A method for optimization of anti-cam mechanism profile and evaluation of dynamic stability

Abstract

The application discloses a method for optimizing a reverse cam mechanism profile and evaluating dynamic stability, comprising the following steps: constructing a simple harmonic motion cam profile equation containing parameter correction based on the motion law of a crank slider mechanism; establishing a four-degree-of-freedom dynamic equation containing time-varying contact stiffness of the reverse cam mechanism based on Newton's second law; calculating the gas pressure and gas stiffness in the cylinder by using the ideal gas polytropic process theory; calculating the curvature radius of each point of the cam profile equation, and constructing a stiffness matrix of the reverse cam mechanism in combination with the time-varying contact stiffness and the gas stiffness; solving the four-order time-varying natural frequency of the reverse cam mechanism corresponding to the stiffness matrix, and analyzing the unstable domain under parameter excitation by using the Floquet theory to determine the parameter value range of the simple harmonic motion cam profile equation containing the parameter correction.

Description

Technical Field

[0001] This invention relates to the field of dynamics of anti-cam mechanisms, and more particularly to a method for optimizing the profile and evaluating the dynamic stability of anti-cam mechanisms. Background Technology

[0002] A cam mechanism is a common high-pair mechanism that uses a cam with a specific profile curve as the driving element to push a driven element in contact with it, converting the rotational motion of the driving element into the reciprocating linear motion or oscillation of the driven element. Its design methods are relatively mature and it is widely used in internal combustion engine valve trains, precision instruments, and high-speed automated equipment. However, in practical engineering applications, some mechanical equipment needs to achieve the reverse motion conversion of "oscillating or linear motion driving rotational motion." Against this backdrop, the reverse cam mechanism, as a motion reversal form of the conventional cam mechanism, has emerged. By reversing the motion relationship, it uses a rocker arm or slider as the driving element to drive the cam to achieve rotation or movement, filling the application gap of conventional cam mechanisms in reverse motion conversion scenarios.

[0003] The reverse cam mechanism inherits the advantages of conventional cam mechanisms, such as compact structure and strong motion controllability. Its fundamental feature lies in the reversal of motion relationships: the cam, originally the driving element, is fixed as part of the frame, while the prismatic pair, originally equipped with the driven element, becomes the driving input element. When the driving element moves along a predetermined trajectory, its rollers move along the groove contour of the fixed cam, thus transforming the linear or simple motion of the driving element into the complex rotation or specific compound motion of the output shaft. In the reverse cam mechanism, the design of the cam profile directly affects combustion characteristics, motion laws, and dynamic characteristics. Improper profile design can lead not only to incomplete combustion, decreased thermal efficiency, increased exhaust emissions, and reduced work efficiency, but also to abrupt changes in motion laws, generating significant residual vibration and impact, causing cam disc detachment or piston cylinder scoring, and accelerating component wear. Summary of the Invention

[0004] The purpose of this invention is to overcome the shortcomings of existing technologies and provide a method for optimizing the profile and evaluating the dynamic stability of an anti-cam mechanism. First, a four-degree-of-freedom dynamic model considering time-varying contact stiffness is established based on Newton's second law, and the gas pressure and stiffness under different cam profiles are solved based on the polytropic process of an ideal gas. Second, the radius of curvature at each point of the cam profile is calculated using the formula for the radius of curvature of a space curve, thereby constructing a stiffness matrix. Based on this, the time-varying natural frequencies under different profiles are solved. Finally, Floquet theory is used to solve the parametric instability domain at different rotational speeds, and a reasonable range of values ​​for the variable parameters is given.

[0005] The objective of this invention is achieved through the following technical solution: A method for optimizing the profile and evaluating the dynamic stability of an anti-cam mechanism includes: Based on the motion law of the crank-slider mechanism, the equation of the cam profile with parameter correction is constructed. Based on Newton's second law, a four-degree-of-freedom dynamic equation is established that includes the time-varying contact stiffness of the anti-cam mechanism; The combustion pressure and combustion stiffness inside the cylinder are calculated using the ideal gas polytropic process theory. Calculate the radius of curvature at each point of the cam profile equation, and construct the stiffness matrix of the anti-cam mechanism by combining the time-varying contact stiffness and the gas stiffness; The fourth-order time-varying natural frequency of the inverse cam mechanism corresponding to the stiffness matrix is ​​solved, and the unstable domain under parameter excitation is analyzed using Floquet theory. The parameter range of the simple harmonic motion cam profile equation with parameter correction is determined by integrating thermodynamic, kinematic and dynamic evaluation criteria.

