A method for characterizing and optimizing the linear motion history of piston based on virtual crankshaft

Abstract

The present invention discloses a method for characterizing and optimizing the linear motion history of a piston based on a virtual crankshaft, comprising the following steps: step 1, determining basic constants and limiting conditions of the piston's cyclic reciprocating linear motion; step 2, selecting decision variables and characterizing the piston's reciprocating linear motion history; step 3, calculating the value of an objective function according to the piston's reciprocating linear motion history and the basic constants of the cyclic motion; step 4, setting piston motion constraints; step 5, forming a calculation model based on the above steps 1 to 4, and iteratively optimizing the decision variables using a sequential quadratic programming method; the method for characterizing and optimizing the linear motion history of a piston based on a virtual crankshaft provided by the present invention improves the possibility of ultimately obtaining a global optimal solution, is easy to implement iterative optimization by self-programming, and improves calculation time efficiency.

Description

Technical Field

[0001] The invention belongs to the technical field of engines, and in particular relates to a method for characterizing and optimizing the linear motion history of a piston based on a virtual crankshaft. Background Art

[0002] Compared with traditional internal combustion engines, the free piston engine eliminates the crank-connecting rod mechanism and has a more compact structure. It has the advantages of light weight, small size, fast response, and wide fuel adaptability. It is widely used in vehicle power, ship transportation, unit power generation, cogeneration and other scenarios.

[0003] Since the movement of the free piston is not restricted and constrained by the uniform speed operation of the crank-connecting rod, its movement history, that is, the relationship between the change of movement quantities such as piston displacement and time, can be independently regulated. Controlling the movement history of the free piston can better match and adapt to the changes in the thermal state in the engine cylinder, and overcome the problem that the movement history and operation rules of the piston of the traditional crank-connecting rod engine are difficult to reduce the cycle exhaust loss and heat transfer loss. It is beneficial to improve the thermal efficiency of the thermal cycle when the engine is running, further improve the operating efficiency of various mechanical systems containing free piston operation modules, reduce the effective fuel consumption rate, improve power endurance, and effectively respond to the increasingly insufficient supply of fossil energy and the increasingly stringent pollution emission regulations. It has broad application prospects.

[0004] The existing free piston motion history characterization and optimization methods mainly focus on processing the displacement-time curve of the piston linear motion. Specifically, the free piston motion history is characterized by using an undetermined explicit function expression or an interpolation calculation method such as a spline curve, and the motion history is optimized by optimizing the undetermined parameters in the expression or the node coordinates of the interpolation curve. The above processing methods are difficult to simultaneously meet many constraints proposed when carrying out actual engineering projects, such as fixed compression ratio, instantaneous piston stillness at the upper and lower dead points, continuous and bounded piston motion acceleration, and a given cycle time. As a result, the characterization of the piston linear motion history curve has problems such as motion impact, i.e., infinite acceleration, discontinuous acceleration, etc., which are not suitable for actual free piston operation control. In addition, the undetermined simple expression and interpolation spline curve method fail to ensure that the curve space it can express is completely consistent with the space of all piston reciprocating linear motion history that meets the given constraints, and it is also difficult to match and optimize with the working fluid-wall heat transfer process and combustion heat release process. Summary of the invention

[0005] The purpose of the present invention is to provide a method for characterizing and optimizing the linear motion history of a piston based on a virtual crankshaft, so as to solve the problems existing in the prior art that the characterization of the linear motion history curve of the piston has motion impact, so it is not suitable for the actual free piston operation regulation, and at the same time, the method of undetermined simple expression and interpolation spline curve is difficult to match and optimize with the working fluid-wall heat transfer process and the combustion heat release history.

[0006] To achieve the above object, the present invention provides a method for characterizing and optimizing the linear motion history of a piston based on a virtual crankshaft, comprising the following steps:

[0007] Step 1: Determine the basic constants and limiting conditions of the piston's cyclic reciprocating linear motion;

[0008] Step 2, select decision variables and characterize the piston reciprocating linear motion process;

[0009] Step 3, calculating the objective function value according to the reciprocating linear motion history of the piston and the basic constants of the cyclic motion;

[0010] Step 4: Set piston motion constraints;

[0011] Step 5: Based on the above steps 1 to 4, a calculation model is formed, and the decision variables are iteratively optimized using the sequential quadratic programming method, wherein the calculation model consists of an objective function, constraints, and decision variables.

