A method for design structure optimization of Roots vacuum unit based on NSGA-II algorithm

Abstract

The present invention discloses a method for optimizing the design structure of a Roots vacuum unit based on an NSGA-Ⅱ algorithm. The method first preliminarily proposes the number of stages, rotor radius, profile equation, rotor thickness and characteristic assembly clearance of a multi-stage Roots vacuum unit, and takes the ultimate pressure, theoretical pumping speed and compression power of the vacuum unit as the target to be optimized; then formulates decision variables, as well as the range of decision variables and the numerical parameters of the remaining variables; then optimizes the design structure of the three-leaf Roots vacuum unit using the NSGA-Ⅱ algorithm; finally, according to the result obtained by the optimization, it is judged whether the corresponding objective function value meets the standard, and if it meets the requirements, all structural parameters are output; if it does not meet the requirements, the decision variables and the numerical values ​​of the remaining variables are re-formulated, and the above steps are repeated. The method of the present invention not only saves the structural optimization cost of the Roots vacuum unit, but also has strong universality, and can be applied to the structural design of Roots pump units in different fields.

Description

Technical Field

[0001] The invention relates to the technical field of structural design optimization, and in particular to a method for optimizing the design structure of a Roots vacuum unit based on an NSGA-II algorithm. Background Art

[0002] Roots vacuum pump is a kind of variable displacement vacuum pump with two blade-shaped rotors rotating synchronously in opposite directions. There is a small gap between the rotors and between the rotors and the inner wall of the pump casing, but they do not touch each other. Roots vacuum pumps are widely used in devices such as petroleum, chemical industry, plastics, pesticides, dynamic balancing of steam turbine rotors, and aerospace space simulation. The ultimate vacuum of Roots pump depends not only on the structure of the pump itself and the manufacturing accuracy of components such as the rotor, but also on the ultimate vacuum of the fore pump. In order to increase the pumping rate and ultimate vacuum of the pump, multiple Roots pumps can be used in series.

[0003] In the process of R&D and production of Roots vacuum units, in the face of corresponding technical requirements, experiments and other methods are often used to test whether the performance of the products produced meets the standards. In a large number of experiments, experience is summarized to obtain design and structural parameters with better performance before putting them into production. It takes a lot of manpower, material and financial resources to formulate the design and structural parameters of Roots vacuum units through a large number of experiments. It takes a long time from design to production, and the design and structural parameters obtained by experimental methods may not meet the preset standards.

[0004] The Chinese patent "CN203641005U A multi-stage Roots pump for ladle degassing" includes Roots pump 1, Roots pump 2, Roots pump 3, Roots pump 4 and Roots pump 5. Roots pump 3, Roots pump 4 and Roots pump 5 are all equipped with a cooling structure that can water-cool the pump body, which solves the problem of the short service life of the Roots vacuum unit in the field of ladle degassing. Moreover, the patent only proposes ways to optimize the life of the Roots vacuum unit in a certain field. When facing other fields, it is often necessary to redesign the structural parameters and conduct a large number of experiments again to design the structure. Summary of the invention

[0005] In view of the above-mentioned deficiencies in the prior art, the present invention provides a method for optimizing the design structure of a Roots vacuum unit based on the NSGA-II algorithm.

[0006] In order to solve the above technical problems, the technical solution adopted by the present invention is: a method for optimizing the design structure of a Roots vacuum unit based on the NSGA-II algorithm, comprising the following steps:

[0007] Step 1: According to actual production needs, the existing multi-stage Roots vacuum unit is used as a prototype for measurement, and the number of stages, rotor radius, profile equation, rotor thickness and characteristic assembly clearance of the multi-stage Roots vacuum unit are preliminarily designed, and the ultimate pressure, theoretical pumping speed and compression power of the vacuum unit are taken as the optimization targets;

[0008] Step 2: Propose decision variables, their ranges and the numerical parameters of other variables;

[0009] The decision variables include: the radial assembly gap δ between the j-th rotor and the rotor 1j , radial assembly clearance δ between the j-th rotor and the pump body 2j , the axial assembly clearance δ between the j-th stage rotor and the rigid support point of the pump body 3j , the axial assembly clearance δ between the j-th stage rotor and the pump body floating support point 4j , the j-th level rotor thickness L j , and the rotor profile coefficient C of the jth stage j .

