Substance removal thickness estimation method

Abstract

A virtual material that is a solid in all temperature regions is assumed, and the temperature in the vicinity of a pulse laser irradiation point is derived by using a heat conduction equation for a solid. A temperature that is increased from an initial temperature Tini preceding laser irradiation by a temperature derived by dividing the energy per unit mass necessary to vaporize a substance by the heat capacity per unit mass of the substance in a solid state is regarded as a virtual boiling point Tb. From a time t1 at which the temperature on a surface of the substance reaches Tb to a first pulse end time t1', the energy Eabsorption per unit area absorbed from the laser by the substance and the energy Erequired per unit area necessary to vaporize the substance from a surface z=0 to z=L1 are regarded as being equal. The thickness L1 by which the substance is removed by the first pulse is estimated.

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 pulsed 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, but pulsed lasers are also widely used as in Non-Patent Document 1. In order to remove surface paint, rust, deposits, etc. using a pulsed laser, the laser irradiation conditions must be optimized. Laser irradiation conditions (parameters) include the laser power, the laser beam diameter at the irradiation point, the speed at which the beam is scanned, the distance the beam is moved in the direction perpendicular to the scan, the number of irradiations when irradiation is repeated, the pulse period, and the length of one pulse.

[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 pulse laser irradiation conditions, without experimental trial and error.

[0008] The method for estimating a material removal thickness according to the present invention is a method for estimating a thickness of a material removed when a pulsed laser is irradiated onto a material formed on a surface of a metal or the like, and the method estimates the thickness of the material removed by irradiating the material with a pulsed laser. 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 virtual boiling point T b The temperature at the surface of the material is T b The first step is to estimate the time t1 at which the laser beam reaches the target point, and the second step is to estimate the energy E per unit area absorbed by the material from the laser between the estimated time t1 and the end time t1' of the first pulse. absorption and the energy E required to vaporize the material from the surface z = 0 to z = L1 per unit area. required The second step is to estimate the thickness L of material removed by the first pulse by setting b If the temperature distribution in the depth direction remaining after removing the material from z = 0 to L1 at time t1 is not reached, the temperature distribution in the depth direction at time t1' is set to t1 = t1', and the temperature at the surface of the material is set to T1' as the temperature distribution in the depth direction at time t1'. In the third step, the temperature at the surface of the material is set to T1' using the heat conduction equation of a solid when a pulse is irradiated so that the temperature at the surface becomes T1' at time t1'. p The fourth step is to calculate the depth dependence of the temperature at the surface, and set the temperature at the surface to T1. The fourth step is to solve the heat conduction equation of the solid, assuming that the temperature of the material just before the next pulse is irradiated is uniform at T1, and calculate the surface temperature at the virtual boiling point T b The fifth step is to determine the time t2 when the temperature at the surface of the material reaches T bIf the time t2 does not reach the next pulse end time t2', the depth dependency of the temperature rise at time t2 is calculated, and the depth dependency of the temperature rise at time t2 and the irradiation start time t2 of the next pulse are calculated. p A sixth step is to add the depth dependency of the temperature at time t to the depth dependency of the temperature at time t, and the temperature at the surface of the material is calculated by subtracting the temperature at the virtual boiling point T b The energy E per unit area absorbed by the material from the laser during the period from the time t2 when the laser reaches the target laser point to the end of the next pulse, t2'. absorption and the energy E required to vaporize the material from the surface z = 0 to z = L2 per unit area. required and a seventh step of estimating the thickness L2 of the material removed by the next pulse by setting the thickness L2 equal to the thickness L2 of the material removed by the next pulse. In the first, second, third, fourth, fifth, sixth, and seventh steps, the temperature at a location near the laser irradiation point is estimated using the heat conduction equation for a solid shown in the following equations (1), (2), and (3), and t i , t i ', L i , T i ', T i (i=1, 2, 3...) the subscript number is incremented by 1, and the irradiation start time of the next pulse is set to t p After increasing the number of thicknesses, the third to seventh steps are repeated a set number of times, and all estimated thicknesses are summed up to estimate the thickness L of the material removed by laser irradiation.

