A five-axis laser impact moldless forming device and a path optimization algorithm thereof

Abstract

This invention provides a moldless forming device for five-axis laser shock and its path optimization algorithm. The method includes a path optimization algorithm based on a five-degree-of-freedom (XYZAC) control system; laser shock is performed by adjusting laser parameters to conduct micro-forming experiments on different metal materials; a five-axis laser shock path optimization model is constructed, and the microstructure forming of the metal surface is controlled by optimizing laser parameters; the influence of laser parameters and shock path on forming quality is studied, and optimization experiments are conducted for different metal materials, significantly improving forming quality and repeatability. This method has broad application prospects in the field of metal micro-forming, improving the accuracy and efficiency of complex shape manufacturing, while enhancing the adaptability and reliability of the equipment.

Description

Technical Field

[0001] This invention relates to laser shock processing technology, and more particularly to a moldless forming device for five-axis laser shock and its path optimization algorithm. Background Technology

[0002] Metal microforming technology is particularly important in modern manufacturing, especially in high-tech fields such as microelectronics, aerospace, and biomedicine. With the increasing demands for miniaturization and high precision, traditional machining methods can no longer meet complex manufacturing requirements, driving the development of new processing technologies.

[0003] High-energy laser shock forming, as an emerging processing method, utilizes the shock waves generated by high-energy laser pulses to impact the metal surface, causing plastic deformation of the material and achieving the formation of complex microstructures. This technology has the following significant advantages: non-contact processing, avoiding tool wear and workpiece deformation; concentrated energy, achieving high-precision microstructure forming; and adjustable laser parameters, providing high flexibility and controllability.

[0004] However, existing technologies still have some shortcomings, such as the potential damage to materials caused by localized heat accumulation due to energy concentration during laser shock, the high requirements for the selection and control of laser parameters, and the low efficiency of existing equipment when processing large-area complex structures.

[0005] Our research aims to address these issues by optimizing the laser shock forming process to improve efficiency and processing quality, thereby promoting the application of this technology in industrial production. Through in-depth research into the influence of laser parameters on microstructure forming, we provide a solid theoretical and practical foundation for the application of high-energy laser shock forming technology in metal microforming. Summary of the Invention

[0006] To address the shortcomings of existing technologies, this invention provides a moldless forming device for five-axis laser impaction and its path optimization algorithm. This invention improves the accuracy and efficiency of complex shape manufacturing, while also enhancing the adaptability and reliability of the equipment.

[0007] To achieve the objectives of this invention, the technical solution adopted is as follows:

[0008] A moldless forming device for five-axis laser impaction and its path optimization algorithm, wherein the specific steps of the method are as follows:

[0009] S1. Obtain current laser parameters (energy, frequency, pulse width);

[0010] S2. Calculate laser shock pressure and strain based on material properties;

[0011] S3. Determine the forming conditions, use a path optimization algorithm for path planning for rapid forming conditions, and adjust laser parameters for micro-forming experiments for fine forming conditions.

[0012] S4. Determine the operating mode, construct a path optimization model to optimize the control microstructure for the normal operating mode, and adjust the laser parameters and path to optimize the forming quality for the abnormal handling mode.

[0013] S5. The optimal impact path is obtained by constructing an optimization model based on the parameters;

[0014] S6. Perform laser shock forming according to the optimal path and laser parameters.

[0015] Furthermore, the acquisition of current laser parameters in step S1 includes real-time measurement of laser energy, frequency, and pulse width.

[0016] Furthermore, the calculation of laser shock pressure and strain in step S2 includes: calculating the pressure and strain generated by laser shock through material properties and laser parameters to determine suitable process parameters.

[0017] Furthermore, the condition determination in step S3 includes: rapid prototyping condition and fine forming condition; the rapid prototyping condition is determined by path planning through a path optimization algorithm; the fine forming condition is determined by micro-forming experiments through adjusting laser parameters.

[0018] The fundamental equation for laser-induced shock waves is derived from the laws of conservation of energy, mass, and momentum, and its one-dimensional planar expression is as follows:

[0019] Energy conservation equation: PU P =1 / 2ρ0U S Up 2 +ρ0U S (E-E0)

[0020] Mass conservation equation: ρ0U S =ρ(U S -U p )

[0021] Momentum conservation equation: (P-P0)=ρ0U S U P

[0022] Where ρ0 is the density before the wavefront, P0 is the pressure before the wavefront, and E0 is the energy before the wavefront; behind the wavefront, ρ is the density of the medium behind the wavefront, P is the shock wave pressure behind the wavefront, and U is the energy before the wavefront. S U is the wavefront spread velocity behind the wavefront, E is the shock wave energy behind the wavefront; p Let U be the velocity of the particle on and behind the wavefront.p If the value is zero, then combining the equation, it can be expressed as follows:

[0023]

[0024] The parameters of the laser-induced shock wave can be obtained by combining the above equations.

