CN110489872B - Piston ring molded line design method based on genetic algorithm - Google Patents
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Abstract
The invention discloses a piston ring molded line design method based on a genetic algorithm, which is characterized by comprising the following steps: 1) Firstly, working conditions of a piston ring are obtained according to operation parameters of an engine, and life cycle calculation step length is determined according to the full life cycle length required to be calculated; 2) Establishing a relation between a piston ring molded line and friction wear of a full life cycle length; 3) Establishing the relation between the ring height, the profile offset rate and the barrel surface height of the piston ring profile and the piston ring profile; finally, a genetic algorithm is used to determine the profile parameters with the lowest frictional wear over the full life cycle length. According to the method, the solving condition of the Reynolds equation is changed from iteration based on the pressure field to iteration based on the demarcation point, and the speed of the pressure field calculated based on the iteration of the demarcation point is far higher than that of the traditional Gaussian delta iteration method, so that a speed difference of thousands of times can be achieved in the actual test, and the improved method can be suitable for a genetic algorithm.
Description
Technical Field
The invention relates to the field of piston ring design, in particular to a piston ring molded line design method based on a genetic algorithm.
Background
In the field of piston ring design, the profile design of a piston ring is an important part. The profile can affect the frictional wear between the piston ring and the cylinder liner. The lubrication conditions of the piston rings throughout 720 degrees of the engine run period change over time. Meanwhile, the lubrication condition of the piston ring can also change along with the progress of abrasion in the whole life cycle of the piston ring.
Therefore, to obtain the friction and wear condition of the full life cycle and the full operation cycle of the piston ring, a great amount of Reynolds equation solving work is needed for a designer to evaluate the friction and wear condition of the piston ring-cylinder sleeve friction pair corresponding to different types of lines.
The solution of the reynolds equation is based on the reynolds boundary condition, which requires the calculated pressure to be not less than 0. In the iteration process, the calculated pressure is directly set to 0, and then the pressure at the end point of the iteration is automatically the required solution. This method has the following disadvantages:
1. the speed is low, and the period for completing one-time molded line evaluation is too long. And further, the piston ring profile design based on tools such as genetic algorithm and the like is almost impossible to use.
2. The algorithm only obtains an approximate solution of the corresponding differential equation, but not an accurate solution, and whether the corresponding differential equation has the accurate solution meeting the condition cannot be judged, so that the original algorithm cannot prompt errors of the differential equation without the solution possibly caused by too thick grids. The presence of errors results in a practically optimal profile parameter of the piston ring.
3. In addition, the existing method is adopted to obtain the friction and wear condition of the full life cycle and the full operation cycle of the piston ring, which takes several months, and the research and development cycle is overlong.
Disclosure of Invention
The invention aims to provide a piston ring molded line design method based on a genetic algorithm aiming at the defects in the prior art so as to solve the problems in the prior art.
The technical problems solved by the invention can be realized by adopting the following technical scheme:
a piston ring molded line design method based on a genetic algorithm comprises the following steps:
1) Firstly, working conditions of a piston ring are obtained according to operation parameters of an engine, and life cycle calculation step length is determined according to the full life cycle length required to be calculated;
2) Establishing a relation between a piston ring molded line and friction wear of a full life cycle length;
firstly, setting the initial state angle of a piston ring to be 0 degree, solving a Reynolds equation, calculating the minimum oil film thickness of a piston ring molded line in a first operation period according to a result, and calculating the oil film thickness of the next angle according to the oil film thickness; since the engine running period is 720 degrees, when the oil film thickness running to 720 degrees is the same as 0 degree, the oil film thickness is considered to be converged; according to the oil film thickness of 720, the friction and abrasion of the piston ring in the whole running period can be calculated;
then, according to the friction and wear of the piston ring, the wear condition of the piston ring molded line of the next piston ring operation period and the molded line of the piston ring after wear are obtained;
repeating the above process until the full life cycle of the piston ring is calculated;
3) Establishing the relation between the ring height, the profile offset rate and the barrel surface height of the piston ring profile and the piston ring profile; finally, a genetic algorithm is used to determine the profile parameters with the lowest frictional wear over the full life cycle length.