[0006] Furthermore, the equation for the simple harmonic motion cam profile with parameter correction is: ; in, For cam rotation angle, λ This is a variable parameter, with a value range of 0 to 1; The characteristic equation of a four-degree-of-freedom dynamic is: ; In the formula , , ; ; In the formula, For the mass of the piston and roller, For the quality of the cam disc, This represents the axial vibration displacement of the piston, with upward movement being positive. Let be the moment of inertia of the cam. This refers to the angular displacement of the cam due to torsional vibration. The time-varying contact stiffness between the roller and the cam. For gas stiffness, This refers to the contact stiffness between the piston and the cylinder wall. Axial stiffness between the cam, thrust bearing, and drive shaft. The torsional stiffness between the cam and the drive shaft; To guide friction and fluid resistance The combined force The periodic cylinder pressure force varies with the rotation angle. The output torque of the cam;l For the length of the roller, d This is the distance from the small end face of the roller to the central axis of the cam. The contact angle between the roller and the cam. This refers to the tangential vibration displacement of the piston along the circumference of the cam. This represents the axial vibration displacement of the cam. The linear displacement and angular displacement of the torsional vibration of the cam are given. .

[0007] Furthermore, the time-varying contact stiffness is expressed as: ; In the formula, Roller radius , Let be the instantaneous radius of curvature of the cam. L The contact length between the roller and the cam surface. E Let be the equivalent elastic modulus of the roller and the cam. F The normal load on the roller caused by the gas pressure.

[0008] Furthermore, the fourth-order time-varying natural frequency of the reverse cam mechanism is solved by applying the generalized eigenvalue decomposition method. Specifically, this includes selecting several cam corner points at equal intervals within one period, calculating the instantaneous stiffness matrix of each corner point, and solving the four-degree-of-freedom dynamic characteristic equation to obtain the fluctuation range of the fourth-order time-varying natural frequency of the reverse cam mechanism.

[0009] Furthermore, the unstable region under parameter excitation is analyzed using Floquet theory, specifically including: constructing a periodic matrix containing state variables and their first derivatives; constructing a transformation matrix using the periodic matrix according to Floquet theory; and determining the stability of the anti-cam mechanism based on the real part of the characteristic exponent.

[0010] Furthermore, in the process of determining the parameter range of the equation for the profile of a simple harmonic motion cam with parameter correction, By comparing the time-varying natural frequency fluctuation range, instability range, and instability degree corresponding to the cam profile motion law under different parameter values, and by comprehensively considering thermodynamic, kinematic, and dynamic evaluation criteria, the parameters are determined. λ The value range is 0.5 to 0.8.

[0011] The present invention also provides a device for optimizing the profile and evaluating the dynamic stability of an anti-cam mechanism, comprising: The module for constructing the simple harmonic motion cam profile equation is used to construct the simple harmonic motion cam profile equation with parameter correction based on the motion law of the crank-slider mechanism. The dynamic equation construction module is used to establish a four-degree-of-freedom dynamic equation that includes the time-varying contact stiffness of the anti-cam mechanism based on Newton's second law. The calculation module is used to calculate the gas pressure and gas stiffness inside the cylinder using the ideal gas polytropic process theory; The stiffness matrix construction module is used to calculate the radius of curvature at each point of the cam profile equation and construct the stiffness matrix of the anti-cam mechanism by combining the time-varying contact stiffness and the gas stiffness. The instability domain determination module is used to solve for the fourth-order time-varying natural frequency of the inverse cam mechanism corresponding to the stiffness matrix, and to analyze the instability domain under parameter excitation using Floquet theory. It also determines the parameter range of the simple harmonic motion cam profile equation with parameter correction by integrating thermodynamic, kinematic and dynamic evaluation criteria.

[0012] The present invention also provides an electronic device, including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the computer program to implement the steps of the method for optimizing the profile and evaluating the dynamic stability of the anti-cam mechanism.

[0013] The present invention also provides a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the steps of the method for optimizing the profile and evaluating the dynamic stability of the anti-cam mechanism.

[0014] Compared with the prior art, the beneficial effects of the technical solution of the present invention are: 1. To address the problem that existing reverse cam profiles easily lead to low combustion efficiency and discontinuous acceleration, resulting in residual vibration and impact, this invention constructs a cam profile equation with parameter-corrected simple harmonic motion by drawing on the motion law of crank-slider mechanisms. Furthermore, based on Newton's second law, a four-degree-of-freedom dynamic equation with time-varying contact stiffness is established. This cam profile equation exhibits excellent thermodynamic and kinematic characteristics within a specific parameter range (…). λ The acceleration is continuous and the jump value is small (0.5~0.8), which avoids the violent impact during the operation of the mechanism and improves the dynamic performance and combustion efficiency of the anti-cam mechanism.

