A shafting friction and vibration reduction method and related device based on coating and profile optimization

Abstract

The application discloses a shafting friction and vibration reduction method and related device based on coating and profile optimization, relates to the field of shafting friction and vibration control, and comprises the following steps: obtaining an optimized cam profile contour based on a cam profile design requirement and constraint condition and a cam profile multi-objective optimization model; determining a transient friction lubrication state based on a cam pair interface contact friction analysis model containing a DLC coating according to the optimized cam profile contour and a target coating parameter set, calculating an interface friction coefficient of the cam pair containing the coating and a driving torque, inputting the driving torque as an excitation into a cam shafting torsional vibration analysis model, and obtaining a shafting dynamic response under a current target coating parameter; comparing and analyzing the shafting dynamic responses under each current target coating parameter, selecting a target coating parameter with the optimal shafting dynamic response as an optimal coating parameter, and taking a corresponding optimized cam profile contour as an optimal cam profile contour.

Description

Technical Field

[0001] This application relates to the field of shaft friction and vibration control, and in particular to a method and related apparatus for reducing shaft friction and vibration based on coating and profile optimization. Background Technology

[0002] The valve train and oil supply camshaft system operates under complex coupled conditions such as alternating impact loads, high-frequency vibration excitation, and mixed lubrication. Surface friction and wear failure, along with excessive shaft vibration, have become key factors restricting the reliability and service life of the shaft system. Coatings exhibit superior surface friction reduction and anti-wear properties under harsh conditions, effectively reducing friction at the cam pair interface and improving lubrication. Meanwhile, cam profile design is also a crucial factor affecting the contact dynamics and friction-lubrication performance of the mechanism.

[0003] Therefore, research on coating and profile optimization has important application value for improving camshaft friction and vibration. Summary of the Invention

[0004] The purpose of this application is to provide a method and device for reducing friction and vibration of shaft systems based on coating and profile optimization, which can effectively reduce the friction coefficient of the cam pair interface, improve the lubrication state, reduce drive torque fluctuations, and significantly suppress shaft vibration response.

[0005] To achieve the above objectives, this application provides the following solution:

[0006] In a first aspect, this application provides a method for reducing friction and vibration in shaft systems based on coating and profile optimization, including:

[0007] Based on the cam profile design requirements and constraints, and using a multi-objective optimization model for cam profiles, the optimized cam profile contour is obtained. The optimization objectives in the multi-objective optimization model for cam profiles are the valve train fullness coefficient and the oil film thickness characterization quantity. The constraints are used to constrain the power exponent values ​​of the valve train fullness coefficient and the oil film thickness characterization quantity in the multi-objective optimization model for cam profiles.

[0008] Based on the optimized cam profile and target coating parameter set, and using the interface contact friction analysis model of the cam pair with DLC coating, the transient friction and lubrication state of the optimized cam pair under each target coating parameter is determined; the target coating parameter set includes several target coating parameters.

[0009] For the transient friction and lubrication state of the cam pair after optimization under each target coating parameter, the interface friction coefficient and driving torque of the coated cam pair are calculated based on the transient friction and lubrication state. The driving torque is then used as an excitation input to the cam shaft torsional vibration analysis model to obtain the shaft dynamic response under the current target coating parameters.

[0010] The dynamic response of the shaft system under each current target coating parameter is compared and analyzed. The target coating parameter with the best dynamic response of the shaft system is selected as the optimal coating parameter, and the corresponding optimized cam profile is selected as the optimal cam profile.

[0011] Optionally, the formula expression for the multi-objective optimization model of the cam profile is:

[0012] minF c (x)=W1F1(-ψ)+W2F2(χ);

[0013] In the formula, W1 and W2 are the weights of the first and second objective functions, respectively, ψ is the fullness coefficient of the valve train cam and χ is the oil film thickness characterization quantity representing the lubrication performance at the tip of the valve train, F1(-ψ) is the optimization function of the fullness coefficient of the valve train cam and F2(χ) is the optimization function of the oil film thickness characterization quantity.

[0014] Optionally, the formula for calculating the fullness coefficient of the valve train camshaft is:

[0015]

[0016] In the formula, α C Let h(α) be the basic segment half-cover angle, and h(α) be the lift function. max This is the maximum valve lift.

[0017] Optionally, the formula for calculating the lift function is:

[0018]

[0019] In the formula, h1 is the rise of the buffer section, h2 is the full rise of the basic section; C k C l C m C n are undetermined coefficients; k, l, m, n are power exponents.

[0020] Optionally, the formula for calculating the oil film thickness, which characterizes the lubrication performance at the tip of the peach, is as follows:

[0021]

[0022] In the formula, ω is the angular velocity of the cam rotation.

[0023] Optionally, the constraints include boundary constraints and minimum radius of curvature constraints;

[0024] The boundary constraint conditions are as follows:

[0025]

[0026] The minimum radius of curvature constraint condition is:

[0027]

[0028] In the formula, p takes a real number between 3 and 8; q takes a real number between 1 and 8, l = 2p, m = 2p + q, n = 2p + 2q, r min For the minimum radius of curvature of the cam profile, [r] min [ ] represents the minimum permissible radius of curvature.

[0029] Optionally, based on the optimized cam profile and target coating parameter set, and using the cam pair interface contact friction analysis model with DLC coating, the transient friction and lubrication state of the optimized cam pair under each target coating parameter is determined, specifically including:

[0030] By convolution Green's function Solve for the elastic deformation of the coated contact surface; where x and y are the position coordinates of the cam pair at contact, and E i * It is the material's equivalent elastic modulus;

[0031] The frequency response function of the convolution Green's function is determined by using discrete convolution-fast Fourier transform and influence coefficient algorithms, thus obtaining the elastic deformation of the coating-substrate contact. The calculation formula for the elastic deformation of the coating-substrate contact is as follows: In the formula, It is a pressure-displacement discrete response function. It refers to the interfacial contact pressure; IFFT is the inverse discrete Fourier transform.