Further, the solution of the Reynolds equation is based on iteration of the demarcation point, and the specific process is as follows:
the preparation steps are as follows: providing operation parameters of an engine, and extracting a demarcation point of which the oil film pressure is smaller than 0 and the oil film pressure is larger than or equal to 0 from the oil film pressure;
step 1: according to the demarcation point, utilizing a sub-method to obtain an oil film pressure field with the oil film pressure greater than a zone 0; simultaneously setting the pressure of a part with the oil film pressure smaller than 0 to be 0;
step 2: performing a plurality of Gaussian-Seidel iteration methods according to the pressure field obtained in the step 1;
step 3: extracting boundary points of which the oil film pressure is smaller than 0 and the oil film pressure is larger than or equal to 0 in the iterated pressure field;
step 4, judging whether the demarcation point is the same as the previous calculation, if so, judging whether the pressure field is the same; if the demarcation point and the pressure field are the same, the calculation convergence is illustrated; if the difference is different, the original differential field is indicated that no proper solution exists, and all possible demarcation point conditions are scanned for judgment.
Further, the method for solving the one-dimensional Reynolds equation under the condition of determining the demarcation point by using the sub-method is characterized in that the process of obtaining the oil film pressure field with the oil film pressure greater than the interval 0 is as follows:
the one-dimensional Reynolds equation is written as follows:
A i p i+1 +B i p i-1 -C i p i ＝D i (2≤i≤n-1)
let p be i ＝x i a+y i b+z i Wherein a and b are undetermined constants, we set
x 1 ＝1,x 2 ＝0；y 1 ＝0,y 2 ＝1；z 1 ＝0；z 2 ＝0；
Then, the method can be recursively obtained according to a difference equation:
can obtain x at the decomposition point 1 ,y 1 ,z 1 ；x n ,y n ,z n From this, a, b and the pressure field can be solved.
Compared with the prior art, the invention has the beneficial effects that:
according to the method, the solving condition of the Reynolds equation is changed from iteration based on the pressure field to iteration based on the demarcation point, and the speed of the pressure field calculated based on the iteration of the demarcation point is far higher than that of the traditional Gaussian delta iteration method, so that a speed difference of thousands of times can be achieved in the actual test, and the improved method can be suitable for a genetic algorithm.
The algorithm can wait for the accurate solution of the corresponding difference equation under the Reynolds boundary condition, and when the difference between two rounds of calculation is 0. Since the demarcation points are calculated in this application and the combinations of demarcation points are limited and small, the present application can determine whether the corresponding differential equation has a solution at the reynolds boundary condition. The method can obtain an accurate solution, and can be applied to the design of molded line parameters of the piston ring to achieve the optimal.
The algorithm solves the friction and wear condition of the full life cycle and the full operation cycle of the piston ring, takes only 1 day, and greatly shortens the research and development cycle.
Drawings
FIG. 1 is a schematic diagram of a solution of Reynolds equation based on demarcation point iteration according to the present invention.
Fig. 2 is a schematic diagram showing three parameters of a piston ring profile according to the present invention.
FIG. 3 is a schematic diagram of the optimization process according to the present invention.
FIG. 4 is a schematic diagram of the total wear amount as an independent variable according to the present invention.
Fig. 5 is a schematic diagram of the wear amounts of the 4 schemes according to the present invention.
Fig. 6 is a schematic diagram of friction power consumption of 4 schemes according to the present invention.
Fig. 7 is a schematic representation of the minimum oil film thickness for the 4 versions of the present invention.
Detailed Description
The invention is further described in connection with the following detailed description, in order to make the technical means, the creation characteristics, the achievement of the purpose and the effect of the invention easy to understand.