[0012] Preferably, the basic constants in step 1 include structural constants, working fluid constants, wall constants, fuel constants, heat transfer model constants, and three-Weber heat release model constants; wherein the structural constants include the cylinder diameter ,stroke , Clearance , the working fluid constant includes the initial working fluid temperature , working fluid quality , gas constant , isochoric specific heat ; Wall constant refers to the wall temperature ; The fuel constant includes the cycle injection amount and low calorific value ; The heat transfer model constant is the average piston speed ; Three Weber heat release model constants including the start time of premixed combustion , duration , Quality Factor , Combustion ratio , the start time of diffusion combustion , duration , Quality Factor , Combustion ratio , the start time of afterburning , duration , Quality Factor and combustion ratio .

[0013] Preferably, in step 1, the constraints include duration constraints and motion constraints; the duration constraint means that the duration of the entire cyclic motion of the piston is a fixed value. The cyclic motion is two-stroke or four-stroke; the motion constraint includes that the maximum acceleration during the piston motion does not exceed a given value The speed of the piston when it moves to the upper and lower dead points is 0, the displacement of the piston at the initial moment is 0, and the maximum displacement at the upper dead point is the stroke. The piston can only change the direction of speed at the upper and lower dead points. The acceleration of the piston movement process must change continuously with time, and no discontinuous points are allowed.

[0014] Preferably, the decision variable in step 2 is: after the imaginary virtual crankshaft rotation motion history corresponding to the piston is divided into intervals in the entire time domain, the value of the virtual crankshaft rotation angular velocity at the endpoints of each time division interval; the specific selection process of the decision variable is as follows: Divide evenly into share, Pick ,form The decision variable is selected as the virtual crankshaft connected to the piston using an imaginary equivalent crank-connecting rod mechanism in the above Angular velocity at characteristic time nodes , so the decision variable is , a total of indivual.

[0015] Preferably, the process of characterizing the piston reciprocating linear motion history in step 2 is specifically as follows:

[0016] S21, using piecewise shape-preserving cubic interpolation method, based on each decision variable Calculate the time history of the virtual crankshaft rotation angular velocity ;

[0017] S22, using the backward difference method (except the first node using the forward difference), based on the virtual crankshaft rotation angular velocity time history Calculate the time history of virtual crankshaft angular acceleration ;

[0018] S23, using the complex trapezoidal numerical integration method, based on the virtual crankshaft rotation angular velocity time history Calculation of virtual crank angle time history ;

[0019] S24, using the connection between the crankshaft rotational motion and the piston linear motion described by the kinematic law of the crank-connecting rod mechanism, according to the virtual crankshaft rotational angular velocity time history obtained above , virtual crankshaft angular acceleration time history , virtual crank angle time history , combined with the derivative law of composite functions, the linear motion history of the piston is mapped and calculated, including the piston displacement ,speed , acceleration The change over time can be used to characterize the linear motion history of the engine piston.

[0020] Preferably, the objective function in step 3 is the cycle indicated thermal efficiency, and the specific calculation process is as follows:

[0021] S31. Based on the energy conservation equations of combustion heat release, heat transfer, volume change work, and internal energy change, combined with the basic constants of cyclic motion, the explicit Euler method is used to iterate from front to back to obtain the working fluid temperature at the corresponding moment. The specific expression is as follows:

[0022] ;

[0023] In the formula, For the The working fluid temperature at a moment; the unit is ; For the The working fluid temperature at a moment; the unit is ; is the time difference between two adjacent time nodes; the unit is ; for The rate of change of working fluid temperature at the moment; the unit is ;

[0024] S32. Calculate the volume change work of the cycle process based on the piston displacement, speed history and working fluid temperature history. , and finally get the cycle indicated thermal efficiency .

[0025] Preferably, the volume change work of the cycle process in S32 is and cycle indicated thermal efficiency The calculation method is as follows:

[0026] The volume change work is calculated by using the complex trapezoidal numerical integration method. , the calculation expression is as follows:

[0027] ;

[0028] Cycle Indicated Thermal Efficiency The calculation expression is as follows:

[0029] ;

[0030] In the formula, For the The piston displacement at the time node is in ; For the The working fluid temperature at a certain moment, in units of ; For the The piston speed at the time node is in , is the time history of the working fluid temperature; is the piston velocity time history; is the time history of piston displacement.

[0031] Preferably, the piston motion constraint conditions set in step 4 are specifically as follows:

[0032] The acceleration of the piston during linear motion does not exceed the given value The constraints are established as follows:

[0033] ;

[0034] In the formula, represents the piston acceleration;

[0035] The duration of a complete piston cycle is given as a value The constraints are established as follows:

[0036] ;

[0037] in, Represents the two-stroke cycle, Represents the four-stroke cycle, Indicates the virtual crankshaft angle corresponding to the moment when the piston cycle motion ends;

[0038] In view of the limitation that the displacement of the piston at the initial moment is 0, the constraints are established as follows:

[0039] ;

[0040] In the formula, Indicates the virtual crankshaft angle corresponding to the initial moment of piston movement;

[0041] In view of the restriction that the piston can and must change the speed direction at the upper and lower dead points, the constraints are established as follows:

[0042] ;

[0043] In the formula, Indicates The virtual crankshaft angular velocity corresponding to each time node.