[0010] Step 3: Use NSGA-II algorithm to optimize the design structure of the three-leaf Roots vacuum unit. The specific process is as follows;

[0011] Step 3.1: Set parameters: Set the upper and lower bounds of the decision variables according to the known mathematical model, set the population size Popsize, the number of genetic evolutions i, and the crossover probability P c and mutation probability P m ; Population size Popsize ranges from 20 to 200, genetic evolution times range from 100 to 2000, crossover probability P c The value range is 0.25~1, and the mutation probability P m The value range is 0.001~0.1, and the value of the setting parameter is determined according to the actual situation of the Roots pump unit;

[0012] Step 3.2: Initialize the population: Set the initial value of the genetic evolution times to 0, set the maximum number of evolution times Gen, and randomly generate the initial population P i ;

[0013] Step 3.3: Calculate the objective function: Calculate the initial population P generated in step 3.2 i The objective function value of each individual in ;

[0014] The objective function includes:

[0015] (1) f i1 =min{compression power of Roots pump unit N};

[0016] (2) f i2=max{Theoretical pumping speed S of Roots pump unit th};

[0017] (3) f i3 =min{Ultimate pressure P of Roots pump unit a}.

[0018] Furthermore, the theoretical pumping speed S of the Roots pump unit is th The calculation process is as follows:

[0019]

[0020] Among them, ω is the rotation speed, L is the thickness of the Roots rotor, R is the rotor radius, η vp is the volume utilization coefficient.

[0021] Furthermore, the calculation process of the total compression power N of the Roots pump unit is as follows:

[0022] Calculate the actual pumping speed S of the Roots pump unit:

[0023]

[0024] Among them, S th is the theoretical pumping speed, P V is the exhaust pressure, P A is the suction pressure, u is the flow conductance. Under actual working conditions, there are two flow states of the counterflow gas in the gap, namely laminar flow and molecular flow. The flow conductance can be simplified to an empirical formula for calculation, as follows:

[0025] Under laminar flow: u = 20.7 × F;

[0026] Under molecular flow conditions: u = 12.7 × F;

[0027] Where F is the gap leakage area, the specific formula is as follows:

[0028] F=((δ1+2δ2)×L+2×(R+a))×(δ3+δ4) / 100

[0029] Among them, δ1 is the radial assembly clearance between the rotors of this stage, δ2 is the radial assembly clearance between the rotor of this stage and the pump body, δ3 is the axial assembly clearance between the rotor of this stage and the rigid support point of the pump body, δ4 is the axial assembly clearance between the rotor of this stage and the floating support point of the pump body, and a is the rotor center distance;

[0030] When the Roots vacuum pump unit is in working state for a long time, the pressure in the pumped container will gradually decrease to the minimum value, that is, the ultimate pressure value; at this time, under the ultimate pressure condition, the actual pumping speed of the vacuum unit S = 0, and the suction ultimate pressure of the i-th level vacuum unit is obtained. for:

[0031]

[0032] in, u i are the theoretical pumping speed and conductance of the i-th vacuum unit respectively; when the vacuum unit works normally under the condition of reaching the limit pressure, the compression power N of the i-th vacuum stage i for:

[0033]

[0034] Among them, η M is the mechanical efficiency, P Vi is the exhaust pressure of the i-th stage, P Ai is the suction pressure of the i-th stage;

[0035] Because the exhaust pressure of the i-1th stage is the suction pressure of the i-th stage, that is:

[0036]

[0037] The exhaust pressure of the last stage is the standard atmospheric pressure P atm , and calculate the compression power of each stage in turn. Assuming that there are k stages in the vacuum unit, the total compression power N is:

[0038]

[0039] Furthermore, the ultimate pressure P of the Roots pump unit is a The calculation process is as follows:

[0040] In the Roots vacuum unit, the exhaust pressure of the previous stage is equal to the suction pressure of the next stage. The ultimate pressure of the vacuum unit is P a That is the suction pressure of the first vacuum stage, and the exhaust pressure of the last stage is the standard atmospheric pressure, that is:

[0041]

[0042] Where k is the number of stages of the multi-stage Roots vacuum unit, P atm is standard atmospheric pressure.

