Parameter optimization design method for power transmission system with centrifugal pendulum damper

Abstract

The application provides a parameter optimization design method of a power transmission system with a centrifugal pendulum absorber, and comprises the following steps: step 1, establishing a power transmission system model with a centrifugal pendulum absorber; wherein the power transmission system model comprises an engine, a double mass flywheel (DMF) and a transmission input shaft which are connected in sequence; the centrifugal pendulum absorber (CPVA) is arranged on the DMF; step 2, constructing an engine thermodynamics and dynamics model; step 3, constructing a DMF dynamics model; step 4, constructing a CPVA dynamics model and a pendulum beating power analysis model; step 5, constructing a dynamics model of the transmission input shaft; step 6, defining decision variables and objective functions in multi-objective optimization; and step 7, adopting MNSGA-II to optimize the decision variables. The application can achieve the target of reducing the pendulum beating power and the transmission system torsional vibration amplitude, and improve the dynamic performance and durability of the system.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of automobile vibration control, and particularly relates to a parameter optimization design method of a power transmission system with a centrifugal pendulum absorber. BACKGROUND

[0002] With the continuous development of the automobile industry, the vibration problem of the vehicle power transmission system has gradually attracted widespread attention. The vibration generated by the main components such as the engine and the transmission during the working process not only affects the comfort and noise level of the vehicle, but also may have an adverse effect on the reliability and service life of the power transmission system. Especially under low-speed working conditions, the torque fluctuation generated by the engine is large, which is easy to cause resonance or unstable vibration phenomenon of the power transmission system, which puts forward higher requirements for the driving experience and vehicle performance.

[0003] In order to effectively suppress these vibrations, researchers have proposed a variety of vibration reduction technologies. Among them, the centrifugal pendulum absorber (CPVA) as a device that reduces torsional vibration through the inertial force of the pendulum mass has been widely used in rotating systems, especially in the aerospace and automotive industries. In the traditional engine and its supporting power transmission system, the installation of CPVA helps to reduce the vibration generated by the irregular work of the engine and improve the stability of the system.

[0004] However, the existing CPVA application mainly focuses on medium and high speed working conditions, while in low speed state, such as engine starting, idling and low speed driving, the vibration reduction effect of CPVA is often limited due to insufficient centrifugal force. In addition, the traditional design usually fails to fully consider the complex working conditions of the automobile power transmission system, resulting in that the vibration reduction performance of CPVA cannot be effectively played in some working conditions. Therefore, how to optimize the parameters of CPVA in the power transmission system so that it can work efficiently under different speeds and working conditions is a problem to be solved in the current technology. SUMMARY

[0005] The purpose of the present application is to provide a parameter optimization design method of a power transmission system with a centrifugal pendulum absorber, which can achieve the goal of reducing the pendulum knock power and the transmission system torsional vibration amplitude, and improve the dynamic performance and durability of the system. The technical scheme adopted is as follows:

[0006] A parameter optimization design method of a power transmission system with a centrifugal pendulum absorber, comprising the following steps:

[0007] Step 1, establishing a power transmission system model with a centrifugal pendulum absorber;

[0008] The power transmission system model comprises an engine, a dual mass flywheel DMF and a transmission input shaft connected in sequence, and a centrifugal pendulum absorber CPVA is arranged on the dual mass flywheel DMF.

[0009] Step 2, constructing an engine thermodynamic and kinetic model;

[0010] Step 3, constructing a DMF kinetic model;

[0011] Step 4, constructing a CPVA kinetic model and a pendulum knock power analysis model;

[0012] Step 5, constructing a kinetic model of the transmission input shaft;

[0013] Step 6, defining decision variables and objective functions in multi-objective optimization:

[0014] The decision variables include parameters in the engine thermodynamic and kinetic model and the CPVA kinetic model.

[0015] The objective functions include an objective function one and an objective function two.

[0016] The objective function one is to minimize a peak factor CF of the transmission input shaft angular acceleration, and the objective function two is to minimize a knock index KI of the CPVA.

[0017] The knock index KI of the CPVA is generated based on the pendulum knock power analysis model.

[0018] Step 7, optimizing the decision variables by using MNSGA-II.