[0032] Based on the optimized cam profile and the elastic deformation of the coating-substrate contact, the transient friction and lubrication state of the optimized cam pair is calculated.

[0033] Secondly, this application provides a shaft system friction reduction and vibration damping device based on coating and profile optimization, comprising:

[0034] The optimization module is used to obtain the optimized cam profile based on the cam profile design requirements and constraints, and on a multi-objective optimization model of the cam profile. The optimization objectives in the multi-objective optimization model of the cam profile are the valve train fullness coefficient and the oil film thickness characterization quantity. The constraints are used to constrain the power exponent values ​​of the valve train fullness coefficient and the oil film thickness characterization quantity in the multi-objective optimization model of the cam profile.

[0035] The transient friction and lubrication state determination module is used to determine the transient friction and lubrication state of the optimized cam pair under each target coating parameter based on the optimized cam profile and target coating parameter set, and on the interface contact friction analysis model of the cam pair with DLC coating; the target coating parameter set includes several target coating parameters.

[0036] The shaft dynamic response calculation module is used to calculate the interface friction coefficient and driving torque of the coated cam pair based on the transient friction and lubrication state of the cam pair after optimization under each target coating parameter, and to input the driving torque as an excitation into the cam shaft torsional vibration analysis model to obtain the shaft dynamic response under the current target coating parameter.

[0037] The output module is used to compare and analyze the dynamic response of the shaft system under each current target coating parameter, and select the target coating parameter with the best dynamic response of the shaft system as the optimal coating parameter, and the corresponding optimized cam profile as the optimal cam profile.

[0038] Thirdly, this application provides a computer 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 shaft friction and vibration reduction method based on coating and profile optimization as described above.

[0039] Fourthly, this application provides a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the shaft friction and vibration reduction method based on coating and profile optimization described above.

[0040] According to the specific embodiments provided in this application, the following technical effects are disclosed:

[0041] This application provides a method and related device for reducing friction and vibration in shaft systems based on coating and profile optimization. The method constructs a multi-objective optimization model for the cam profile based on design requirements and constraints. The optimization targets are the valve train cam fullness coefficient and oil film thickness, with constraints on the power exponent values, resulting in an optimized cam profile contour. Based on this contour and the target coating parameter set, the transient friction and lubrication state of the optimized cam pair under each target coating parameter is determined using a cam pair interface contact friction analysis model with a DLC coating. The interface friction coefficient and driving torque of the coated cam pair are calculated, and the driving torque is input into a cam shaft torsional vibration analysis model to obtain the dynamic response of the shaft system. The optimal parameters are selected through comparative analysis. In this way, the optimized cam profile contour and optimal coating parameters work together to effectively improve the lubrication state of the cam pair interface, thereby reducing the friction coefficient. Stable lubrication and a lower friction coefficient reduce driving torque fluctuations. The reduction in driving torque fluctuations makes the excitation transmitted to the shaft system more stable, thus significantly suppressing the shaft system vibration response. Attached Figure Description

[0042] To more clearly illustrate the technical solutions in the embodiments of this application or the prior art, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0043] Figure 1 This is an application environment diagram of a shaft system friction reduction and vibration reduction method based on coating and profile optimization according to an embodiment of this application;

[0044] Figure 2 A schematic flowchart illustrating a shaft friction and vibration reduction method based on coating and profile optimization, provided in an embodiment of this application;

[0045] Figure 3 This is a schematic diagram of a coated cam pair contact according to an embodiment of this application;

[0046] Figure 4 A flowchart illustrating the friction reduction and vibration reduction analysis of a coated camshaft system according to an embodiment of this application;

[0047] Figure 5 Analysis diagram of valve train-fuel cam pair interface coating modification and shaft vibration reduction provided in an embodiment of this application;

[0048] Figure 6 A graph showing the variation of the friction coefficient of a coated valve train cam pair provided in an embodiment of this application;

[0049] Figure 7This is a schematic diagram of the relative torsion angle of a coated valve train / fuel supply camshaft system according to an embodiment of this application;

[0050] Figure 8 This is a schematic diagram of the front and rear contours of the valve train cam optimized according to an embodiment of this application;

[0051] Figure 9 A comparison diagram of the friction and lubrication performance of the valve train camshaft pair before and after optimization design, provided for an embodiment of this application;

[0052] Figure 10 A comparison diagram of the vibration characteristics of the valve train camshaft system before and after optimization design provided in an embodiment of this application;

[0053] Figure 11 A schematic diagram of the functional modules of a shaft friction reduction and vibration reduction device based on coating and profile optimization provided in an embodiment of this application;

[0054] Figure 12 This is a schematic diagram of the structure of a computer device provided in an embodiment of this application. Detailed Implementation

[0055] The technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this application, and not all embodiments. Based on the embodiments of this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application.

[0056] To make the above-mentioned objectives, features and advantages of this application more apparent and understandable, the application will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0057] The shaft friction and vibration reduction method based on coating and profile optimization provided in this application can be applied to, for example... Figure 1 In the application environment shown, terminal 102 communicates with server 104 via a network. A data storage system can store the data that server 104 needs to process. The data storage system can be set up independently, integrated into server 104, or placed in the cloud or on another server.

[0058] The terminal 102 can be, but is not limited to, various desktop computers, laptops, smartphones, tablets, IoT devices, and portable wearable devices. IoT devices can include smart speakers, smart TVs, smart air conditioners, and smart in-vehicle devices. Portable wearable devices can include smartwatches, smart bracelets, and head-mounted devices. The server 104 can be implemented using a standalone server or a server cluster composed of multiple servers, or it can be a cloud server.