[0044] Preferably, the specific content of iterative optimization of decision variables using sequential quadratic programming in step 5 is: randomly generate multiple groups of virtual crankshaft angular velocity decision variable sequences, calculate their corresponding cycle indicated thermal efficiencies respectively, select a group of decision variables with the largest thermal efficiency as the initial values ​​of the algorithm iterative optimization, reduce the initial value sensitivity of the subsequent optimization process, use sequential quadratic programming, based on the established mapping relationship between decision variables and objective functions, set the minimum iteration step tolerance and the maximum constraint violation tolerance, iteratively optimize and solve the decision variables starting from the initial values, and output the solution results when the iterative optimization is completed.

[0045] Therefore, the present invention adopts the above-mentioned piston linear motion history characterization and optimization method based on virtual crankshaft, which has the following beneficial effects:

[0046] (1) The method provided by the present invention automatically satisfies many motion constraints, which is conducive to reducing constraints in the actual optimization process;

[0047] (2) The constraint expression of the actual iterative optimization process is more concise and efficient, reducing the difficulty of optimization;

[0048] (3) The optimization process is efficient and has a high iteration speed;

[0049] (4) Reducing the initial value sensitivity of the iterative optimization process is conducive to increasing the possibility of obtaining the global optimal solution in the end;

[0050] (5) It is easy to write a program to implement iterative optimization, and the calculation time is good.

[0051] The technical solution of the present invention is further described in detail below through the accompanying drawings and embodiments. BRIEF DESCRIPTION OF THE DRAWINGS

[0052] Figure 1 It is an overall flow chart of a method for characterizing and optimizing the linear motion history of a piston based on a virtual crankshaft of the present invention;

[0053] Figure 2 A schematic diagram of the relationship between the crankshaft angle and the piston displacement driven by the virtual crank-connecting rod mechanism according to an embodiment of the present invention;

[0054] Figure 3 A schematic diagram of a mapping relationship between decision variables, motion history and optimization objectives established in an embodiment of the present invention;

[0055] Figure 4 The engine piston displacement time history curve diagram obtained after optimization of the embodiment of the present invention;

[0056] Figure 5 This is a time history curve diagram of the engine piston speed obtained after optimization of an embodiment of the present invention. DETAILED DESCRIPTION

[0057] The following detailed description of the embodiments of the present invention provided in the accompanying drawings is not intended to limit the scope of the invention claimed for protection, but merely represents selected embodiments of the present invention. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0058] See also Figure 1-5 , a method for characterizing and optimizing the linear motion history of a piston based on a virtual crankshaft, comprising the following steps:

[0059] Step 1: Determine the basic constants and constraints of the piston's reciprocating linear motion; the basic constants include structural constants, working fluid constants, wall constants, fuel constants, heat transfer model constants, and three-Weber heat release model constants; the structural constants include the cylinder diameter ,stroke , Clearance , the working fluid constant includes the initial working fluid temperature , working fluid quality , gas constant , isochoric specific heat ; Wall constant refers to the wall temperature ; The fuel constant includes the cycle injection amount and low calorific value ; The heat transfer model constant is the average piston speed ; Three Weber heat release model constants including the start time of premixed combustion , duration , Quality Factor , Combustion ratio , the start time of diffusion combustion , duration , Quality Factor , Combustion ratio , the start time of afterburning , duration , Quality Factor and combustion ratio ; Among them, the instantaneous average heat transfer coefficient in the heat transfer model is Calculated using the Eichelberg formula:

[0060] ;

[0061] The basic constant is the average piston speed. ;

[0062] The constraints include duration constraints and motion constraints; the duration constraint means that the duration of the entire piston cycle motion is a fixed value. The cyclic motion is two-stroke or four-stroke; the motion constraint includes that the maximum acceleration during the piston motion does not exceed a given value The speed of the piston when it moves to the upper and lower dead points is 0, the displacement of the piston at the initial moment is 0, and the maximum displacement at the upper dead point is the stroke. The piston can only change the direction of speed at the upper and lower dead points. The acceleration of the piston movement process must change continuously with time, and no discontinuous points are allowed.

