Modeling method of annular composite beam laser welding heat source model

Abstract

The invention discloses a modeling method of an annular composite beam laser welding heat source model, and relates to the technical field of laser welding. The modeling method of the annular composite beam laser welding heat source model comprises the steps that 1, an existing Gaussian plane distribution heat source model is improved, and the limitation that the power in the radius of a heat source accounts for 95% of the total power in the existing model is improved into any power proportion; 2, establishing an annular plane distribution heat source model; 3, establishing a Gaussian volume distribution heat source model based on the improved Gaussian plane distribution heat source model; and 4, establishing an annular volume distribution heat source model based on the annular plane distribution heat source model. The problem that a heat source is difficult to establish accurately in the laser welding numerical simulation process is solved.

Description

Technical Field

[0001] The present invention relates to the technical field of laser welding, and specifically to a modeling method for a laser welding heat source model of an annular composite beam. Background Technique

[0002] As an efficient and precise welding method, laser welding technology has currently achieved rapid development and wide application globally. In fields such as power batteries, automobiles, and consumer electronics, the application of laser welding has gradually increased, and the market scale has continued to expand. With the development of the high-end precision manufacturing industry, the demand for laser welding in fields such as 3C products, automotive lightweighting, power and energy storage batteries, etc. is continuously growing, showing a broad market prospect. The heat source model is the basis of laser welding numerical simulation, and it needs to accurately reflect the physical process of laser welding, including the distribution of laser energy on the welded part. To improve the weld quality of laser welding, composite beam lasers are gradually being applied in production. As shown in Figure 1 , the optical fiber of the composite laser includes a central core and an annular core. Among them, the laser conducted in the central core forms a circular light spot on the surface of the welded part, and its power density distribution conforms to the Gaussian distribution; the laser conducted in the annular core forms an annular light spot on the surface of the welded part, and the power density distribution on the annular cross-section also conforms to the Gaussian distribution; the two are combined to form the composite laser heat source for laser welding.

[0003] The power density distribution of the commonly used Gaussian plane distribution heat source model is:

[0004]

[0005] Where: Q c is the laser power; r H is the radius of the circular light spot; r is the distance from any point inside the light spot to the center of the light spot.

[0006] There are mainly three types of existing laser beam annular light spot heat source models, and their power density distributions are respectively:

[0007] a. The power density on the annular light spot is equal, that is, the energy of the laser is evenly distributed:

[0008]

[0009] Where: Q r is the total power of the annular light spot; r o is the outer diameter of the annular light spot; r i is the inner diameter of the annular light spot.

[0010] b. Modified from the circular light spot plane Gaussian heat source:

[0011]

[0012] Where: is the position where the maximum power density of the annular light spot is located at the center; is the half-width of the annular light spot.

[0013] c. Set the maximum power density q m as a value to be determined, and modify the exponential part by the circular light spot formula:

[0014]

[0015] where q m is the maximum power density on the annular light spot.

[0016] Since the power density distribution of the laser on the cross-section of the annular light spot and the circular light spot conforms to the Gaussian distribution, when defining the radius of the circular light spot and the inner and outer diameters of the annular light spot, it is necessary to clearly define the proportion of the power within a given range to the total laser power. As Figure 2 shown, the commonly used Gaussian plane heat source model at present assumes that the integral of the power density within the range of radius r H accounts for 95% of the total power. However, the standards adopted in practice for determining the light spot radius are different, and other ratios may be used, such as 86.5%. Taking the circular light spot as an example, under the ratio of the power within different radius r H regions to the total power, using the existing Gaussian light spot plane distribution heat source model, the relative error of the total power is shown in Table 1. It can be seen from the table that when the ratio is 0.95, since it is the same as the assumed ratio of the existing model, the relative error is zero, and when the ratio deviates more from 0.95, the relative error is greater. Therefore, it is necessary to modify the existing Gaussian plane distribution heat source model to make its application range more extensive.