[0009] r (vector): Position near the laser irradiation point t: Time (instance) J (vector): Thermal energy passing through unit time / unit area ρ: Density of material c: Heat capacity per unit mass of material T: Temperature of material A: Energy generated in material by laser irradiation per unit time / unit volume K: Thermal conductivity of material 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 pulse 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. 3 is an explanatory diagram showing the state of irradiating rust with a laser. FIG. 4A is a characteristic diagram showing the time dependence of the temperature at the surface of a material (rust) irradiated with the first (first) pulse. FIG. 4B is a characteristic diagram showing the depth dependence of the temperature of a material (rust) irradiated with the first (first) pulse at time t1. FIG. 4C is a characteristic diagram showing the depth dependence of the temperature of a material (rust) irradiated with the first (first) pulse at time t1'. FIG. 5A is a characteristic diagram showing the peak power density of the laser at power A, such that the temperature reaches T1' at time t1'. p 5B is a characteristic diagram showing the time dependence of the temperature on the surface of a material (rust) when irradiated with light having a temperature of T1′ at time t1′. p When light having the following characteristics is irradiated, time t p 6A is a characteristic diagram showing the depth dependence of the temperature of the material (rust) at time t. FIG. 6B is a characteristic diagram showing the time dependence of the temperature at the surface of the material (rust) irradiated with the second pulse. p When the temperature at time t is assumed to be uniform at T1, p 6C is a characteristic diagram showing the depth dependence of the temperature of the material (rust) at time t p 6D is a characteristic diagram showing the time dependence of the temperature rise on the surface of the material (rust) irradiated with the second pulse, assuming that the temperature at time t is uniform at T1. p When the temperature at time t is assumed to be uniform at T1,p 6E is a characteristic diagram showing the depth dependence of the temperature rise of the material (rust) at time t p 6A is a characteristic diagram showing the depth dependency of the temperature rise of the material (rust) at time t2 when it is assumed that the temperature at time t2 is uniform at T1. FIG. 6F is a characteristic diagram showing the depth dependency of the temperature of the material (rust) irradiated with the second pulse at time t2. FIG. 6G is a characteristic diagram showing the depth dependency of the temperature of the material (rust) irradiated with the second pulse at time t2'. FIG. 7A is a characteristic diagram showing the depth dependency of the temperature of the material (rust) irradiated with the second pulse at time t2' when the peak power density of the laser is power A, so that the temperature becomes T2' at time t2'. p 7B is a characteristic diagram showing the time dependence of the temperature on the surface of a material (rust) when irradiated with light having a peak power density of power A, so that the temperature becomes T at time t. p When light having the following value is irradiated, time 2t p 8A is a characteristic diagram showing the depth dependence of the temperature of the material (rust) at time 2t. FIG. 8B is a characteristic diagram showing the time dependence of the temperature at the surface of the material (rust) irradiated with the third pulse. p When the temperature at time 2t is assumed to be uniform at T2, p 8C is a characteristic diagram showing the depth dependence of the temperature of the material (rust) at time 2t p 8D is a characteristic diagram showing the time dependence of the temperature rise on the surface of the material (rust) irradiated with the third pulse, assuming that the temperature at time 2t is uniform at T2. p When the temperature at time 2t is assumed to be uniform at T2, p FIG. 8E is a characteristic diagram showing the depth dependence of the temperature rise of the material (rust) at time 2t pFIG. 8F is a characteristic diagram showing the depth dependence of the temperature rise of the material (rust) at time t3, assuming that the temperature at time t2 is uniform at T2. FIG. 8F is a characteristic diagram showing the depth dependence of the temperature of the material (rust) irradiated with the third pulse at time t3. FIG. 9 is a characteristic diagram showing the time dependence of the temperature at the surface of the material (rust) when irradiated with three pulses. FIG. 10 is a diagram explaining the estimation of the removal thickness by irradiation with three pulses in Example 1. FIG. 11 is a characteristic diagram summarizing the results obtained in Example 1. FIG. 12 is a photograph showing the appearance of rusted steel after irradiating it with a pulse laser under different conditions. FIG. 13 is an explanatory diagram explaining the estimation of the removal thickness by irradiation with three pulses in Example 3. FIG. 14 is a characteristic diagram showing the results obtained in Example 3.

[0012] A method for estimating a material removal thickness according to an embodiment of the present invention will now be described. In the method for estimating a material removal thickness according to an embodiment of the present invention, when a pulsed laser beam is irradiated onto paint, rust, deposits, etc. on the surface of a material such as a metal, the temperature in the vicinity of the laser irradiation 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 of the solid in the vicinity of the laser irradiated point 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, when 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. When the number of pulses is 1, q(t) = 0 in other regions. Also, for example, when the period is t p and when the number of pulses is two, t p ≦t≦t p +τ, q(t) = 1. p When the number of pulses is three, p ≦t≦2t p +τ region, q(t) = 1. 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 numerically solved to determine the temperature T of a material near the laser irradiation site. However, if the temperature of the 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 site using the heat conduction equation for a solid. The thickness L of the material removed is estimated from the temperature of this virtual material.

[0022] 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.

[0023] 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.

[0024] 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.

[0025] 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.

[0026] 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.

[0027] 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.

[0028] Figure 3 shows how a laser is irradiated onto rust. Figure 3 is a cross-sectional view of the rust and steel viewed from the y-axis direction. The z-axis is taken as the depth direction, with z = 0 at the surface of the rust. The direction of laser scanning is taken as the x-axis. The scanning speed is taken as 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:

[0029]

[0030] 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. p , R, and α are constants that do not depend on temperature.

[0031] In addition, 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) may be set to 0.

[0038]

[0039] Consider a pulse laser that outputs a pulse train with a certain period. Let the pulse period be t p The pulse width is τ. The thickness of the material (rust) removed at this time is estimated.

[0040] [First step] Estimation of the boiling point arrival time t1 during the first pulse irradiation (FIG. 4A).

[0041] When performing laser cleaning, pulses are usually irradiated while moving (scanning) the beam, rather than repeatedly irradiating the same spot. If the irradiation start time and irradiation end time of the first (first) pulse are 0 and t1', respectively, then t1' = τ. Before time t1', the temperature of the material (rust) will reach the hypothetical boiling point T bIf the temperature exceeds t, it can be assumed that the material (rust) will be removed. Figure 4A shows the time dependence of the 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) removed is evaluated. Expressed mathematically, this is expressed as Equation (8), where 0≦t≦t1'.