[0063] Step 2, select decision variables and characterize the piston reciprocating linear motion history; wherein the decision variables are: after the virtual crankshaft rotational motion history corresponding to the piston is divided into intervals in the entire time domain, the values ​​of the virtual crankshaft rotational angular velocity at the endpoints of each time division interval; the specific selection process of the decision variables is as follows: Divide evenly into share, Pick ,form The decision variable is selected as the virtual crankshaft connected to the piston using an imaginary equivalent crank-connecting rod mechanism in the above Angular velocity at characteristic time nodes , so the decision variable is , a total of indivual;

[0064] The process of characterizing the piston's reciprocating linear motion is specifically as follows:

[0065] S21, using piecewise shape-preserving cubic interpolation method, based on each decision variable Calculate the time history of the virtual crankshaft rotation angular velocity ; Specifically: for the whole process time domain Divide evenly into share, Much greater than ,form The virtual crankshaft angular velocity at the general time node , using piecewise shape-preserving cubic interpolation method, based on characteristic time nodes and their corresponding virtual crankshaft angular velocity Calculate and form the virtual crankshaft rotation angular velocity time history ,Right now by General time points and its corresponding virtual crankshaft angular velocity Represents. Piecewise conformal cubic interpolation can ensure The first-order derivative of is continuous, that is, the virtual crankshaft angular acceleration is continuous;

[0066] S22, using the backward difference method (except the first node using the forward difference), based on the virtual crankshaft rotation angular velocity time history Calculate the time history of virtual crankshaft angular acceleration ; Specifically: virtual crankshaft angular acceleration time history General time points and its corresponding virtual crankshaft angular acceleration It indicates that the calculation is based on The backward difference formula of , except that the first node uses forward difference calculation, is as follows:

[0067] ;

[0068] ;

[0069] In the formula, Indicates The moment of a general time node; the unit is ; Indicates The moment of a general time node; the unit is ; Indicates The virtual crankshaft angular velocity corresponding to the time node; the unit is ; Indicates The virtual crankshaft angular velocity at the time node; the unit is ,in, ;

[0070] S23, using the complex trapezoidal numerical integration method, based on the virtual crankshaft rotation angular velocity time history Calculate the time history of the virtual crankshaft angular displacement ; Specifically: virtual crankshaft angle displacement time history by General time points and its corresponding virtual crankshaft angular displacement The expression is calculated based on The complex trapezoidal integral formula is as follows:

[0071] ;

[0072] In the formula, Indicates the time difference between two adjacent general time nodes; the unit is ; Indicates that the virtual crankshaft is The angular velocity at a general time node; the unit is ;

[0073] S24, using the connection between the crankshaft rotational motion and the piston linear motion described by the kinematic law of the crank-connecting rod mechanism, according to the virtual crankshaft rotational angular velocity time history obtained above , virtual crankshaft angular acceleration time history , virtual crank angle time history , combined with the derivative law of composite functions, the linear motion history of the piston is mapped and calculated, including the piston displacement ,speed , acceleration The change over time can be used to characterize the linear motion history of the engine piston. The details are as follows:

[0074] Based on the crankshaft angle time history , calculate the piston displacement time history , by General time points and its corresponding piston displacement The expression is as follows:

[0075] ;

[0076] In the formula, Indicates the length of the virtual connecting rod; the unit is ; Represents the virtual crank length, which is the basic structural constant stroke Half of ;

[0077] According to the law of composite function derivation, the piston displacement is differentiated with respect to time, and the calculation expression of the piston velocity time history is obtained as follows:

[0078] ;

[0079] Similarly, the piston speed time history by General time points and its corresponding piston speed The expression is calculated as follows:

[0080] ;

[0081] Similarly, the calculation expression of the piston acceleration time history is obtained by differentiating the piston velocity with respect to time, as follows:

[0082] ;

[0083] in,

[0084] ;

[0085] ;

[0086] Piston acceleration time history Likewise General time points and its corresponding piston acceleration The expression is calculated as follows:

[0087] ;

[0088] Step 3: Calculate the objective function value according to the reciprocating linear motion history of the piston and the basic constants of the cyclic motion; wherein the objective function is the cyclic indicated thermal efficiency, and the specific calculation process is as follows:

[0089] S31. Based on the energy conservation equations of combustion heat release, heat transfer, volume change work, and internal energy change, combined with the basic constants of cyclic motion, the explicit Euler method is used to iterate from front to back to obtain the working fluid temperature at the corresponding moment. The specific expression is as follows:

[0090] ;