[0043] Step 3.4: Non-dominated sorting and crowding calculation: Sort the individuals in the initial parent population according to the non-dominated level, and sort them according to the crowding degree for the same non-dominated level;

[0044] Step 3.5: Generate the initial parent population Q i :Use the competitive selection method to select parents suitable for reproduction and make the initial parent population Q i The size is equal to Popsize;

[0045] The process of selecting suitable parents for breeding by the competition selection method is as follows:

[0046] Randomly select two participating individuals, compare them according to the non-dominated sorting level, and choose the individual with a smaller dominance level. When the non-dominated sorting levels are the same, the individual with a larger crowding degree is preferentially selected as the parent suitable for reproduction.

[0047] Step 3.6: Crossover: Apply the crossover operator to the parent population, replace and recombine the structures of the two parent individuals to generate new individuals, according to the given crossover probability P c , if the generated random number between 0 and 1, rand(0,1), is less than the crossover probability P c When , the crossover operation is performed; otherwise, the crossover operation is not performed;

[0048] Step 3.7: Mutation: Apply the mutation operator to the population, and change one or some genes in the selected individuals to obtain the offspring population R i , according to the given mutation probability P m , when the random number rand(0,1) between 0 and 1 is less than the mutation probability P m , the mutation operation is performed; otherwise, the mutation operation is not performed; after crossover mutation, the offspring population R is generated. i ;

[0049] Step 3.8: Merge and select a new parent population: Merge the offspring population obtained by crossover mutation with the corresponding parent population into a new population T i , calculate the new population T i The objective function value of the individual in the population is calculated, and each individual is sorted and crowded. According to the set population size, individuals with high non-dominated levels are selected to form a new population. When the non-dominated levels are consistent, individuals with larger crowding are selected to form a new parent population Q. i+1 ;

[0050] Step 3.9: Determine whether i satisfies the maximum number of evolutions. If not, add 1 to the evolution count and repeat steps 3.6 to 3.8 until the maximum number of evolutions is met. If the maximum number of evolutions is met, select the required individuals from the remaining individuals based on the non-dominated sorting and crowding calculation as the final Pareto solution, and output the relevant parameters.

[0051] Step 4: Based on the result obtained in step 3, determine whether the corresponding objective function value meets the standard. If it meets the requirements, output all structural parameters; if it does not meet the requirements, re-draft the decision variables and the values ​​of the remaining variables, and repeat steps 2 to 4.

[0052] The beneficial effects of adopting the above technical solution are:

[0053] 1. The method provided by the present invention is based on the NSGA-II algorithm to optimize the design structure of the Roots vacuum unit. It has strong universality and can be applied to the structural design of Roots pump units in different fields.

[0054] 2. The method provided by the present invention reduces the calculation complexity and adds an elite strategy to the algorithm. It does not rely on a large number of experiments and only uses fewer computing resources to obtain excellent unit performance. Therefore, there is no need to consume a lot of manpower and material resources. A relatively good solution can be obtained through only a small amount of resources, which greatly reduces the R&D and design costs. BRIEF DESCRIPTION OF THE DRAWINGS

[0055] Figure 1 It is a flow chart of a method for optimizing the design structure of a Roots vacuum unit based on the NSGA-II algorithm in an embodiment of the present invention;

[0056] Figure 2 Flow chart of the NSGA-II algorithm in an embodiment of the present invention. DETAILED DESCRIPTION

[0057] The specific implementation of the present invention is further described in detail below in conjunction with the accompanying drawings and examples. The following examples are used to illustrate the present invention, but are not intended to limit the scope of the present invention.

