# Optimization mathematical model of process paramet

2022-07-25
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The mathematical model of process parameter optimization for green manufacturing

1 introduction

the problem of resource utilization and environmental behavior is an important research topic in the world, and the resource utilization and environmental behavior optimization of manufacturing systems (including mechanical manufacturing systems) is an important part of it. For a long time, the research on mechanical manufacturing system has focused on production cost, productivity, product quality and so on, but paid little attention to the rational use of resources and environmental protection. In recent years, with people's increasing attention to saving earth resources, improving environmental quality and protecting human health, the mechanical manufacturing system can no longer be described only by traditional indicators such as cost, efficiency and quality. Based on the above considerations, this paper is one of the necessary equipment in rubber quality inspection MP (3) type grinding machine optimizes and analyzes the typical machining process in mechanical manufacturing, establishes a mathematical model of process parameter optimization for green manufacturing, which takes cutting parameters AP, N, f (or VF, AF) and cutting fluid as design variables, quality as constraints, productivity, cost, resource consumption and environmental pollution as objective functions, and gives an application example

2 establishment of optimization mathematical model

2.1 determination of design variables

in the machining process, once the material, machining requirements, machine tools and cutting tools of the workpiece are determined, the selection of cutting parameters and cutting fluid becomes the key to affect the objective function. Therefore, the cutting parameters and cutting fluid are taken as design variables, that is, the cutting parameters n=x1, (f or VF, AF) =x2, ap=x3, and the cutting fluid is X4, Then

x=[x1, X2, X3, x4]t=[n, (f or VF, AF), AP, cutting fluid]t

2.2 determine the objective function

1) in order to improve productivity, take the shortest single work hour TW as the first objective function F1 (x), That is,

f1 (x) =mintw=min (tm+tct+tot)

where: TM - cutting time (min) of the process (see the concise manual of cutting parameters (Third Edition) by AI Xing and Xiao Shigang published by the machinery industry press in 1994)

tot - other auxiliary time (min) except tool change

2) to improve economy, Take the lowest single piece process cost C as the second objective function F2 (x), that is,

f2 (x) =minc=min (tmm+tctmtm/t+tmct/t+totm)

where: m - the factory expenditure shared by the process per unit time (yuan/min)

ct - the cost related to the tool during the tool durability period (including tool grinding cost and tool depreciation cost) (yuan)

t - tool durability (min)

3) is a reasonable use of resources, Determine the following objective function:

a. in order to reduce the power required for cutting and reduce the consumption of power resources, the third objective function F3 (x) is to minimize the power PI consumed by cutting the metal ZW per unit volume, That is,

f3 (x) =min (pi/zw) =min[(pu+apc)/zw]

where: Pu - the no-load power of the machine tool (kw) (for the relationship between Pu and N of the lathe, see the energy characteristics and application of the machining system written by Liu Fei, xuzongjun, etc. published by the Mechanical Industry Press in 1995)

α—— Power balance equation coefficient, α= 1.15 ~ 1.25

pc - cutting power of machine tool during machining (kw) (see concise manual of cutting parameters (Third Edition) by AI Xing and Xiao Shigang published by China Machine Press in 1994 for the calculation formula)

zw - metal removal amount per unit time (mm3/mi can also determine whether to increase color, plasticizer, conductive material or other materials n)

b. in order to reduce tool wear during machining and reduce the consumption of tool resources, Taking the minimum tool wear rate WR within the processing time as the fourth objective function f - may4,2013 (x), That is,

where: WRA - the mechanical wear rate of the tool (for the calculation formula, see an analytical approach for determining the environmental impact of machine processes written by a a Munoz and P Sheng in the Journal of materials processing technology in november1995) wrd - the thermochemical wear rate of the tool (for the calculation formula, see the same literature as WRA)

c. reduce the consumption of cutting fluid. The cutting fluid required in the machining process includes the cutting fluid covered on the chip and workpiece (M chip, m workpiece), the cutting fluid vaporized into the environment (M vaporization) and the recyclable cutting fluid (M Cycle), that is, the total amount of cutting fluid m=m chip +m workpiece +m vaporization +m cycle, because m cycle can be recycled, Therefore, reducing the sum of the first three parts in the formula (M chip +m workpiece +m vaporization) (see the same literature as WRA for the calculation formula) can reduce the consumption of cutting fluid resources. Therefore, taking the minimum of (M chip +m workpiece +m vaporization) as the fifth objective function F5 (x), that is,

f5 (x) =min (M chip +m workpiece +m vaporization)

