Multi-objective optimization of the molding size o

2022-09-26
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Multi-objective optimization of the molding size of precision cavity mold

preface

the molding size of precision cavity film tools is divided into three categories, namely, the size of cavity cavity, the size of cavity core and the size of center distance. The design criterion is that all kinds of errors caused by molding materials, mold design and manufacturing, use and maintenance and other factors must be included in the dimensional tolerance of product parts. These errors mainly include the dimensional tolerance caused by the selection error of linear shrinkage of molding materials, the dimensional error caused by mold manufacturing error, the dimensional error caused by the repair modulus reserved during mold design and maintenance, and the wear amount in the use process. In optimization, these influencing factors need to be comprehensively analyzed in order to get reasonable and effective results

1 probability calculation of linear shrinkage of forming materials

the linear shrinkage of materials is affected by many factors, and there is a variation range [Kmin, kmax], which is regarded as a random variable, and it is approximate to the normal distribution. Its mathematical expectation is( μ= Kmax + Kmin)/2, set its standard deviation as σ, Because the value of normal random variable is μ ±4 σ The probability outside is almost zero, so it can be considered as Kmin= μ- four σ, kmax= μ+ four σ, Any form of the two formulas can be obtained σ= (kmax - Kmin)/8, according to 3 of normal distribution σ Rule, the actual possible linear shrinkage range [K ′ min, K ′ Max] can be set at μ ±3 σ The inner bent core is fixed on the bent core base, that is, K 'min= μ- three σ, k′max = μ+ three σ, The reliability probability is 99.73%, so the calculation formula of the actual linear shrinkage of various materials in the sense of probability is k ′ min= (K  max+7kmin)/8, K ′ max= (7kmax+kmin)/8, and the actual comprehensive linear shrinkage of forming materials in the sense of probability is μ′= (k′max + k′min)/2。 Table 1 lists the actual linear shrinkage data of various common formed alloy materials in the sense of probability. Table 1 Analysis of the actual comprehensive linear shrinkage of the alloy in the sense of probability

2 molding size

2.1 cavity size

according to the principle of integration, the overall physical size of the product parts should be marked as LZ0, which undoubtedly provides energy for the industrial transformation of Nanzhuang- Δ, The size of the corresponding cavity is lc0+ δ, When the cavity is processed to the maximum allowable size, there is

lcmax=lz (1+ μ′) -ηΔ+δ (1)

where h is the repair coefficient, D is the dimensional tolerance of product parts, δ Accuracy tolerance for mold manufacturing. If the actual linear shrinkage at this time is the minimum linear shrinkage, the solid size of the product part is the maximum

lzmax=lcmax-lcmax K ′ min (2)

substitute formula (2) into formula (1), omit the high-order minor term, then there is

lzmax=lz (1+ μ′- k′min) - h D + δ (3)

at this time, the constraint condition lzmax ≤ LZ should be met, then there is

H ≥ LZ( μ′- k′max + δ)/D (4)

when the size and material of the product parts are determined, the right end of this formula can be regarded as the mold manufacturing tolerance δ The function of is written as f( δ)。

when the cavity is processed to the minimum allowable size and the actual linear shrinkage is the maximum, the solid size is the minimum. At this time, lzmin ≥ LZ shall be met- Δ, Then it can be analyzed that

h ≤ LZ( μ′- K ′ max)/d+1 (5)

mark the right end of this formula as Dmax, and the solid size error of product parts cannot exceed D, that is, lzmax - lzmax ≤ D, then there is

δ ≤ d-lz (k 'max - K' min) (6)

record the right end of this formula as δ Max, for δ The lower limit of, according to the highest precision that can be achieved by precision cavity mold processing, can reach it5, take δ min = 0.01mm。

2.2 cavity and core size

according to the principle of entering the body, the hole size of product parts is marked as LZ0+ Δ, The corresponding core size is l0c- δ, When the core is processed to the maximum allowable size and the actual linear shrinkage is the maximum, the hole size is the maximum; when the core is processed to the minimum allowable size and the actual shrinkage is the minimum, the hole size is the minimum. According to this principle, h and δ The upper and lower limits of (4), (5) and (6) are the same and will not be listed

2.3 center distance dimension

this kind of dimension does not involve repair modulus and wear, but only related to linear shrinkage. For product parts, it can be marked as LZ ± d/2, and the corresponding mold center distance dimension can be marked as LC ± δ/2. You can get δ Upper limit of δ Max is shown in equation (6), and is no longer listed

3 multi-objective optimization of cavity forming dimension

both require mold manufacturing accuracy tolerance δ As large as possible to reduce the mold manufacturing cost and process difficulty, while requiring the mold repair coefficient h to be as small as possible. At this time, there is a stronger fault tolerance for the selection error of linear shrinkage, so the optimization model is

using the efficiency coefficient method to solve this optimization problem. The efficiency coefficients D1 and D2 are the best when they are 1 and the worst when they are 0. According to this, equation (7) is transformed into a standard type

s.t. f( δ)- h≤0

h-hmax≤0

δ min- δ ≤0

δ-δ Max ≤ 0

where hmin=f( δ Min), the outer point penalty function method is used to solve this model, because the objective function is constructed as a quadratic function, and the penalty term of the outer point method is also a quadratic function. Then, using the quadratic convergence property, without one-dimensional search of iteration step size, a minimization sequence can be obtained in one step by Newton method. When the penalty factor tends to infinity, the sequence converges to the optimal solution h* and δ*, And the convergence is guaranteed. So far, the molding size in the sense of optimization can be obtained. The calculation formulas of cavity size, core size and center distance size are

lc0 respectively+ δ*=[ Lz(1+ μ′)- h*D]0+ δ* (9)

Lc- δ* 0=[Lz(1- μ′)+ h* Δ]-δ* 0 (10)

Lc± δ*/2=[Lz(1+ μ′)] ± δ*/2 (11)

(11) δ* Take as δ Max, see formula (6)

4 example

Table 2 lists the forming size data of aluminum bronze alloy product parts obtained by optimization method and traditional method at the same time. Table 2 molding size under optimization method and traditional method

(Note: in traditional method, δ= (0.15~0.35)h; H induce tissue regeneration such as ligaments and central nerves =0.5 ~ 0.75)

it can be seen from the table that the processing accuracy requirements of each molding size obtained by the optimization method are lower than those obtained by the traditional method (the public value obtained by the optimization method must be greater by some means), and the optimized modification coefficients are less than the modification modulus of the traditional method except for the second size, Thus, the fault tolerance of the selection error of linear shrinkage is considered to the greatest extent

5 conclusion

this paper comprehensively analyzes the relationship between various factors that affect the dimensional accuracy of product parts. The multi-objective optimization model established takes into account the comprehensive effect of various important influencing factors, and provides a quantitative analysis method, which is more reasonable and economical than selecting based on experience, and has certain theoretical and practical value. (end)

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