[0017]

[0018] For the power density distribution of the plane distribution heat source, the following conditions are required to be met:

[0019] (1) In the target region, that is, the circular region within the circular light spot where the distance from the center is less than r H , and the region within the annular light spot where the distance from the center is greater than the inner diameter r i , and less than the outer diameter r o , the integral of the power density accounts for a fixed value η c of the total laser power;

[0020] Circular light spot:

[0021] Annular light spot:

[0022] (2) The integral of the power density within an infinite range is equal to the total laser power Q

[0023] ∫0 ∞ q(r)2πrdr = Q

[0024] According to relevant experimental data, the power density distribution within the annular light spot is not uniform. Therefore, formula (1) is only applicable to rough calculations; the formula for the power density distribution of the annular light spot shown in formula (2) is directly modified from the power density formula of the circular light spot without rigorous derivation. Taking r p = 0.5mm, r i = 0.3mm as an example:

[0025]

[0026] Therefore, formula (2) does not meet condition (2). For the formula for the power density distribution of the annular light spot shown in formula (3), according to condition (1), we have:

[0027]

[0028] The integral of the power density within an infinite range is:

[0029]

[0030] Less than Q r , which does not meet condition (2). Summary of the Invention

[0031] Aiming at the deficiencies of the prior art, the present invention provides a modeling method for a laser welding heat source model of an annular composite beam, which solves the problems raised in the above background technology.

[0032] To achieve the above objectives, the present invention is realized through the following technical solutions: A modeling method for a laser welding heat source model of an annular composite beam specifically includes the following steps:

[0033] S1. Construct a Gaussian plane distribution heat source formula for the laser circular light spot:

[0034] A1. Assume that the power density distribution of the Gaussian plane distribution heat source is:

[0035]

[0036] Where q m is the maximum power density, and K is the heat energy concentration coefficient.

[0037] A2. For condition (2) of the power density distribution of the plane distribution heat source, we have:

[0038]

[0039] Solve to get: The conditions for the power density distribution of the planar distributed heat source (1) are as follows:

[0040] After simplification, we get: In summary, we can obtain: S2. Construct the Gaussian planar distributed heat source formula for the laser annular spot:

[0041] B1. Assume that on the cross-section of the annular spot, the power density distribution follows a Gaussian distribution, and the maximum power density is q m . The power density distribution of the annular spot can be expressed as:

[0042]

[0043] where σ is the standard deviation of the Gaussian distribution.

[0044] B2. According to the condition (1) of the power density distribution of the planar distributed heat source, we have:

[0045]

[0046] Since the power density distribution on the annular spot is symmetric about the midline r = r p of the ring, and the integral of the Gaussian distribution over the infinite interval is 1, we can obtain: B3. According to the condition (2) of the power density distribution of the planar distributed heat source, let the ratio of the power in the region between the inner diameter and the outer diameter of the annular spot to the total power be η r , then:

[0047]

[0048] Let According to the properties of the Gaussian distribution, we can obtain the relationship curve between η r and 1 / β, as shown in Figure 3 . Determine the corresponding value of β from the curve according to the value of η r .

[0049] In summary, the power density distribution formula for the annular spot is:

[0050]

[0051] S3. Construct the power density distribution of the planar distributed heat source model for the annular composite beam laser:

[0052] q f (r) = q c (r0 + q r (r0; (3)

[0053] S4. Construct the Gaussian volume distributed heat source formula for the laser circular spot. The volume distribution model of the circular laser heat source is as shown in Figure 4 .

[0054] C1. Basic assumptions: (1) The radius of the heat source action area decreases linearly with the increase of the molten pool depth; (2) At the planes where different molten pool depths z are located, the power density at the center is equal.

[0055] C2. Assume that the power density distribution formula of the circular laser heat source volume distribution model is:

[0056]

[0057] C3. According to the law of conservation of energy:

[0058]

[0059] C4. From the fact that the radius of the heat source action area decreases linearly with the increase of the molten pool depth, it can be obtained that:

[0060]

[0061] C5. Obtain the power density volume distribution formula of the circular light spot:

[0062]

[0063] S5. Construct the Gaussian volume distribution heat source formula of the laser annular light spot, and the annular laser heat source volume distribution model is as Figure 5 shown.

[0064] D1. Basic assumptions: (1) The width of the annular area of the heat source action area decreases linearly with the increase of the molten pool depth; (2) At the planes where different molten pool depths z are located, the position of the center line of the annular area remains unchanged; (3) At the planes where different molten pool depths z are located, the power density of the center line of the annular area is the largest and equal.

[0065] D2. Assume that the power density distribution formula of the annular laser heat source volume distribution model is:

[0066]

[0067] It can be transformed into: D3. According to the law of conservation of energy:

[0068]

[0069] D4. Since on the annular cross-section, the power density distribution is symmetric about r = r p then

[0070]

[0071] D5. In the molten pool plane at a depth of z, there is

[0072]

[0073] It can be obtained that:

[0074]

[0075] Let Then:

[0076]

[0077] D6. According to condition (1), in the molten pool plane at depth z, there is

[0078]

[0079] where z s and z b are the values of the molten pool surface and bottom surface in the z-axis direction respectively; r so , r bo , r si and r bi are the outer diameter and inner diameter of the action area of the annular volume heat source on the molten pool surface and bottom surface respectively.