[0015] 2. To address the problems of crude gas pressure calculations in existing technologies, which fail to accurately reflect the in-cylinder combustion process, leading to incomplete combustion, decreased thermal efficiency, and increased emissions, this invention innovatively introduces the theory of ideal gas polymorphic processes into gas pressure calculations. Simulation verification was performed using AVL BOOST software. A time-varying stiffness matrix was constructed based on gas stiffness, and Floquet theory was used to analyze the unstable domain under parameter excitation. This accurately reveals the influence of profile parameters on the dynamic characteristics of the anti-cam mechanism, expands the analytical methods for the dynamic characteristics of the anti-cam mechanism, and improves the accuracy and computational efficiency of dynamic characteristic analysis.

[0016] 3. Addressing the lack of clear dynamic characteristic evaluation standards in existing anti-cam mechanism designs, the time-varying natural frequency solution and profile comparison analysis framework proposed in this invention possesses universality. By accurately identifying the parametric instability domains at different speeds, it provides clear parameter value criteria for the efficient design and reliability improvement of anti-cam mechanisms, achieving accurate prediction of dynamic response. Furthermore, by comparing the fourth-order time-varying natural frequencies and instability domains of different cam profiles, the universality and effectiveness of the method presented in this invention are verified, facilitating its application in engineering practice.

[0017] In summary, this invention proposes a variable-parameter inverse cam profile equation based on existing profiles. This equation addresses existing technical problems by achieving more complete combustion of fuel gas to improve work efficiency, smoothing the motion, and suppressing vibration and impact to reduce wear. Based on thermodynamic and kinematic evaluation standards, the dynamic characteristics of this profile are analyzed, and the range of values ​​for the variable parameters is given. Attached Figure Description

[0018] Figure 1-1 This is a schematic diagram of the model corresponding to the profile equation of a variable-parameter inverse cam mechanism proposed in this invention. Figure 1-2 Figures (a) to (d) are schematic diagrams of piston displacement, velocity, acceleration and jump curves corresponding to the profile equation of the anti-cam mechanism proposed in this invention. Figure 2 A schematic diagram of the profile equation of an ideal anti-cam mechanism provided by the present invention; Figure 3-1 This is a schematic diagram of the coordinate system of the anti-cam mechanism provided by the present invention; Figure 3-2 A piston force diagram provided according to the present invention; Figure 4 This is a schematic diagram of the four-degree-of-freedom equivalent dynamic model provided by the present invention; Figure 5-1 This invention provides a cylinder pressure-volume relationship diagram based on an ideal gas polytropic process. Figure 5-2 This is a comparison chart of the AVL BOOST simulation results and the theoretical calculation results provided by the present invention; Figure 5-3 This is a comparison diagram of gas pressure under different cam profile equations provided by the present invention; Figure 6 The fourth-order time-varying natural frequency diagram of the anti-cam mechanism under sinusoidal family, simple harmonic modified shape, cycloid and simple harmonic type lines provided by the present invention; Figure 7-1The present invention provides a parametric instability domain diagram for an anti-cam mechanism under sinusoidal family, simple harmonic modified shape, cycloid and simple harmonic type lines. Figure 7-2 The diagram shows the para-excited instability region of the anti-cam mechanism under a simple harmonic profile with different parameter values ​​provided by the present invention. Detailed Implementation

[0019] The present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments. It should be understood that the specific embodiments described herein are only for explaining the present invention and are not intended to limit the present invention.

[0020] Example 1 This embodiment discloses a method for optimizing the profile and evaluating the dynamic stability of an anti-cam mechanism, including: S1. Based on the motion law of the crank-slider mechanism, construct the simple harmonic motion cam profile equation with parameter correction; the simple harmonic motion cam profile equation with parameter correction is: ; in, For cam rotation angle, λ This is a variable parameter, with a value range of 0 to 1; Figure 1-1 This is a schematic diagram illustrating the variation law of the cam profile equation with parameter correction. Figure 1-2 Figures (a) to (d) are schematic diagrams of the piston displacement, velocity, acceleration, and jump curves corresponding to the profile equation of this inverse cam mechanism. Figure 2 The curve showing the variation of the ideal profile equation of the reverse cam mechanism can be seen as it changes with the parameters. λ As the coefficient of performance increases, the profile changes become increasingly gentle during the intake and exhaust phases, followed by a rise in slope and a faster curve change. This is beneficial for the mixing and combustion of oil and gas, and its motion pattern conforms to the requirements of thermodynamic design. When the parameters... λ When the value increases, the jump value of the acceleration curve at the point of abrupt change in slope rises significantly, indicating that the impact of the anti-cam mechanism is relatively severe; while when λ is less than 0.9, the jump value decreases significantly, and the impact is within an acceptable range.