[0042]

[0043] When a laser is irradiated under certain conditions, the temperature reaches the virtual boiling point T b Assume that we have reached

[0044] In the first step, the initial temperature T ini The temperature rise from the room temperature (for example, RT) by the temperature 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 virtual boiling point T b The temperature at the surface of the material is T b The time t1 at which the

[0045] [Second step] The thickness L of the material (rust) vaporized by the first pulse irradiation １ Estimation of (Fig. 4B).

[0046] In this case, the energy E per unit area absorbed by the material (rust) from the laser during the time period t1 to t1' is absorption can be written as follows:

[0047]

[0048] Here, we assume that the laser is completely absorbed without passing through the material (rust). 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 follows:

[0049]

[0050] FIG. 4B shows the temperature dependence T(x0, y0, z, t1) in the depth direction at coordinates (x0, y0) and time t1. This is obtained by substituting t=t1 into equation (10). The temperature at the surface z=0 is the virtual boiling point T bThe energy E required to vaporize the material (rust) from z = 0 to z = L1 per unit area is required can be written as follows:

[0051]

[0052] Here, T(x0, y0, z, t1) is as shown in FIG. 4B.

[0053] Energy E per unit area absorbed by the material (rust) from the laser at time t1 to t1' absorption and the energy E required to vaporize the material (rust) from z = 0 to z = L1 per unit area. required By assuming that these are equal, the thickness L1 of the material (rust) vaporized by the first pulse irradiation can be estimated.

[0054] In the second step, the energy E per unit area absorbed by the material from the laser between the estimated time t1 and the end time t1' of the first pulse is calculated. absorption and the energy E required to vaporize the material from the surface z = 0 to z = L1 per unit area. required By equating L1 with L2, the thickness of material removed by the first pulse is estimated.

[0055] Next, consider the removal of material (rust) by the second pulse (next pulse). To estimate the thickness L2 removed by the second pulse at coordinates (x0, y0), the following steps are taken:

[0056] [Third step] Remove the material (rust) from z=0 to L1 and determine the surface temperature T1' at the end time t1' of the first pulse irradiation (FIG. 4C).

[0057] Because it is estimated that the material (rust) from z = 0 to L1 was removed by the first pulse, the depth position L1 is set to z = 0. Also, it is assumed that the temperature distribution does not change between times t1 and t1'. That is, the portion of the temperature distribution T(x0, y0, z, t = t1) obtained by substituting t = t1 into equation (10) where z ≥ L1 is set as the temperature distribution T(x0, y0, z, t = t1'). The surface temperature at time t1' is denoted as T1'.

[0058] The temperature at the surface of the material is T b If the temperature does not reach the predetermined value, t1 is set to t1', and in the third step, the temperature distribution in the depth direction remaining after removing the material from z = 0 to L1 at time t1 is set to the temperature distribution in the depth direction at time t1', and the temperature at the surface of the material is set to T1'.

[0059] [Fourth step] Next (second) pulse irradiation start time t = t p Estimation of temperature distribution in (Fig. 5).

[0060] Consider light irradiation such that the temperature at the surface z=0 becomes T1' at time t1'. That is, in equation (8), the peak power density of the laser is power A so that T=T1' at time t=t1'. p Consider light irradiation with the following formula: Figure 5A shows the time dependence of temperature at x = x0, y = y0, z = 0.

[0061] The pulse period is t p When , the second pulse starts at t = t p At time t = t p The depth dependence of ρ (FIG. 5B) can be written as follows:

[0062]

[0063] Here, the upper limit of the integral range is t p Instead, it is t1' because the time t1' to t p This is because the laser is not irradiated during this time. Also, the temperature T(x0, y0, 0, t p ) will be written as T1.

[0064] In the fourth step, the heat conduction equation of a solid when a pulse is incident so that the temperature on the surface becomes T1' at time t1' is used to calculate the temperature at the start time t1' of the next pulse. p The depth dependence of the temperature at the surface is determined and the temperature at the surface is defined as T1.

[0065] [Fifth step] Estimation of the boiling point arrival time t2 during the next (second) pulse irradiation (FIGS. 6A, 6B, 6C, and 6D).

[0066] When the second pulse starts to be applied, the temperature of the material (rust) rises. However, if there is a spatial temperature distribution as shown in FIG. 5B, it becomes difficult to solve the heat conduction equation. Therefore, as shown in FIG. 6B, p The temperature at the point is assumed to be uniform at T1. By making this assumption, it becomes possible to easily solve the heat conduction equation.

[0067] When the temperature is uniform at T1, the temperature at the surface is the boiling point T b To reach b The temperature only needs to rise by -T1. Figures 6C and 6D show the temperature rise plotted on the vertical axis.

[0068] FIG. 6A can be expressed by equation (8').

[0069]

[0070] Equation (8') is obtained by changing the constant from RT to T1 in equation (8) and setting the lower limit of integration to t p This is what we have decided.

[0071] If the irradiation of the second pulse ends at time t2', the temperature rise on the surface of the material (rust) T(x0, y0, 0, t)-T1 will reach T b If the temperature exceeds -T1, it can be assumed that the material (rust) will be removed. b The time when it becomes -T1 is defined as t2.

[0072] In the fifth step, the temperature of the material immediately before the next pulse is irradiated is assumed to be uniform at T1, and the heat conduction equation of the solid is solved to determine whether the surface temperature is equal to the virtual boiling point T b The time t2 at which the

[0073] [Sixth step] Estimation of the temperature distribution at the boiling point arrival time t2 during the next (second) pulse irradiation (FIGS. 6E and 6F).