[0080] w z = r zo - r zi

[0081] D7. Obtain the annular light spot power density volume distribution formula:

[0082]

[0083] S6. Construct the power density distribution of the annular composite beam laser volume distribution heat source model:

[0084] q Vf (r) = q Vc (r) + q Vr (r). (6)

[0085] Preferably, the steps for constructing the Gaussian plane distribution heat source formula of the laser annular light spot specifically include the following:

[0086] B1. Assume that on the cross-section of the annular light spot, the power density distribution follows a Gaussian distribution, and the maximum value of the power density is q m , and the power density distribution of the annular light spot can be expressed as:

[0087]

[0088] B2. According to condition (1) of the power density distribution of the plane distribution heat source, there is:

[0089]

[0090] Since the power density distribution on the annular light spot is symmetric about the midline r = r of the ring, and the integral of the Gaussian distribution over the infinite interval is 1, the following can be obtained: p Symmetric, and the integral of the Gaussian distribution over the infinite interval is 1, so the following can be obtained:

[0091] B3. According to condition (2) of the power density distribution of the planar distributed heat source, let the ratio of the power of the region between the inner diameter and the outer diameter of the annular light spot to the total power be η r , then:

[0092]

[0093] Let According to the properties of the Gaussian distribution, the relationship curve of η r and 1 / β can be obtained;

[0094] According to the value of η r to determine the corresponding value of β from the curve;

[0095] In summary, the power density distribution formula of the annular light spot:

[0096]

[0097] Preferably, in the above A1, q m is the maximum power density, and K is the heat energy concentration coefficient.

[0098] Preferably, in the above B1, σ is the standard deviation of the Gaussian distribution.

[0099] Preferably, in the above D6, z s and z b are the values of the molten pool surface and bottom surface in the z-axis direction respectively; r so , r bo , r si and r bi are the outer diameter and inner diameter of the action region of the annular volume heat source on the molten pool surface and bottom surface respectively.

[0100] Beneficial effects

[0101] The present invention provides a modeling method for an annular composite beam laser welding heat source model. Compared with the prior art, it has the following beneficial effects:

[0102] This modeling method for the annular composite beam laser welding heat source model, by introducing the parameter η c representing the proportion of the energy within the radius range of the circular light spot to the total energy, derives the Gaussian planar distributed heat source model under any η c . Introduces the parameter η r, the power density distribution formula of the annular light spot that strictly meets Condition 1 and Condition 2 under any η is derived, that is, a plane distribution heat source model of the annular light spot is established. According to the same inventive concept, a volume distribution heat source model is established, which has high accuracy and good guiding significance. r Under r , the power density distribution formula of the annular light spot that strictly meets Condition 1 and Condition 2 is derived, that is, a plane distribution heat source model of the annular light spot is established. According to the same inventive concept, a volume distribution heat source model is established, which has high accuracy and good guiding significance. BRIEF DESCRIPTION OF THE DRAWINGS

[0103] Figure 1 is a schematic diagram of the composite beam laser of the present invention;

[0104] Figure 2 is a schematic diagram of the definition of the heat source radius of the present invention;

[0105] Figure 3 is η of the present invention r and the relationship curve diagram of 1 / β;

[0106] Figure 4 is a schematic diagram of the volume distribution model of the circular laser heat source of the present invention;

[0107] Figure 5 is a schematic diagram of the volume distribution model of the annular laser heat source of the present invention;

[0108] Figure 6 is the plane distribution diagram of the laser power density of the central circular heat source of the present invention;

[0109] Figure 7 is the plane distribution diagram of the laser power density of the annular heat source of the present invention;

[0110] Figure 8 is the plane distribution diagram of the laser power density of the composite heat source of the present invention;

[0111] Figure 9 is the power density distribution diagram on the y = 0 section under different power ratios of the central circular heat source of the present invention;

[0112] Figure 10 is the power density distribution diagram on the y = 0 section under different power ratios of the annular heat source of the present invention;

[0113] Figure 11 is the power density distribution diagram on the y = 0 section under different power ratios of the composite heat source of the present invention;

[0114] Figure 12 is the power density distribution diagram of the volume distribution model of the composite heat source on the surface of the welded part of the present invention;

[0115] Figure 13 is the power density distribution diagram of the volume distribution model of the composite heat source inside the welded part of the present invention. DETAILED DESCRIPTION OF THE INVENTION

[0116] Next, the technical solutions in the embodiments of the present invention will be clearly and completely described in conjunction with the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all the embodiments. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative efforts shall fall within the protection scope of the present invention.