[0021] S2. Based on Newton's second law, establish a four-degree-of-freedom dynamic equation that includes the time-varying contact stiffness of the anti-cam mechanism; Figure 3-1 This is a schematic diagram of the coordinate system of the anti-cam mechanism. Figure 3-2 This is a schematic diagram of a piston. Figure 4 The equivalent dynamic model of the inverse cam mechanism is given; according to Newton's second law, the differential equation of the four-degree-of-freedom inverse cam mechanism can be expressed as: ; In the formula , , ; ; In the formula, For the mass of the piston and roller, Let be the moment of inertia of the cam. For the cam disc mass; The contact stiffness between the roller and the cam. For gas stiffness, This refers to the contact stiffness between the piston and the cylinder wall. Axial stiffness between the cam, thrust bearing, and drive shaft. The torsional stiffness between the cam and the drive shaft; To guide friction and fluid resistance The combined force The periodic cylinder pressure force varies with the rotation angle. This is the output torque of the cam. l For the length of the roller, d This is the distance from the small end face of the roller to the central axis of the cam. The contact angle between the roller and the cam; This represents the axial vibration displacement of the piston. This refers to the tangential vibration displacement of the piston along the circumference of the cam. This represents the axial vibration displacement of the cam. The linear displacement and angular displacement of the torsional vibration of the cam are given. .

[0022] S3. The gas pressure and gas stiffness inside the cylinder were calculated using the ideal gas polytropic process theory, and the results were verified by simulation using AVLBOOST software.

[0023] Engineering thermodynamics states that during most of the engine's operation, the fundamental state parameters of the gas satisfy the following: ; In the formula, This refers to the instantaneous pressure of the gas inside the cylinder. This refers to the instantaneous volume of gas inside the cylinder. is the variable coefficient.

[0024] The various processes in thermal equipment can be approximated as isochoric, isobaric, isothermal, and adiabatic processes. For the sake of simplification, irreversible losses in the actual process are temporarily disregarded and treated as reversible processes.

[0025] In reality, the change in the working fluid state within the cylinder of the anti-cam mechanism is a continuous and complex non-equilibrium thermodynamic process with a high polytropic coefficient. The heat release efficiency during combustion and the heat transfer boundary conditions of the cylinder wall change in real time, reflecting the heat exchange characteristics between the anti-cam mechanism and the external environment. To construct an analytical model that facilitates dynamic solution, this embodiment simplifies the working process into a segmented process controlled by different polytropic coefficients based on the Schmidt cycle theory.

[0026] Based on the two-stroke operating characteristics of this mechanism, a complete working cycle is divided into the following four stages: Polymorphic compression stage: During this stage, the piston moves from bottom dead center to top dead center. At this time, the intake and exhaust ports are closed, and the working fluid is compressed. The polytropic coefficient of ideal air... Therefore, when the heliotropic coefficient During compression, the process is adiabatic, meaning the cylinder wall does not exchange heat with the outside environment. In actual operation, during the initial compression phase, the cylinder wall is hotter than the gas, causing the gas to absorb heat. At this time, the heliotropy... During the later stages of compression, the gas is hotter than the cylinder wall, at which point the polytropic coefficient increases. In summary, considering the slight leakage caused by poor cylinder wall sealing, the average compression polytropic coefficient is selected. [Reference: Zhou Longbao. Internal Combustion Engine].

[0027] At this point, the pressure equation is: ; P atm Atmospheric pressure, This refers to the instantaneous volume of the cylinder. This is the maximum volume of the combustion chamber; Constant volume combustion stage: In an ideal combustion cycle, this stage of combustion is assumed to be completed at the instant of top dead center. At this point, the cylinder volume remains constant, and the pressure increases from the pressure at the end of compression. The pressure suddenly increased to the maximum. In actual simulations, this process is treated as a sustained combustion rotation near top dead center. Rapid pressure transitions within a given range are replaced by smooth curves.

[0028] ; In the formula , ; P max This is the maximum combustion pressure that occurs within the cylinder. The compression ratio is defined below.

[0029] Variable expansion phase: During this stage, the piston moves from top dead center to bottom dead center. The high-temperature, high-pressure combustion gas pushes the piston to do work, and the gas intensely dissipates heat to the cylinder walls. However, combustion does not end instantaneously at top dead center; instead, there is a delayed combustion phenomenon. In the initial stage of expansion, the gas temperature continues to rise, but overall, the temperature trend is downward, although the rate of temperature decrease is slightly slower than in an adiabatic process. Therefore, the average polytropic coefficient of expansion is selected as... [Reference: Zhou Longbao. Internal Combustion Engine].

[0030] The pressure equation at this point is: ; In the formula ; This refers to the cylinder volume at the start of combustion.