[0074] FIG. 6E shows the time t p The temperature rise at the surface z=0 is T b-T1. FIG. 6E can be expressed by equation (10').

[0075]

[0076] Equation (10') is obtained by changing the constant from RT to T1 in equation (10) and moving it to the left side, and setting the lower limit of the integral to t p Then, t=t2 is substituted.

[0077] The temperature distribution in the depth direction at the actual time t2 is shown in FIG. p From the temperature distribution in the depth direction at the temperature T, it is considered that there is a temperature rise as shown in FIG. 6E, and it is considered that these are added together. b If the time t2 does not reach the next pulse end time t2', the depth dependency of the temperature rise at time t2 is calculated, and the depth dependency of the temperature rise at time t2 and the irradiation start time t2 of the next pulse are calculated. p The depth dependence of temperature at time t2 is obtained by adding the depth dependence of temperature at time t1 and time t2.

[0078] The depth dependence of temperature T(x0, y0, z, t2) at time t2 obtained in this manner is shown in FIG. 6F.

[0079] [Seventh step] Estimation of the thickness L2 of the material (rust) that will be vaporized by the next (second) pulse irradiation (Fig. 6F).

[0080] The energy E per unit area absorbed by the material (rust) from the laser at time t2 to t2' absorption can be written as follows:

[0081]

[0082] Here, it is assumed that the laser is completely absorbed without passing through the material (rust). Equation (9') is obtained by setting the lower limit of the integral of equation (9) to t2 and the upper limit to t2'.

[0083] The energy E required to vaporize the material (rust) from z = 0 to z = L2 per unit area required can be written as follows:

[0084]

[0085] Here, T(x0, y0, z, t2) is as shown in Fig. 6F. Equation (11') is obtained by setting the upper limit of the integral of equation (11) to L2 and the time to t2.

[0086] The energy E per unit area absorbed by the material (rust) from the laser at time t2 to t2' absorption and the energy E required to vaporize the material (rust) from z = 0 to z = L2 per unit area. required By assuming that these are equal, the thickness L2 of the material (rust) vaporized by the second pulse irradiation can be estimated.

[0087] In the seventh step, the temperature at the surface of the material is adjusted to the hypothetical boiling point T b The energy E per unit area absorbed by the material from the laser during the period from the time t2 when the laser reaches the target laser point to the end of the next pulse, t2'. absorption and the energy E required to vaporize the material from the surface z = 0 to z = L2 per unit area. required By equating L2 with L2, we estimate the thickness of material removed by the next pulse.

[0088] From the above steps, the thickness of the material (rust) vaporized by the first pulse irradiation and the second pulse irradiation can be estimated to be L1 + L2.

[0089] t i , t i ', L i , T i ', T i (i=1, 2, 3...) the subscript number is incremented by 1, and the irradiation start time of the next pulse is set to t p After increasing the number of pulses, steps 3 to 7 are repeated a set number of times, and all estimated thicknesses are added together to estimate the thickness L of the material removed by laser irradiation. For example, when considering the thickness L3 removed by the third pulse irradiation at coordinates (x0, y0), the same procedures as steps 3 to 7 are carried out, and the thickness L of the material removed by pulse laser irradiation is estimated as L1 + L2 + L3.

[0090] [Third step'] The material (rust) from z=0 to L2 is removed, and the surface temperature T2' at the end time t2' of the second pulse irradiation is determined (FIG. 6G).

[0091] Because it is estimated that the second pulse removed the material (rust) from z=0 to L2, the depth position L2 is set to z=0. Also, it is assumed that the temperature distribution does not change between times t2 and t2'. That is, the portion of the temperature distribution T(x0, y0, z, t=t2) where z≧L2 is set to temperature distribution T(x0, y0, z, t=t2'). The surface temperature at time t2' is denoted as T2'.

[0092] [4th step] Next (third) pulse irradiation start time t=2t p Estimation of temperature distribution in (Fig. 7).

[0093] Consider light irradiation such that the temperature at the surface z=0 becomes T2' at time t2'. That is, in equation (8), the lower limit of the integral is set to t p Then, when t = t2', T = T2', the peak power density of the laser is power A p Consider light irradiation with the following formula: Figure 7A shows the time dependence of temperature at x = x0, y = y0, z = 0.

[0094] The pulse period is t p When the third pulse starts, the irradiation time is t = 2t p x = x0, y = y0, time t = 2t p Depth dependence of temperature T(x0, y0, z, 2t p ) (FIG. 7B) can be written as follows:

[0095]

[0096] Equation (12') defines the lower limit of the integral of equation (12) as t p , the upper limit is t2', and time t is 2t p This is what we have decided.

[0097] Here, the upper limit of the integral range is 2t p Instead, it is t2' from time t2' to 2t p This is because the laser is not irradiated during this time. Also, the temperature T(x0, y0, 0, 2t p) will be written as T2.

[0098] [5' step] Estimation of boiling point arrival time t3 during the next (third) pulse irradiation (FIGS. 8A, 8B, 8C, and 8D).

[0099] When the irradiation of the third pulse begins, the temperature of the material (rust) rises. However, if there is a spatial temperature distribution as shown in Figure 7B, it becomes difficult to solve the heat conduction equation. Therefore, as shown in Figure 8B, p The temperature at the point is assumed to be uniform at T2. By making this assumption, it becomes possible to easily solve the heat conduction equation.