[0059] In one exemplary embodiment, such as Figure 2 As shown, a method for reducing friction and vibration of shaft systems based on coating and profile optimization is provided. This method is executed by computer equipment, specifically by a terminal or server alone, or by both a terminal and a server. In this embodiment, the method is applied to... Figure 1 Taking server 104 as an example, the explanation includes the following steps 201 to 204. Wherein:

[0060] Step 201: Based on the cam profile design requirements and constraints, and based on the cam profile multi-objective optimization model, the optimized cam profile contour is obtained; the optimization objectives in the cam profile multi-objective optimization model are the valve train fullness coefficient and the oil film thickness characterization quantity; the constraints are used to constrain the power exponent values ​​of the valve train fullness coefficient and the oil film thickness characterization quantity in the cam profile multi-objective optimization model.

[0061] Step 202: Based on the optimized cam profile and target coating parameter set, and using the cam pair interface contact friction analysis model with DLC coating, determine the transient friction and lubrication state of the optimized cam pair under each target coating parameter; the target coating parameter set includes several target coating parameters.

[0062] Step 203: For the transient friction and lubrication state of the cam pair after optimization under each target coating parameter, calculate the interfacial friction coefficient and driving torque of the coated cam pair based on the transient friction and lubrication state, and use the driving torque as an excitation input to the cam shaft system torsional vibration analysis model to obtain the shaft system dynamic response under the current target coating parameter.

[0063] Step 204: Compare and analyze the dynamic response of the shaft system under each current target coating parameter, select the target coating parameter with the best dynamic response of the shaft system as the optimal coating parameter, and select the corresponding optimized cam profile as the optimal cam profile.

[0064] In an engine, the camshaft system, which supplies valves and fuel, operates under complex conditions. It is subjected to alternating impact forces and high-frequency vibrations, and lubrication is also poor. Under these circumstances, the camshaft surface is prone to wear due to friction, and the shaft system may vibrate excessively. Both of these problems seriously affect the reliability and service life of the shaft system.

[0065] Surface coatings are widely used, especially under harsh working conditions, due to their excellent friction-reducing and wear-resistant properties, significantly reducing interfacial friction and improving lubrication. Therefore, surface overcoating can be used to increase the thickness of the contact oil film, thereby separating the roughness of the contact surfaces to achieve friction reduction and efficiency enhancement. Diamond-like carbon (DLC) coatings possess high hardness, high wear resistance, and self-lubricating properties, achieving significant results in improving the friction and lubrication of contact surfaces. In camshaft pairs, sliding and rolling alternate between interfaces, with drastic changes in relative velocity, contact geometry, and stress state, making friction and lubrication analysis conditions complex and variable. Therefore, this paper considers the instantaneous friction and vibration coupling conditions of the camshaft system and, combining macroscopic contact mechanics and microscopic three-dimensional lubrication characteristics, establishes a tribological analysis model of the camshaft pair with DLC coating under mixed lubrication conditions, thus achieving a comprehensive analysis of the friction, lubrication, and vibration performance of the camshaft system under coated contact.

[0066] This embodiment primarily studies the role of camshaft coatings in improving the wear resistance of contact surfaces. Taking into account both valve timing performance and lubrication characteristics, a cam shape optimization method is designed to simultaneously meet multiple objectives. The changes in camshaft vibration response after coating and cam shape optimization are systematically investigated, clarifying how coating technology and cam shape optimization work synergistically to improve camshaft vibration. Ultimately, the goal of optimizing both camshaft surface friction characteristics and improving system vibration is achieved, providing a theoretical basis and practical method for enhancing the overall performance of diesel engine camshaft systems.

[0067] Specifically, when executing step 201, the following can be done:

[0068] Because the camshaft profile directly affects the valve lift curve, thus determining the diesel engine's charging efficiency and exhaust performance, an optimized profile can increase the valve opening "time-section" value and fullness coefficient, improving cylinder intake and exhaust efficiency and increasing diesel engine power and fuel economy. The contact stress and lubrication characteristics between the camshaft and tappet are closely related to the profile design; an optimized profile can increase the minimum radius of curvature and reduce local contact stress, thereby reducing friction and wear. This paper proposes an optimized camshaft profile design scheme based on camshaft pair wear failure, combining mathematical models and simulation tools with multi-objective optimization methods.

[0069] (1) Design of the buffer section of the valve train profile:

[0070] The buffer section adopts a cosine-constant velocity buffer section design, consisting of a cosine section and a constant velocity section. This effectively smooths the transition of cam motion and reduces the impact of acceleration changes on the system. Its equation is:

[0071]

[0072] In the formula, α1 is the wrap angle of the cosine segment, α2 is the wrap angle of the buffer segment, λ is the period of the cosine function, and λ=π / 2α1.

[0073] (a) When α=α2, the total lift of the buffer section is h1, from which we can obtain:

[0074] A0+A1α2=h1.

[0075] (b) At the dividing point α = α1, the lift h(α) remains continuous, and we can obtain:

[0076] A0+A1α1=C1(1-cosλα1).

[0077] (c) At the boundary point α = α1, dh(α) / dα remains continuous, so we can obtain:

[0078] A1 = C1λsin(λα1).

[0079] (d) The fourth condition is a supplementary condition, so we can obtain:

[0080] α1 = Gα2.

[0081] The entire lift curve can be obtained:

[0082]

[0083] In the formula, h1 is the rise of the buffer segment, and G is the cosine segment wrap angle coefficient, with a value of G = α1 / α2.

[0084] Taking into account the operating frequency of the gas distribution mechanism, load conditions, and other key factors, the acceleration at the end of the buffer section should be zero, and there should be a certain clearance to ensure the working characteristics of the valve. Therefore, the selection of the buffer section wrap angle α2 should be coordinated with the buffer section lift h1.