[0025] In the laser shock forming process, the relationship between laser power density I0 and pulse width τ, pulse energy E, and spot diameter d can be expressed by the following formula:

[0026]

[0027] To improve the peak pressure of shock waves, we propose an innovative constraint model. During laser shock forming, by coating the metal surface with an absorption layer and a constraint layer, the peak pressure of the shock wave can be significantly increased. This paper mainly introduces our method for estimating the peak pressure of laser-induced shock waves under the constraint model, and the macroscopic equations of plasma motion proposed based on the law of energy conservation and the theory of macroscopic gas expansion. Based on the law of energy conservation and the theory of macroscopic gas expansion, the macroscopic equations of plasma motion are given:

[0028]

[0029] Where: I(t) is the laser power density, P(t) is the laser-induced shock wave pressure, L(t) is the absorption layer thickness, V(t) is the plasma expansion velocity, Z1 is the acoustic impedance of the impacted target, and Z2 is the acoustic impedance of the confinement layer. From the above two equations, the formula for calculating the peak pressure of the laser-induced shock wave can be obtained:

[0030]

[0031] In the above formula, P max Here, I0 is the peak pressure, α is the laser power density, and α is the interaction efficiency between the laser and the metal material, typically taken as 0.1 to 0.2. In the formula, Z1 is the acoustic impedance of the material being impacted by the laser, Z2 is the acoustic impedance of the confinement layer, and Z is the composite acoustic impedance of Z1 and Z2. The Fabbro model makes some ideal assumptions, such as uniform heating of the surface of the impacted material within the laser irradiation range; isotropic confinement layer and impacted material; plasma vaporization state is considered as ideal gas; and plasma diffusion direction is only axial. In summary, the Fabbro formula fully considers the influence of the acoustic impedance of the absorption layer and confinement layer on the induced shock wave, and also considers the interaction efficiency between the laser and the metal foil. Moreover, the formula parameters are relatively easy to select, and it can accurately estimate the peak pressure of the nanosecond laser-induced shock wave.

[0032] Estimating the strain rate of laser-induced plastic deformation is a crucial step in understanding the behavior of materials under laser shock. Strain rate describes the rate at which a material deforms per unit time. Typically, during high-energy laser shock, the strain rate is extremely high, exceeding 10^6 s^-1. The following are the methods and steps for estimating the strain rate of laser-induced plastic deformation:

[0033] Laser shock wave pressure: When a laser pulse acts on the surface of a material, it generates an instantaneous high-pressure shock wave. This pressure is usually calculated using the energy density of the laser.

[0034] strain rate Defined as the rate of change of strain ε with time t, the formula is:

[0035]

[0036] The laser shock wave pressure (P) can be estimated using the following formula:

[0037]

[0038] I is the energy density of the laser, c is the sound velocity of the material, and R is the reflectivity of the material;

[0039] Calculate the plastic strain rate: Plastic strain rate It can be estimated using the shock wave pressure, material density, and wave velocity, as shown in the formula:

[0040]

[0041] ρ is the density of the material.

[0042] Furthermore, the operation mode determination in step S4 includes: normal operation mode and abnormal handling mode; in the normal operation mode, a path optimization model is constructed to optimize the control of the microstructure forming on the metal surface; in the abnormal handling mode, laser parameters and impact path are adjusted, and optimization experiments are conducted to improve the forming quality.

[0043] In this case, using only linear interpolation, i.e., connecting discrete points one by one to form a tangent path, in the case of five-axis cladding, it is also necessary to specify the AC turning angle for the discrete points on the path. That is, the definition format of the printing path for a discrete point is:

[0044] X_Y_Z_A_C

[0045] In the above formula, the horizontal line represents the coordinate value or rotation angle. For two adjacent points, their X, Y, Z coordinate values ​​are usually very close. However, if the path normal vector planning is unreasonable, the deviation of the AC rotation angle of adjacent points can be large.

[0046] Suppose there are two neighboring points with similar X, Y, Z coordinates. and When the normal of the impact point on a workpiece coincides with the beam, and the cladding surface is the region at the top of a sphere, the X, Y, Z coordinate values ​​of P_1 and P_2 are very similar. Due to data noise, Δθ and The difference is larger in the top region of the curved surface (Δθ may be close to π). (Possibly close to π / 4), the control system interpolates based on the travel distance in the axis direction corresponding to a pulse signal. Therefore, for some coordinate positions between P_1 and P_2, the interpolation of the X, Y, and Z axes may stop, that is, the coordinates remain stationary and wait for the A and C axes to continue to rotate significantly. At this time, interference may occur.