[0091] In the formula, For the The working fluid temperature at a moment; the unit is ; For the The working fluid temperature at a moment; the unit is ; is the time difference between two adjacent time nodes; the unit is ; for The rate of change of working fluid temperature at the moment; the unit is ; Among them, the working fluid temperature change rate ;

[0092] Heat transfer rate ;

[0093] Volume change power ;

[0094] Instantaneous heat release rate of combustion ;

[0095] Instantaneous heat release rate of diffusion combustion

[0096] ;

[0097] Premixed combustion instantaneous heat release rate

[0098] ;

[0099] Afterburning combustion instantaneous heat release rate

[0100] ;

[0101] S32. Calculate the volume change work of the cycle process based on the piston displacement, speed history and working fluid temperature history. , and finally get the cycle indicated thermal efficiency ; The volume change work and cycle indicated thermal efficiency The calculation method is as follows:

[0102] The volume change work is calculated by using the complex trapezoidal numerical integration method. , the calculation expression is as follows:

[0103] ;

[0104] Cycle Indicated Thermal Efficiency The calculation expression is as follows:

[0105] ;

[0106] In the formula, For the The piston displacement at the time node is in ; For the The working fluid temperature at a certain moment, in units of ; For the The piston speed at the time node is in , is the time history of the working fluid temperature; is the piston velocity time history; is the time history of piston displacement.

[0107] Step 4: Set the piston motion constraints; details are as follows:

[0108] The acceleration of the piston during linear motion does not exceed the given value The constraints are established as follows:

[0109] ;

[0110] In the formula, represents the piston acceleration;

[0111] The duration of a complete piston cycle is given as a value The constraints are established as follows:

[0112] ;

[0113] in, Represents the two-stroke cycle, Represents the four-stroke cycle, Indicates the virtual crankshaft angle corresponding to the moment when the piston cycle motion ends;

[0114] In view of the limitation that the displacement of the piston at the initial moment is 0, the constraints are established as follows:

[0115] ;

[0116] In the formula, Indicates the virtual crankshaft angle corresponding to the initial moment of piston movement;

[0117] In view of the restriction that the piston can and must change the speed direction at the upper and lower dead points, the constraints are established as follows:

[0118] ;

[0119] In the formula, Indicates The virtual crankshaft angular velocity corresponding to each time node.

[0120] Step 5. Based on the above steps 1 to 4, a calculation model is formed, and the decision variables are iteratively optimized using the sequential quadratic programming method, wherein the calculation model consists of an objective function, constraints and decision variables; the specific contents are as follows: randomly generate multiple sets of virtual crankshaft angular velocity decision variable sequences, calculate their corresponding cycle indicated thermal efficiencies respectively, select a set of decision variables with the largest thermal efficiency as the initial values ​​of the algorithm iterative optimization, reduce the initial value sensitivity of the subsequent optimization process, use the sequential quadratic programming method, based on the established mapping relationship between the decision variables and the objective function, set the minimum iteration step tolerance and the maximum constraint violation tolerance, iteratively optimize and solve the decision variables starting from the initial values, and output the solution results when the iterative optimization is completed.

[0121] Example

[0122] Step 1: Determine the basic constants and constraints of the piston's cyclic reciprocating linear motion.

[0123] For structural constants, stroke , cylinder diameter , clearance ; For the working fluid constant, the initial working fluid temperature , working fluid quality , gas constant , isochoric specific heat ; For the wall constant, the wall temperature . For the fuel constant, the cycle injection amount , low calorific value ; For the three-Weber heat release model constant, the start time of premixed combustion is , duration , Quality Factor , Combustion ratio , the start time of diffusion combustion , duration , Quality Factor , Combustion ratio , the start time of afterburning , duration , Quality Factor , Combustion ratio .

[0124] Due to the motion constraint, the total duration of the piston cycle is fixed. ; The cyclic motion is defined as a two-stroke. The maximum acceleration during the piston motion does not exceed the given value. ; The speed of the piston when it moves to the upper and lower dead points is 0, and the piston is at the lower dead point at the initial moment, the piston is at the upper dead point at the end of the compression stroke, and the piston is at the lower dead point at the end of the expansion stroke; the displacement of the piston at the initial moment is 0, and the maximum displacement at the upper dead point is the stroke The piston can and must change the direction of speed at the upper and lower dead points. The acceleration of the piston movement process must change continuously with time, and discontinuous points are not allowed.

[0125] Step 2: Select decision variables and characterize the piston reciprocating linear motion process.

[0126] 2-1 Time domain of the whole process Divide evenly into share, Take 14 and form That is, 15 characteristic time nodes, the selected decision variables are the angular velocity of the virtual crankshaft connected to the piston using an imaginary equivalent crank-connecting rod mechanism at the above 15 characteristic time nodes , so the decision variable is , there are 15 in total.

