefore, ρc is the heat capacity of the material per unit volume. A is the energy generated in the material by laser irradiation per unit time / unit volume, and is a function of the position and time t.

[0016] Furthermore, the following Fourier's law holds between J and T: In equation (2), K is the thermal conductivity.

[0017]

[0018] The heat source term A (energy generated in a substance per unit time and per unit volume) is expressed by the following equation (3):

[0019]

[0020] Here, f(r) (r is a vector) is the spatial dependency of the intensity of the irradiated laser, and is normalized to be greater than or equal to 0 and less than or equal to 1. When the position where the laser is irradiated moves at a speed v (v is a vector), it becomes f(r-vt). Also, q(t) is the time dependency of the intensity of the irradiated laser, and is normalized to be greater than or equal to 0 and less than or equal to 1. For example, if irradiation of a rectangular pulse laser (pulse width τ) in the time domain begins at time 0, q(t) = 1 in the region 0≦t≦τ. If the number of pulses is 1, q(t) = 0 in other regions. Also, for example, if irradiation of a CW laser begins at time 0, q(t) = 0 in the region t<0, and q(t) = 1 in the region t>0. A p is the peak power density of the incident laser on the surface of the material [W / m 2 ]. R is the reflectance of the laser irradiated onto the material. α is the laser absorption coefficient of the material. z is the position in the depth direction from the surface of the material.

[0021] By providing appropriate initial and boundary conditions, equations (1), (2), and (3) can be solved numerically to determine the temperature T of the material near the point irradiated with the laser.

[0022] However, when the temperature of a material rises due to laser irradiation and exceeds its melting point or boiling point, equation (1) no longer holds. To avoid this problem, the present invention introduces a virtual material that is solid over the entire temperature range, and derives the temperature of the material near the laser irradiation point using the heat conduction equation for a solid. The thickness L of the material to be removed is estimated from the temperature of this virtual material.

[0023] The method for estimating material removal thickness according to an embodiment of the present invention will be described in more detail below, taking rust on a steel surface as an example and irradiating the rust with a laser. Steel is iron containing 0.02% to 2.1% carbon.

[0024] Figure 1 shows the temperature dependence of rust energy. The rust composition was assumed to be Fe2O3. The energy at room temperature (298K) was set to 0. The heat capacity per unit mass, c, is a physical quantity that is inherently dependent on temperature, but for simplicity, it was set to a constant value of 0.9 J / (gK). The melting point of Fe2O3 was set to 1800K, and the boiling point was set to 2973K.

[0025] Since I was unable to find literature values ​​for the heat of fusion and heat of vaporization of Fe2O3, I substituted the literature values ​​for FeO listed in Reference 2, adopting a heat of fusion of 430 J / g and a heat of vaporization of 3200 J / g. Therefore, the energy required (per unit mass) to vaporize Fe2O3 at room temperature (298 K) is (2973 K - 298 K) x 0.9 J / (gK) + 430 J / g + 3200 J / g = 6037.47 J / g. Here, I introduce hypothetical rust, which is solid across the entire temperature range. Furthermore, I assume that the heat capacity c is a constant value of 0.9 J / (gK) across the entire temperature range.

[0026] Figure 2(b) shows the temperature dependence of hypothetical rust energy. The slope of the line showing the temperature dependence of hypothetical rust energy shown in Figure 2(b) is the heat capacity of hypothetical rust [c = 0.9 J / (gK)]. Figure 2(a) shows the temperature dependence of the actual rust energy shown in Figure 1.

[0027] The energy (per unit mass) required to vaporize Fe2O3 at room temperature is 6037.47 J / g, as shown by the dashed line in Figure 2(c), and the temperature at which the above-mentioned hypothetical rust has this energy will be called the hypothetical boiling point. The difference between the hypothetical boiling point of rust and room temperature is calculated by dividing the energy per unit mass required to vaporize Fe2O3 (substance) by the heat capacity per unit mass of Fe2O3 (substance) in the solid state, which is 6037.47 J / g ÷ 0.9 J / (gK) = 6708.3 K.

