CN114218688B - Sectional type inclined groove blade characteristic parameter optimization method for ventilated brake disc - Google Patents
Sectional type inclined groove blade characteristic parameter optimization method for ventilated brake disc Download PDFInfo
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- G06F30/00—Computer-aided design [CAD]
- G06F30/10—Geometric CAD
- G06F30/17—Mechanical parametric or variational design
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- F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
- F16—ENGINEERING ELEMENTS AND UNITS; GENERAL MEASURES FOR PRODUCING AND MAINTAINING EFFECTIVE FUNCTIONING OF MACHINES OR INSTALLATIONS; THERMAL INSULATION IN GENERAL
- F16D—COUPLINGS FOR TRANSMITTING ROTATION; CLUTCHES; BRAKES
- F16D65/00—Parts or details
- F16D65/02—Braking members; Mounting thereof
- F16D65/12—Discs; Drums for disc brakes
- F16D65/128—Discs; Drums for disc brakes characterised by means for cooling
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- F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
- F16—ENGINEERING ELEMENTS AND UNITS; GENERAL MEASURES FOR PRODUCING AND MAINTAINING EFFECTIVE FUNCTIONING OF MACHINES OR INSTALLATIONS; THERMAL INSULATION IN GENERAL
- F16D—COUPLINGS FOR TRANSMITTING ROTATION; CLUTCHES; BRAKES
- F16D65/00—Parts or details
- F16D65/78—Features relating to cooling
- F16D65/84—Features relating to cooling for disc brakes
- F16D65/847—Features relating to cooling for disc brakes with open cooling system, e.g. cooled by air
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- F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
- F16—ENGINEERING ELEMENTS AND UNITS; GENERAL MEASURES FOR PRODUCING AND MAINTAINING EFFECTIVE FUNCTIONING OF MACHINES OR INSTALLATIONS; THERMAL INSULATION IN GENERAL
- F16D—COUPLINGS FOR TRANSMITTING ROTATION; CLUTCHES; BRAKES
- F16D65/00—Parts or details
- F16D65/78—Features relating to cooling
- F16D2065/788—Internal cooling channels
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- G06F2119/00—Details relating to the type or aim of the analysis or the optimisation
- G06F2119/08—Thermal analysis or thermal optimisation
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Abstract
The invention discloses a method for optimizing characteristic parameters of sectional type inclined groove blades of a ventilated brake disc, which comprises the following steps: step one, establishing a sectional type inclined groove blade model of a brake disc; determining structural characteristic parameters required to be optimized for the sectional type inclined groove blade; determining an optimization target and constraint conditions; step two, adopting a sectional inclined groove blade model to carry out numerical simulation, carrying out data sampling based on an optimal Latin hypercube method, fitting a response surface agent model and verifying the accuracy of the agent model; step three, solving a Pareto optimal solution set obtained by two objective functions by adopting NSGA-II; and step four, obtaining an optimal solution in the Pareto optimal solution set by a TOPSIS decision method, and carrying out CFD verification. The optimization method can optimize and improve the characteristic parameters of the sectional type inclined groove blades in the brake disc, and improves the convective heat dissipation performance of the brake disc.
Description
Technical Field
The invention relates to the technical field of vehicle braking, in particular to a method for optimizing sectional type inclined groove blade characteristic parameters of a ventilated brake disc.
Background
The inside straight blade that adopts of current ventilation formula brake disc that vehicle braking used more, ventilation formula straight blade brake disc have two outer friction surfaces, and the brake disc internal surface passes through straight blade connection, allows the air flow, and the brake disc can reach higher temperature when braking, and the air current of continuous passing through the blade provides good cooling, has prolonged the life of brake disc. However, when a straight-blade brake disc rotates counterclockwise, the left side of the heat dissipation channel is subjected to high pressure relative to the right side, which are respectively referred to as the pressure side and the suction side, because of the presence of the air inflow angle, the flow velocity along the radial suction side gradually decreases, and the kinetic energy of the fluid itself is insufficient to carry away the suction side fluid, so that a backflow zone exists on the suction side in the flow channel. The existence of the backflow area in the ventilation type brake disc channel seriously blocks the flow of air, new cooling air is difficult to exchange with the internal air, uneven flow on two sides is caused, uneven heat dissipation in the channel is finally caused, and the convection heat dissipation performance of the brake disc is seriously reduced.