[0127] 2-2 For the whole process time domain Divide evenly into share, Much greater than , take 799, form That is, 800 general time nodes. For the virtual crankshaft angular velocity at the general time node , using piecewise shape-preserving cubic interpolation method, based on characteristic time nodes and their corresponding virtual crankshaft angular velocity Calculate and form the virtual crankshaft rotation angular velocity time history ,Right now With 800 general time nodes and its corresponding virtual crankshaft angular velocity Represents. Piecewise conformal cubic interpolation can ensure The first-order derivative of is continuous, that is, the virtual crankshaft angular acceleration is continuous. Similarly, the time history of the virtual crankshaft angular acceleration With 800 general time nodes and its corresponding virtual crankshaft angular acceleration It indicates that the calculation is based on The backward difference formula of , except for the first node which uses forward difference calculation, is as follows:

[0128] ;

[0129] ;

[0130] In the formula, Indicates The moment of a general time node; the unit is ; Indicates The moment of a general time node; the unit is ; Indicates The virtual crankshaft angular velocity corresponding to the time node; the unit is ; Indicates The virtual crankshaft angular velocity at the time node; the unit is ,in, ;

[0131] Virtual crank angle time history With 800 general time nodes and its corresponding virtual crankshaft angular displacement The expression is calculated based on The complex trapezoidal integral formula is as follows:

[0132] ;

[0133] In the formula, Indicates the time difference between two adjacent general time nodes; the unit is ; Indicates that the virtual crankshaft is The angular velocity at a general time node; the unit is ;

[0134] 2-3 Piston displacement described by the kinematics of the crank-connecting rod mechanism and crankshaft angle relationship, such as Figure 2 As shown, based on the above virtual crankshaft angle time history , calculate the piston displacement time history , With 800 general time nodes and its corresponding piston displacement The expression is as follows:

[0135] ;

[0136] In the formula, Indicates the length of the virtual connecting rod; the unit is ; Represents the virtual crank length, which is the basic structural constant stroke Half of ;

[0137] According to the law of composite function derivation, the piston displacement is differentiated with respect to time, and the calculation expression of the piston velocity time history is obtained as follows:

[0138] ;

[0139] Similarly, the piston speed time history With 800 general time nodes and its corresponding piston speed The expression is calculated as follows:

[0140] ;

[0141] Similarly, the calculation expression of the piston acceleration time history is obtained by differentiating the piston velocity with respect to time, as follows:

[0142] ;

[0143] in,

[0144] ;

[0145] ;

[0146] Piston acceleration time history Also with 800 general time nodes and its corresponding piston acceleration The expression is calculated as follows:

[0147] ;

[0148] Step 3, calculate the objective function value according to the piston's reciprocating linear motion history and the basic constants of the cyclic motion.

[0149] 3-1 Time history of working fluid temperature With 800 general time nodes And its corresponding working fluid temperature The calculation is based on the energy conservation equations of combustion heat release, heat transfer, volume change work, and internal energy change. Combined with the basic constants of the basic cyclic motion mentioned above, the classic explicit Euler method is used to iterate from front to back, as follows:

[0150] ;

[0151] in,

[0152] Working fluid temperature change rate ;

[0153] Heat transfer rate ;

[0154] Volume change power ;

[0155] Instantaneous heat release rate of combustion ;

[0156] Instantaneous heat release rate of diffusion combustion

[0157] ;

[0158] Premixed combustion instantaneous heat release rate

[0159] ;

[0160] Afterburning combustion instantaneous heat release rate

[0161] ;

[0162] 3-2 Using the piston displacement, velocity history and working fluid temperature history obtained in the above process, calculate the volume change work of the cycle process , and then the cycle indicated thermal efficiency is obtained ;

[0163] The complex trapezoidal numerical integration method is used to calculate the volume change work, as follows:

[0164] ;

[0165] Calculate the objective function, i.e., cycle indicated thermal efficiency ,

[0166] ;

[0167] At this point, through steps 2 and 3, the functional mapping relationship between the decision variable, i.e., the angular velocity of the virtual crankshaft at the characteristic time node and the optimization target, i.e., the cycle indicated thermal efficiency, is established. The schematic diagram of this process is shown in FIG. Figure 3 shown.

[0168] Step 4: Set the piston motion constraints.