[0085] (2) Design of the basic segment of the valve train profile:

[0086] When designing the basic section profile equation of the valve train, using a higher-order quintic equation is a more effective method because increasing the number of terms does not significantly affect the characteristic parameters. Therefore, it is preferable to avoid using too many terms, which not only maintains a good curve fit but also avoids computational complexity and increased analytical workload. Thus, the lift function of the basic section takes the following form;

[0087]

[0088] In the formula, α C h1 is the half-wrap angle of the basic segment, h2 is the full lift of the basic segment, and C is the full lift of the basic segment. k C l C m C nare undetermined coefficients, and k, l, m, n are power exponents.

[0089] Analysis of the power exponent values ​​revealed four unknowns in the equation. Therefore, to simplify the calculation and improve efficiency, the power exponent was simplified to two unknowns, and the following power exponent values ​​were selected:

[0090] k=2, l=2p, m=2p+q, n=2p+2q.

[0091] In the formula, p takes a real number between 3 and 8; q takes a real number between 1 and 8. From the continuity condition, we know that:

[0092] (a) When α = α2, h(α) = h1, we can obtain:

[0093] h1+C0+C k +C l +C m +C n =h1.

[0094] (b) When α = α2, the velocity of the tappet at the end of the buffer section is the same as that at the beginning of the basic section. To ensure continuity, therefore:

[0095] kC k +lC l +mC m +nC n =v1.

[0096] (c) When α = α2, d 2 h α / dα 2 =0, therefore we can obtain:

[0097] k(k-1)C k +l(l-1)C l +m(m-1)C m +n(n-1)C n =0.

[0098] (d) When α=α2, d 3 h α / dα 3 =0, therefore we can obtain:

[0099] k(k-1)(k-2)C k +l(l-1)(l-2)C l +m(m-1)(m-2)C m +n(n-1)(n-2)C n =0.

[0100] (e) When α = α² + α C At that time, h α=h1+h2 is the known basic segment elevation, so we get:

[0101] C0 = h2.

[0102] Solving for:

[0103]

[0104] The cam profile design plays a decisive role in the valve movement of the valve train, directly affecting the diesel engine's performance. Therefore, optimizing the cam profile design is particularly important. The cam fullness coefficient is a key parameter affecting the charging and exhaust performance of the valve train. Optimization should aim for the largest possible fullness coefficient to improve the overall efficiency and power output of the diesel engine. The cam profile fullness coefficient ψ can be defined as:

[0105]

[0106] In the formula, α C Let h(α) be the basic segment half-cover angle, and h(α) be the lift function. max This is the maximum valve lift.

[0107] Considering the importance of the body coefficient to the charging and exhaust performance of the valve train, this objective aims to maximize the body coefficient value while meeting the calculation conditions. Through derivation of the basic equation, the specific expression for the body coefficient can be obtained as follows:

[0108]

[0109] Therefore, the fullness coefficient is chosen as the first objective function for the optimization design, and it is ensured that...

[0110] F1(x) = maxψ.

[0111] Minimum oil film thickness calculation formula:

[0112]

[0113] Substituting the formulas for entrainment speed and radius of curvature, we get:

[0114]

[0115] make but

[0116] from It can be analyzed that θ is called the hydrodynamic evaluation coefficient. Within the interval 0 ≤ θ ≤ 0.5, when θ = 0 or 0.5, h min =0, while in the interval θ > 0.5, h min This will increase sharply with increasing θ. A larger lubrication coefficient helps improve lubrication performance, therefore:

[0117]

[0118] Since the "peach tip" area is where the lubrication effect of the cam pair is poor, this area is selected as the key research object. A mathematical model for the second objective function—oil film thickness—is established, and the oil film thickness characterization quantity can be obtained by deriving the formula:

[0119]

[0120] In the formula, ω is the angular velocity of the cam rotation.

[0121] To ensure optimal lubrication at the cam tip, the oil film thickness should be maximized, i.e., the lubrication coefficient should be maximized. For higher-order cams, the lubrication coefficient at the cam tip should be... α The calculated value is generally negative, therefore it is required to take its minimum value within the calculation range. Based on the above analysis, selecting the cam fullness coefficient and oil film thickness as optimization objectives, the objective function F can be obtained. c (x):

[0122] min F c (x)=W1F1(-ψ)+W2F2(χ).

[0123] In the formula, W1 and W2 are the weights of the first and second objective functions, respectively, with the weight coefficients taking the same value of 0.5, which can also be adjusted according to the specific situation. ψ is the fullness coefficient of the valve train cam and χ is the oil film thickness characterization quantity representing the lubrication performance at the tip of the valve. F1(-ψ) is the optimization function of the fullness coefficient of the valve train cam and F2(χ) is the optimization function of the oil film thickness characterization quantity.

[0124] (3) After analyzing the above problem, it is found to be a multi-objective constrained nonlinear minimization problem. The following constraints are introduced to carry out the cam profile optimization design.

[0125] (a) Boundary constraints:

[0126]

[0127] (b) Minimum radius of curvature constraint:

[0128]

[0129] In the formula, r min For the minimum radius of curvature of the cam profile, [r] min [ ] represents the minimum permissible radius of curvature.

[0130] (c) Maximum acceleration constraint:

[0131] The maximum acceleration was constrained, but analysis revealed that when the oil film thickness was used as the objective function, the result was the vertical acceleration at the cam tip. Therefore, constraining the oil film thickness is essentially an indirect limitation on the acceleration, and thus there is no need to repeatedly constrain the acceleration.