[0117] Please refer to Figures 1-5 , the present invention provides a technical solution: a modeling method for a heat source model of an annular composite beam laser welding, specifically including the following steps:

[0118] S1. Construct the Gaussian plane distribution heat source formula for the laser circular spot:

[0119] A1. Assume that the power density distribution of the Gaussian plane distribution heat source is:

[0120]

[0121] where q m is the maximum power density, and K is the heat energy concentration coefficient.

[0122] A2. The condition (2) of the power density distribution of the plane distribution heat source is:

[0123]

[0124] Solve to get: A3. The condition (1) of the power density distribution of the plane distribution heat source is:

[0125]

[0126] Simplify to get: In summary, it can be obtained: S2. Construct the Gaussian plane distribution heat source formula for the laser annular spot:

[0127] B1. Assume that on the cross-section of the annular spot, the power density distribution follows a Gaussian distribution, and the maximum power density is q m . The power density distribution of the annular spot can be expressed as:

[0128]

[0129] where σ is the standard deviation of the Gaussian distribution.

[0130] B2. According to the condition (1) of the power density distribution of the plane distribution heat source, there is:

[0131]

[0132] Since the power density distribution on the annular light spot is symmetric about the midline r = r of the ring, and the integral of the Gaussian distribution over the infinite interval is 1, we can obtain: p Symmetric, and the integral of the Gaussian distribution over the infinite interval is 1, so we can get: B3. According to condition (2) of the power density distribution of the planar distributed heat source, let the ratio of the power of the region between the inner diameter and the outer diameter of the annular light spot to the total power be η r , then:

[0133]

[0134] Let According to the properties of the Gaussian distribution, the relationship curve between η r and 1 / β can be obtained, as shown in Figure 3 . Determine the corresponding β value from the curve according to the value of η r .

[0135] In summary, the power density distribution formula of the annular light spot:

[0136]

[0137] S3. Construct the power density distribution of the annular composite beam laser planar distributed heat source model:

[0138] q f (r) = q c (r) + q r (r);

[0139] S4. Construct the Gaussian volume distribution heat source formula of the laser circular light spot, and the circular laser heat source volume distribution model is as shown in Figure 4 .

[0140] C1. Basic assumptions: (1) The radius of the heat source action area decreases linearly with the increase of the molten pool depth; (2) The power density at the center is equal in the plane where the molten pool depth z is located;

[0141] C2. Assume that the power density distribution formula of the circular laser heat source volume distribution model is:

[0142]

[0143] C3. According to the law of conservation of energy:

[0144]

[0145] C4. From the fact that the radius of the heat source action area decreases linearly with the increase of the molten pool depth, we can get:

[0146]

[0147] C5. Obtain the circular light spot power density volume distribution formula:

[0148]

[0149] S5. Construct the Gaussian volume distribution heat source formula for the laser ring-shaped spot. The volume distribution model of the ring-shaped laser heat source is as Figure 5 shown:

[0150] D1. Basic assumptions: (1) The width of the ring-shaped area in the heat source action area decreases linearly with the increase of the molten pool depth; (2) The position of the center line of the ring-shaped area remains unchanged in the plane at different molten pool depths z; (3) The power density at the center line of the ring-shaped area is the largest and equal in the plane at different molten pool depths z;

[0151] D2. Assume that the power density distribution formula of the volume distribution model of the ring-shaped laser heat source is:

[0152]

[0153] It can be transformed into: D3. According to the law of conservation of energy:

[0154]

[0155] D4. Since on the ring-shaped cross-section, the power density distribution is symmetric about r = r p then

[0156]

[0157] D5. In the plane of the molten pool at depth z, there is

[0158]

[0159] It can be obtained that:

[0160]

[0161] Let Then:

[0162]

[0163] D6. According to assumption (1), in the plane of the molten pool at depth z, there is

[0164]

[0165] where, z s and z b are the values of the molten pool surface and bottom surface in the z-axis direction respectively; r so , r bo , r si and r biThey are the outer diameter and inner diameter of the action areas of the annular volume heat source on the molten pool surface and bottom surface respectively.