[0100] If the temperature is uniform at T2, the temperature at the surface will be the boiling point T b To reach b The temperature only needs to rise by -T2. Figures 8C and 8D show the temperature rise plotted on the vertical axis.

[0101] FIG. 8A can be expressed by equation (8").

[0102]

[0103] Equation (8″) is obtained by changing the constant from RT to T2 in equation (8) and setting the lower limit of integration to 2t p This is what we have decided.

[0104] If the irradiation of the third pulse ends at time t3', the temperature rise on the surface of the material (rust) T(x0, y0, 0, t)-T2 will reach T b If the temperature exceeds -T2, it can be assumed that the material (rust) will be removed. b The time when it becomes -T2 is set to t3.

[0105] [Sixth step] Estimation of the temperature distribution at the boiling point arrival time t3 in the next (third) pulse irradiation (FIGS. 8E and 8F).

[0106] FIG. 8E shows the time 2t p The temperature rise at the surface z=0 is T(x0, y0, z, t3)-T2, which is the depth dependency of the temperature rise at the coordinates (x0, y0) and time t3, when the temperature at the surface z=0 is considered to be uniform. b-T2. FIG. 8E can be expressed by equation (10").

[0107]

[0108] Equation (10″) is obtained by changing the constant from RT to T2 in equation (10) and moving it to the left side, and setting the lower limit of the integral to 2t p Then, t=t3 is substituted.

[0109] The temperature distribution in the depth direction at the actual time t3 is the temperature distribution at the time 2t shown in FIG. p It is considered that there was a temperature rise as shown in FIG. 8E from the temperature distribution in the depth direction at

[0110] The depth dependence of temperature T(x0, y0, z, t3) at time t3 obtained in this manner is shown in FIG. 8F.

[0111] [Seventh step] Estimation of the thickness L3 of the material (rust) vaporized by the next (third) pulse irradiation (FIG. 8F).

[0112] The energy E per unit area absorbed by the material (rust) from the laser at times t3 to t3' absorption can be written as follows:

[0113]

[0114] Here, it is assumed that the laser is completely absorbed without passing through the material (rust). Equation (9") is obtained by setting the lower limit of the integral of equation (9) to t3 and the upper limit to t3'. Note that equation (9") can be expressed as equation (9'"), which will be described later.

[0115] The energy E required to vaporize the material (rust) from z = 0 to z = L3 per unit area required can be written as follows:

[0116]

[0117] Here, T(x0, y0, z, t3) is as shown in FIG. 8F. Equation (11") is obtained by setting the upper limit of the integral of equation (11) to L3 and the time to t3. Note that equation (11") can be expressed as equation (11'"), which will be described later.

[0118] The energy E per unit area absorbed by the material (rust) from the laser at times t3 to t3' absorption and the energy E required to vaporize the material (rust) from z = 0 to z = L3 per unit area. required By assuming that these are equal, the thickness L3 of the material (rust) vaporized by the third pulse irradiation can be estimated.

[0119] From the above steps, the thickness of the substance (rust) vaporized by the first pulse irradiation, the second pulse irradiation, and the third pulse irradiation can be estimated to be L1 + L2 + L3.

[0120] Figure 9 shows a graph illustrating the time dependence of the temperature on the surface of the material (rust) described above. Furthermore, when considering the thickness removed by the fourth or subsequent pulse irradiation at coordinates (x0, y0), the same procedures as steps 3 to 7 are followed. The thickness L of the material (rust) vaporized by pulse irradiation is the sum of all estimated thicknesses.

[0121] [Example 1: Estimation of removal thickness by three pulse irradiation (FIG. 10)] Pulse width τ = 100 ns, pulse period t p = 10 μs (= 10000 ns), beam diameter d = 30 μm, scan speed in the x direction v = 2.5 m / s, peak power density A p = 3.21 x 10 12 W / m 2 In the case of , we consider the case where the removal thickness is estimated taking into account three pulse irradiations. The spatial interval at which the pulses are irradiated is vt p = 25 μm. At time 0, the first pulse irradiation starts with the coordinates x = 0, y = 0 as the center. As the coordinates (x0, y0) for evaluating the temperature, x0 = 37.5 μm and y0 = 0 μm are selected.

[0122] When the time dependency of temperature was evaluated using the procedure in the first step above, the hypothetical boiling point was not reached by the time t' (= τ) when the first pulse irradiation ended. Therefore, L = 0 μm. Therefore, the temperature T' on the surface at the time t' when the first pulse irradiation ended can be calculated by substituting t = t' in equation (8). T' = 4162.53 K + RT.

[0123] Using the procedure of the fourth step, the second pulse irradiation start time, t p The surface temperature T1 at the time of the test was evaluated and found to be T1 = 1622.34 K + RT. b The time t2 at which −T1 occurred was evaluated and found to be t2 = 10029.52 ns. L2 was estimated using the procedure in the seventh step and found to be L2 = 7.2 μm.

[0124] Furthermore, when the surface temperature T2' at the end time t2' of the second pulse irradiation was evaluated using the procedure of the third step, it was found to be T2' = 802.24K + RT.