[0047] In Δθ and In larger cases, raising the laser emitter to rotate the workpiece into position before lowering it to continue cladding, or performing point interpolation densification on the paths represented by line segments P_1 and P_2, is essential for protecting the workpiece. Although these methods can prevent workpiece damage, they still cannot prevent damage caused by heat accumulation in the optical fiber during prolonged heating.

[0048] Furthermore, the step S5, which obtains the optimal impact path by constructing an optimization model based on parameters, includes: calculating the optimal laser impact path using laser parameters and a path optimization algorithm;

[0049] Since the normal vector is only a direction vector, we can assume that for n = (n x ,n y ,n z ) T Let's say the center of rotation is the origin of the coordinate system. To make n coincide with the positive direction of the Z-axis, the specific process is as follows:

[0050] ① Rotate the workpiece around the Z-axis by an angle θ, so that the normal vector is located in the yOz plane;

[0051] ② Rotate the workpiece around the X-axis by an angle φ, so that the normal vector coincides with the positive direction of the Z-axis;

[0052] This allows us to first calculate the vector [n] x ,n y The angle θ between the vector and the positive Y-axis ∈ [-π,π] is then determined by the vector. Calculate angle Based on the processing conditions, since n z ≥0 means that the positive direction of the normal vector always points to the side where the nozzle is located, and when optimizing the two corners A and C without considering the normal vector, the range of values ​​does not need to be considered. Therefore, by The defined normal vector can be written as

[0053]

[0054] The above formula is used for estimation Defined normal vector The deviation from the target surface normal vector is the objective function used to construct the optimization model;

[0055] For the AC turning angle obtained by the above method, there may be cases where the C turning angle of neighboring points deviates by approximately ±2π. This is because when optimizing each turning angle using subsequent optimization iterative methods, the initial values ​​of the iterations also need to be as close as possible to the optimal values. Therefore, in order to minimize the deviation of the turning angle of neighboring points, the C turning angle of each point is first optimized based on the 2π periodicity of the trigonometric function. Assume that the points on the discrete path are arranged in sequence [p0, p1, ... p1]. i p n ], where p i =[x i y i , z i a i c i Then, the following formula is used to apply the formula to each c. i Update:

[0056]

[0057] After performing the first round of optimization on the C-angle of each point using the above formula, the difference in the C-angle between any two adjacent points can be made no greater than π.

[0058] Assume all C-turns are arranged in sequence C = [c0, c1, ... c n ],|C|=[|c0|,|c1|…|c n |],ΔC=[…,C i -c i-1 Then you can use

[0059] min(max(|ΔC|))

[0060] This means that the deviation of the angle at the nearest point C should be as small as possible; similarly,

[0061] min(max(|ΔA|))

[0062] This means minimizing the deviation of the angle at the nearest point A;

[0063] Let n i and n(a i c i ) represent the normal vector of the i-th discrete point on the theoretical path and the normal vector of the i-th point in the rotation optimization, defined by the AC rotation angle according to the formula.

[0064] V (A, C) = [acos (n0n (a0, c0), acos (n1n (a1, c1)), ..., acos (n n n(α n c n ))],then,

[0065] min(max(|V(A,C)|))

[0066] The deviation between the normal vector defined by the current AC turning angle at each point and the normal vector of the theoretical path should be as small as possible;

[0067] A mathematical model for optimizing each point on the processing path can be obtained:

[0068]

[0069] In the above optimization model, t = α + β + γ, A = (a0 + a1, ..., a n C = (c0, c1, ..., c) n Let A and C represent the vectors formed by the A and C angles of each point, respectively, and Δ represent the forward difference operator. The first two constraints are determined based on the software algorithm and actual working conditions. The first constraint is that the A-axis always deflects in the positive direction and does not exceed 90°. The second constraint is that the deviation between the nozzle axis and the normal vector of the cladding surface does not exceed 45°. There is no constraint on C, which means that the C-axis angle C∈(-∞,∞). The last two constraints are constraints on the starting angle when iterating the vectors formed by the AC angles of each point in each row as individuals. There is no constraint on the first row. The deviation between the end point of the subsequent row and the starting point of the current row cannot be greater than the threshold of the deviation of the angle of the neighboring point. In the objective function, α, β, and γ represent the weights of each sub-optimal objective. Since C is much more sensitive to error than A, we take β>α≥γ, and β>0, α>0, γ>0 to ensure that the values ​​of the three sub-objectives are as small as possible when f(A,C) reaches its optimum.