[0031] The fourth stage is the exhaust transition stage, which simulates the rapid drop in cylinder pressure after the exhaust valve opens. A linear weighted transition function is introduced. In the formula , Given the exhaust advance angle, the relationship between cylinder pressure and volume can be obtained, see... Figure 5-1 .

[0032] In summary, the gas pressure curve is a periodic function formed by splicing two variable curves: compression and expansion.

[0033] Let the cross-sectional area of ​​the cylinder be... Piston lift is H The piston displacement function is The minimum volume of the combustion chamber is When the piston moves downwards, the instantaneous volume of the cylinder... for: ; Introducing compression ratio , Substituting into the above equation, we get: ; The analytical expression for gas pressure is: ; According to gas stiffness The definitions include: ; In the formula: ; To verify the correctness of the above gas pressure model, a single-cylinder thermodynamic coupling model was established using AVL BOOST software. First, the engine structural parameters (bore, stroke, compression ratio), initial boundary conditions, and key combustion process parameters from the theoretical gas pressure model were passed to this model as input. This model is based on the first law of thermodynamics for variable mass systems, integrates the Vibe two-stage combustion model and the Woschni instantaneous heat transfer model, and iteratively solves the instantaneous in-cylinder pressure within a complete working cycle using one-dimensional gas dynamics equations. The specific fitting parameter values ​​for the theoretical and simulation models are shown in Table 1.

[0034] Table 1. Basic parameters for gas pressure fitting; Figure 5-2 The figure shows a comparison between the simulation results of AVL BOOST and the theoretical model. According to the results, the peak gas pressure angle of the simulation model is slightly earlier, the transition process is smoother, and the peak gas pressure is slightly lower. However, the difference between the two is not significant. Therefore, the theoretical formula can be used to calculate the gas pressure under different profiles.

[0035] Figure 5-3 A comparison chart of gas pressure under different cam profile equations shows that, for example... k Variable family of sine curves with smaller values, λ Curves with larger harmonic profile values, where piston displacement changes more slowly in the initial stage, show a slower decrease in combustion pressure. This indicates that if the cylinder volume changes too rapidly at the initial moment, the combustion pressure will drop rapidly, and the fuel and air will enter the later stages of expansion before they are fully mixed and combusted, thus reducing engine efficiency. Conversely, curves with slower displacement changes in the initial stage can maintain a longer pressure plateau period, providing more favorable thermodynamic conditions for uniform mixing and complete combustion of fuel and air, thus helping to improve engine thermal efficiency. Therefore, the novel harmonic profile equation proposed in this invention has better thermodynamic performance.

[0036] S4. Calculate the radius of curvature at each point of the cam profile equation to solve for the contact stiffness, and construct the stiffness matrix of the four-degree-of-freedom reverse cam mechanism by combining the time-varying contact stiffness of the reverse cam mechanism and the gas stiffness. Coordinates of the contact point between the piston roller and the cam It can be represented as: ; Expanding the equation of the convex profile along the circumference, we can transform it into an expression for a curve in a Cartesian coordinate system: ; ; Contact angle The expression: ; coordinate transformation matrix for: ; The spatial curve equation of the contact point can then be expressed as: ; The velocity and acceleration at that point can then be expressed as: ; ; Its acceleration can be decomposed into two parts: one is the tangential acceleration parallel to the velocity direction, and the other is the normal acceleration perpendicular to the velocity direction.

[0037] The equation for circular motion is: ; in Normal acceleration, Instantaneous velocity This is the required radius of curvature.

[0038] The magnitude of tangential acceleration is the projection of the acceleration vector onto the velocity vector. The magnitude of tangential acceleration can be calculated using the rules of vector operations: ; The magnitude of the normal acceleration is: ; Then the radius of curvature : ; The principal normal direction of the space curve is: ; For a cylindrical cam, the outward normal of the surface at the contact point, along the radial direction of the cylinder, can be represented as: ; By comparing the principal normals of the curves and the outer normal of the cam surface The sign of the radius of curvature can be determined by its relative direction. ; The radius of curvature can then be obtained.

[0039] Time-varying contact stiffness can be expressed as: ; In the formula, Roller radius , Let be the instantaneous radius of curvature of the cam. L The contact length between the roller and the cam surface. E Let be the equivalent elastic modulus of the roller and the cam. F The normal load on the roller caused by the gas pressure.

[0040] S5. Solve for the fourth-order time-varying natural frequency of the four-degree-of-freedom inverse cam mechanism corresponding to the stiffness matrix, and use Floquet theory to analyze the unstable domain under parameter excitation, so as to analyze the advantages and disadvantages of the dynamic characteristics of the modified harmonic motion cam profile equation under different parameter values.