[0132] Specifically, when executing step 202, the following can be done:

[0133] like Figure 3 The diagram shows a coated cam pair contact, where both the cam and follower surfaces have a certain thickness of coating, and the coating is completely bonded to the substrate material. Since the coating thickness is small, typically on the order of micrometers, its impact on the cam pair's structural dimensions can be ignored. Because the contact length in the y-direction is much greater than that in the x-direction during cam pair contact, the cam pair contact can be equivalent to a roller contacting a semi-infinite space. The coating thickness on the roller surface at the contact point is h. c1 The thickness of the semi-infinite surface coating is h. c2 Compared to the uncoated model, the only change after considering the coating is in the elastic deformation equation. Therefore, the other equations in the cam pair friction and lubrication analysis equation set remain unchanged, and the effect of the coating on elastic deformation is taken into account in the film thickness equation.

[0134] The calculation of elastic deformation at the coating-substrate interface can be divided into two cases. The first case is when the elastic modulus and Poisson's ratio of the coating are the same as those of the substrate, and the semi-infinite space formula derived from elasticity theory can still be used for calculation. The second case is when the elastic modulus or Poisson's ratio of the coating is different from that of the substrate, and the elastic deformation needs to be solved using numerical methods such as the finite element method and boundary element method. The calculation is based on the deformation formula of the infinitely long coating half-space interface. For the uncoated contact surface, the elastic deformation caused by pressure distribution can be obtained by the formula, while the elastic deformation of the contact surface with coating is solved by the following convolutional Green's function:

[0135]

[0136] In the formula, x and y are the position coordinates when the cam pair is in contact, and E i * It is the equivalent elastic modulus of the material.

[0137] The corresponding frequency response function in the frequency domain is:

[0138]

[0139] For a coated half-space plane, both the coating and the substrate can undergo elastic deformation. In this case, the normal displacement in the spatial domain cannot be expressed using an explicit Green's function. However, its frequency response function can be expressed in the frequency domain using the following formula:

[0140]

[0141] in,

[0142] By using discrete convolution-fast Fourier transform and influence coefficient algorithms, the frequency response function of the Green's function can be obtained, thus yielding the elastic deformation of the coating-substrate contact. Since the elastic deformation is caused by the contact pressure of the interfacial oil film and micro-protrusions, the elastic deformation of the coating-substrate line contact can be calculated using the following formula:

[0143]

[0144] In the formula, It is a pressure-displacement discrete response function. It refers to the interfacial contact pressure, and IFFT (Inverse Fast Fourier Transform) is the inverse discrete Fourier transform.

[0145] like Figure 4 The flowchart shown illustrates the friction and vibration reduction analysis of a coated camshaft system. First, input parameters for the camshaft system are provided, including geometric, operating condition, material, and lubrication parameters, as well as coating mechanical and thermal parameters. Dynamic calculations of the camshaft system under coupled friction and vibration conditions are then performed to obtain the dynamic response characteristics (instantaneous load, microstructure, etc.) and instantaneous motion (entrainment speed, radius of curvature, etc.) within the contact micro-region. Subsequently, the contact elastic deformation of the coated surface is solved, as shown in the formula... The grid size for discretizing the mid-frequency response function in the frequency domain corresponds to the grid size for pressure calculation, resulting in significant calculation errors. Therefore, Gaussian integrals are used to overcome these errors. The frequency response function singularity is located, and then the IFFT method is applied to the discrete matrix of the frequency response function to extract the influence coefficients. The DC-FFT fast algorithm is then used to calculate the elastic deformation of the coated surface.

[0146] Based on the transient operating conditions of the contact area and considering the influence of microstructure and non-Newtonian fluid effects, the quasi-system numerical method and fast Fourier transform method are used to calculate the friction and lubrication state and shear distribution under the rough contact surface of the cam pair, so as to obtain the transient friction and lubrication state of the coated cam pair. The solution process includes alternating iterative solutions of the pressure field and temperature field until the pressure and temperature solutions meet the convergence criteria to enter the next time cycle. Finally, based on the contact state of the cam pair, the transient drive torque change of the multi-valve valve train-fuel camshaft is calculated, and a quantitative study on the interface friction and vibration suppression of the camshaft system coating is carried out. The contact friction state and dynamic performance changes of the valve train-fuel camshaft system coating are analyzed until the dynamic performance evaluation of the friction reduction and vibration reduction of the camshaft system interface coating is completed within the operating cycle.

[0147] Specifically, when performing steps 203-204, the specific steps can be as follows:

[0148] Under high-speed / alternating load coupling conditions, the camshaft pair is subjected to a complex and harsh working environment, often leading to increased interfacial friction loss and frequent pitting failures. To analyze the transient dynamics of the camshaft pair and the mixed lubrication and wear characteristics under coating contact, based on the convolutional Green's function and fast Fourier transform method, and considering the complex structure, multiple excitation sources, and transient operating conditions of the valve train-fuel camshaft system, a three-dimensional roughness contact-based thermo-mechanical-vibration multi-field coupled friction reduction analysis method for the camshaft system interface coating is proposed. A multi-scale optimization experiment for the application of the camshaft pair wear-resistant coating is also designed. The cam profile design directly affects the contact dynamics and lubrication performance of the valve train mechanism; considering valve train performance and lubrication characteristics, a multi-objective optimization design method for the cam profile is proposed. The analysis diagrams of the valve train-fuel camshaft pair interface coating modification and shaft vibration reduction are shown below. Figure 5 As shown, this provides a theoretical basis and technical support for the failure analysis of cam pair interface and surface friction reduction and wear resistance.