Referring to fig. 1, the piston ring profile design method based on the genetic algorithm provided by the invention comprises the following steps:
1) Firstly, working conditions of a piston ring are obtained according to operation parameters of an engine, and life cycle calculation step length is determined according to the full life cycle length required to be calculated;
2) Establishing a relation between a piston ring molded line and friction wear of a full life cycle length;
firstly, setting the initial state angle of a piston ring to be 0 degree, solving a Reynolds equation, calculating the minimum oil film thickness of a piston ring molded line in a first operation period according to a result, and calculating the oil film thickness of the next angle according to the oil film thickness; since the engine running period is 720 degrees, when the oil film thickness running to 720 degrees is the same as 0 degree, the oil film thickness is considered to be converged; according to the oil film thickness of 720, the friction and abrasion of the piston ring in the whole running period can be calculated;
then, according to the friction and wear of the piston ring, the wear condition of the piston ring molded line of the next piston ring operation period and the molded line of the piston ring after wear are obtained;
repeating the above process until the full life cycle of the piston ring is calculated;
3) Establishing the relation between the ring height, the profile offset rate and the barrel surface height of the piston ring profile and the piston ring profile; finally, a genetic algorithm is used to determine the profile parameters with the lowest frictional wear over the full life cycle length.
3) Further, the solution of the Reynolds equation is based on iteration of the demarcation point, and the specific process is as follows:
the preparation steps are as follows: providing operation parameters of an engine, and extracting a demarcation point of which the oil film pressure is smaller than 0 and the oil film pressure is larger than or equal to 0 from the oil film pressure;
step 1: according to the demarcation point, utilizing a sub-method to obtain an oil film pressure field with the oil film pressure greater than a zone 0; simultaneously setting the pressure of a part with the oil film pressure smaller than 0 to be 0;
step 2: performing a plurality of Gaussian-Seidel iteration methods according to the pressure field obtained in the step 1;
step 3: extracting boundary points of which the oil film pressure is smaller than 0 and the oil film pressure is larger than or equal to 0 in the iterated pressure field;
step 4, judging whether the demarcation point is the same as the previous calculation, if so, judging whether the pressure field is the same; if the demarcation point and the pressure field are the same, the calculation convergence is illustrated; if the difference is different, the original differential field is indicated that no proper solution exists, and all possible demarcation point conditions are scanned for judgment.
Further, the method for solving the one-dimensional Reynolds equation under the condition of determining the demarcation point by using the sub-method is characterized in that the process of obtaining the oil film pressure field with the oil film pressure greater than the interval 0 is as follows:
the one-dimensional Reynolds equation is written as follows:
A i p i+1 +B i p i-1 -C i p i ＝D i (2≤i≤n-1)
let p be i ＝x i a+y i b+z i Wherein a and b are undetermined constants, we set
x 1 ＝1,x 2 ＝0；y 1 ＝0,y 2 ＝1；z 1 ＝0；z 2 ＝0；
Then, the method can be recursively obtained according to a difference equation:
can obtain x at the decomposition point 1 ,y 1 ,z 1 ；x n ,y n ,z n From this, a, b and the pressure field can be solved.
In the design process of the piston ring molded line of the internal combustion engine, the working condition of the piston ring within the range of 0-720 degrees of the crank angle of the engine is obtained according to the running parameters of the engine. And determines a life cycle calculation step size (for example, a wear condition requiring 1000 hours to be calculated, the calculation step size may be set to 1 hour) according to the life cycle length to be calculated.
Next, a relationship between the piston ring profile and full life cycle frictional wear is established.
The specific method comprises the following steps: first, according to the teachings of the present invention, the Reynolds equation is solved and the wear level and frictional power consumption of the piston ring over an engine cycle are calculated based on the result. And then, calculating the wear condition of the molded line and a new molded line of the next life cycle calculation point according to the wear amount just calculated and the life cycle step length. The algorithm of the invention is repeatedly used for solving the Reynolds equation and calculating the friction and wear amount until the whole life cycle is calculated.
In this way, a relationship between the piston ring profile and full life cycle frictional wear is established. And then three basic parameters of the molded line are established, the molded line offset rate, the piston ring height, the piston ring width and the molded line of the piston ring are related. Genetic algorithms can then be used to find the profile parameters that have the lowest frictional wear throughout the life cycle.
Examples
1 establishment of piston ring friction model
1.1 representation of piston ring molded lines
The piston ring profile is characterized by three parameters, namely the ring height, the profile offset rate and the barrel height of the piston ring, as shown in fig. 2. In FIG. 2, L is the ring height of the piston ring, L a ,L b Respectively the distance from the highest point of the molded line of the piston ring to the upper side surface and the lower side surface of the piston ring, and the molded line offset rate O is used s ＝L b L represents the offset of the piston ring profileIn the case, BH is the height of the barrel surface of the piston ring. The present application characterizes the piston ring profile with these three parameters.