[0028] Therefore, if we consider irradiating a virtual rust, which is solid across the entire temperature range, with a laser and solve the heat conduction equation for solids, and the temperature of the virtual rust rises from room temperature by 6708.3 K or more, we can estimate that the rust is removable. Similarly, if the temperature is less than 6708.3 K, we can estimate that the rust is not removable.

[0029] Figure 3A shows how a laser is irradiated onto rust. Figure 3A is a cross-sectional view of the rust and steel viewed from the y-axis direction. The z-axis is the depth direction, with z = 0 at the surface of the rust. The direction of laser scanning is the x-axis, and its speed is v. Furthermore, if a Gaussian beam is used as the spatial dependence f(r) of the laser beam intensity, irradiation begins at time 0, and the laser irradiation position at time 0 is (x, y) = (0, 0), the heat source term A can be written as follows:

[0030]

[0031] Here, d is the 1 / e radius of the laser beam on the rust surface (the radius at which the power density is 1 / e of the maximum value). p : the peak power density of the laser incident on the surface, R: the laser reflectivity of the rust, and α: the light absorption coefficient of the rust. pLet us consider the case where R and α are constants independent of temperature. Also, assuming that thermal radiation from the rust surface can be ignored, the following boundary conditions are adopted:

[0032]

[0033] If we assume that the temperature of the rust is the ambient temperature (room temperature RT) regardless of location before the laser light irradiation begins, the temperature T of the rust at time t and location (x, y, z) after laser irradiation can be written as follows (Reference 1):

[0034]

[0035]

[0036] Here, ρ is the density of rust, c is the heat capacity per unit mass of rust, and κ is the thermal diffusivity of rust (=K / (ρc), where K is the thermal conductivity of rust), which are constants that are independent of temperature. In the following evaluation, ρ=5.2×10 3 kg / m 3 , c = 9.0 × 10 2 J / (kgK), κ=9.2×10 -7 m 2 / s, R = 0.3, α = 4.5 × 10 5 / m.

[0037] Furthermore, when laser irradiation starts from time 0, the lower limit of the integral range of equation (6) can be set to 0 as shown in the following equation (6').

[0038]

[0039] Next, the case where the laser is a pulsed laser and the case where the laser is a CW laser will be described in detail.

[0040] [1. When the laser is a pulsed laser] Consider a pulsed laser that outputs a pulse train at a certain period, as shown in Figure 3B (a). The pulse width is τ. Estimate the thickness of the material (rust) removed at this time. When performing laser cleaning, pulses are usually irradiated while moving (scanning) the beam, rather than repeatedly irradiating the same location with pulses. If the start time of pulse irradiation is set to 0, the end time of irradiation is τ. If the temperature of the material (rust) exceeds the virtual boiling point before time τ, it can be assumed that the material (rust) will be removed. When the laser is a pulsed laser, the thickness of the material removed can be estimated at the point (x, y) where laser irradiation begins.

[0041] Figure 4A shows the time dependence of temperature on the surface (coordinates (x0, y0)) of the material (rust) being irradiated with a pulse. The coordinates (x0, y0) are the location where the thickness of the material (rust) being removed is evaluated. Expressed mathematically, this is given by Equation (8), where 0 ≤ t ≤ τ.

[0042]

[0043] When a laser is irradiated under certain conditions, the temperature reaches the virtual boiling point T b In this case, the energy per unit area absorbed by the material (rust) from the laser during the time period t1 to τ is E absorption can be written as follows:

[0044]

[0045] Here, the laser is assumed to be completely absorbed without passing through the material (rust). ０ , y ０ ) at a certain time t, the temperature dependence T(x ０ , y ０ , z, t) can be written as follows:

[0046]

[0047] 4B shows the temperature dependence T(x0, y0, z, t1) in the depth direction at coordinates (x0, y0) and time t1, which is obtained by substituting t=t1 into equation (10).

[0048] The temperature at the surface z = 0 is the virtual boiling point T b The energy E required to vaporize the material (rust) from z = 0 to z = L per unit area is required can be written as follows:

[0049]

[0050] Here, T(x0, y0, z, t1) is as shown in FIG. 4B.

[0051] Energy E per unit area absorbed by the material (rust) from the laser at times t1 to τ absorption and the energy E required to vaporize the material (rust) from z = 0 to z = L per unit area. required By setting these to be equal, the thickness L of the vaporized material (rust) can be estimated.