[0149] in, Figure 6 Figures (a) and (b) show the variation of the friction coefficient of the coated intake and exhaust camshaft pairs under transient dynamic conditions. Analysis of the results shows that applying a coating to the camshaft pair surface significantly reduces its friction coefficient, especially in the critical section affecting the valve train's operating conditions, where the friction coefficient can be reduced by nearly 0.015, thus improving its frictional contact state. This phenomenon is mainly attributed to the increased oil film thickness, the reduced contact probability of surface roughness and micro-protrusions leading to a decrease in oil film shear force, and the higher temperature generated by the DLC coating resulting in a decrease in extreme shear modulus, thereby reducing lubricant viscosity and lowering the contact friction coefficient.

[0150] Specifically, the free end of the shaft exhibits a large instantaneous speed fluctuation range. Therefore, analyzing the instantaneous speed change at the valve train / fuel supply camshaft end is crucial. Figure 7 As shown in the figure. Analysis of the results shows that due to the increased thickness of the oil film at the interface of the coated camshaft pair, the contact friction excitation is reduced, leading to a weakening of the inter-surface oil film excitation effect. The instantaneous speed fluctuation range of the camshaft system shows a decreasing trend, especially for the instantaneous speed range of the fuel supply camshaft end, where it decreases from 140 r / min to 135 r / min at 44 inertia, a decrease of approximately 3.6%. The relative torsion angle change between the valve train and fuel supply camshaft ends is shown in the figure. Figure 7 As shown in the results, the overturning interface coating at the valve train-fuel camshaft end reduces the instantaneous angular displacement by about 18% and further decreases the high-frequency response.

[0151] In this embodiment, the study on the improvement of camshaft system friction and vibration by profile optimization is as follows:

[0152] This embodiment utilizes the profile data obtained from the proposed multi-objective optimization method for cam profiles, which can improve the contact friction and lubrication state between cam pairs, especially in improving the dynamic characteristics of lubricating film thickness. The design of the fuel injection cam pair profile is not easily changed, mainly due to its core role in the fuel injection system and the systemic impact of design changes. Therefore, a vibration characteristic analysis model of the camshaft system under elastodynamic conditions is used to explore the degree of influence of the optimized design of the valve train cam profile on the friction and vibration performance of the camshaft system.

[0153] The optimized front and rear profiles of the valve train camshaft studied in this embodiment are as follows: Figure 8 As shown in (a) and (b) in the figure. While keeping the basic structure (parameters of the basic segment and the buffer segment) unchanged, increasing the profile of the profile within the basic segment will improve the inflation performance. The degree to which profile optimization improves the friction and lubrication state of the valve train camshaft pair was analyzed, such as... Figure 9 As shown in (a) and (b) in the figure. The results analysis shows that after the profile optimization design, the oil film thickness of the valve train cam pair increases and the friction coefficient decreases. The optimized profile can increase the oil film thickness by about 15% and reduce the friction coefficient by about 6% near the "peach tip" of the intake and exhaust cam pairs, respectively, thus improving the oil film formation capability between the cam pairs.

[0154] Optimize the vibration characteristics of the front and rear camshaft systems, such as Figure 10 Figures (a) and (b) primarily illustrate the additional stress and speed fluctuations of each inertia shaft segment. The optimization design mainly focuses on the valve train cam profile and does not explore its impact on the vibration characteristics of the multi-part control valve-fuel camshaft system. Analysis of the results shows that profile optimization can reduce the contact friction coefficient between the valve train cam pairs, thereby reducing frictional excitation and improving the shaft system's driving torque characteristics. This results in a reduction of approximately 4.0% and 5% in the additional stress and speed fluctuations of the valve train camshaft caused by frictional torque, respectively. Compared to improving the vibration characteristics of the camshaft system, profile optimization is more beneficial for enhancing the contact friction lubrication characteristics of the cam pairs, thus achieving synergistic optimization of the cam pair profile design with the shaft system's friction performance and vibration characteristics.

[0155] Based on the same inventive concept, this application also provides a shaft friction and vibration reduction device based on coating and profile optimization for implementing the aforementioned shaft friction and vibration reduction method. The solution provided by this device is similar to the solution described in the above method. Therefore, the specific limitations of one or more embodiments of the shaft friction and vibration reduction device based on coating and profile optimization provided below can be found in the limitations of the shaft friction and vibration reduction method based on coating and profile optimization described above, and will not be repeated here.

[0156] In one exemplary embodiment, such as Figure 11 As shown, a shaft friction reduction and vibration damping device based on coating and profile optimization is provided, comprising:

[0157] Optimization module 1101 is used to obtain the optimized cam profile based on the cam profile design requirements and constraints, and based on the cam profile multi-objective optimization model. The optimization objectives in the cam profile multi-objective optimization model are the valve train fullness coefficient and the oil film thickness characterization quantity. The constraints are used to constrain the power exponent values ​​of the valve train fullness coefficient and the oil film thickness characterization quantity in the cam profile multi-objective optimization model.

[0158] The transient friction and lubrication state determination module 1102 is used to determine the transient friction and lubrication state of the optimized cam pair under each target coating parameter based on the optimized cam profile and target coating parameter set, and on the interface contact friction analysis model of the cam pair with DLC coating; the target coating parameter set includes several target coating parameters.

[0159] The shaft dynamic response calculation module 1103 is used to calculate the interface friction coefficient and driving torque of the coated cam pair based on the transient friction and lubrication state of the cam pair after optimization under each target coating parameter, and to input the driving torque as an excitation into the cam shaft torsional vibration analysis model to obtain the shaft dynamic response under the current target coating parameter.

[0160] The output module 1104 is used to compare and analyze the dynamic response of the shaft system under each current target coating parameter, select the target coating parameter with the best dynamic response of the shaft system as the optimal coating parameter, and select the corresponding optimized cam profile as the optimal cam profile.