[0041] Contact stiffness Gas stiffness and contact angle All have been determined, and the stiffness matrix of the anti-cam mechanism can be established. K Select the corner. From 0 to For multiple discrete points, the instantaneous stiffness matrix corresponding to each rotation position is calculated, and the time-varying natural frequency of the reverse cam mechanism at that moment is solved by the generalized eigenvalue decomposition method: In the formula, K Here is the stiffness matrix. M For the quality matrix, Φ n Given the modal vectors, the time-varying natural frequencies under different profiles can be calculated using the above formula. The values ​​of each parameter are shown in Table 2.

[0042] Table 2. Values ​​of basic parameters for the dynamic equations; The time-varying natural frequency ranges under different cam-type lines were obtained, such as... Figure 6 As shown in Table 3.

[0043] Table 3. Time-varying natural frequency range under different cam types; It can be observed that for simple harmonic shaping curves, the parameters λ The effect of the natural frequency of the reverse cam mechanism exhibits a relationship with the sinusoidal family of parameters. k Completely opposite evolutionary trends. With λAs the value increases from 0 to 0.9, the fluctuation range of the low-order natural frequencies of the anti-cam mechanism becomes significantly more divergent. Specifically, the lower limit of the first-order natural frequency drops sharply from 0.9361 to 0.8732, widening the bandwidth in the low-frequency range and increasing the time-varying instability of the anti-cam mechanism in low-frequency modes. Simultaneously, the fluctuation range of the fourth-order natural frequency shows a converging trend, with its fluctuation range becoming increasingly smaller. Furthermore, with the parameter... λ As the value increases, the fluctuation range of the higher-order natural frequencies of the anti-cam mechanism decreases significantly, while the fluctuation range of the lower-order natural frequencies increases slowly, indicating that the lower-order frequencies have a greater impact on the parameters. λ Its sensitivity is low.

[0044] To explore the dynamic characteristics of the novel profile, Floquet theory is used to solve the instability region of the reverse cam mechanism.

[0045] ; In the formula , , ; It is an 8×1 matrix containing the state variables and their first derivatives. It is an 8×8 periodic matrix with a period of . Take the damping ratio According to Floquet theory, a transformation matrix can be constructed using a periodic matrix, and then the stability of the anti-cam mechanism can be determined based on the real part of the characteristic exponent. The instability regions for different profiles are as follows: Figure 7-1 and Figure 7-2 As shown, it can be observed that with the parameter λ As the value increases, the fluctuation range of the first three natural frequencies of the anti-cam mechanism will increase, while the fluctuation range of the fourth natural frequency will decrease. Furthermore, with the increase of parameters... λ As the frequency increases, the instability region of the anti-cam mechanism increases at low excitation frequencies, but the degree of instability in the instability region decreases. From Figure 5-3 It can be seen that when the parameter λ When the gas pressure drops to 0.8, the gas pressure decreases relatively slowly, which is consistent with existing profiles ( λ Compared to (=0), its gas pressure drop process is delayed by approximately T / 8 cycles; from Figure 1-2 It can be seen that when the parameter λ When the acceleration is 0.8, the acceleration curve is continuous, with a jump value of approximately 10, while the existing profile ( λ When the jump value is 3 (=0), both are at a low level, indicating a small impact. Therefore, considering thermodynamic, kinematic, and dynamic evaluation indicators, the parameters of the novel anti-cam mechanism profile described in this invention are... λThe value range can be 0.5~0.8. Within this parameter range, the peak duration of the profile gas pressure is long, the combustion efficiency is high, and the acceleration curve is continuous with a small jump value, so there will be no impact. Its dynamic performance is also excellent.

[0046] In summary, this embodiment establishes a four-degree-of-freedom dynamic model considering time-varying contact stiffness, solves for the gas pressure and stiffness under different cam profiles based on the polytropic process of an ideal gas, and calculates the radius of curvature at each point of the cam profile using the formula for the radius of curvature of a space curve, thereby constructing a time-varying stiffness matrix. The fourth-order time-varying natural frequency of the inverted cam mechanism is solved using the generalized eigenvalue decomposition method; further, Floquet theory is applied to analyze the parametric instability domain at different speeds, identifying the instability region of the inverted cam mechanism. The study found that the variation of the variable parameters has a significant impact on the dynamic characteristics of the inverted cam mechanism. Comparative analysis with various typical cam profiles such as sinusoidal, harmonic, polynomial, and cycloidal cam profiles verifies the universality and effectiveness of the method of this invention. Based on this, a reasonable range of values ​​for the variable parameters is given, providing a theoretical basis and technical support for the efficient design of the inverted cam mechanism.