[0166] w z = r zo - r zi

[0167] D7. Obtain the formula for the volume distribution of the power density of the annular light spot:

[0168]

[0169] S6. Construct the power density distribution of the laser volume distribution heat source model of the annular composite beam:

[0170] q Vf (r) = q Vc (r) + q Vr (r).

[0171] Preferably, the specific steps for constructing the Gaussian plane distribution heat source formula of the laser annular light spot are as follows:

[0172] B1. Assume that on the cross-section of the annular light spot, the power density distribution follows a Gaussian distribution, and the maximum value of the power density is q m , and the power density distribution of the annular light spot can be expressed as:

[0173]

[0174] B2. According to condition (1) of the power density distribution of the plane distribution heat source, we have:

[0175]

[0176] Since the power density distribution on the annular light spot is symmetric about the midline r = r p of the ring, and the integral of the Gaussian distribution in the infinite interval is 1, we can obtain:

[0177] B3. According to condition (2) of the power density distribution of the plane distribution heat source, let the ratio of the power in the area between the inner diameter and the outer diameter of the annular light spot to the total power be η r , then:

[0178]

[0179] Let According to the properties of the Gaussian distribution, the relationship curve between η r and 1 / β can be obtained;

[0180] According to the value of η r to determine the corresponding value of β from the curve;

[0181] In summary, the formula for the power density distribution of the annular light spot is as follows:

[0182]

[0183] In the present invention, in A1, q m is the maximum power density, and K is the heat energy concentration coefficient.

[0184] In the present invention, in B1, σ is the standard deviation of the Gaussian distribution.

[0185] In the present invention, in D6, z s and z b are respectively the values of the molten pool surface and bottom surface in the z-axis direction; r so , r bo , r si and r bi are respectively the outer diameter and inner diameter of the action area of the annular volume heat source on the molten pool surface and bottom surface.

[0186] In the prior art, as Figure 1 shown, the annular composite laser beam is formed by irradiating lasers with different powers through double-layer optical fiber conduction, as Figure 2 shown. The annular composite laser welding heat source consists of a central circular heat source and a peripheral annular heat source.

[0187] As Figure 3 shown, the heat source model of the laser includes the plane power density distribution of the laser irradiated on the surface of the welded part and the distribution of the laser energy in the molten pool space, that is, the volume power density distribution.

[0188] Aiming at the shortcomings of the above prior art, the present invention introduces the parameter η c characterizing the proportion of the energy within the radius range of the circular light spot to the total energy, and derives the Gaussian plane distribution heat source model for any η c . The parameter η r representing the proportion of the energy within the bandwidth range of the annular light spot to the total energy is introduced, and the power density distribution formula of the annular light spot that strictly meets Condition 1 and Condition 2 for any η r is derived, that is, a plane distribution heat source model of the annular light spot is established. And according to the same inventive concept, a volume distribution heat source model is established.

[0189] The following takes specific embodiments to illustrate this process in detail.

[0190] (1) Laser heat source plane distribution model

[0191] According to formula (3), the variable parameters are set as follows. The central laser power is Q c = 4000 W; the annular laser power is the power Q r = 2000 W; the effective heating radius of the central laser is rH =1mm; the inner diameter of the effective heating area of ​​the ring laser heat source is r i =1mm; outer diameter is r o =3mm. Figure 6 , Figure 7 and Figure 8 The power density distribution in the composite planar laser heat source model, the central improved Gaussian circular plane heat source, the surrounding annular plane heat source and the sum of the two composite planar distribution heat source models are given respectively. Figure 9 , Figure 10 and Figure 11 A curve showing the change of power density with x-coordinate at different power density ratios within the action range on the y=0 section is given.

[0192] (2) Laser heat source volume distribution model

[0193] According to formula (6), the variable parameters are set as follows: the central laser power is Qc = 2000W; the ring laser power is Qr = 10000W; the effective heating radius of the central laser on the molten pool surface is r sH =1mm; the inner diameter of the effective heating area of ​​the ring laser heat source is r si =1mm; outer diameter is r so =3mm; the effective heating radius of the laser at the bottom of the molten pool is r bH =0.5mm; the inner diameter of the effective heating area of ​​the ring laser heat source is r bi =1.4mm; outer diameter is r bo =2.6mm; the molten pool depth is H=3mm. Figure 12 and Figure 13 The spatial power density distribution of the composite heat source model distribution model is given.