[0161] In one exemplary embodiment, a computer device is provided, which may be a server or a terminal, and its internal structure diagram may be as follows. Figure 12 As shown, the computer device includes a processor, memory, input / output (I / O) interfaces, and a communication interface. The processor, memory, and I / O interfaces are connected via a system bus, and the communication interface is also connected to the system bus via the I / O interfaces. The processor provides computational and control capabilities. The memory includes non-volatile storage media and internal memory. The non-volatile storage media stores the operating system, computer programs, and a database. The internal memory provides the environment for the operating system and computer programs stored in the non-volatile storage media. The database stores data on shaft friction and vibration reduction based on coating and profile optimization. The I / O interfaces are used for information exchange between the processor and external devices. The communication interface is used for communication with external terminals via a network connection. When the computer program is executed by the processor, it implements a shaft friction and vibration reduction method based on coating and profile optimization.

[0162] Those skilled in the art will understand that Figure 12 The structure shown is merely a block diagram of a portion of the structure related to the present application and does not constitute a limitation on the computer device to which the present application is applied. Specific computer devices may include more or fewer components than those shown in the figure, or combine certain components, or have different component arrangements.

[0163] In one exemplary embodiment, a computer device is also provided, including a memory and a processor, wherein the memory stores a computer program, and the processor executes the computer program to implement the steps in the above-described method embodiments.

[0164] In one exemplary embodiment, a computer-readable storage medium is provided storing a computer program that, when executed by a processor, implements the steps in the above-described method embodiments.

[0165] It should be noted that the user information (including but not limited to user device information, user personal information, etc.) and data (including but not limited to data used for analysis, data stored, data displayed, etc.) involved in this application are all information and data authorized by the user or fully authorized by all parties, and the collection, use and processing of the relevant data must comply with relevant regulations.

[0166] Those skilled in the art will understand that all or part of the processes in the methods of the above embodiments can be implemented by a computer program instructing related hardware. The computer program can be stored in a non-volatile computer-readable storage medium, and when executed, it can include the processes of the embodiments of the above methods. Any references to memory, databases, or other media used in the embodiments provided in this application can include at least one of non-volatile and volatile memory. Non-volatile memory can include read-only memory (ROM), magnetic tape, floppy disk, flash memory, optical memory, high-density embedded non-volatile memory, resistive random access memory (ReRAM), magnetic random access memory (MRAM), ferroelectric random access memory (FRAM), phase change memory (PCM), graphene memory, etc. Volatile memory can include random access memory (RAM) or external cache memory, etc. By way of illustration and not limitation, RAM can take many forms, such as Static Random Access Memory (SRAM) or Dynamic Random Access Memory (DRAM).

[0167] The databases involved in the embodiments provided in this application may include at least one type of relational database and non-relational database. Non-relational databases may include, but are not limited to, blockchain-based distributed databases. The processors involved in the embodiments provided in this application may be general-purpose processors, central processing units, graphics processing units, digital signal processors, programmable logic devices, quantum computing-based data processing logic devices, etc., and are not limited to these.

[0168] In summary, this application has the following technical effects:

[0169] (1) Considering the characteristics of structural vibration, multi-source excitation, and transient operating conditions of the valve train and oil supply mechanism, a multi-scale lubrication analysis model of the cam pair coating interface under the coupling effect of friction and vibration was developed. The friction reduction and efficiency enhancement mechanism of the cam pair interface coating was systematically revealed. An equivalent test simulating the wear resistance of the cam pair coating surface was carried out. The effects of the cam pair interface coating on reducing contact friction, reducing shaft vibration, and improving wear resistance were investigated. Furthermore, by optimizing the valve train cam pair profile to reduce valve train vibration and improve contact lubrication characteristics, the following conclusions were drawn:

[0170] (2) The effects of the coating on friction reduction and shaft vibration reduction of the cam pair under fluctuating operating conditions were evaluated. The results showed that the rough peak contact area ratio of the cam pair with DLC coating was reduced, resulting in a decrease in the interfacial contact friction coefficient, especially in the basic section of the valve train cam pair and the oil supply section of the fuel supply cam pair under harsh operating conditions. The above-mentioned coating contact and friction coupling effect reduced the driving torque between the cam pairs by about 4 N·m, and the instantaneous speed fluctuation and additional stress of the shaft system showed a decreasing trend.

[0171] (3) Multi-scale optimization tests of wear-resistant coatings for simulated cam pairs were conducted. The results showed that the wear-resistant coating specimens could reduce the width of wear marks and the depth of contact wear, indicating that the wear resistance of the coated specimens was improved, especially under high-speed and heavy-load conditions. Under the same test conditions, the uncoated specimens showed the most severe wear, and the average wear depth of the WC-coated specimens was 0.5 times that of the uncoated specimens, demonstrating the superiority of surface wear-resistant strengthening.

[0172] (4) A profile optimization design method integrating valve body fullness and tribological parameters was proposed. Using high-order cam profile equations and operating constraints as optimization conditions, and combining the cam pair fullness coefficient and oil film thickness as optimization objectives, corresponding optimization designs were carried out on cam pair wear and shaft vibration. Results show that after cam pair profile optimization design, the fullness coefficient increases, the lubricating oil film thickness increases, the probability of interface wear problems decreases, and the friction and vibration characteristics of the cam shaft system can be improved.

[0173] The technical features of the above embodiments can be combined in any way. For the sake of brevity, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0174] This embodiment uses specific examples to illustrate the principles and implementation methods of this application. The description of the above embodiments is only for the purpose of helping to understand the method and core ideas of this application; at the same time, for those skilled in the art, there will be changes in the specific implementation methods and application scope based on the ideas of this application. In summary, the content of this specification should not be construed as a limitation of this application.