[0070] Furthermore, the laser shock forming process in step S6 based on the optimal path and laser parameters includes: performing the laser shock forming process based on the optimized laser shock path and laser parameters to improve forming accuracy and repeatability.

[0071] Compared with the prior art, the present invention has the following beneficial effects: The present invention proposes a moldless forming equipment for five-axis laser impact and its path optimization algorithm, which improves the accuracy and efficiency of complex shape manufacturing, while enhancing the adaptability and reliability of the equipment. Attached Figure Description

[0072] Figure 1 This is a flowchart of a moldless forming device for five-axis laser shock and its path optimization algorithm according to the present invention.

[0073] Figure 2 This is a schematic diagram of the five-axis laser shock processing path and beam irradiation direction of the present invention;

[0074] Figure 3 This is a flowchart illustrating the process of generating cladding machining commands from theoretical toolpaths with normal vectors according to the present invention.

[0075] Figure 4 This is a schematic diagram illustrating the steps of calculating the AC rotation angle from the normal vector according to the present invention. Detailed Implementation

[0076] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0077] like Figure 1 As shown, a five-axis laser impact dieless forming device and its path optimization algorithm specifically include the following steps:

[0078] S1. Obtain current laser parameters (energy, frequency, pulse width);

[0079] S2. Calculate laser shock pressure and strain based on material properties;

[0080] S3. Determine the forming conditions, use a path optimization algorithm for path planning for rapid forming conditions, and adjust laser parameters for micro-forming experiments for fine forming conditions.

[0081] S4. Determine the operating mode, construct a path optimization model to optimize the control microstructure for the normal operating mode, and adjust the laser parameters and path to optimize the forming quality for the abnormal handling mode.

[0082] S5. The optimal impact path is obtained by constructing an optimization model based on the parameters;

[0083] S6. Perform laser shock forming according to the optimal path and laser parameters.

[0084] Furthermore, the acquisition of current laser parameters in step S1 includes real-time measurement of laser energy, frequency, and pulse width.

[0085] Furthermore, the calculation of laser shock pressure and strain in step S2 includes: calculating the pressure and strain generated by laser shock through material properties and laser parameters to determine suitable process parameters.

[0086] Furthermore, the condition determination in step S3 includes: rapid prototyping condition and fine forming condition; the rapid prototyping condition is determined by path planning through a path optimization algorithm; the fine forming condition is determined by micro-forming experiments through adjusting laser parameters.

[0087] The fundamental equation for laser-induced shock waves is derived from the laws of conservation of energy, mass, and momentum, and its one-dimensional planar expression is as follows:

[0088] Energy conservation equation: PU P =1 / 2ρ0U S Up 2 +ρ0U S (E-E0)

[0089] Mass conservation equation: ρ0U S =ρ(U S -U p )

[0090] Momentum conservation equation: (P-P0)=ρ0U S U P

[0091] Where ρ0 is the density before the wavefront, P0 is the pressure before the wavefront, and E0 is the energy before the wavefront; behind the wavefront, ρ is the density of the medium behind the wavefront, P is the shock wave pressure behind the wavefront, and U is the energy before the wavefront. S U is the wavefront spread velocity behind the wavefront, E is the shock wave energy behind the wavefront; p Let U be the velocity of the particle on and behind the wavefront. p If the value is zero, then combining the equation, it can be expressed as follows:

[0092]

[0093] The parameters of the laser-induced shock wave can be obtained by combining the above equations;

[0094] In the laser shock forming process, the relationship between laser power density I0 and pulse width τ, pulse energy E, and spot diameter d can be expressed by the following formula:

[0095]

[0096] To improve the peak pressure of shock waves, we propose an innovative constraint model. During laser shock forming, by coating the metal surface with an absorption layer and a constraint layer, the peak pressure of the shock wave can be significantly increased. This paper mainly introduces our method for estimating the peak pressure of laser-induced shock waves under the constraint model, and the macroscopic equations of plasma motion proposed based on the law of energy conservation and the theory of macroscopic gas expansion. Based on the law of energy conservation and the theory of macroscopic gas expansion, the macroscopic equations of plasma motion are given:

[0097]

[0098] Where: I(t) is the laser power density, P(t) is the laser-induced shock wave pressure, L(t) is the absorption layer thickness, V(t) is the plasma expansion velocity, Z1 is the acoustic impedance of the impacted target, and Z2 is the acoustic impedance of the confinement layer. From the above two equations, the formula for calculating the peak pressure of the laser-induced shock wave can be obtained:

[0099]

[0100] In the above formula, P max Here, I0 is the peak pressure, α is the laser power density, and α is the interaction efficiency between the laser and the metal material, typically taken as 0.1 to 0.2. In the formula, Z1 is the acoustic impedance of the material being impacted by the laser, Z2 is the acoustic impedance of the confinement layer, and Z is the composite acoustic impedance of Z1 and Z2. The Fabbro model makes some ideal assumptions, such as uniform heating of the surface of the impacted material within the laser irradiation range; isotropic confinement layer and impacted material; plasma vaporization state is considered as ideal gas; and plasma diffusion direction is only axial. In summary, the Fabbro formula fully considers the influence of the acoustic impedance of the absorption layer and confinement layer on the induced shock wave, and also considers the interaction efficiency between the laser and the metal foil. Moreover, the formula parameters are relatively easy to select, and it can accurately estimate the peak pressure of the nanosecond laser-induced shock wave.

[0101] Estimating the strain rate of laser-induced plastic deformation is a crucial step in understanding the behavior of materials under laser shock. Strain rate describes the rate at which a material deforms per unit time. Typically, during high-energy laser shock, the strain rate is extremely high, exceeding 10^6 s^-1. The following are the methods and steps for estimating the strain rate of laser-induced plastic deformation:

[0102] Laser shock wave pressure: When a laser pulse acts on the surface of a material, it generates an instantaneous high-pressure shock wave. This pressure is usually calculated using the energy density of the laser.

[0103] strain rate Defined as the rate of change of strain ε with time t, the formula is:

[0104]

[0105] The laser shock wave pressure (P) can be estimated using the following formula:

[0106]

[0107] I is the energy density of the laser, c is the sound velocity of the material, and R is the reflectivity of the material;

[0108] Calculate the plastic strain rate: Plastic strain rate It can be estimated using the shock wave pressure, material density, and wave velocity, as shown in the following formula.

[0109]

[0110] ρ is the density of the material.

[0111] like Figure 2 As shown, the beam travels along the row tangent, reciprocating along the line tangent. In this study, only linear interpolation is used, representing the path by connecting discrete points one by one. Figure 2 The line cutting path in the code. In the case of five-axis cladding, it is also necessary to specify the AC rotation angle for discrete points on the path. That is, the definition format of the print path for a discrete point is:

[0112] X_Y_Z_A_C

[0113] In the above formula, the horizontal line represents the coordinate value or rotation angle. For two adjacent points, their X, Y, Z coordinate values ​​are usually very close. However, if the path normal vector planning is unreasonable, the deviation of the AC rotation angle of adjacent points can be large. Suppose there are two adjacent points with similar X, Y, Z coordinate values. and When the normal of the impact point on a workpiece coincides with the beam, and the cladding surface is the region at the top of a sphere, the X, Y, Z coordinate values ​​of P_1 and P_2 are very similar. Due to data noise, Δθ and The difference is larger in the top region of the curved surface (Δθ may be close to π). (Possibly close to π / 4), the control system interpolates based on the travel distance in the axis direction corresponding to a pulse signal. Therefore, for some coordinate positions between P_1 and P_2, the interpolation of the X, Y, and Z axes may stop, that is, the coordinates remain stationary and wait for the A and C axes to continue to rotate significantly. At this time, interference may occur.

[0114] In Δθ and In larger cases, raising the laser emitter to rotate the workpiece into position before lowering it to continue cladding, or performing point interpolation densification on the paths represented by line segments P_1 and P_2, is essential for protecting the workpiece. Although these methods can prevent workpiece damage, they still cannot prevent damage caused by heat accumulation in the optical fiber during prolonged heating.

[0115] like Figure 3 As shown, the process of generating the cladding machining command from the theoretical toolpath with normal vectors involves first calculating the conversion between the normal vector and the AC angle. Based on this, the AC angle at each point on the path is initially optimized. Then, an optimization model is constructed based on the initial optimization to minimize the deviation of the AC angle between any two adjacent points.

[0116] like Figure 4 As shown, since the normal vector is only a direction vector, it can be assumed that for n = (n x ,n y ,n z ) T Let's say the center of rotation is the origin of the coordinate system. This is so that n coincides with the positive direction of the Z-axis:

[0117] ① Rotate the workpiece around the Z-axis by an angle θ, so that the normal vector is located in the yOz plane;

[0118] ② Rotate the workpiece around the X-axis by an angle φ so that the normal vector coincides with the positive direction of the Z-axis.