[0047] Example 2 Based on the same inventive concept, this application also provides a device for optimizing the profile and evaluating the dynamic stability of an anti-cam mechanism, which can be used to implement the method described in the above embodiments, specifically including the following: The module for constructing the simple harmonic motion cam profile equation is used to construct the simple harmonic motion cam profile equation with parameter correction based on the motion law of the crank-slider mechanism. The dynamic equation construction module is used to establish a four-degree-of-freedom dynamic equation that includes the time-varying contact stiffness of the anti-cam mechanism based on Newton's second law. The calculation module is used to calculate the gas pressure and gas stiffness inside the cylinder using the ideal gas polytropic process theory; The stiffness matrix construction module is used to calculate the radius of curvature at each point of the cam profile equation and construct the stiffness matrix of the four-degree-of-freedom inverse cam mechanism by combining the time-varying contact stiffness and the gas stiffness. The instability domain determination module is used to solve for the fourth-order time-varying natural frequency of the four-degree-of-freedom inverse cam mechanism corresponding to the stiffness matrix, and to analyze the instability domain under parameter excitation using Floquet theory, so as to determine the parameter value range of the simple harmonic motion cam profile equation with parameter correction.

[0048] Preferably, embodiments of this application also provide a specific implementation of an electronic device capable of implementing all steps in the anti-cam mechanism profile optimization and dynamic stability evaluation method described in the above embodiments. The electronic device specifically includes the following: Processor, memory, communications interface, and bus; The processor, memory, and communication interface communicate with each other via a bus; the communication interface is used to realize information transmission between server-side devices, metering devices, and user-side devices.

[0049] The processor is used to call the computer program in the memory. When the processor executes the computer program, it implements all the steps in the method for optimizing the profile and evaluating the dynamic stability of the anti-cam mechanism in the above embodiments.

[0050] Embodiments of this application also provide a computer-readable storage medium capable of implementing all steps of the method for optimizing the profile and evaluating the dynamic stability of the anti-cam mechanism in the above embodiments. The computer-readable storage medium stores a computer program that, when executed by a processor, implements all steps of the method for optimizing the profile and evaluating the dynamic stability of the anti-cam mechanism in the above embodiments.

[0051] The various embodiments in this specification are described in a progressive manner. Similar or identical parts between embodiments can be referred to interchangeably. Each embodiment focuses on its differences from other embodiments. In particular, hardware + program embodiments are relatively simple in description because they are fundamentally similar to method embodiments; relevant parts can be referred to the descriptions in the method embodiments.

[0052] While this application provides method operation steps as shown in the embodiments or flowcharts, more or fewer operation steps may be included based on conventional or non-inventive labor. The order of steps listed in the embodiments is merely one possible execution order among many and does not represent the only execution order. In actual device or client product execution, the method can be executed in the order shown in the embodiments or drawings or in parallel (e.g., in a parallel processor or multi-threaded processing environment).

[0053] Those skilled in the art will understand that embodiments of the present invention can be provided as methods, systems, or computer program products. Therefore, the present invention can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, the present invention can take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0054] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means that implement the functions specified in one or more flowcharts and / or one or more block diagrams.

[0055] These computer program instructions may also be loaded onto a computer or other programmable data processing apparatus to cause a series of operational steps to be performed on the computer or other programmable apparatus to produce a computer-implemented process, such that the instructions, which execute on the computer or other programmable apparatus, provide steps for implementing the functions specified in one or more flowcharts and / or one or more block diagrams.

[0056] This invention is not limited to the embodiments described above. The above description of specific embodiments is intended to illustrate and explain the technical solutions of this invention. The specific embodiments described above are merely illustrative and not restrictive. Without departing from the spirit and scope of the claims, those skilled in the art can make many specific modifications based on the teachings of this invention, and these modifications all fall within the scope of protection of this invention.

Claims

1. A method for optimizing the profile and evaluating the dynamic stability of an anti-cam mechanism, characterized in that, include: Based on the motion law of the crank-slider mechanism, the equation of the cam profile with parameter correction is constructed. Based on Newton's second law, a four-degree-of-freedom dynamic equation is established that includes the time-varying contact stiffness of the anti-cam mechanism; The combustion pressure and combustion stiffness inside the cylinder are calculated using the ideal gas polytropic process theory. Calculate the radius of curvature at each point in the cam profile equation, and construct the stiffness matrix of the anti-cam mechanism by combining the time-varying contact stiffness and the gas stiffness; The fourth-order time-varying natural frequency of the inverse cam mechanism corresponding to the stiffness matrix is ​​solved, and the unstable domain under parameter excitation is analyzed using Floquet theory. The parameter range of the simple harmonic motion cam profile equation with parameter correction is determined by integrating thermodynamic, kinematic and dynamic evaluation criteria.