[0019] Preferably, in step 6, the decision variables include an ignition advance angle, an injection advance angle, an average throttle opening, a combustible mixture formation time in the engine thermodynamic and kinetic model and a pendulum transient position at vehicle startup in the CPVA kinetic model.

[0020] Preferably, in step 6, the objective function one is:

[0021]

[0022] wherein, is a peak value of the transmission input shaft angular acceleration;

[0023] is a root mean square value of the transmission input shaft angular acceleration.

[0024] Preferably, in step 6, the objective function two is:

[0025]

[0026]

[0027]

[0028] and are the normalized values of the peak and average knock power respectively.

[0029] ω1 and ω2 represent the weights of the peak and average values respectively.

[0030] Compared with the prior art, the present application has the following advantages:

[0031] 1. By accurate dynamic modeling and optimal design, the knock power and torsional vibration generated by the CPVA pendulum during engine starting process are effectively reduced.

[0032] 2. The improved MNSGA-II algorithm is used to optimize the key parameters, improving the accuracy and stability of vibration control; the overall scheme improves the performance of the power transmission system while significantly improving the NVH performance and vehicle comfort. BRIEF DESCRIPTION OF DRAWINGS

[0033] Figure 1 is a structural schematic diagram of the power transmission system.

[0034] Figure 2 is a structural schematic diagram of the engine model.

[0035] Figure 3 is a dynamic model diagram of the secondary flywheel in the DMF.

[0036] Figure 4 is a structural schematic diagram of the centrifugal pendulum shock absorber.

[0037] Figure 5 is a flowchart of the multi-objective optimization algorithm.

[0038] Figure 6 is the optimization result after multiple iterations. DETAILED DESCRIPTION

[0039] The parameter optimization design method of the power transmission system with the added centrifugal pendulum shock absorber of the present application will be described in more detail below in conjunction with the accompanying schematic diagrams, which represent the preferred embodiments of the present application. It should be understood that those skilled in the art can modify the present application described herein while still achieving the advantageous effects of the present application. Therefore, the following description should be understood as a broad knowledge to those skilled in the art and not as a limitation of the present application.

[0040] This invention provides a method for optimizing the design parameters of a vehicle powertrain system with added CPVA, aiming to significantly improve the vibration reduction performance of CPVA during vehicle startup.

[0041] Step 1: Establish a power transmission system model with centrifugal pendulum shock absorbers.

[0042] like Figure 1 As shown, this method is based on the torque transmission path of each component in the vehicle powertrain system. Starting from the engine output torque, it is transmitted to the CPVA rotor via the primary flywheel of the DMF. After inertial tuning is achieved inside the CPVA to weaken torsional vibration, the torque is further transmitted to the secondary flywheel of the DMF and finally acts on the transmission input shaft, thus completing the efficient power transmission and vibration reduction functions.

[0043] This optimization design method first requires: constructing an accurate powertrain system model, including dynamic models of key components such as the engine, DMF, CPVA, and transmission input shaft, to ensure that the dynamic characteristics and mutual coupling of each component can be fully reflected, laying the foundation for subsequent parameter optimization.

[0044] like Figure 1 As shown, the powertrain system model mainly includes the following key components and their interconnections:

[0045] 1. Engine

[0046] The engine provides torque to the entire powertrain system through its output shaft, and is the power source of the system.

[0047] 2. Dual Mass Flywheel (DMF)

[0048] The DMF consists of a primary flywheel, a ring-shaped long-arc helical spring, and a secondary flywheel.

[0049] (1) Primary flywheel: directly connected to the engine output shaft to receive the engine torque input.

[0050] (2) Annular long arc helical spring: It is the core elastic element of DMF and is set in the channel opened on the circumference of the secondary flywheel.

[0051] (3) Secondary flywheel: It receives the smooth torque transmitted by the primary flywheel through a ring-shaped long arc helical spring and is fixedly connected to the rotor of the centrifugal pendulum vibration damper (CPVA).

[0052] 3. Centrifugal pendulum vibration damper (CPVA)

[0053] The CPVA is mounted on the secondary flywheel of the DMF, and its main components include the rotor, pendulum, and limit mechanism.

[0054] (1) Rotor: Fixed on the secondary flywheel of DMF, it rotates synchronously with the secondary flywheel to provide installation and motion support for the pendulum.