At present, most students at home and abroad are mainly concentrated on simulation analysis, prediction and experimental verification on the aerodynamic performance and heat exchange effect of the brake disc in the aspect of research on improving the heat dissipation efficiency of the ventilated brake disc, but less research on optimizing the characteristic parameters of the sectional type inclined groove blades aiming at the internal channel backflow area.
There is therefore a need for a method of improving the heat dissipation performance of a brake disc by improving the parameters of the ventilated brake disc segmented inclined slot vane characteristics to compromise mass flow and heat transfer.
Disclosure of Invention
In view of the above, the invention provides a method for optimizing the characteristic parameters of sectional type inclined groove blades of a ventilated brake disc, which can optimize and improve the characteristic parameters of sectional type inclined groove blades in the brake disc and improve the convective heat dissipation performance of the brake disc.
The invention adopts the following specific technical scheme:
a sectional type inclined groove blade characteristic parameter optimization method of a ventilated brake disc comprises the steps that the ventilated brake disc is provided with two outer friction surfaces, two oppositely arranged inner surfaces and a plurality of radiating blades connected between the two inner surfaces; the plurality of radiating blades are uniformly distributed around the circumference of the brake disc; each radiating blade is divided into an inner blade and an outer blade which are arranged along the radial direction of the brake disc by an intermediate inclined groove; an included angle formed by the inclined groove and the radial center line of the inner blade, wherein the included angle is formed by the opening of the inclined groove towards the outside of the brake disc, and the inclined groove is used for introducing fluid on the pressure side to the suction side so as to reduce a backflow area; the optimization method comprises the following steps:
step one, establishing a sectional type inclined groove blade model of a brake disc; the structural characteristic parameters required to be optimized for the sectional type inclined groove blades of the ventilated brake disc are determined, wherein the structural characteristic parameters comprise the inclined groove opening width H, the inclined groove opening inclination angle alpha and the number N of the sectional type inclined groove blades; determining optimization targets and constraint conditions, wherein the two optimization targets are a maximum mass flow m and a maximum heat exchange coefficient h passing through an internal channel;
step two, adopting a sectional inclined groove blade model to carry out numerical simulation, carrying out data sampling based on an Optimal Latin Hypercube (OLHS) method, fitting a response surface (Response Surface Methodology, RSM) agent model and verifying the accuracy of the agent model;
step three, solving a Pareto (Pareto) optimal solution set obtained by two objective functions (m, h) by adopting NSGA-II;
and step four, obtaining an optimal solution in the Pareto optimal solution set by a TOPSIS (Technique for Order Preference by Similarity to an Ideal Solution) decision method, and carrying out CFD (Computational Fluid Dynamics ) verification on the result.
Further, in the first step, the structural feature parameters in the design variables are varied within the following ranges:
the value distribution interval of the opening width H of the optimized parameter inclined groove is 8 mm-13 mm;
the value distribution interval of the opening inclination angle alpha of the optimized parameter inclined groove is 30-60 degrees;
the value distribution interval of the number N of the optimized parameter blades is 20-40.
Furthermore, in the second step, the response surface agent model is a polynomial of the objective function fitted by a least square method, so as to realize the display of the objective function; the basic expression of the objective function is:
wherein x is i An ith component, beta, of an n-dimensional argument x 0 Is a constant term undetermined coefficient, beta i Is the primary term undetermined coefficient, beta ij Is the coefficient to be determined of the quadratic term, the column vector beta, n is the number of design variables, and epsilon is the error.
Further, for the accuracy of the calculation result, the accuracy of the fitting equation is determined in the form of variance, and the basic expression of the determination is:
wherein N is the number of sample points, y i As a result of the true response value,calculated response value for response surface model, +.>Is the average of the true response values.