[0058] like Figure 1 As shown, the method for optimizing the design structure of the Roots vacuum unit based on the NSGA-II algorithm in this embodiment is as follows.

[0059] Step 1: According to actual production needs, the existing multi-stage Roots vacuum unit is used as a prototype for measurement, and the number of stages, rotor radius, profile equation, rotor thickness and characteristic assembly clearance of the multi-stage Roots vacuum unit are preliminarily designed, and the ultimate pressure, theoretical pumping speed and compression power of the vacuum unit are taken as the optimization targets;

[0060] Step 2: Propose decision variables, their ranges and the numerical parameters of other variables;

[0061] The decision variables include: the radial assembly gap δ between the j-th rotor and the rotor 1j , radial assembly clearance δ between the j-th rotor and the pump body 2j , the axial assembly clearance δ between the j-th stage rotor and the rigid support point of the pump body 3j , the axial assembly clearance δ between the j-th stage rotor and the pump body floating support point 4j , the j-th level rotor thickness L j , and the rotor profile coefficient C of the jth stage j .

[0062] In this embodiment, the optimization object is a 7-stage Roots pump unit, and the rotor shape coefficients of the 1st and 2nd stages are set to C1, the rotor shape coefficients of the 3rd and 4th stages are set to C2, and the rotor shape coefficients of the 5th, 6th and 7th stages are set to C3. In this embodiment, the final decision variables total 38, as follows:

[0063] X(L1, L2, L3, L4, L5, L6, L7, δ 11 , δ 21 , δ 31 , δ 41 , δ 12 , δ 22 , δ 32 , δ 42 , δ 13 , δ 23 , δ 33 , δ 43 , δ 14 , δ 24 , δ 34 , δ 44 , δ 15 , δ 25 , δ 35 , δ 45 , δ 16 , δ 26 , δ 36 , δ 46 , δ 17 , δ 27 , δ 37 , δ 47 , C1, C2, C3)

[0064] Step 3: Use NSGA-II algorithm to optimize the design structure of the three-leaf Roots vacuum unit. The process is as follows: Figure 2 As shown, the specific process is as follows:

[0065] Step 3.1: Set parameters: Set the upper and lower bounds of the decision variables according to the known mathematical model, set the population size Popsize, the number of genetic evolutions i, and the crossover probability P c and mutation probability P m ;

[0066] In this embodiment, the population size Popsize is set to 80, the number of genetic evolutions is i, and the crossover probability P is set to c =0.9 and mutation probability P m =0.1.

[0067] Step 3.2: Initialize the population: Set the initial value of the genetic evolution times to 0, set the maximum number of evolution times Gen, and randomly generate the initial population P i ;

[0068] Step 3.3: Calculate the objective function: Calculate the initial population P generated in step 3.2 i The objective function value of each individual in ;

[0069] The objective function includes:

[0070] (1) f i1 =min{compression power of Roots pump unit N};

[0071] (2) f i2 =max{Theoretical pumping speed S of Roots pump unit th};

[0072] (3) f i3 =min{Ultimate pressure P of Roots pump unit a}.

[0073] Furthermore, the theoretical pumping speed S of the Roots pump unit is th The calculation process is as follows:

[0074]

[0075] Among them, ω is the rotation speed, L is the thickness of the Roots rotor, R is the rotor radius, η vp is the volume utilization coefficient.

[0076] Volume utilization coefficient η vp The calculation formula is: Where A1 is the volume of the pump chamber and A2 is the cross-sectional area of ​​the rotor.