[0055] (2) Pendulum: Mounted on the rotor via a hinge point, it can swing around the center of the rotor under the action of centrifugal force. The periodic motion of the pendulum generates a reverse inertial force to counteract torsional vibrations of a specific order, thereby optimizing the dynamic performance of the system.

[0056] (3) Limiting mechanism: installed at the end of the pendulum's stroke to limit the pendulum's swing amplitude, avoid excessive swinging that could cause mechanical impact or damage, and ensure the system's reliability and durability.

[0057] 4. Gearbox input shaft

[0058] The DMF secondary flywheel is rigidly connected to the transmission input shaft, transmitting smooth torque, which has been vibration-damped and dynamically optimized, to the transmission to support subsequent power delivery and vehicle drive.

[0059] The overall structure of the power transmission system is as follows:

[0060] Engine output shaft → DMF primary flywheel → DMF secondary flywheel → CPVA rotor → CPVA pendulum → transmission input shaft.

[0061] In step 1, the dynamic parameters of each component, such as inertia, stiffness, and damping coefficient, are determined to provide a basic mathematical model for subsequent optimization analysis.

[0062] Step 2: Engine thermodynamics and dynamics modeling.

[0063] A zero-dimensional transient model of a four-cylinder four-stroke engine is established. By assuming that the working medium is an ideal gas and combining the mass conservation equation in the cylinder and the first law of thermodynamics, a mathematical expression for transient torque is derived. Based on the transient torque analysis, the effects of ignition advance angle, injection advance angle, throttle opening and the formation time of combustible mixture on transient torque output are analyzed and used as decision variables for multi-objective optimization.

[0064] like Figure 2 As shown, the torque output of an engine is closely related to the thermodynamic processes of the working medium within its cylinder. To accurately describe the state evolution within the cylinder, it is assumed that the working medium is an ideal gas, and that its state parameters (temperature, pressure, etc.) are uniformly distributed within the cylinder.

[0065] First, from the perspective of mass conservation, the mass balance equation of the medium inside the cylinder is established:

[0066]

[0067] dm e =τ(dm)s + g(φ ia )dx)

[0068] wherein, m c is the working medium mass in the cylinder;

[0069] m s is the air mass flowing into the cylinder;

[0070] m e is the exhaust gas mass discharged from the cylinder;

[0071] τ is a correction coefficient considering exhaust gas residue, and is a set value;

[0072] φ ia is the fuel injection advance angle, and is a set value, while being one of the decision variables of the multi-objective optimization;

[0073] g(φ ia ) is the cycle injection volume, and is a set value;

[0074] is the percentage of the fuel mixture, and is a table value according to the instantaneous crank angle calibration;

[0075] φ is the instantaneous crank angle, φ = 0 represents the top dead center, and φ = π represents the bottom dead center, and is a simulation output value.

[0076] Due to the volume lag effect of the intake system, the intake flow is affected by the periodic change of the crank angle.

[0077] Therefore, the state parameters of the intake and exhaust systems are calculated using the volume method, and the change rate of the intake mass is as follows:

[0078]

[0079] ω is the crank angle speed, and is a simulation output value;

[0080] μ is the exhaust flow coefficient, representing the formation time of the combustible mixture, and is a set value, while being one of the decision variables of the multi-objective optimization;

[0081] A s is the intake valve flow area, and is a set value;

[0082] p s is the pressure of the intake gas before the valve, and is a table value according to the instantaneous crank angle calibration;

[0083] χ to is the average opening degree of the throttle, and is a set value, while being one of the decision variables of the multi-objective optimization;v s is the mass volume of the intake gas, and is a table value according to the instantaneous crank angle calibration;

[0084] To describe the dynamic characteristics of heat release in the cylinder during combustion, the combustion heat release rate equation is introduced:

[0085]

[0086] where Q B is the heat released by combustion;

[0087] η u is the combustion efficiency, which is a set value;

[0088] m B0 is the mass of gas supplied per cycle, which is a set value;

[0089] H u is the lower heating value of the fuel, which is a set value;

[0090] Δφ is the crank angle of the combustion process, which is a simulation output value;

[0091] φ VB is the ignition advance angle, which is a set value and also one of the decision variables for multi-objective optimization;

[0092] z is the combustion mass index, which is a set value;

[0093] It can be seen that, which depends on key factors such as combustion efficiency, fuel lower heating value, and ignition advance angle.