Further, the third step comprises the following specific steps:
generating an initial population with a scale of N in a random manner, performing non-dominant sorting on the initial population, and obtaining a first generation offspring population through basic operations of three genetic algorithms of selection, intersection and variation;
starting from the second generation, merging the child population and the parent population, carrying out rapid non-dominant sorting, simultaneously carrying out crowding degree calculation on individuals in each non-dominant layer, and selecting N individuals to form a new next generation population according to the non-dominant relationship of the individuals and the crowding degree of the individuals and the selection condition;
and generating new offspring population through selection, crossover and mutation operation, and sequentially cycling until the condition of ending the program is met.
Further, the fourth step comprises the following specific steps:
assuming that n evaluation objects are provided, each evaluation object has m indexes, the decision matrix is:
X＝(x ij ) n×m (i＝1，2，…，n；j＝1，2，…，m)；
normalizing the initial matrix:
setting a weighting factor w j Weighting the normalization matrix as follows:
a ij ＝w j ×b ij ；
determining a positive ideal solution Z + And negative ideal solution Z - ：
Calculating the distance from each evaluation object to the positive idealAnd distance +/of each evaluation object to negative ideal solution>
Calculating the closeness r i ：
The beneficial effects are that:
according to the sectional type inclined groove blade characteristic parameter optimization method, through theoretical analysis on the convection heat radiation performance of the ventilation type brake disc, the structural characteristic parameters required to be optimized for the sectional type inclined groove blade are determined to be the inclined groove opening width H, the inclined groove opening inclination angle alpha and the blade number N of the sectional type inclined groove blade; firstly, obtaining each group of design variable values through simulation test, performing simulation calculation according to an established finite element simulation model, obtaining response sampling data corresponding to a plurality of sampling points by using an OLHS method, and obtaining a fitting function of an optimization target by using a response surface model; solving a second generation non-inferior sorting genetic algorithm NSGA-II based on the Pareto optimal solution to obtain a Pareto optimal solution set with the mass flow m and the convection heat transfer coefficient h being maximum; the optimal solution is found based on the TOPSIS principle, and the sectional type inclined groove blade structure is set according to the optimal value, so that the ventilated brake disc with stronger convection heat transfer performance is obtained, and the rationality optimization of the sectional type inclined groove blade structure characteristic parameters of the ventilated brake disc is realized. The optimization method has wider applicability and higher accuracy in the field of engineering design.
Drawings
FIG. 1 is a flow chart of a method of optimizing parameters of a segmented inclined slot blade feature of a ventilated brake disc in accordance with the present invention;
FIG. 2 is a schematic illustration of the straight inter-blade passage recirculation zone of a ventilated brake disc of the prior art;
FIG. 3 is a schematic view of a straight blade construction of a prior art ventilated brake disc;
FIG. 4 is a schematic illustration of two-dimensional characterization parameters of a segmented inclined slot blade of a ventilated brake disc;
FIG. 5 is a schematic diagram of a segmented inclined slot vane CFD numerical simulation fluid domain grid;
FIG. 6 is a schematic view of a ventilated brake disc optimized for use with the present invention;
FIG. 7 is a Pareto optimal solution set diagram obtained by the optimization method of the present invention;
FIG. 8 is a graph comparing the results of optimization according to the present invention with the average temperature of the blade surface according to the prior art.
Wherein 1-outer friction surface, 2-inner surface, 3-inclined groove, 4-inner blade, 5-outer blade, 6-cooling channel, 7-suction side, 8-pressure side, 9-straight blade
Detailed Description
The invention will now be described in detail by way of example with reference to the accompanying drawings.