[0052] Figure 5 shows the results of model calculations when a laser is irradiated onto rusted steel under different conditions. The model calculations were performed under the conditions of pulse width τ = 100 ns, beam diameter d = 30 μm, scan speed v = 2.5 m / s, and peak power density A p 1.73 x 10 12 W / m 2 (Condition A.), 3.21 x 10 12 W / m 2 (Condition B) was changed in two ways. Laser irradiation started at time 0, centered on the coordinates x = 0, y = 0, and the thickness of the vaporized material (rust) at time t = τ = 100 ns and the coordinates x = 0, y = 0 was calculated.

[0053] Figure 5A shows the time dependence of the temperature rise at the surface, T(0,0,0,t)-RT, under condition A.

[0054] Using equation (8), the hypothetical boiling point of 6708.3 K was reached 62.34 ns after the start of irradiation. Figure 5B shows the depth-wise distance dependence of the temperature rise at time 62.34 ns, T(0,0,z,t=62.34 ns)-RT, calculated using equation (10). Using equations (9) and (11), the thickness of the material (rust) removed was estimated to be 3.2 μm under condition A.

[0055] On the other hand, Figure 5C shows the time dependence of the temperature rise at the surface under condition B. Calculations using equation (8) show that the hypothetical boiling point of 6708.3 K was reached 32.87 ns after the start of irradiation.

[0056] Figure 5D shows the depth-distance dependence of the temperature rise at time 32.87 ns calculated using Equation (10). Using Equations (9) and (11), we estimated the thickness of the material (rust) removed under Condition B, which was 6.9 μm.

[0057] Table 1 shows a summary of the model calculation results for the above pulse laser.

[0058]

[0059] Figure 6 shows photographs (experimental results) of the appearance of rusted steel after laser irradiation under various conditions. The pulse width τ, beam diameter d, scan speed v, and peak power density are the same as those in the model calculations. The pulse period is 10 μs (frequency 100 kHz), the movement distance in the vertical direction of the scan is 25 μm, and the number of cleanings is 1, 2, 3, or 4. Visual inspection shows that under condition B, almost all of the rust is removed after three times.

[0060] On the other hand, under condition A, some rust remains even after four passes. Using the estimated removal thickness from the model calculation, the rust thickness before laser irradiation can be estimated to be approximately 20 μm. However, in this case, due to the pulse period (10 μs) and scan speed (2.5 m / s), the beam is irradiated every 25 μm, so there is a possibility that rust may also be removed by pulses before and after the pulse focused on in the calculation. Therefore, the actual rust thickness before laser irradiation can be estimated to be thicker than approximately 20 μm.

[0061] [2. When the laser is a CW laser] Unlike pulsed lasers, CW lasers, such as those shown in Figure 3B (b), have no concept of pulse width. Therefore, the time when the temperature reaches its maximum value is considered to be the end of laser irradiation, and the same process is carried out as with pulsed lasers. Figure 7A shows the time dependence of the temperature on the surface (coordinates (x0, y0)) of a material (rust) being irradiated with scanned CW laser light. Expressed mathematically, this is given by Equation (8').

[0062]

[0063] The coordinates (x0, y0) are chosen so that the laser light gradually approaches as time passes, passes the center of the laser light at a certain time, and then gradually moves away. When the laser is irradiated and scanned under certain conditions, the temperature reaches a virtual boiling point at time t2 and reaches its maximum value at time t3. In this case, the energy E per unit area absorbed by the material (rust) from the laser between times t2 and t3 is absorption can be written as follows, similar to the case of a pulsed laser:

[0064]

[0065] Here, it is assumed that the laser is completely absorbed without passing through the material (rust). Equation (9') can be expressed as equation (9'') described later. The temperature dependence T(x0, y0, z, t) in the depth direction at a certain time t on the coordinates (x0, y0) can be written as the following equation.

[0066]

[0067] 7B shows the temperature dependence T(x0, y0, z, t2) in the depth direction at coordinates (x0, y0) and time t2, which is obtained by substituting t=t2 into equation (10').