[0094] Combining equations (1) and (2), it can be seen that the heat released by combustion directly affects the thermodynamic state change of the gas in the cylinder.

[0095] Based on the ideal gas state equation, the instantaneous pressure in the cylinder can be expressed as:

[0096]

[0097]

[0098] where V c is the working volume of the cylinder, which is a set value;

[0099] c v is the specific heat capacity in the cylinder, which is a set value;

[0100] R is the gas constant, which is a set value;

[0101] is the heat dissipation rate of the cylinder;

[0102] Q w is the heat dissipation in the cylinder;

[0103] a gThe average heat dissipation coefficient is denoted as , and is a set value.

[0104] A w The heat dissipation area is a set value.

[0105] ΔT is the temperature difference between the working fluid inside the cylinder and the cylinder wall, and is a set value;

[0106] The above formula dynamically correlates combustion heat release with cylinder pressure, serving as the basis for calculating gas pressure torque T. g The key item.

[0107] To obtain the engine's power output, a dynamic model is further introduced.

[0108] Instantaneous torque is derived from reciprocating inertial torque M m and gas pressure torque M g It consists of two parts, represented as follows:

[0109]

[0110]

[0111] Where, m p The equivalent reciprocating mass of the piston, piston rings, piston pin, and connecting rod is a set value.

[0112] r is the crank radius, which is a set value;

[0113] λ s This is the ratio of the crank radius to the connecting rod length, and is a set value;

[0114] t is the crank rotation time, which is a set value;

[0115] d p Where is the piston diameter, and is the set value;

[0116] Combining the cylinder pressure calculated in equation (4), equation (6) describes the direct effect of gas pressure on torque.

[0117] Ultimately, the total torque output by the engine is:

[0118] M e =M m +M g (7)

[0119] Equation (7) is the instantaneous engine output torque M e The final expression fully integrates the thermodynamic and kinetic models.

[0120] Through the logical connections of the above formulas, the influence of multiple parameters such as injection advance angle, combustible mixture formation time, and throttle opening on engine output torque can be quantitatively analyzed.

[0121] Step 3, Establish DMF dynamic model.

[0122] As shown in Figure 3 , the discrete method is used to model the long arc ring helical spring, which is decomposed into an equivalent system composed of multiple masses and short arc springs. Combined with the torsional dynamic equation of the primary and secondary flywheels, the torsional response characteristics of the DMF are derived, and the adjustment effect on the vibration of the power transmission system is analyzed.

[0123] The double-mass flywheel (DMF) model with long arc ring helical spring is composed of three main parts: primary flywheel, long arc ring spring and secondary flywheel. The long arc ring spring on the circumference of the flywheel is continuously compressed and released in the channel, thereby transmitting torque from the primary flywheel to the secondary flywheel.

[0124] The dynamic differential equations of the primary flywheel and the secondary flywheel are as follows:

[0125]

[0126] Where, J d1 and J d2 are the moments of inertia of the primary flywheel and the secondary flywheel, respectively;

[0127] θ1 is the torsional angle of the primary flywheel, θ2 is the torsional angle of the secondary flywheel, and is the simulation output value;

[0128] k d is the equivalent spring stiffness, which is a set value;

[0129] γ0, γ1, γ n are the central angles of the discrete short springs when not compressed, the central angle of the first equivalent spring deformation, and the central angle of the nth equivalent spring deformation, respectively, and are simulation output values;

[0130] M d2 is the output torque of the secondary flywheel, and is the simulation output value;

[0131] M seal is the damping force caused by the sealing element between the primary flywheel and the secondary flywheel, which is a table value calibrated according to the instantaneous crank angle;

[0132] Step 4, Construct CPVA dynamic model and pendulum knocking power analysis model.

[0133] As shown in Figure 4 , considering that there are two identical pendulums installed on the rotor in the CPVA, the motion trajectory is an epitrochoid, where X-Y is a fixed coordinate system on the rotor shaft, and x i -y i is a non-fixed coordinate system rotating with the pendulum.