[0119] This allows us to first calculate the vector [n] x ,n y The angle θ between the vector and the positive Y-axis ∈ [-π,π] is then determined by the vector.

[0120]

[0121] Calculate angle Based on the processing conditions, since n z ≥0 means that the positive direction of the normal vector always points to the side where the nozzle is located, and when optimizing the two corners A and C without considering the normal vector, the range of values ​​does not need to be considered. Therefore, by The defined normal vector can be written as

[0122]

[0123] The formula is used for estimation Defined normal vector The deviation from the target surface normal vector is the objective function used to construct the optimization model.

[0124] Additionally, for Figure 3The AC turning angle obtained by the method shown may have deviations of approximately ±2π from the C turning angle of neighboring points. Since subsequent optimization iterations of each turning angle require initial values ​​to be as close as possible to the optimal value, the C turning angle of each point is first optimized based on the 2π periodicity of trigonometric functions to minimize the deviation of the turning angle from neighboring points. According to 2a, assume that the points on the discrete path are arranged in sequence [p0, p1, ... p...]. i p n ], where p i =[x i y i , z i a i c i Then, the following formula is used to apply the formula to each c. i Update:

[0125]

[0126] After performing the first round of optimization on the C-angle of each point using the above formula, the difference in the C-angle between any two adjacent points can be made no greater than π.

[0127] Assume all C-turns are arranged in sequence C = [c0, c1, ... c n ],|C|=[|c0|,|c1|…|c n |],ΔC=[…,c i -c i-1 ], then we can use

[0128] min(max(|ΔC|))

[0129] This means minimizing the deviation of the angle at the nearest point C. Similarly,

[0130] min(max(|ΔA|))

[0131] This means that the deviation of the angle of the nearest point A should be as small as possible.

[0132] Let n i and n(a i c i ) represent the normal vector of the i-th discrete point on the theoretical path and the normal vector of the i-th point in the corner optimization, defined by the AC corner according to the above formula.

[0133] V(A,C)=[acos(n0n(a0,c0), acos(n1n(a1,c1)),…acos(n n n(a n c n ))],then,

[0134] min(max(|V(A,C)|))

[0135] The deviation between the normal vector defined by the current AC turning angle at each point and the normal vector of the theoretical path should be as small as possible.

[0136] A mathematical model for optimizing each point on the processing path can be obtained.

[0137]

[0138] In the above optimization model, t = α + β + γ, A = (a0 + a1, ..., a n C = (c0, c1, ..., c) n Let A and C represent the vectors formed by the A and C angles at each point, respectively, and Δ represent the forward difference operator. The first two constraints are determined based on the software algorithm and actual working conditions. The first constraint is that the A-axis always deflects in the positive direction and does not exceed 90°. The second constraint is that the deviation between the nozzle axis and the normal vector of the cladding surface does not exceed 45°. There is no constraint on C, meaning that the C-axis angle C∈(-∞,∞). The latter two constraints are constraints on the starting angle when iterating the vectors formed by the AC angles of each point in each row as individuals. There is no constraint on the first row, and the deviation of the angle between the end point of subsequent rows and the starting point of the current row cannot be greater than the threshold of the angle deviation of neighboring points. In the objective function, α, β, and γ represent the weights of each sub-optimal objective. Since C is much more sensitive to error than A, we take β>α≥γ, and β>0, α>0, γ>0, to ensure that the values ​​of the three sub-objectives are as small as possible when f(A,C) reaches its optimum.