1.2 establishment of lubrication model
The basic lubrication condition of the piston ring is determined by the radial stress balance of the piston ring, and the radial force balance equation of the piston ring is as follows:
F ten +F gas ＝F hdr +F asp (1.1)
wherein F is ten Is the elasticity of piston ring, F gas Back pressure for gas generation, F hdr F is oil film supporting force asp Is the solid contact force of the microprotrusions.
The oil film support force is determined by the average reynolds equation:
wherein h is the thickness of the oil film, phi x ,φ c ,φ s μ is the oil viscosity, p is the average pressure, and U is the tangential velocity.
The microprotrusion contact force is given by the microprotrusion contact model, and the microprotrusion contact force on the unit circumference is as follows:
wherein eta, beta and sigma are respectively the density of the microprotrusions, the curvature radius of the peak top and the surface roughness, E is the elastic modulus, F 2.5 And F 2 Is a function derived from a gaussian distribution.
1.3 Friction wear calculation
The friction force between the piston ring and the cylinder sleeve is as follows:
wherein τ 0 For shear stress constant, A c Is connected with the microprotrusionsA contact area; alpha 0 For boundary friction coefficient, W A Normal force generated for the microprotrusion contact. Within the integral is fluid friction, where μ is lube viscosity, U is tangential velocity, h is nominal oil film thickness, p is average oil film pressure, φ f ,φ fs ,φ fp Is a shear stress factor.
Wear between the piston ring and the cylinder liner is given by the Archard model:
wherein k is m For the wear coefficient, F A The solid contact force, H is the hardness of the material, and x is the relative sliding distance. 2. Optimizing results and analysis
The initial design parameters of the piston ring are that the piston ring height L=1.2E-3 m, the piston ring barrel height BH=3.6E-6 m and the line offset rate O s =0.5; the design result is that the friction power consumption is 6.14J, and the abrasion loss is 8.01E-18m 3 . The preset search interval is 1E-3m less than or equal to L less than or equal to 2E-3m,5E-7m less than or equal to BH less than or equal to 1E-5m, and 0.2 less than or equal to O s Less than or equal to 0.8. The Reynolds equation is solved by a finite difference method, and the number of grids is 5000. The population number of the AMGA algorithm is 40, and 5000 different molded line schemes are calculated in total. The optimization process is shown in fig. 3, and in order to analyze the relationship between the design parameters and the design indexes on the pareto front, the parameters on the pareto front are divided by the initial design parameters, and then the total wear amount is taken as an independent variable to draw fig. 4.
In order to analyze a specific optimization effect, the application compares 3 different schemes with an original scheme from the pareto front, and the schemes are a scheme for optimizing power consumption, a scheme for optimizing abrasion and a scheme for comprehensively optimizing. The profile parameters and optimization results are shown in table 1. The wear amounts for the 4 schemes are shown in fig. 5, the friction power consumption is shown in fig. 6, and the minimum oil film thickness is shown in fig. 7.
TABLE 1 molded line parameters and optimization results
From the final optimization combination and the variation of the parameters along with the optimization index, the line offset rate is close to 0.35, so that the line offset rate can be considered to have an optimal range; for the other two parameters, overall, the smaller the ring height, the greater the wear, and the less power consumption; the smaller the height of the bucket, the less wear and power consumption.
From the specific lubrication condition, the abrasion loss of the 3 optimized schemes in the crank angle range from 360 degrees to 540 degrees is far lower than that of the original scheme; of the minimum oil film thicknesses, only the optimized wear scheme has an oil film thickness after 450 degrees that is lower than the original scheme, and other schemes have an oil film thickness between 360 and 540 degrees that is greater than the original scheme. The lubrication conditions in other sections are good and bad. This means that the lubrication conditions of the original solution in this interval have a lot of room for improvement throughout the piston ring operating cycle. In other intervals, optimizing friction power consumption may lead to an increase in wear, and optimizing wear may lead to an increase in friction power consumption.
3. Conclusion(s)
1) The method establishes a model between friction and abrasion of the piston ring, and obtains the relation between the molded line of the piston ring and the friction and abrasion by solving the model.