[0125] In the procedure of the above-mentioned step 4′, the second pulse irradiation is performed at time t p The lower limit of the integral of equation (8) is t p In the formula, A p = 1.56 x 10 11 W / m 2 Using equation (12'), the third pulse irradiation start time, time 2t p The surface temperature T2 at the time of measurement was evaluated and found to be T2 = 296.41 K + RT.

[0126] Using the procedure of step 5′ above, the temperature rise of the surface is T b The time t3 at which -T2 occurred was evaluated and found to be t3 = 20037.55 ns. L3 was estimated using the procedure in step 7' above and found to be L3 = 6.0 μm. Therefore, the removal thickness L due to pulse train irradiation at position x0 = 37.5 μm, y0 = 0 μm was estimated to be L = L1 + L2 + L3 = 13.2 μm. Figure 11 and the following Tables 1, 2, and 3 summarize the results obtained.

[0127]

[0128]

[0129]

[0130] [Example 2: Peak power density dependence of removal thickness considering three pulse irradiation] Under the conditions of Example 1, the removal thickness was evaluated by changing the peak power density. The results are shown in Table 4 below. For example, to remove 30 μm of rust, A p = 1.73 x 10 12 W / m 2 5 times, A p = 3.21 x 10 12 W / m 2 It can be estimated that cleaning must be repeated three times.

[0131]

[0132] Figure 12 shows photographs (experimental results) of the appearance of rusted steel after irradiating it with a laser at different peak power densities. p The beam diameter d, scanning speed v, and peak power density are the same as those in the model calculation. The moving distance in the vertical direction of the scan is 25 μm, and the number of cleanings is 1, 2, 3, 4, and 5.

[0133] In visual inspection, condition B. (peak power density A p = 3.21 x 10 12 W / m 2 ), almost all of the rust was removed after three passes. p = 1.73 x 10 12 W / m 2 ) some rust remains even after four times. Using the estimated removal thickness from model calculations, the rust thickness before laser irradiation can be estimated to be about 30 μm.

[0134] Example 3: Location Dependence of Removal Thickness Considering Three Pulse Irradiation (FIG. 13) Under the same conditions as in Example 1, the location where the temperature was evaluated was changed to evaluate the removal thickness. The first pulse irradiation was started at time 0, centered on the coordinates x = 0, y = 0. The coordinates (x0, y0) for evaluating the temperature were selected to be x0 = 25 μm and y0 = 0 μm. When the time dependency of the temperature was evaluated using the procedure in the first step described above, the virtual boiling point was reached at time t1 = 67.0 ns.

[0135] Calculating the equation (9) in the second step above, E absorption =37448.9J / m 2 When L1 was estimated using equation (11), it was found to be L1 = 2.9 μm. When the surface temperature T1' at time t1' was found according to the procedure in the third step, it was found to be T1' = 1985.61 K + RT. In the procedure in the fourth step, the first pulse irradiation was started from time 0, and T1' = 1985.61 K + RT at the end of irradiation time t1', because in equation (8), A p = 6.47 x 10 11 W / m 2 It is time.

[0136] Using equation (12), the second pulse irradiation start time t p The surface temperature T1 at the time of the test was evaluated and found to be T1 = 748.45 K + RT. b When the time t2 at which −T1 occurs was evaluated, it was found to be t2=10029.11 ns.

[0137] When calculating the equation (9') in the seventh step, E absorption =159410.7J / m 2 When L2 was estimated using equation (11'), it was found to be L2 = 7.6 μm.

[0138] Furthermore, when the surface temperature T2' at the time t2' when the second pulse irradiation was completed was evaluated using the procedure of the third step, it was found to be T2' = 450.57 K + RT. p Starting from t2′, at the irradiation time t2′, T2′=450.57K+RT is obtained by setting the lower limit of the integral of equation (8) to t p In the formula, A p = 7.39 x 10 10 W / m 2 It is time.

[0139] Using equation (12'), the third pulse irradiation start time is time 2t p The surface temperature T2 at the time of the test was evaluated and found to be T2 = 165.39 K + RT.b The time t3 at which -T2 occurred was evaluated and found to be t3 = 20065.92 ns. L3 was estimated using the procedure in step 7' above and found to be L3 = 2.9 μm. Therefore, the removal thickness L due to pulse train irradiation at position x0 = 25.0 μm, y0 = 0 μm was estimated to be L = L1 + L2 + L3 = 13.4 μm. The results obtained are summarized in Figure 14 and Tables 5, 6, and 7 below.

[0140]

[0141]

[0142]

[0143] The removal thickness L at the position x = 37.5 μm and y = 0 μm estimated in Example 1 was L = 13.2 μm. Comparing the two, it was estimated that the removal thicknesses were almost the same.

[0144] In Example 3, the location dependency of the removal thickness under one condition was estimated, but by estimating the location dependency of the removal thickness under different conditions, it is possible to estimate conditions under which the location dependency of the removal thickness is small.

[0145] In the above Examples 1 to 3, the thickness of material (rust) removed was considered taking into account three pulses, but two pulses or four or more pulses may also be considered. Also, the temperature may be evaluated at any location, but in order to evaluate how much material (rust) is removed by pulse irradiation, it is preferable to evaluate it at a position near the laser irradiation point.

[0146] In the above Examples 1 to 3, room temperature RT was used as the initial temperature of the substance. ini It may be.

[0147] As described above, according to the present invention, a virtual substance that is solid over the entire temperature range is assumed, and the temperature in the vicinity of the pulsed laser irradiation point is estimated using the heat conduction equation for a solid.