[0068] The temperature at the surface z = 0 is the virtual boiling point T b The energy E required to vaporize the material (rust) from z = 0 to z = L per unit area is required can be written as follows, similar to the case of a pulsed laser:

[0069]

[0070] Here, T(x0, y0, z, t2) is as shown in FIG. 7B. Equation (11') can be expressed as equation (11"), which will be described later. The energy E per unit area absorbed by the material (rust) from the laser between times t2 and t3 is absorption and the energy E required to vaporize the material (rust) from z = 0 to z = L per unit area.required By setting these to be equal, the thickness L of the vaporized material (rust) can be estimated.

[0071] Figure 8 shows the results of model calculations when a laser is irradiated onto rusted steel under different conditions. The model calculations were performed with a beam diameter d of 36 μm and the scanning speed v changed to two conditions: 1 m / s (condition C) and 2 m / s (condition D). Peak power density A p is 2.06 x 10 10 W / m 2 At time 0, laser irradiation was started with the coordinates x = 0, y = 0 as the center. Under condition C, the thickness of the vaporized material (rust) was calculated at x = 100 μm and y = 0 μm.

[0072] On the other hand, under condition D, a similar calculation was performed with x = 300 μm and y = 0 μm. Considering the scan speed, under condition C, the center of the beam passes through x = 100 μm and y = 0 μm at time 100 μs. Under condition D, the center of the beam passes through x = 300 μm and y = 0 μm at time 150 μs.

[0073] Figure 8A shows the time dependence of temperature rise under condition C. Calculations using equation (8') showed that the hypothetical boiling point was reached at time 78.9 μs. The maximum temperature was reached at time 125.1 μs. Figure 8B shows the depth dependence of temperature rise at time 78.9 ns, calculated using equation (10'). Estimating the thickness of the material (rust) removed using equations (9') and (11') revealed that 24.6 μm was removed under condition C.

[0074] Figure 8C shows the time dependence of temperature rise under condition D. Calculations using equation (8') showed that the hypothetical boiling point was reached at time 145.34 μs. The maximum temperature was reached at time 164.04 μs. Figure 8D shows the depth dependence of temperature rise at time 145.34 μs, calculated using equation (10'). Estimating the thickness of the material (rust) removed using equations (9') and (11') revealed that 12.6 μm was removed under condition D.

[0075] Table 2 shows a summary of the model calculation results for the above CW laser.

[0076]

[0077] Figure 9 shows photographs (experimental results) of the appearance of rusted steel after irradiating it with a CW laser under different conditions. The beam diameter d, scan speed v, and peak power density A p is the same as the model calculation. The movement distance in the vertical direction of the scan is 20 μm, and the number of cleanings is 1 and 3. Visual inspection shows that after one cleaning, condition C removes more rust than condition D. On the other hand, after three cleanings, both conditions C and D remove rust. Using the estimated removal thickness from the model calculation, the rust thickness can be estimated to be about 30 μm.

[0078] In the above explanation, room temperature RT was used as the initial temperature of the substance. ini It may be.

[0079] As described above, according to the present invention, a virtual material is assumed to be solid over the entire temperature range, and the temperature in the vicinity of the laser irradiation point is derived using the heat conduction equation for a solid. ini The temperature rise calculated by dividing the energy per unit mass required to vaporize the substance by the heat capacity per unit mass of the substance in a solid state is called the hypothetical boiling point T b Let's call it this.

[0080] When the laser is a pulsed laser, the temperature at the surface of the material is equal to or higher than the virtual boiling point T b The energy per unit area absorbed by the material from the laser between the time it reaches the target and the time the pulse ends is E absorption and the energy E required to vaporize the material from surface z = 0 to z = L per unit area. required By equating , the thickness L of material removed is estimated.

[0081] When the laser is a CW laser, the temperature at the surface of the material is equal to or higher than the virtual boiling point T b The energy E per unit area absorbed by the material from the laser between the time when the temperature reaches its maximum and the time when the temperature reaches its maximum. absorptionand the energy E required to vaporize the material from surface z = 0 to z = L per unit area. required By assuming that σ is equal to σ, the thickness L of the material to be removed is estimated. In this way, according to the present invention, it is possible to estimate the amount of material to be removed from the surface by simple calculation. Information on the estimated removal thickness can be used to determine the laser irradiation conditions in a shorter time without experimental trial and error.