The embodiment of the invention provides a method for optimizing characteristic parameters of sectional type inclined groove blades of a ventilated brake disc, wherein the structure of a straight blade 9 of the existing ventilated brake disc is shown in fig. 2 and 3, while the structure of the ventilated brake disc in the embodiment of the invention is shown in fig. 6, the ventilated brake disc of the embodiment of the invention is provided with two outer friction surfaces 1, two oppositely arranged inner surfaces 2 and a plurality of radiating blades connected between the two inner surfaces 2, a cooling channel 6 is formed between two adjacent radiating blades, one side of the cooling channel 6 is a Pressure side 8, and the other side of the cooling channel is a Suction side 7; the plurality of radiating blades are uniformly distributed around the circumference of the brake disc; each radiating blade is divided into an inner blade 4 and an outer blade 5 which are arranged along the radial direction of the brake disc by an intermediate inclined groove 3, and the specific structure is shown in figure 4; the inclined groove 3 forms an angle with the radial centre line of the inner blade 4, which opening is directed towards the outside of the brake disc, the inclined groove 3 being used to introduce fluid at the pressure side 8 to the suction side 7 to reduce the recirculation zone; as shown in fig. 1, the optimization method includes the steps of:
step one, establishing a sectional type inclined groove blade model of a brake disc; the structural characteristic parameters required to be optimized for the sectional type inclined groove blades of the ventilated brake disc are determined, wherein the structural characteristic parameters comprise the opening width H of the inclined groove 3 of the sectional type inclined groove blades, the opening inclination angle alpha of the inclined groove 3 and the number N of the blades; determining optimization targets and constraint conditions, wherein the two optimization targets are a maximum mass flow m and a maximum heat exchange coefficient h passing through an internal channel;
performing numerical simulation by adopting the constructed sectional inclined groove blade model, performing data sampling based on an Optimal Latin Hypercube (OLHS) method, fitting a response surface agent model and verifying the accuracy of the agent model;
step three, solving a Pareto optimal solution set obtained by two objective functions (m, h) by adopting NSGA-II;
and step four, obtaining an optimal solution in the Pareto optimal solution set by a TOPSIS decision method, and carrying out CFD verification on the result, as shown in fig. 5.
In a specific embodiment, in the step one, the variation range of the structural feature parameter in the design variable specifically includes:
the value distribution interval of the opening width H of the optimized parameter inclined groove 3 is 8 mm-13 mm;
the value distribution interval of the opening inclination angle alpha of the optimized parameter inclined groove 3 is 30-60 degrees;
the value distribution interval of the number N of the optimized parameter blades is 20-40.
Furthermore, in the second step, the response surface proxy model is a polynomial of the objective function fitted by a least square method, so as to realize the display of the objective function; the basic expression of the objective function is:
wherein x is i An ith component, beta, of an n-dimensional argument x 0 Is a constant term undetermined coefficient, beta i Is the primary term undetermined coefficient, beta ij Is the coefficient to be determined of the quadratic term, the column vector beta, n is the number of design variables, and epsilon is the error.
In order to calculate the accuracy of the result, the accuracy of the fitting equation needs to be judged, the accuracy of the fitting equation is judged in a variance form, and the basic expression of the judgment is as follows:
wherein N is the number of sample points, y i As a result of the true response value,calculated response value for response surface model, +.>Is the average of the true response values.
According to the embodiment of the invention, sampling points are obtained by using an Optimal Latin Hypercube (OLHS) method, each set of design variable values is obtained according to a simulation test, simulation calculation is performed according to the finite element simulation model established in the step one, and response sampling data corresponding to 30 sampling points are obtained, as shown in the following table 1.
Table 1 sample data results
The embodiment of the invention uses R 2 To measure the degree of conformity of the approximation model with the sample point term, if R 2 The closer the value is to 1, the closer the approximation model is to the true value, i.e., the higher the model accuracy is established. R of average mass flow m and average convective heat transfer coefficient h in the embodiment of the invention 2 The values are 0.93647 and 0.91848 respectively, which are both larger than the set 0.9, so that the accuracy requirement of the response surface agent model is met, and the method can be used for multi-objective optimization.
Specifically, the third step may include the following specific steps:
generating an initial population with a scale of N in a random manner, performing non-dominant sorting on the initial population, and obtaining a first generation offspring population through basic operations of three genetic algorithms of selection, intersection and variation;
starting from the second generation, merging the child population and the parent population, carrying out rapid non-dominant sorting, simultaneously carrying out crowding degree calculation on individuals in each non-dominant layer, and selecting N individuals to form a new next generation population according to the non-dominant relationship of the individuals and the crowding degree of the individuals and the selection condition;
and generating new offspring population through selection, crossover and mutation operation, and sequentially cycling until the condition of ending the program is met.
In the embodiment of the invention, the mathematical expression of multi-objective optimization is established based on the objective function of the agent model in the second step, as follows:
wherein: p (alpha, N, H) is an objective function, m max For maximum mass flow of cross section, h max The maximum average convection heat transfer coefficient in the channel is called alpha, N and H as design variables.