[0169] The acceleration of the piston during linear motion does not exceed the given value. The constraints are established as follows:

[0170] ;

[0171] The duration of the two-stroke movement of a complete piston cycle is given as a given value The constraints are established as follows:

[0172] ;

[0173] In view of the limitation that the displacement of the piston at the initial moment is 0, the constraints are established as follows:

[0174] ;

[0175] In view of the restriction that the piston can and must change the speed direction at the upper and lower dead points, the constraints are established as follows:

[0176] ;

[0177] In addition, it is worth noting that the speed of the piston when it moves to the upper and lower dead points is 0, and the maximum displacement at the upper dead point is the stroke. The restriction that the acceleration of the piston motion process needs to change continuously with time can be automatically satisfied using the piston linear motion history characterization method described in step 2.

[0178] Step 5: Based on the above steps 1 to 4, a calculation model is formed, and the decision variables are iteratively optimized using the sequential quadratic programming method; specifically: 2000 sets of virtual crankshaft angular velocity decision variable sequences are randomly generated, and their corresponding cycle indicated thermal efficiencies are calculated respectively, and a set of decision variables with the largest thermal efficiency is selected as the initial value of the algorithm iteration optimization, in order to reduce the initial value sensitivity of the subsequent optimization process. Based on the mapping relationship between the decision variables and the objective function established above, the sequential quadratic programming optimization algorithm is used, and the minimum iteration step size tolerance is set to and the maximum constraint violation tolerance is , by constructing and solving a series of constrained quadratic programming subproblems, determining the search direction and step size for each step and making adjustments to the decision variables Perform iterative optimization and solve. After the iteration is completed, output the solution result to obtain the optimized piston linear motion history, such as Figure 4 , 5 As shown, the optimization target value is 48.3974%, which is 2.3774% higher than the indicated thermal efficiency of 46.02% of the original engine, i.e. the traditional motion history of the piston.

[0179] Therefore, the present invention adopts the above-mentioned method for characterizing and optimizing the linear motion history of the piston based on a virtual crankshaft. Based on the principle that there is a one-to-one correspondence between the linear motion of the piston and the rotational motion of the crankshaft in a traditional engine due to the connection of the crank-connecting rod mechanism, the imaginary virtual crankshaft rotational motion history corresponding to the piston is divided into intervals in the entire time domain, and the values ​​of the virtual crankshaft rotation angular velocity at the endpoints of each time-divided interval are used as decision variables. The time history of the free piston motion is calculated using the kinematic law of the crank-connecting rod. Under the given basic constants of the thermodynamic cycle motion, the indicated thermal efficiency is maximized as the optimization goal, and iterative optimization constraints are set to meet the restriction requirements in the process of the linear motion of the piston. The sequential quadratic programming optimization algorithm is used to construct and solve a series of constrained quadratic programming sub-problems, determine the search direction and step size of each step, and iterate the decision variables to achieve the optimization solution of the linear motion history of the engine piston.

[0180] Finally, it should be noted that the above embodiments are only used to illustrate the technical solution of the present invention rather than to limit it. Although the present invention has been described in detail with reference to the preferred embodiments, those skilled in the art should understand that they can still modify or replace the technical solution of the present invention with equivalents, and these modifications or equivalent replacements cannot cause the modified technical solution to deviate from the spirit and scope of the technical solution of the present invention.