[0148] Initial temperature T before laser irradiation iniThe 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 The temperature at the surface of the material is T b The energy E per unit area absorbed by the material from the laser between the time t1 when the laser reaches the target and the time t1' when the first pulse ends is absorption and the energy E required to vaporize the material from the surface z = 0 to z = L1 per unit area. required By setting these values ​​equal, the thickness L1 of the material removed by the first pulse is estimated (first step, second step).

[0149] The temperature at the surface of the material is T b If it does not reach t1, t1 = t1' is set, and the temperature distribution in the depth direction remaining after removing the rust from z = 0 to L1 at time t1 is considered to be the temperature distribution in the depth direction at time t1', and the temperature at this surface is set to T1' (third step).

[0150] Next, using the heat conduction equation of a solid when a pulse is incident so that the temperature becomes T1' at time t1', the irradiation start time t p The depth dependence of the temperature at the surface is determined and the temperature at the surface is set to T1 (fourth step).

[0151] Just before the next (second) pulse is irradiated, the temperature of the material is assumed to be uniform at T1, and the heat conduction equation of the solid is solved to find that the surface temperature reaches the virtual boiling point T b The time t2 at which the value of

[0152] Also, the depth dependency of the temperature rise at time t2 is calculated. However, if the temperature at the surface of the material is T b If the time t does not reach the second pulse end time t, the time t is considered to be equal to the second pulse end time t'. p The depth dependence of temperature at time t2 is calculated by adding the depth dependence of temperature at time t1 and time t2 (sixth step).

[0153] Virtual boiling point T bThe energy E per unit area absorbed by the material from the laser during the period from the time t2 when the laser reaches the target point to the time t2' when the second pulse ends is absorption and the energy E required to vaporize the material from the surface z = 0 to z = L2 per unit area. required By assuming that L is equal to L, the thickness L2 of the material removed by the next (second) pulse is estimated (seventh step). Thereafter, steps 3 to 7 are repeated as necessary.

[0154] All estimated thicknesses are summed to estimate the thickness of material removed by laser irradiation, L. For example, when two pulses are considered, L = L + L, and when three pulses are considered, L = L + L + L.

[0155] Thus, according to the present invention, it is possible to estimate the amount of material removed from the surface by simple calculation, and the information on the estimated removal thickness can be used to determine the laser irradiation conditions in a shorter time without experimental trial and error.

[0156] Some or all of the above-described embodiments may also be described as, but are not limited to, the following supplementary notes.

[0157] [Supplementary Note 1] A method for estimating the thickness of a material removed when a pulsed laser is irradiated onto a material formed on a surface of a metal or the like, comprising: ini The temperature rise by the temperature obtained 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 virtual boiling point T b and the temperature at the surface of the material is T b The first step is to estimate the time t1 at which the laser beam reaches the target laser beam, and the second step is to estimate the energy E per unit area absorbed by the material from the laser between the estimated time t1 and the end time t1' of the first pulse. absorption and the energy E required to vaporize the substance from the surface z = 0 to z = L1 per unit area. requireda second step of estimating the thickness L of the material removed by the first pulse by setting b If the temperature distribution in the depth direction remaining after removing the substance from z=0 to L1 at time t1 is set to t1=t1', the temperature distribution in the depth direction at time t1' is set to the temperature at the surface of the substance, and the temperature at the surface of the substance is set to T1'. In the third step, the temperature distribution in the depth direction at time t1' is set to T1'. In the third step, the temperature distribution in the depth direction remaining after removing the substance from z=0 to L1 at time t1' is set to the temperature at the surface of the substance, and the temperature at the surface of the substance is set to T1'. In the third step, the temperature distribution in the depth direction at time t1' ... p The fourth step is to calculate the depth dependence of the temperature at the surface, and set the temperature at the surface to T1. The fourth step is to solve the heat conduction equation of the solid, assuming that the temperature of the material immediately before the next pulse is uniform at T1, and calculate the surface temperature at the virtual boiling point T b A fifth step of determining the time t2 when the temperature at the surface of the substance reaches T b If the time t2 does not reach the next pulse end time t2', the depth dependency of the temperature rise at time t2 is calculated, and the depth dependency of the temperature rise at time t2 and the irradiation start time t2 of the next pulse are calculated. p a sixth step of determining the depth dependence of the temperature at time t2 as the depth dependence of the temperature at time t2; and b From the time t2 when the laser beam reaches the end of the next pulse, the energy E per unit area absorbed by the material from the laser is absorption and the energy E required to vaporize the substance from the surface z = 0 to z = L2 per unit area. required and a seventh step of estimating the thickness L2 of the material removed by the next pulse by setting equal to t. In the first step, the second step, the third step, the fourth step, the fifth step, the sixth step, and the seventh step, the temperature at a location near the laser irradiation location is estimated using the heat conduction equation for a solid shown in the following equations (1), (2), and (3), and t i , t i ', L i , T i ', T i(i=1, 2, 3...) the subscript number is incremented by 1, and the irradiation start time of the next pulse is set to t p The method for estimating the thickness of material removed by laser irradiation includes increasing the number of times, repeating the third to seventh steps a set number of times, and adding up all the estimated thicknesses to estimate the thickness L of the material removed by laser irradiation.