[0082] Thus, according to the present invention, the thickness of material removed from the surface can be estimated by simple calculation, and the laser irradiation conditions can be determined in a shorter time by estimating the thickness of material removed depending on the laser irradiation conditions without experimental trial and error. Information on the estimated removal thickness can be used to determine the laser irradiation conditions in a shorter time without experimental trial and error.

[0083] Some or all of the above-described embodiments may also be described as, but are not limited to, the following supplementary notes.

[0084] [Supplementary Note 1] A method for estimating the thickness of a material removed when a laser is irradiated onto a material formed on the surface of a metal or the like, is provided. The method estimates the temperature caused by laser irradiation near the laser irradiation point using the solid heat conduction equations shown in the following equations (1), (2), and (3), and calculates the initial temperature T before laser irradiation. ini The temperature rise calculated by dividing the energy per unit mass required to vaporize the substance by the heat capacity per unit mass of the substance in a solid state is called the hypothetical boiling point T b When the laser is a pulsed laser, the temperature at the surface of the material is equal to or greater than the virtual boiling point T b The energy E per unit area absorbed by the material from the laser between the time when the laser reaches the target and the time when the pulse ends. absorption and the energy E required to vaporize the substance from the surface z = 0 to z = L per unit area. required The thickness L of the material removed is estimated by setting the thickness L equal to the virtual boiling point Tｂ The energy E per unit area absorbed by the material from the laser between the time when the temperature reaches the maximum and the time when the temperature reaches the maximum. absorption and the energy E required to vaporize the substance from the surface z = 0 to z = L per unit area. required and estimating the thickness L of the material removed by setting the thickness L to be equal to the thickness L of the material removed.

[0085] r (r is a vector): Position near the laser irradiation point t: Time (point in time) J (J is a vector): Thermal energy passing through unit time / unit area ρ: Density of the substance c: Heat capacity per unit mass of the substance T: Temperature rise of the substance A: Energy generated in the substance by laser irradiation per unit time / unit volume K: Thermal conductivity of the substance f(r): Spatial dependence of the intensity of the irradiated laser (0≦f(r)≦1) q(t): Time dependence of the intensity of the irradiated laser (0≦q(t)≦1) A p : Peak power density of the laser incident on the surface of the material R: Reflectance of the laser irradiated to the material α: Laser absorption coefficient of the material z: Position in the depth direction from the surface of the material

[0086] [Supplementary Note 2] In the method for estimating a material removal thickness described in Supplementary Note 1, the density ρ of the material, the heat capacity c of the material, the thermal conductivity K of the material, the reflectance R of the material, and the absorption coefficient α of the material are constants independent of temperature, and the heat conduction equation of the solid satisfies the boundary condition shown in the following equation (5).

[0087]

[0088] [Supplementary Note 3] In the method for estimating a material removal thickness according to Supplementary Note 1 or 2, when the location where the thickness of the material to be removed is evaluated is set to r0 (vector) = (x0, y0), absorption is represented by the following formula (9'"), and the E required is a material removal thickness estimation method shown in the following equation (11 ″).

[0089] t1: The temperature due to laser irradiation is the virtual boiling point T bt1': When the laser is a pulsed laser, this is the pulse end time. When the laser is a CW laser, this is the time when the temperature due to laser irradiation reaches its highest point. v (vector): Scanning speed of the laser beam. d: 1 / e radius of the laser beam.

[0090] [Supplementary Note 4] In the method for estimating a material removal thickness according to any one of Supplementary Notes 1 to 3, when the laser is a pulsed laser, the material removal thickness estimation is performed at a point (x, y) where laser irradiation is started.

[0091] [Supplementary Note 5] The method for estimating whether or not a material can be removed according to any one of Supplementary Notes 1 to 4, wherein the material is Fe2O3.