Claims

1. A method for characterizing and optimizing the linear motion history of a piston based on a virtual crankshaft, characterized in that: The following steps are involved: Step 1: Determine the basic constants and limiting conditions of the piston's cyclic reciprocating linear motion; Step 2, select decision variables and characterize the piston reciprocating linear motion process; Step 3, calculating the objective function value according to the reciprocating linear motion history of the piston and the basic constants of the cyclic motion; Step 4: Set piston motion constraints; Step 5: Based on the above steps 1 to 4, a calculation model is formed, and the decision variables are iteratively optimized using a sequential quadratic programming method, wherein the calculation model consists of an objective function, constraints, and decision variables; In step 1, the constraints include duration constraints and motion constraints; The duration constraint means that the duration of the entire piston cycle is a fixed value. The cyclic motion is two-stroke or four-stroke; the motion constraint includes that the maximum acceleration during the piston motion does not exceed a given value The speed of the piston when it moves to the upper and lower dead points is 0, the displacement of the piston at the initial moment is 0, and the maximum displacement at the upper dead point is the stroke. , the piston can only change the direction of speed at the upper and lower dead points, and the acceleration of the piston movement process must change continuously with time, and no discontinuous points are allowed; The decision variables in step 2 are: the values ​​of the virtual crankshaft rotation angular velocity at the endpoints of each time-divided interval after the virtual crankshaft rotation motion history corresponding to the piston is divided into equal intervals in the entire time domain; the specific selection process of the decision variables is as follows: Divide evenly into share, Pick ,form The decision variable is selected as the virtual crankshaft connected to the piston using an imaginary equivalent crank-connecting rod mechanism in the above Angular velocity at characteristic time nodes , so the decision variable is , a total of indivual; The process of characterizing the piston reciprocating linear motion history in step 2 is specifically as follows: S21, using piecewise shape-preserving cubic interpolation method, based on each decision variable Calculate the time history of the virtual crankshaft rotation angular velocity ; S22, using the backward difference method, based on the virtual crankshaft rotation angular velocity time history Calculate the time history of virtual crankshaft angular acceleration ; S23, using the complex trapezoidal numerical integration method, based on the virtual crankshaft rotation angular velocity time history Calculation of virtual crank angle time history ; S24, based on the above obtained virtual crankshaft rotation angular velocity time history , virtual crankshaft angular acceleration time history , virtual crank angle time history , combined with the derivative law of composite functions, the linear motion history of the piston is mapped and calculated, including the piston displacement ,speed , acceleration The change over time can be used to characterize the linear motion history of the engine piston; The objective function in step 3 is the cycle indicated thermal efficiency, and the specific calculation process is as follows: S31. Based on the energy conservation equations of combustion heat release, heat transfer, volume change work, and internal energy change, combined with the basic constants of cyclic motion, the explicit Euler method is used to iterate from front to back to obtain the working fluid temperature at the corresponding moment. The specific expression is as follows: ； In the formula, For the The working fluid temperature at a moment; the unit is ; For the The working fluid temperature at a moment; the unit is ; is the time difference between two adjacent time nodes; the unit is ; for The rate of change of working fluid temperature at the moment; the unit is ; S32. Calculate the volume change work of the cycle process based on the piston displacement, speed history and working fluid temperature history. Finally, the cycle indicated thermal efficiency is obtained ; Volume change work in the cycle process of S32 and cycle indicated thermal efficiency The calculation method is as follows: The volume change work is calculated by using the complex trapezoidal numerical integration method. , the calculation expression is as follows: ； Cycle Indicated Thermal Efficiency The calculation expression is as follows: ； In the formula, For the The piston displacement at the time node is in ; For the The working fluid temperature at a certain moment, in units of ; For the The piston speed at the time node is in , is the time history of the working fluid temperature; is the piston velocity time history; is the piston displacement time history; The piston motion constraints set in step 4 are as follows: The acceleration of the piston during linear motion does not exceed the given value The constraints are established as follows: ； In the formula, represents the piston acceleration; The duration of a complete piston cycle is a given value. The constraints are established as follows: ； in, stands for two-stroke cycle, Represents the four-stroke cycle, Indicates the virtual crankshaft angle corresponding to the moment when the piston cycle motion ends; In view of the limitation that the displacement of the piston at the initial moment is 0, the constraint conditions are established as follows: ； In the formula, Indicates the virtual crankshaft angle corresponding to the initial moment of piston movement; In view of the restriction that the piston can and must change the speed direction at the upper and lower dead points, the constraints are established as follows: ； In the formula, Indicates The virtual crankshaft angular velocity corresponding to each time node.

2. The method for characterizing and optimizing the piston linear motion history based on a virtual crankshaft according to claim 1 is characterized in that: The basic constants in step 1 include structural constants, working fluid constants, wall constants, fuel constants, heat transfer model constants, and three-Weber heat release model constants; the structural constants include the cylinder diameter ,stroke , Clearance , the working fluid constant includes the initial working fluid temperature , working fluid quality , gas constant , isochoric specific heat ; The wall constant refers to the wall temperature ; The fuel constant includes the cycle injection amount and low calorific value ; The heat transfer model constant is the average piston speed ; Three Weber heat release model constants including the start time of premixed combustion , duration , Quality Factor , Combustion ratio , the start time of diffusion combustion , duration , Quality Factor , Combustion ratio , the start time of afterburning , duration , Quality Factor and combustion ratio .

3. The method for characterizing and optimizing the piston linear motion history based on a virtual crankshaft according to claim 2 is characterized in that: The specific content of iterative optimization of decision variables using sequential quadratic programming in step 5 is as follows: randomly generate multiple sets of virtual crankshaft angular velocity decision variable sequences, calculate their corresponding cycle indicated thermal efficiencies respectively, select a set of decision variables with the largest thermal efficiency as the initial values ​​of the algorithm iterative optimization, use sequential quadratic programming, based on the established mapping relationship between decision variables and objective functions, set the minimum iteration step tolerance and the maximum constraint violation tolerance, iteratively optimize and solve the decision variables starting from the initial values, and output the solution results when the iterative optimization is completed.

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