Claims

1. A path optimization method for a moldless forming device based on five-axis laser shock, characterized in that, The specific steps of the method are as follows: S1. Obtain the current laser parameters, including energy, frequency, and pulse width; S2. Calculate laser shock pressure and strain based on material properties; S3. Determine the forming conditions, use a path optimization algorithm for path planning for rapid forming conditions, and adjust laser parameters for micro-forming experiments for fine forming conditions. S4. Determine the operating mode, construct a path optimization model to optimize the control microstructure for the normal operating mode, and adjust the laser parameters and path to optimize the forming quality for the abnormal handling mode. S5. The optimal impact path is obtained by constructing an optimization model based on the parameters; S6. Perform laser shock forming according to the optimal path and laser parameters; The condition determination in step S3 includes: rapid prototyping condition and fine forming condition; the rapid prototyping condition is determined by path planning through a path optimization algorithm; the fine forming condition is determined by micro-forming experiments through adjusting laser parameters. The fundamental equation for laser-induced shock waves is derived from the laws of conservation of energy, mass, and momentum, and its one-dimensional planar expression is as follows: Energy conservation equation: PU P =1 / 2ρ0U S Up 2 +ρ0U S (E-E0) Mass conservation equation: ρ0U S =ρ(U S -U p ) Momentum conservation equation: (P-P0)=ρ0U S U P Where ρ0 is the density before the wavefront, P0 is the pressure before the wavefront, and E0 is the energy before the wavefront; ρ is the density of the medium behind the wavefront, P is the shock wave pressure behind the wavefront, and U... S U is the wavefront spread velocity behind the wavefront, E is the shock wave energy behind the wavefront; p Let U be the velocity of the particle on and behind the wavefront. p If the value is zero, then combining the equation, it can be expressed as follows: The parameters of the laser-induced shock wave can be obtained by combining the above equations. In the laser shock forming process, the relationship between laser power density I0 and pulse width τ, pulse energy E, and spot diameter d can be expressed by the following formula: To improve the peak pressure of the shock wave, a constraint model is proposed. During laser shock forming, by covering the metal surface with an absorption layer and a constraint layer, the peak pressure of the shock wave can be significantly increased. A method for estimating the peak pressure of the laser-induced shock wave under the constraint model is presented, along with a macroscopic equation for plasma motion based on the law of energy conservation and the theory of macroscopic gas expansion. The macroscopic equation for plasma motion is given based on the law of energy conservation and the theory of macroscopic gas expansion. Where: I(t) is the laser power density, P(t) is the laser-induced shock wave pressure, L(t) is the absorption layer thickness, V(t) is the plasma expansion velocity, Z1 is the acoustic impedance of the impacted target, and Z2 is the acoustic impedance of the confinement layer. From the above two equations, the formula for calculating the peak pressure of the laser-induced shock wave can be obtained: In the above formula, P max I0 is the peak pressure, I0 is the laser power density, and α is the interaction efficiency between the laser and the metal material, typically taken as 0.1 to 0.

2. In the formula, Z1 is the acoustic impedance of the material impacted by the laser, Z2 is the acoustic impedance of the confinement layer, and Z is the composite acoustic impedance of Z1 and Z2. The above model includes ideal assumptions, assuming that the surface of the impacted material is heated uniformly within the laser irradiation range; the confinement layer and the impacted material are isotropic; the plasma vaporization state is considered as an ideal gas; and the plasma diffusion direction is only axial. Estimating the strain rate of laser-induced plastic deformation is a crucial step in understanding the behavior of materials under laser shock. Strain rate describes the rate at which a material deforms per unit time. Typically, during high-energy laser shock, the strain rate is extremely high, exceeding 10^6 s^-1. The following are the methods and steps for estimating the strain rate of laser-induced plastic deformation: Laser shock wave pressure: When a laser pulse acts on the surface of a material, it generates an instantaneous high-pressure shock wave. This pressure is usually calculated using the energy density of the laser. strain rate Defined as the rate of change of strain ε with time t, the formula is: The laser shock wave pressure P can be estimated using the following formula: I is the energy density of the laser, c is the sound velocity of the material, and R is the reflectivity of the material; Calculate the plastic strain rate. It can be estimated using the shock wave pressure, material density, and wave velocity, as shown in the formula: ρ is the density of the material.

2. The path optimization method for a moldless forming device based on five-axis laser shock according to claim 1, characterized in that, The acquisition of current laser parameters in step S1 includes real-time measurement of laser energy, frequency, and pulse width.

3. The path optimization method for a moldless forming device based on five-axis laser shock according to claim 1, characterized in that, The calculation of laser shock pressure and strain in step S2 includes: calculating the pressure and strain generated by laser shock through material properties and laser parameters to determine suitable process parameters.

4. The path optimization method for a moldless forming device based on five-axis laser shock according to claim 1, characterized in that, The operation mode determination in step S4 includes: normal operation mode and abnormal handling mode; in the normal operation mode, a path optimization model is constructed to optimize the control of the forming of microstructures on the metal surface; in the abnormal handling mode, laser parameters and impact path are adjusted, and optimization experiments are conducted to improve the forming quality. In this case, using only linear interpolation, i.e., connecting discrete points one by one to form a tangent path, in the case of five-axis cladding, it is also necessary to specify the AC turning angle for the discrete points on the path. That is, the definition format of the printing path for a discrete point is: X_Y_Z_A_C In the above formula, the horizontal line represents the coordinate value or rotation angle. For two adjacent points, their X, Y, Z coordinate values ​​are usually very close. However, if the path normal vector planning is unreasonable, the deviation of the AC rotation angle of adjacent points can be large. Suppose there are two adjacent points with similar X, Y, Z coordinate values. and When the normal of the impact point on a workpiece coincides with the beam, and the cladding surface is the region at the top of a sphere, the X, Y, Z coordinate values ​​of P_1 and P_2 are very similar. Due to data noise, Δθ and The difference is greater in the region at the top of the curved surface, where Δθ may be close to π. It may be close to π / 4. The control system interpolates based on the travel distance in the axis direction corresponding to a pulse signal. Therefore, for some coordinate positions between P_1 and P_2, the interpolation of the three axes X, Y, and Z may stop, that is, the coordinates remain stationary and wait for the two axes A and C to continue to rotate significantly. At this time, interference may occur. In Δθ and In cases where the workpiece is large, the laser emitter can be raised to rotate it into position before the laser emitter is lowered to continue cladding, or the paths represented by line segments P_1 and P_2 can be interpolated and densified.