The agent model, the constraint parameters and the range thereof are input into a genetic algorithm, and in the embodiment of the invention, the population number is set to be 50, the maximum iteration number is 200, the crossover probability is 0.8, and the variation probability is 0.1; a Pareto optimal solution set of mass flow m and convective heat transfer coefficient h is obtained as shown in fig. 7.
The fourth step comprises the following specific steps:
assuming that n evaluation objects are provided, each evaluation object has m indexes, the decision matrix is:
X＝(x ij ) n×m (i＝1，2，…，n；j＝1，2，…，m)；
normalizing the initial matrix:
setting a weighting factor w j Weighting the normalization matrix as follows:
a ij ＝w j ×b ij ；
determining a positive ideal solution Z + And negative ideal solution Z - ：
Calculating the distance between each evaluation object and the positive and negative ideal solutions:
calculating the closeness r i ：
To verify the accuracy of the solution of the multi-objective genetic algorithm of NSGA-II based on the Pareto solution set, the embodiment of the present invention uniformly selects 5 discrete points from the Pareto front shown in fig. 7 in proportion to compare with the CFD simulation result, as shown in the following table 2 in detail:
table 2 simulation and Pareto solution comparison
As can be seen from Table 2, the average error between the simulation results of the mass flow and the convective heat transfer coefficient and the solution value of the genetic algorithm is 2.03% and 0.88%, respectively, and the two are well matched; it is illustrated that the result of the multi-objective genetic algorithm solution of NSGA-II based on the Pareto solution set in the embodiment of the invention is reliable.
To obtain the optimal solution in the Pareto optimal solution set by TOPSIS decision method, the proximity r of the feasible solution in FIG. 7 is calculated i The optimal point is selected as a solution of the embodiment of the present invention according to the sorting result of the proximity.
In the implementation process, the optimal structural parameter of the finally selected sectional type inclined groove blade is that the groove opening width H is 12.7mm, the groove opening inclination angle alpha is 56.38 degrees, and the number N of the blades is 36. The mass flow rate through the brake disc after optimization is 49.88g/s, which is improved by 12.37% compared with the mass flow rate 44.39g/s through the brake disc before optimization. The average convection heat transfer coefficient of the optimized brake disc is 91.23W/m 2 K, compared with the heat exchange coefficient 82.16W/m of the brake disc before optimization 2 K is improved by 9.9%. Therefore, the optimized brake disc has good heat radiation performance compared with the brake disc before optimization.
FIG. 5 compares the average temperature of the blade surfaces before and after optimization with the change of the rotation speed using CFD. Under the working condition that the wheel rotation speed is 200-1200 rpm, the average surface temperature of the Straight blade 9 (Straight vane) and the sectional inclined groove blade (Vane with channel) is reduced along with the increase of the rotation speed; and the sectional type inclined groove blade structural design is better than the straight blade 9 radiating effect, and the average temperature of sectional type inclined groove blade surface is lower than straight blade 9 temperature, and the maximum 1.51% is reached to Reduction rate (Reduction rate) when the rotational speed is 900rpm, as shown in fig. 8.
According to the sectional type inclined groove blade characteristic parameter optimization method, through theoretical analysis on the convection heat radiation performance of the ventilation type brake disc, the structural characteristic parameters required to be optimized for the sectional type inclined groove blade are determined to be the opening width H of the inclined groove 3, the opening inclination angle alpha of the inclined groove 3 and the number N of the blades; firstly, obtaining each group of design variable values through simulation test, performing simulation calculation according to an established finite element simulation model, obtaining response sampling data corresponding to a plurality of sampling points by using an OLHS method, and obtaining a fitting function of an optimization target by using a response surface model; solving a second generation non-inferior sorting genetic algorithm NSGA-II based on the Pareto optimal solution to obtain a Pareto optimal solution set with the mass flow m and the convection heat transfer coefficient h being maximum; the optimal solution is found based on the TOPSIS principle, and the sectional type inclined groove blade structure is set according to the optimal value, so that the ventilated brake disc with stronger convection heat transfer performance is obtained, and the rationality optimization of the sectional type inclined groove blade structure characteristic parameters of the ventilated brake disc is realized. The optimization method has wider applicability and higher accuracy in the field of engineering design.