[0134] Considering the superposition of the centrifugal force field and the gravitational field, the differential equations of motion for the rotor and the pendulum, based on the second kind of Lagrange equation, are as follows:

[0135]

[0136] Where α is the rotation angle of the rotor, and is the simulation output value;

[0137] S i For the transient displacement of the pendulum, the pendulum is defined in y i S on the axis i =0, which is the simulation output value; in addition, S at t=0 i As one of the decision variables in multi-objective optimization;

[0138] E is the kinetic energy of the system, and is the calculated value obtained according to the existing formula;

[0139] V is the potential energy of the system, and is the calculated value obtained according to the existing formula;

[0140] U p Let be the elastic potential energy of the limiting mechanism, and be the calculated value obtained according to the existing formula;

[0141] i is the pendulum number;

[0142] μ α is the viscous damping coefficient of the rotor, and is a set value;

[0143] M d1 The excitation torque acting on the rotor is denoted as , and is the simulation output value.

[0144] μ si is the viscous damping coefficient of the pendulum, and is a set value;

[0145] μ ri is the rolling damping coefficient of the pendulum, and is a set value;

[0146] F ni Let be the normal force acting on the pendulum, and be the calculated value obtained based on the existing formula;

[0147] To compare the performance of the pendulum under startup conditions, the striking power of the pendulum is defined as an indicator of the strength of the pendulum's impact on the limiting mechanism.

[0148] Constructing a pendulum striking power analysis model:

[0149] A mathematical expression for the pendulum's striking power is defined to describe its dynamic response under different start-up conditions. The average striking power and peak striking power of the pendulum are incorporated into the evaluation index of multi-objective optimization through normalization.

[0150] Peak hitting power of pendulum ω2 and average hitting power The calculation formula is as follows:

[0151]

[0152]

[0153] Wherein, P ij is the hitting power of the i-th pendulum at the j-th time;

[0154] S ij is the displacement of the i-th pendulum at the j-th hitting, which is the simulation output value;

[0155] S pi is the position of the pendulum limiting mechanism, which is a set value, and its reference coordinate system is consistent with S i .

[0156] k si is the stiffness of the pendulum limiting mechanism, which is a set value;

[0157] t start and t end are the start and end times of the hitting, respectively, which are set values;

[0158] Q is the sum of the number of times that all pendulums hit the limiting mechanism according to the time history, and N is the number of pendulums.

[0159] Step 5, modeling the dynamics model of the transmission input shaft.

[0160] The end of the power transmission system is the transmission input shaft.

[0161] The motion differential equation of the input shaft is as follows:

[0162]

[0163] Wherein, J s is the moment of inertia, which is a set value;

[0164] is the angular velocity of the input shaft, which is a simulation output value;

[0165] k s is the equivalent stiffness, which is a set value;

[0166] c s is the equivalent damping coefficient, which is a set value;

[0167] M r is the load torque, which is a set value;

[0168] The torsional dynamics equation of the drive shaft is established, the transient torsional vibration response of the engine starting stage is analyzed, the inertia parameters, equivalent damping coefficient and load torque of the input shaft are defined, and the influence of the dynamic characteristics on the performance of the overall drive system is quantified.

[0169] Step 6, define the parameters in multi-objective optimization.

[0170] The peak factor (CF) of the transmission input shaft angular acceleration and the knock index (KI) of the CPVA are selected as the objective functions, the five parameters of the spark advance angle, the fuel injection advance angle, the idle throttle opening, and the pendulum starting position are selected as the decision variables, and a multi-objective optimization problem is constructed.

[0171] The embodiment focuses on the dynamic behavior of the power transmission system during the engine starting process, and aims to minimize the knock power generated by the CPVA pendulum and the torsional vibration of the drive system input shaft by optimizing the combination of system parameters.

[0172] Through numerical simulation of the system model, the initial pendulum position of the optimization is determined. The angular acceleration amplitude spectrum of different initial positions is calculated, and the positions with large angular acceleration amplitude are preferentially optimized.

[0173] The first objective function is to minimize the peak factor CF of the transmission input shaft angular acceleration, and the calculation formula is as follows:

[0174]

[0175] wherein, is the peak value of the transmission input shaft angular acceleration;

[0176] is the root mean square value of the transmission input shaft angular acceleration.

[0177] The second objective function is to minimize the knock index (KI) considering the dynamic characteristics of the CPVA, and the calculation formula is as follows:

[0178]

[0179] wherein, and are the normalized values of the peak knock power and the average knock power in formula (12) and formula (13), respectively.