5. The path optimization method for a moldless forming device based on five-axis laser shock according to claim 1, characterized in that, The step S5, which obtains the optimal impact path by constructing an optimization model based on parameters, includes: calculating the optimal laser impact path using laser parameters and a path optimization algorithm. Since the normal vector is only a direction vector, we can assume that for n = (n x ,n y ,n z ) T Let's say the center of rotation is the origin of the coordinate system. To make n coincide with the positive direction of the Z-axis, the specific process is as follows: ① Rotate the workpiece around the Z-axis by an angle θ, so that the normal vector is located in the yOz plane; ② Rotate the workpiece around the X-axis by an angle φ, so that the normal vector coincides with the positive direction of the Z-axis; First calculate the vector [n] x ,n y The angle θ between the vector and the positive Y-axis ∈ [-π,π] is then determined by the vector. Calculate angle Based on the processing conditions, since n z ≥0 means that the positive direction of the normal vector always points to the side where the nozzle is located, and when optimizing the two corners A and C without considering the normal vector, the range of values ​​does not need to be considered. Therefore, by The defined normal vector can be written as The above formula is used for estimation Defined normal vector The deviation from the target surface normal vector is the objective function used to construct the optimization model; First, optimize the C-angle of each point based on the 2π periodicity of trigonometric functions. Assume that the points on the discrete path are arranged in sequence [p0, p1, ... p1]. i ,p n ], where p i =[x i y i , z i a i c i Then, the following formula is used to apply the formula to each c. i Update After performing the first round of optimization on the C-angle of each point using the above formula, the difference in the C-angle between any two adjacent points can be made no greater than π. Assume all C-turns are arranged in a sequence C = [c0, c1, ... c n ],|C|=[|c0|,|c1|,…|c n |],ΔC=[…,c i -c i-1 ], then we can use min(max(|ΔC|)) This means that the deviation of the angle at the nearest point C should be as small as possible; similarly, min(max(|ΔA|)) This means minimizing the deviation of the angle at the nearest point A; Let n i and n(a i ,c i ) represent the normal vector of the i-th discrete point on the theoretical path and the normal vector of the i-th point in the rotation optimization, defined by the AC rotation angle according to the formula. V(A,C)=[acos(n0n(a0,c0),acos(n1n(a1,c1)),…,acos(n n n(a n ,c n Therefore, min(max(|V(A,C)|)) The deviation between the normal vector defined by the current AC turning angle at each point and the normal vector of the theoretical path should be as small as possible; A mathematical model for optimizing each point on the processing path can be obtained: In the above optimization model, t = α + β + γ, A = (a0 + a1, ..., a n C = (c0, c1, ..., c) n Let A and C represent the vectors formed by the A-angle and C-angle of each point, respectively, and Δ represent the forward difference operator. The first two constraints are determined based on the software algorithm and actual working conditions. The first constraint is that the A-axis always deflects in the positive direction and does not exceed 90°. The second constraint is that the deviation between the nozzle axis and the normal vector of the cladding surface does not exceed 45°. There is no constraint on C, which means that the C-axis angle C∈(-∞,∞). The last two constraints are constraints on the starting angle when iterating the vector formed by the AC-angle of each point in each row as an individual. There is no constraint on the first row. The deviation between the end point of the subsequent row and the starting point of the current row cannot be greater than the threshold of the deviation of the angle of the neighboring point. In the objective function, α, β, and γ represent the weights of each sub-optimization objective. We take β>α≥γ, and β>0, α>0, and γ>0.

6. The path optimization method for a moldless forming device based on five-axis laser shock according to claim 1, characterized in that, The laser shock forming process in step S6, which involves performing laser shock forming based on the optimized laser shock path and laser parameters, includes: performing the laser shock forming process based on the optimized laser shock path and laser parameters to improve forming accuracy and repeatability.

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