In summary, the above embodiments are only preferred embodiments of the present invention, and are not intended to limit the scope of the present invention. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention should be included in the protection scope of the present invention.
Claims (4)
1. A method for optimizing the characteristic parameters of sectional type inclined groove blades of a ventilated brake disc is characterized in that the ventilated brake disc is provided with two outer friction surfaces, two oppositely arranged inner surfaces and a plurality of radiating blades connected between the two inner surfaces; the plurality of radiating blades are uniformly distributed around the circumference of the brake disc; each radiating blade is divided into an inner blade and an outer blade which are arranged along the radial direction of the brake disc by an intermediate inclined groove; an included angle formed by the inclined groove and the radial center line of the inner blade, wherein the included angle is formed by the opening of the inclined groove towards the outside of the brake disc, and the inclined groove is used for introducing fluid on the pressure side to the suction side so as to reduce a backflow area; the optimization method comprises the following steps:
step one, establishing a sectional type inclined groove blade model of a brake disc; the structural characteristic parameters required to be optimized for the sectional type inclined groove blades of the ventilated brake disc are determined, wherein the structural characteristic parameters comprise the inclined groove opening width H, the inclined groove opening inclination angle alpha and the number N of the sectional type inclined groove blades; determining optimization targets and constraint conditions, wherein the two optimization targets are a maximum mass flow m and a maximum heat exchange coefficient h passing through an internal channel;
step two, adopting a sectional inclined groove blade model to carry out numerical simulation, carrying out data sampling based on an optimal Latin hypercube method, fitting a response surface agent model and verifying the accuracy of the agent model;
step three, solving a Pareto optimal solution set obtained by two objective functions (m, h) by adopting NSGA-II;
step four, obtaining an optimal solution in a Pareto optimal solution set by a TOPSIS decision method, and carrying out CFD verification on the result;
in the second step, the response surface agent model is a polynomial of an objective function fitted through a least square method, so that the objective function is displayed; the basic expression of the objective function is:
wherein xi is the ith component of the n-dimensional independent variable x, beta 0 is a constant term undetermined coefficient, beta i is a primary term undetermined coefficient, beta ij is a secondary term undetermined coefficient, a column vector beta is formed, n is the number of design variables, and epsilon is an error;
for the accuracy of the calculation result, the accuracy of the fitting equation is judged in the form of variance, and the basic expression of the judgment is as follows:
wherein N is the number of sample points, y i As a result of the true response value,calculated response value for response surface model, +.>Is the average of the true response values.
2. The optimization method of claim 1, wherein in the first step, a variation range of the structural feature parameter in the design variable is:
the value distribution interval of the opening width H of the optimized parameter inclined groove is 8 mm-13 mm;
the value distribution interval of the opening inclination angle alpha of the optimized parameter inclined groove is 30-60 degrees;
the value distribution interval of the number N of the optimized parameter blades is 20-40.
3. The optimization method of claim 2, wherein step three comprises the specific steps of:
generating an initial population with a scale of N in a random manner, performing non-dominant sorting on the initial population, and obtaining a first generation offspring population through basic operations of three genetic algorithms of selection, intersection and variation;
starting from the second generation, merging the child population and the parent population, carrying out rapid non-dominant sorting, simultaneously carrying out crowding degree calculation on individuals in each non-dominant layer, and selecting N individuals to form a new next generation population according to the non-dominant relationship of the individuals and the crowding degree of the individuals and the selection condition;
and generating new offspring population through selection, crossover and mutation operation, and sequentially cycling until the condition of ending the program is met.
4. The optimization method of claim 3, wherein step four comprises the specific steps of:
assuming that n evaluation objects are provided, each evaluation object has m indexes, the decision matrix is:
X＝(x ij ) n×m (i＝1，2，…，n；l＝1，2，…，m)；
normalizing the initial matrix:
setting a weighting factor w j Weighting the normalization matrix as follows:
a ij ＝w j ×b ij ；
determining a positive ideal solution Z + And negative ideal solution Z - ：
Calculating the distance between each evaluation object and the positive and negative ideal solutions:
calculating the closeness r i ：
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