[0077] Furthermore, the calculation process of the total compression power N of the Roots pump unit is as follows:

[0078] Calculate the actual pumping speed S of the Roots pump unit:

[0079]

[0080] Among them, S th is the theoretical pumping speed, P V is the exhaust pressure, P A is the suction pressure, u is the flow conductance. Under actual working conditions, there are two flow states of the counterflow gas in the gap, namely laminar flow and molecular flow. The flow conductance can be simplified to an empirical formula for calculation, as follows:

[0081] Under laminar flow: u = 20.7 × F;

[0082] Under molecular flow conditions: u = 12.7 × F;

[0083] Where F is the gap leakage area, the specific formula is as follows:

[0084] F=((δ1+2δ2)×L+2×(R+a))×(δ3+δ4) / 100

[0085] Among them, δ1 is the radial assembly clearance between the rotors of this stage, δ2 is the radial assembly clearance between the rotor of this stage and the pump body, δ3 is the axial assembly clearance between the rotor of this stage and the rigid support point of the pump body, δ4 is the axial assembly clearance between the rotor of this stage and the floating support point of the pump body, and a is the rotor center distance;

[0086] When the Roots vacuum pump unit is in working state for a long time, the pressure in the pumped container will gradually decrease to the minimum value, that is, the ultimate pressure value; at this time, under the ultimate pressure condition, the actual pumping speed of the vacuum unit S = 0, and the suction ultimate pressure of the i-th level vacuum unit is obtained. for:

[0087]

[0088] in, u i are the theoretical pumping speed and conductance of the i-th vacuum unit respectively; when the vacuum unit works normally under the condition of reaching the limit pressure, the compression power N of the i-th vacuum stage i for:

[0089]

[0090] Among them, η M is the mechanical efficiency, P Vi is the exhaust pressure of the i-th stage, P Ai is the suction pressure of the i-th stage;

[0091] Because the exhaust pressure of the i-1th stage is the suction pressure of the i-th stage, that is:

[0092]

[0093] The exhaust pressure of the last stage is the standard atmospheric pressure P atm , and calculate the compression power of each stage in turn. Assuming that there are k stages in the vacuum unit, the total compression power N is:

[0094]

[0095] Furthermore, the ultimate pressure P of the Roots pump unit is a The calculation process is as follows:

[0096] In the Roots vacuum unit, the exhaust pressure of the previous stage is equal to the suction pressure of the next stage. The ultimate pressure of the vacuum unit is P a That is the suction pressure of the first vacuum stage, and the exhaust pressure of the last stage is the standard atmospheric pressure, that is:

[0097]

[0098] Where k is the number of stages of the multi-stage Roots vacuum unit, P atm is standard atmospheric pressure.

[0099] Step 3.4: Non-dominated sorting and crowding calculation: Sort the individuals in the initial parent population according to the non-dominated level, and sort them according to the crowding degree for the same non-dominated level;

[0100] Step 3.5: Generate the initial parent population Q i :Use the competitive selection method to select parents suitable for reproduction and make the initial parent population Q i The size is equal to Popsize;

[0101] The process of selecting suitable parents for breeding by the competition selection method is as follows:

[0102] Randomly select two participating individuals, compare them according to the non-dominated sorting level, and choose the individual with a smaller dominance level. When the non-dominated sorting levels are the same, the individual with a larger crowding degree is preferentially selected as the parent suitable for reproduction.

[0103] Step 3.6: Crossover: Apply the crossover operator to the parent population, replace and recombine the structures of the two parent individuals to generate new individuals, according to the given crossover probability P c , if the generated random number between 0 and 1, rand(0,1), is less than the crossover probability P c When , the crossover operation is performed; otherwise, the crossover operation is not performed;

[0104] Step 3.7: Mutation: Apply the mutation operator to the population, and change one or some genes in the selected individuals to obtain the offspring population R i , according to the given mutation probability P m , when the random number rand(0,1) between 0 and 1 is less than the mutation probability P m , the mutation operation is performed; otherwise, the mutation operation is not performed; after crossover mutation, the offspring population R is generated. i ;

[0105] Step 3.8: Merge and select a new parent population: Merge the offspring population obtained by crossover mutation with the corresponding parent population into a new population T i , calculate the new population T i The objective function value of the individual in the population is calculated, and each individual is sorted and crowded. According to the set population size, individuals with high non-dominated levels are selected to form a new population. When the non-dominated levels are consistent, individuals with larger crowding are selected to form a new parent population Q. i+1 ;

[0106] Step 3.9: Determine whether i satisfies the maximum number of evolutions. If not, add 1 to the evolution count and repeat steps 3.6 to 3.8 until the maximum number of evolutions is met. If the maximum number of evolutions is met, select the required individuals from the remaining individuals based on the non-dominated sorting and crowding calculation as the final Pareto solution, and output the relevant parameters.