4), in order to reduce environmental pollution and protect workers' health, Determine the following objective function:

a. reduce the machine tool noise. The machine tool noise is mainly the noise generated by the mechanical structure (especially the noise generated by gears, motors, bearings, etc.). The noise level is related to its frequency, so the minimum noise frequency is taken as the sixth objective function F6 (x) (for relevant calculation, see the noise of machine tools - principle and control written by Zhang CE published by Tianjin Science and Technology Press in 1984), that is,

f6 (x) =min (nz/60+c)

where: Z - number of main shaft gear teeth

c - natural frequency

b. reduce the pollution of cutting fluid. The cutting fluid attached to the workpiece and chip will pollute the work site, And it has certain toxicity and flammability as volatile cutting fluids, so the minimum weighted mass MW is taken as the seventh objective function F7 (x), that is,

f7 (x) =minmw

the calculation method of MW in the formula is shown in an analytical approach for determining the environmental impact of machine processes written by a Munoz and P Sheng in the Journal of materials processing technology in november1995

2.3 determining constraints

in the production process, due to the limitations of processing equipment, processing conditions and workpiece quality requirements, the range of design variables available for selection is limited, Therefore, the following constraints must be taken into account when establishing the optimization mathematical model:

1) back feed: apmin ≤ AP ≤ apmax

2) machine speed: Nmin ≤ n ≤ nmax

3) machine feed: Fmin ≤ f ≤ Fmax (during milling: Vmin ≤ VF ≤ Vmax)

4) machine effective power: PC HPE ≤ 0

where: PE - main motor power (kw)

h -- machine tool efficiency

5) machine tool feed mechanism strength: FF ≤ FM

in the formula, FF -- feed resistance (n) (for the calculation formula, see the concise manual of cutting parameters (Third Edition) written by AI Xing and Xiao Shigang published by China Machine Press in 1994)

fm -- maximum allowable feed resistance (n)

6) machine tool torque: MC ≤ mm

in the formula, MC -- torque (nm) (for the calculation formula, see the concise manual of cutting parameters (Third Edition) by AI Xing and Xiao Shigang published by China Machine Press in 1994)

mm - maximum allowable torque of machine tool (nm)

7) tool dulling standard:

where T - tool durability (min) (for the calculation formula, see the concise manual of cutting parameters (Third Edition) by AI Xing and Xiao Shigang published by China Machine Press in 1994) ）

8) workpiece machining surface roughness: Ramin ≤ RA ≤ ramax

where ra - cutting surface roughness (m)

if necessary, the requirements for productivity can also be reduced to constraints. The above constraints are only the general conditions that should be considered in general machining. For different processing methods, it is often necessary to add some other constraints according to the actual processing conditions to ensure the realization of processing requirements

2.4 establishment of optimization mathematical model

in conclusion, degradable packages for typical machining processes of mechanical manufacturing can be established to facilitate the buyer and the seller. The high cost of new materials faces the promotion problem. The optimization mathematical model is the optimization design method of multi-objective function

the optimization mathematical model of typical machining processes established in this paper is a multi-objective function optimization model, and its objective function can be treated by weighted sum method. The objective function after weighted sum is

f (x) =l1f1 (x) +l2f2 (x) +... +l7f7 (x)

where L1, L2,..., L7 are weighting factors respectively, and l1+l2+l3+l4+l5+l6+l7=1. The weighting factor can be determined by using the hierarchical single sorting in the analytic hierarchy process. By establishing the analytic hierarchy process structure model as shown in Figure 1, the 7 indicators in the indicator layer can be sorted and their sorting weights can be obtained

the meanings of the indicators of layer C in the figure: C1 is the man hour of a single piece, C2 is the process cost of a single piece, C3 is the power consumption, C4 is the tool wear rate, C5 is the consumption of cutting fluid, C6 is the noise, and C7 is the toxicity and flammability of cutting fluid

4 application example of optimization mathematical model

according to the established optimization mathematical model, we have compiled the corresponding process parameter optimization software. Figure 2 shows the known conditions and optimization results of turning process parameters optimization for green manufacturing. (end)

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