[0180] The maximum-minimum value method is selected for normalization.

[0181] ω1 and ω2 represent the weights of the peak and average values, respectively, and are set values.

[0182] Five key parameters of the engine and the CPVA are selected as decision variables in multi-objective optimization. Table 1 shows all decision variables and the value range of the defined decision variables.

[0183] Table 1 All decision variables and the range of values defining the decision variables

[0184]

[0185] Step 7, design of the target optimization algorithm.

[0186] By using the improved non-dominated sorting genetic algorithm (MNSGA-II), the better Pareto solution set is found in the multi-objective optimization problem by dynamically adjusting the population size and diversity preservation strategy, avoiding the problems of premature convergence of the population and uneven distribution of optimization solutions.

[0187] As shown in Figure 5 , the optimization process starts with the initial parameter setting, and the population diversity is realized by generating the initial population and using crossover and mutation operations. Then, fitness evaluation is carried out, and the selection and retention of the optimal individual are determined by using the non-dominated sorting and crowding degree calculation of the merged population. After the initial optimization, further local search is carried out for the five decision variables in Table 1 to improve the globality and stability of the solution. Finally, through multiple iterations, the optimization results are output until the convergence condition is met. The whole process fully combines the global search ability of genetic algorithm with the engineering constraint characteristics of the problem itself, effectively improving the efficiency and accuracy of parameter optimization.

[0188] Step 8, numerical verification of the optimization results.

[0189] Based on multi-body dynamics simulation, the improvement effect of the optimization design on the vibration characteristics of the system is verified, and the Figure 6 Pareto front solution in the above is substituted into the dynamic transmission system model, and the improvement of the swing child knocking power and the torsional vibration response of the transmission system after optimization is analyzed, to prove the effectiveness and feasibility of the optimization model.

[0190] The above is only the preferred embodiment of the present application, and does not limit the present application in any way. Any person skilled in the art, without departing from the scope of the technical solutions of the present application, can make any form of equivalent replacement or modification of the technical solutions and technical contents disclosed in the present application, and still belong to the protection scope of the present application.

Claims

1. A method for parameter optimization design of power transmission system equipped with centrifugal pendulum vibration absorber, characterized in that, The method comprises the following steps: Step 1, establishing a power transmission system model with a centrifugal pendulum absorber; Wherein, the power transmission system model comprises an engine, a dual mass flywheel DMF and a transmission input shaft connected in sequence; the centrifugal pendulum absorber CPVA is arranged on the dual mass flywheel DMF; Step 2, constructing an engine thermodynamics and dynamics model; Step 3, constructing a DMF dynamics model; Step 4, constructing a CPVA dynamics model and a pendulum knocking power analysis model; Step 5, constructing a dynamics model of the transmission input shaft; Step 6, defining decision variables and objective functions in multi-objective optimization: The decision variables include: several parameters in the engine thermodynamics and dynamics model and the CPVA dynamics model; The objective functions include objective function one and objective function two; Objective function one is to minimize a peak factor of the transmission input shaft angular acceleration CF Objective function two is to minimize a jerk index of the CPVA KI ; wherein the CPVA has a knock index of KI generated based on a pendulum knock power analysis model; Step 7, optimizing the decision variables by using MNSGA-II; In step 6, the decision variables include: the ignition advance angle, the fuel injection advance angle, the average throttle opening, the time of forming combustible mixture in the engine thermodynamics and dynamics model and the pendulum transient position at the start of the vehicle in the CPVA dynamics model; In step 6, the objective function one is: ； wherein, is the peak value of the transmission input shaft angular acceleration; the root mean square value of the angular acceleration of the transmission input shaft; In step 6, the objective function two is: ； ； ； and normalized values of peak tap power and average tap power respectively; and denote the weight of peak and average value, respectively; is the first pendulum at the first knock power; is the displacement of the th pendulum at the th tap, which is the simulation output value; For the pendulum position limiting mechanism, the setting value; R is the rigidity of the pendulum limiting mechanism, which is a set value; and are the time instants of the beginning and end of the tap, respectively, and are set values. to sum all the number of times the escapement has been limited as a function of time; is the number of pendulums.

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