[0107] Step 4: Based on the result obtained in step 3, determine whether the corresponding objective function value meets the standard. If it meets the requirements, output all structural parameters; if it does not meet the requirements, re-draft the decision variables and the values ​​of the remaining variables, and repeat steps 2 to 4.

Claims

1. A method for optimizing the design structure of a Roots vacuum unit based on the NSGA-Ⅱ algorithm, characterized in that: The steps include: Step 1: According to actual production needs, the existing multi-stage Roots vacuum unit is used as a prototype for measurement, and the number of stages, rotor radius, profile equation, rotor thickness and characteristic assembly clearance of the multi-stage Roots vacuum unit are preliminarily designed, and the ultimate pressure, theoretical pumping speed and compression power of the vacuum unit are taken as the optimization targets; Step 2: Propose decision variables, their ranges and the numerical parameters of other variables; The decision variables include: the radial assembly clearance between the j-th rotor and the rotor , radial assembly clearance between the j-th rotor and the pump body , the axial assembly clearance between the j-stage rotor and the rigid support point of the pump body , the axial assembly clearance between the j-stage rotor and the pump body floating support point , the rotor thickness of the jth stage , and the rotor profile coefficient of the jth stage ; Step 3: Use NSGA-Ⅱ algorithm to optimize the design structure of the three-leaf Roots vacuum unit; Step 3.1: Set parameters: Set the upper and lower bounds of the decision variables according to the known mathematical model, set the population size Popsize, the number of genetic evolutions i, and the crossover probability and mutation probability ; Step 3.2: Initialize the population: Set the initial value of the genetic evolution times to 0, set the maximum number of evolution times Gen, and randomly generate the initial population ; Step 3.3: Calculate the objective function: Calculate the initial population generated in step 3.2 The objective function value of each individual in ; Step 3.4: Non-dominated sorting and crowding calculation: Sort the individuals in the initial parent population according to the non-dominated level, and sort them according to the crowding degree for the same non-dominated level; Step 3.5: Generate the initial parent population Q i :Use the competitive selection method to select parents suitable for reproduction and make the initial parent population The size is equal to Popsize; Step 3.6: Crossover: Apply the crossover operator to the parent population, replace and recombine the structures of the two parent individuals to generate new individuals according to the given crossover probability. , if the generated random number between 0 and 1, rand(0,1), is less than the crossover probability When , the crossover operation is performed; otherwise, the crossover operation is not performed; Step 3.7: Mutation: Apply the mutation operator to the population, and change one or some genes in the selected individuals to obtain the offspring population. , according to the given mutation probability , when the random number rand(0,1) between 0 and 1 is less than the mutation probability When , the mutation operation is performed; otherwise, the mutation operation is not performed; after crossover mutation, the offspring population is generated ; Step 3.8: Merge and select a new parent population: merge the offspring population obtained by crossover mutation with the corresponding parent population into a new population , calculate the new population The objective function value of the individual in the population is calculated, and each individual is sorted and the crowding degree is calculated. According to the set population size, individuals with high non-dominated levels are selected to form a new population. When the non-dominated levels are consistent, individuals with high crowding degrees are selected to form a new parent population. ; Step 3.9: Determine whether i meets the maximum number of evolutions. If not, add 1 to the evolution count and repeat steps 3.6 to 3.8 until the maximum number of evolutions is met. If the maximum number of evolutions is met, select the required individuals from the remaining individuals according to the non-dominated sorting and crowding calculation as the final Pareto solution, and output the relevant parameters. Step 4: Based on the result obtained in step 3, determine whether the corresponding objective function value meets the standard. If it meets the requirements, output all structural parameters; if it does not meet the requirements, re-determine the decision variables and the values ​​of the remaining variables, and repeat steps 2 to 4.