[0194] It should be noted that, in this article, relational terms such as first and second, etc. are only used to distinguish one entity or operation from another entity or operation, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Moreover, the terms "include", "comprise" or any other variants thereof are intended to cover non-exclusive inclusion, so that a process, method, article or device including a series of elements includes not only those elements, but also other elements not explicitly listed, or also includes elements inherent to such process, method, article or device.

[0195] Although embodiments of the present invention have been shown and described, it will be appreciated by those skilled in the art that various changes, modifications, substitutions and variations may be made to the embodiments without departing from the principles and spirit of the present invention, and that the scope of the present invention is defined by the appended claims and their equivalents.

Claims

1. A modeling method for a circular composite beam laser welding heat source model, characterized in that: The specific steps include: S1. Construct the Gaussian plane distribution heat source formula of the laser circular spot: A1. Assuming that the power density distribution of the Gaussian plane distribution heat source is: A2. The conditions (2) for the power density distribution of a planar distributed heat source are: The solution is: A3. The conditions for the power density distribution of a planar distributed heat source (1) are: Simplified: In summary, we can get: S2, construct the Gaussian plane distribution heat source formula of the laser ring spot; S3. Construct the power density distribution of the planar distribution heat source model of the annular composite beam laser: q f (r)=q c (r)+q r (r); S4. Construct the Gaussian volume distribution heat source formula of the laser circular spot: C1. Basic assumptions: (1) The radius of the heat source action area decreases linearly with the increase of the molten pool depth; (2) The power density at the center is equal in the plane at different molten pool depths z; C2. Assuming the power density distribution formula of the circular laser heat source volume distribution model is: C3. According to the law of conservation of energy: C4. From the fact that the radius of the heat source action area decreases linearly with the increase of the molten pool depth, we can get: C5. Get the volume distribution formula of circular spot power density: S5. Construct the Gaussian volume distribution heat source formula of the laser annular spot: D1. Basic assumptions: (1) The width of the annular region in the heat source action area decreases linearly with the increase of the molten pool depth; (2) The position of the middle line of the annular region remains unchanged in the plane where the molten pool depth z is different; (3) The power density of the middle line of the annular region is the largest and equal in the plane where the molten pool depth z is different; D2. Assume that the power density distribution formula of the ring laser heat source volume distribution model is: Can be transformed into: D3. According to the law of conservation of energy: D4. Since the power density distribution on the annular cross section is about r = r p Symmetric Rule D5. In the molten pool plane at depth z, there are: We can get: make but: D6. According to assumption (1), in the molten pool plane at depth z, we have: w z ＝r zo -r zi ； D7. Get the volume distribution formula of the annular spot power density: S6. Construct the power density distribution of the annular composite beam laser volume distribution heat source model: q Vf (r)=q Vc (r)+q Vr (r)。 2. The modeling method of a circular composite beam laser welding heat source model according to claim 1, characterized in that: The Gaussian plane distribution heat source formula for constructing the laser annular spot specifically includes the following steps: B1. Assume that the distribution of power density on the cross section of the annular spot obeys Gaussian distribution, and the maximum value of power density is q m , the power density distribution of the annular spot can be expressed as: B2. According to the conditions (1) for the power density distribution of the planar heat source, we have: Since the power density distribution on the annular spot is about the center line of the ring r = r p Symmetric, and the Gaussian distribution integrates to 1 in an infinite interval, so we can get: B3. According to the condition (2) of the power density distribution of the planar heat source, let the ratio of the power in the area between the inner and outer diameters of the annular spot to the total power be η r ,but: make According to the properties of Gaussian distribution, we can get η r Relationship curve with 1 / β; According to η r The value of determines the corresponding value of β from the curve; In summary, the annular spot power density distribution formula is:

3. The modeling method of a circular composite beam laser welding heat source model according to claim 1, characterized in that: In A1, q m is the maximum power density, and K is the thermal energy concentration coefficient.

4. The modeling method of a circular composite beam laser welding heat source model according to claim 1, characterized in that: In B1, σ is the standard deviation of the Gaussian distribution.

5. The modeling method of a circular composite beam laser welding heat source model according to claim 1, characterized in that: In D6, z s and z b are the values ​​of the molten pool surface and bottom in the z-axis direction respectively; r so 、r bo 、r si and r bi are the outer diameter and inner diameter of the action area of ​​the annular volume heat source on the surface and bottom of the molten pool respectively.

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