[0092] The present invention is not limited to the above-described embodiments, and it is clear that many modifications and combinations can be implemented by those skilled in the art within the technical spirit of the present invention. For example, while the above description describes the removal of rust formed on the surface of steel, the present invention is not limited to the above-described embodiments. For example, phenomena occurring when a laser is irradiated onto a material such as paint, deposits, or oxides present on the surface of a metal or the like can also be included in the scope of the present invention by calculating the material's physical properties using appropriate values. Furthermore, for example, the above description employs a Gaussian beam as the spatial dependency of the laser beam intensity, but this is not limiting. If the spatial dependency of the irradiated laser beam intensity is f(r), the energy E per unit area absorbed by the material (rust) from the laser between times t1 and t1' is: absorption can be written as follows instead of equation (9'):

[0093]

[0094] where r0 (r0 is a vector) is the location where the material (rust) removal thickness is evaluated, and v (v is a vector) is the scanning speed of the beam.

[0095] [Reference 1] J. H. Bechtel, "Heating of solid targets with laser pulses", Journal of Applied Physics, vol. 46, pp. 1585-1593, 1975. [Reference 2] B. Koroglu et al., "Gas Phase Chemical Evolution of Uranium, Aluminum, and Iron Oxides", Scientific Reports, vol. 8, Article number 10451, 2018.

Claims

1. A method for estimating the thickness of material removed when a laser is irradiated onto a material formed on the surface of a metal or the like, in which the temperature due to laser irradiation near the laser irradiation point is estimated using the solid heat conduction equation shown in the following formulas (1), (2), and (3), and the initial temperature T before laser irradiation is estimated. ini The temperature rise calculated by dividing the energy per unit mass required to vaporize the substance by the heat capacity per unit mass of the substance in a solid state is called the hypothetical boiling point T b When the laser is a pulsed laser, the temperature at the surface of the material is equal to or greater than the virtual boiling point T b The energy E per unit area absorbed by the material from the laser between the time when the laser reaches the target and the time when the pulse ends. absorption and the energy E required to vaporize the substance from the surface z = 0 to z = L per unit area. required The thickness L of the material removed is estimated by setting the temperature at the surface of the material equal to the virtual boiling point T ｂ The energy E per unit area absorbed by the material from the laser between the time when the temperature reaches the maximum and the time when the temperature reaches the maximum. absorption and the energy E required to vaporize the substance from the surface z = 0 to z = L per unit area. required and estimating the thickness L of the material removed by setting the thickness L to be equal to the thickness L of the material removed. r (r is a vector): Position near the laser irradiation point t: Time (point in time) J (J is a vector): Thermal energy passing through unit time / unit area ρ: Density of the substance c: Heat capacity per unit mass of the substance T: Temperature rise of the substance A: Energy generated in the substance by laser irradiation per unit time / unit volume K: Thermal conductivity of the substance f(r): Spatial dependence of the intensity of the irradiated laser (0≦f(r)≦1) q(t): Time dependence of the intensity of the irradiated laser (0≦q(t)≦1) A p : Peak power density of the laser incident on the surface of the material R: Reflectance of the laser irradiated to the material α: Laser absorption coefficient of the material z: Position in the depth direction from the surface of the material 2. A method for estimating a material removal thickness according to claim 1, wherein the density ρ of the material, the heat capacity c of the material, the thermal conductivity K of the material, the reflectance R of the material, and the absorption coefficient α of the material are constants independent of temperature, and the heat conduction equation of the solid satisfies the boundary condition shown in the following equation (5).

3. In the method for estimating a material removal thickness according to claim 1, when the location where the thickness of the material to be removed is evaluated is set to r0 (vector) = (x0, y0), E absorption is shown in the following equation (9'"), and E required is a material removal thickness estimation method shown in the following equation (11 ″). t1: The temperature due to laser irradiation is the virtual boiling point T b t1': if the laser is a pulsed laser, this is the pulse end time. If the laser is a CW laser, this is the time when the temperature reaches its highest point due to laser irradiation. v (vector): scanning speed of the laser beam. d: 1 / e radius of the laser beam.

4. A method for estimating a material removal thickness according to claim 1, wherein, when the laser is a pulsed laser, the material removal thickness is estimated at a point (x, y) where laser irradiation starts.

5. A method for estimating whether a material can be removed, according to any one of claims 1 to 4, wherein the material is Fe2O3.

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