[0158] r (vector): Position near the laser irradiation point t: Time (point in time) J (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 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

[0159] [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).

[0160]

[0161] [Supplementary Note 3] In the method for estimating material removal thickness according to Supplementary Note 1 or 2, required is a material removal thickness estimation method shown in the following equation (11''').

[0162] (x0, y0): Location t where the temperature is evaluated i During the i-th pulse irradiation, the temperature of the substance reaches the virtual boiling point T b The time when L is reached i : the thickness T(x0, y0, z, t i ): location (x0, y0), time ti Depth dependence of temperature in

[0163] [Supplementary Note 4] In the method for estimating a material removal thickness according to any one of Supplementary Note 1 to Supplementary Note 3, when the initial position of laser irradiation is (0, 0), E absorption is the material removal thickness estimation method shown in the following equation (9''').

[0164] r0 (vector): Location t where the temperature is evaluated i ': End time of the i-th pulse irradiation v (vector): Scanning speed of the laser beam d: 1 / e radius of the laser beam

[0165] [Supplementary Note 5] The method for estimating a material removal thickness according to any one of Supplementary Notes 1 to 4, wherein the material is Fe2O3.

[0166] It should be noted that the present invention is not limited to the above-described embodiments, and it is clear that many modifications and combinations can be implemented by a person of ordinary skill in the art within the technical spirit of the present invention. For example, in the above-described embodiments, the removal of rust formed on the surface of steel is described, but 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 using appropriate values ​​as the physical property values ​​of the material. Furthermore, for example, in the above description, a Gaussian beam is used as the spatial dependency of the laser beam intensity, but this is not limiting. If the spatial dependency of the intensity of the irradiated laser beam is f(r), then at time t i ~t i The energy per unit area absorbed by the material (rust) from the laser is E absorption can be written as follows instead of equations (9), (9'), and (9''):

[0167]

[0168] 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.

[0169] [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 a material removed when a pulsed laser is irradiated onto a material formed on the surface of a metal or the like, comprising: ini The temperature rise by the temperature obtained 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 virtual boiling point T b and the temperature at the surface of the material is T b a first step of estimating the time t1 at which the laser beam reaches the end of the first pulse, and a second step of estimating the energy E per unit area absorbed by the material from the laser during the period from the estimated time t1 to the end time t1' of the first pulse; absorption and the energy E required to vaporize the substance from the surface z = 0 to z = L1 per unit area. required a second step of estimating the thickness L of the material removed by the first pulse by setting b If the temperature distribution in the depth direction remaining after removing the substance from z=0 to L1 at time t1 is set to t1=t1', the temperature distribution in the depth direction at time t1' is set to the temperature distribution in the depth direction at time t1', and the temperature at the surface of the substance is set to T1'. A third step is to calculate the temperature at the start time t1 of the next pulse irradiation using the heat conduction equation of a solid when a pulse is irradiated so that the temperature at the surface becomes T1' at time t1'. p The fourth step is to calculate the depth dependence of the temperature at the surface, and set the temperature at the surface to T1. The fourth step is to solve the heat conduction equation of the solid, assuming that the temperature of the material immediately before the next pulse is irradiated is uniform at T1, and set the surface temperature at the virtual boiling point T b A fifth step of determining the time t2 when the temperature at the surface of the substance reaches T b If the time t2 does not reach the next pulse end time t2', the depth dependency of the temperature rise at time t2 is calculated, and the depth dependency of the temperature rise at time t2 and the irradiation start time of the next pulse t2 are compared. p a sixth step of setting the depth dependency of the temperature at time t2 to the sum of the depth dependency of the temperature at time t2 and the depth dependency of the temperature at time t1; b From the time t2 when the laser beam reaches the end of the next pulse, the energy E per unit area absorbed by the material from the laser is absorption and the energy E required to vaporize the substance from the surface z = 0 to z = L2 per unit area. required and a seventh step of estimating a thickness L2 of the material removed by the next pulse by setting equal to t, wherein in the first step, the second step, the third step, the fourth step, the fifth step, the sixth step, and the seventh step, the temperature at a location near the laser irradiation location is estimated using the heat conduction equation for a solid shown in the following equations (1), (2), and (3), i , t i ', L i , T i ', T i (i=1, 2, 3...) the subscript number is incremented by 1, and the irradiation start time of the next pulse is set to t p and repeating the third to seventh steps a set number of times after increasing the number of thicknesses, and adding up all the estimated thicknesses to estimate the thickness L of the material removed by laser irradiation. r (vector): Position near the laser irradiation point t: Time (point in time) J (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 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. The method for estimating material removal thickness according to claim 1, required is a material removal thickness estimation method shown in the following equation (11'''). (x0, y0): Location t where the temperature is evaluated i During the i-th pulse irradiation, the temperature of the substance reaches the virtual boiling point T b The time when L is reached i : the thickness T(x0, y0, z, t i ): location (x0, y0), time t i Depth dependence of temperature in 4. In the method for estimating material removal thickness according to claim 1, when the initial position of laser irradiation is (0,0), E absorption is the material removal thickness estimation method shown in the following equation (9'''). r0 (vector): Location t where the temperature is evaluated i ': End time of the i-th pulse irradiation v (vector): Scanning speed of the laser beam d: 1 / e radius of the laser beam 5. A method for estimating a material removal thickness according to any one of claims 1 to 4, wherein the material is Fe2O3.

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