2. The method for optimizing the profile and evaluating the dynamic stability of the anti-cam mechanism according to claim 1, characterized in that, The equation for the simple harmonic motion cam profile with parameter correction is: ； in, For cam rotation angle, λ This is a variable parameter, with a value range of 0 to 1; The characteristic equation of a four-degree-of-freedom dynamic is: ； In the formula ， ， ； ； In the formula, For the mass of the piston and roller, For the quality of the cam disc, This represents the axial vibration displacement of the piston, with upward movement being positive. Let be the moment of inertia of the cam. This refers to the angular displacement of the cam due to torsional vibration. The time-varying contact stiffness between the roller and the cam. For gas stiffness, This refers to the contact stiffness between the piston and the cylinder wall. Axial stiffness between the cam, thrust bearing, and drive shaft. The torsional stiffness between the cam and the drive shaft; To guide friction and fluid resistance The combined force The periodic cylinder pressure force varies with the rotation angle. The output torque of the cam; l For the length of the roller, d This is the distance from the small end face of the roller to the central axis of the cam. The contact angle between the roller and the cam. This refers to the tangential vibration displacement of the piston along the circumference of the cam. This represents the axial vibration displacement of the cam. The linear displacement and angular displacement of the torsional vibration of the cam are given. .

3. The method for optimizing the profile and evaluating the dynamic stability of the anti-cam mechanism according to claim 1, characterized in that, The time-varying contact stiffness is expressed as: ； In the formula, Roller radius , Let be the instantaneous radius of curvature of the cam. L The contact length between the roller and the cam surface. E Let be the equivalent elastic modulus of the roller and the cam. F The normal load on the roller caused by the gas pressure.

4. The method for optimizing the profile and evaluating the dynamic stability of the anti-cam mechanism according to claim 1, characterized in that, The fourth-order time-varying natural frequency of the reverse cam mechanism is solved by applying the generalized eigenvalue decomposition method. Specifically, this involves selecting several cam corner points at equal intervals within one cycle, calculating the instantaneous stiffness matrix of each corner point, and solving the four-degree-of-freedom dynamic characteristic equation to obtain the fluctuation range of the fourth-order time-varying natural frequency of the reverse cam mechanism.

5. The method for optimizing the profile and evaluating the dynamic stability of the anti-cam mechanism according to claim 1, characterized in that, The unstable region under parameter excitation is analyzed using Floquet theory, specifically including: constructing a periodic matrix containing state variables and their first derivatives; constructing a transformation matrix using the periodic matrix according to Floquet theory; and determining the stability of the anti-cam mechanism based on the real part of the characteristic exponent.

6. The method for optimizing the profile and evaluating the dynamic stability of the anti-cam mechanism according to claim 1, characterized in that, In the process of determining the range of parameter values ​​for the equation of the simple harmonic motion cam profile with parameter correction, By comparing the time-varying natural frequency fluctuation range, instability range, and instability degree corresponding to the cam profile motion law under different parameter values, and by comprehensively considering thermodynamic, kinematic, and dynamic evaluation criteria, the parameters are determined. λ The value range is 0.5 to 0.

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7. A device for optimizing the profile and evaluating the dynamic stability of an anti-cam mechanism, characterized in that, include: The module for constructing the simple harmonic motion cam profile equation is used to construct the simple harmonic motion cam profile equation with parameter correction based on the motion law of the crank-slider mechanism. The dynamic equation construction module is used to establish a four-degree-of-freedom dynamic equation that includes the time-varying contact stiffness of the anti-cam mechanism based on Newton's second law. The calculation module is used to calculate the gas pressure and gas stiffness inside the cylinder using the ideal gas polytropic process theory; The stiffness matrix construction module is used to calculate the radius of curvature at each point in the cam profile equation and construct the stiffness matrix of the anti-cam mechanism by combining the time-varying contact stiffness and the gas stiffness. The instability domain determination module is used to solve for the fourth-order time-varying natural frequency of the inverse cam mechanism corresponding to the stiffness matrix, and to analyze the instability domain under parameter excitation using Floquet theory. It also determines the parameter range of the simple harmonic motion cam profile equation with parameter correction by integrating thermodynamic, kinematic and dynamic evaluation criteria.

8. An electronic device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, When the processor executes the computer program, it implements the steps of the method for optimizing the profile and evaluating the dynamic stability of the anti-cam mechanism as described in any one of claims 1 to 6.

9. A computer-readable storage medium having a computer program stored thereon, characterized in that, When executed by a processor, the computer program implements the steps of the method for optimizing the profile and evaluating the dynamic stability of the anti-cam mechanism as described in any one of claims 1 to 6.

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