Claims

1. A method for reducing friction and vibration in shaft systems based on coating and profile optimization, characterized in that... include: Based on the design requirements and constraints of the cam profile, and using a multi-objective optimization model for the cam profile, the optimized cam profile contour is obtained. The optimization objectives in the multi-objective optimization model of the cam profile are the valve train fullness coefficient and the oil film thickness characterization quantity; the constraint conditions are used to constrain the power exponent values ​​of the valve train fullness coefficient and the oil film thickness characterization quantity in the multi-objective optimization model of the cam profile. Based on the optimized cam profile and target coating parameter set, and using the interface contact friction analysis model of the cam pair with DLC coating, the transient friction and lubrication state of the optimized cam pair under each target coating parameter is determined. The target coating parameter set includes several target coating parameters; For the transient friction and lubrication state of the cam pair after optimization under each target coating parameter, the interface friction coefficient and driving torque of the coated cam pair are calculated based on the transient friction and lubrication state. The driving torque is then used as an excitation input to the cam shaft torsional vibration analysis model to obtain the shaft dynamic response under the current target coating parameters. The dynamic response of the shaft system under each current target coating parameter is compared and analyzed. The target coating parameter with the best dynamic response of the shaft system is selected as the optimal coating parameter, and the corresponding optimized cam profile is selected as the optimal cam profile.

2. The shaft friction reduction and vibration reduction method based on coating and profile optimization according to claim 1, characterized in that, The formula expression for the multi-objective optimization model of the cam profile is: minF c (x)=W1F1(-ψ)+W2F2(χ); In the formula, W1 and W2 are the weights of the first and second objective functions, respectively, ψ is the fullness coefficient of the valve train cam and χ is the oil film thickness characterization quantity representing the lubrication performance at the tip of the valve train, F1(-ψ) is the optimization function of the fullness coefficient of the valve train cam and F2(χ) is the optimization function of the oil film thickness characterization quantity.

3. The shaft friction reduction and vibration reduction method based on coating and profile optimization according to claim 2, characterized in that, The formula for calculating the fullness coefficient of the valve train camshaft is: In the formula, α C Let h(α) be the basic segment half-cover angle, and h(α) be the lift function. max This is the maximum valve lift.

4. The shaft friction reduction and vibration reduction method based on coating and profile optimization according to claim 3, characterized in that, The formula for calculating the lift function is as follows: In the formula, h1 is the rise of the buffer section, h2 is the full rise of the basic section; C k C l C m C n are undetermined coefficients; k, l, m, n are power exponents.

5. The shaft friction reduction and vibration reduction method based on coating and profile optimization according to claim 4, characterized in that, The formula for calculating the oil film thickness, a characterizing factor for lubrication performance at the tip of a peach, is as follows: In the formula, ω is the angular velocity of the cam rotation.

6. The shaft friction reduction and vibration reduction method based on coating and profile optimization according to claim 5, characterized in that, The constraints include boundary constraints and minimum radius of curvature constraints. The boundary constraint conditions are as follows: The minimum radius of curvature constraint condition is: In the formula, p takes a real number between 3 and 8; q takes a real number between 1 and 8, l = 2p, m = 2p + q, n = 2p + 2q, r min For the minimum radius of curvature of the cam profile, [r] min [ ] represents the minimum permissible radius of curvature.

7. The shaft friction reduction and vibration reduction method based on coating and profile optimization according to claim 6, characterized in that, Based on the optimized cam profile and target coating parameter set, and using the cam pair interface contact friction analysis model with DLC coating, the transient friction and lubrication state of the optimized cam pair under each target coating parameter is determined, specifically including: By convolution Green's function Solve for the elastic deformation of the coated contact surface; where x and y are the position coordinates of the cam pair at contact, and E i * It is the material's equivalent elastic modulus; The frequency response function of the convolution Green's function is determined by using discrete convolution-fast Fourier transform and influence coefficient algorithms, thus obtaining the elastic deformation of the coating-substrate contact. The calculation formula for the elastic deformation of the coating-substrate contact is as follows: In the formula, It is a pressure-displacement discrete response function. It refers to the interfacial contact pressure; IFFT is the inverse discrete Fourier transform. Based on the optimized cam profile and the elastic deformation of the coating-substrate contact, the transient friction and lubrication state of the optimized cam pair is calculated.

8. A shaft system friction reduction and vibration damping device based on coating and profile optimization, characterized in that, include: The optimization module is used to obtain the optimized cam profile based on the cam profile design requirements and constraints, and based on the cam profile multi-objective optimization model. The optimization objectives in the multi-objective optimization model of the cam profile are the valve train fullness coefficient and the oil film thickness characterization quantity; the constraint conditions are used to constrain the power exponent values ​​of the valve train fullness coefficient and the oil film thickness characterization quantity in the multi-objective optimization model of the cam profile. The transient friction and lubrication state determination module is used to determine the transient friction and lubrication state of the optimized cam pair under each target coating parameter based on the optimized cam profile and target coating parameter set and the interface contact friction analysis model of the cam pair with DLC coating. The target coating parameter set includes several target coating parameters; The shaft dynamic response calculation module is used to calculate the interface friction coefficient and driving torque of the coated cam pair based on the transient friction and lubrication state of the cam pair after optimization under each target coating parameter, and to input the driving torque as an excitation into the cam shaft torsional vibration analysis model to obtain the shaft dynamic response under the current target coating parameter. The output module is used to compare and analyze the dynamic response of the shaft system under each current target coating parameter, and select the target coating parameter with the best dynamic response of the shaft system as the optimal coating parameter, and the corresponding optimized cam profile as the optimal cam profile.

9. A computer device, comprising: A memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that the processor executes the computer program to implement the shaft friction and vibration reduction method based on coating and profile optimization as described in any one of claims 1-7.

10. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by the processor, it implements the shaft friction reduction and vibration reduction method based on coating and profile optimization as described in any one of claims 1-7.

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