2) The friction and abrasion of the piston ring are optimally calculated, and the friction and abrasion of the piston ring are remarkably reduced. The feasibility of the piston ring molded line optimization design through an optimization algorithm is verified. The full-period friction power consumption can be reduced by 13.8% by the optimized power consumption scheme, the abrasion loss can be reduced by 25.8% by the optimized abrasion scheme, the friction power consumption can be reduced by 9.9% by the comprehensive optimization scheme, and the abrasion is reduced by 18.5%.
The foregoing has shown and described the basic principles and main features of the present invention and the advantages of the present invention. It will be understood by those skilled in the art that the present invention is not limited to the embodiments described above, and that the above embodiments and descriptions are merely illustrative of the principles of the present invention, and various changes and modifications may be made without departing from the spirit and scope of the invention, which is defined in the appended claims. The scope of the invention is defined by the appended claims and equivalents thereof.
Claims (1)
1. A piston ring molded line design method based on a genetic algorithm is characterized by comprising the following steps:
1) Firstly, working conditions of a piston ring are obtained according to operation parameters of an engine, and life cycle calculation step length is determined according to the full life cycle length required to be calculated;
2) Establishing a relation between a piston ring molded line and friction wear of a full life cycle length;
firstly, setting the initial state angle of a piston ring to be 0 degree, solving a Reynolds equation, calculating the minimum oil film thickness of a piston ring molded line in a first operation period according to a result, and calculating the oil film thickness of the next angle according to the oil film thickness; since the engine running period is 720 degrees, when the oil film thickness running to 720 degrees is the same as 0 degree, the oil film thickness is considered to be converged; according to the oil film thickness of 720, the friction and abrasion of the piston ring in the whole running period can be calculated;
then, according to the friction and wear of the piston ring, the wear condition of the piston ring molded line of the next piston ring operation period and the molded line of the piston ring after wear are obtained;
repeating the above process until the full life cycle of the piston ring is calculated;
3) Establishing the relation between the ring height, the profile offset rate and the barrel surface height of the piston ring profile and the piston ring profile; finally, determining the molded line parameter with the lowest friction and abrasion in the whole life cycle length by using a genetic algorithm;
the solution of the Reynolds equation is based on iteration of the demarcation point, and the specific process is as follows:
the preparation steps are as follows: providing operation parameters of an engine, and setting a demarcation point of which the oil film pressure is smaller than 0 and the oil film pressure is larger than or equal to 0 in the oil film pressure;
step 1: according to the demarcation point, utilizing a sub-method to obtain an oil film pressure field with the oil film pressure greater than a zone 0; simultaneously setting the pressure of a part with the oil film pressure smaller than 0 to be 0;
step 2: performing a plurality of Gaussian-Seidel iteration methods according to the pressure field obtained in the step 1;
step 3: extracting boundary points of which the oil film pressure is smaller than 0 and the oil film pressure is larger than or equal to 0 in the iterated pressure field;
step 4, judging whether the demarcation point is the same as the previous calculation, if so, judging whether the pressure field is the same; if the demarcation point and the pressure field are the same, the calculation convergence is illustrated; if the difference is different, the fact that the original differential field does not have a proper solution is indicated, and then all possible demarcation point conditions are scanned to judge;
the method for solving the one-dimensional Reynolds equation under the condition of determining the demarcation point by using the sub-method comprises the following steps of:
the one-dimensional Reynolds equation is written as follows:
A i p i+1 +B i p i-1 -C i p i ＝D i (2≤i≤n-1)
let p be i ＝x i a+y i b+z i Wherein a and b are undetermined constants, we set
x 1 ＝1,x 2 ＝0；y 1 ＝0,y 2 ＝1；z 1 ＝0；z 2 ＝0；
Then, the method can be recursively obtained according to a difference equation:
can obtain x on the decomposition boundary point 1 ,y 1 ,z 1 ；x n ,y n ,z n And all x within the boundary i ,y i ,z i According to the pressure of 0 on the demarcation point, the equation can be usedSolving a and b; will a, bBack to p i ＝x i a+y i b+z i The whole pressure field can be obtained.
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