2. The method for optimizing the design structure of a Roots vacuum unit based on the NSGA-Ⅱ algorithm according to claim 1, characterized in that: The objective function includes: (1) f i1 = min {Compression power of Roots pump unit N }; (2) f i2 = max {Theoretical pumping speed of Roots pump unit }; (3) f i3 = min {The ultimate pressure of Roots pump unit }.

3. The method for optimizing the design structure of a Roots vacuum unit based on the NSGA-Ⅱ algorithm according to claim 2, characterized in that: The theoretical pumping speed of the Roots pump unit The calculation process is as follows: in, is the rotation speed, L is the thickness of the Roots rotor, R is the rotor radius, is the volume utilization coefficient.

4. The method for optimizing the design structure of a Roots vacuum unit based on the NSGA-Ⅱ algorithm according to claim 3 is characterized in that: The total compression power of the Roots pump unit N The calculation process is as follows: Calculate the actual pumping speed S of the Roots pump unit: in, is the theoretical pumping speed, P V is the exhaust pressure, P A is the suction pressure, u is the flow conductance. Under actual working conditions, there are two flow states of the counterflow gas in the gap, namely laminar flow and molecular flow. Its flow conductance can be simplified to an empirical formula for calculation, as follows: Under laminar flow: ; In molecular flow state: ; Where F is the gap leakage area, the specific formula is as follows: in, is the radial assembly clearance between the rotors of this stage, is the radial assembly clearance between the rotor of this stage and the pump body, It is the axial assembly clearance between the rotor of this stage and the rigid support point of the pump body. It is the axial assembly clearance between the rotor of this stage and the floating support point of the pump body. is the rotor center distance; When the Roots vacuum pump unit is in working state for a long time, the pressure in the pumped container will gradually decrease to the minimum value, that is, the ultimate pressure value; at this time, under the ultimate pressure condition, the actual pumping speed of the vacuum unit S=0, and the suction ultimate pressure of the i-th level vacuum unit is obtained. for: in, , are the theoretical pumping speed and conductance of the i-th vacuum unit respectively; when the vacuum unit works normally under the condition of reaching the ultimate pressure, the compression power of the i-th vacuum stage for: in, is the mechanical efficiency, P Vi is the exhaust pressure of the i-th stage, P Ai is the suction pressure of the i-th stage; Because the exhaust pressure of the i-1th stage is the suction pressure of the i-th stage, that is: in is the exhaust pressure of the i-1th stage; The exhaust pressure of the last stage is the standard atmospheric pressure P atm , and calculate the compression power of each stage in turn. Assuming that there are k stages in the vacuum unit, the total compression power N is: 。 5. The method for optimizing the design structure of a Roots vacuum unit based on the NSGA-Ⅱ algorithm according to claim 4 is characterized in that: The ultimate pressure of the Roots pump unit The calculation process is as follows: In the Roots vacuum unit, the exhaust pressure of the previous stage is equal to the suction pressure of the next stage. The ultimate pressure of the vacuum unit is P a That is the suction pressure of the first vacuum stage, and the exhaust pressure of the last stage is the standard atmospheric pressure, that is: Where k is the number of stages of the multi-stage Roots vacuum unit, P atm is standard atmospheric pressure.

6. The method for optimizing the design structure of a Roots vacuum unit based on the NSGA-Ⅱ algorithm according to claim 5, characterized in that: The process of selecting the parent generation suitable for breeding by the competitive selection method in step 3.5 is as follows: Two participating individuals are randomly selected and compared according to their non-dominated sorting levels. The individual with a smaller dominance level is selected. When the non-dominated sorting levels are consistent, the individual with a larger crowding degree is preferentially selected as the parent suitable for reproduction.

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