A cam profile design and spring selection method for a marine jet system plunger pump

Abstract

This invention relates to a method for designing the cam profile and selecting springs for a plunger pump in a marine injection system. Based on a polynomial piecewise function, a smooth and controllable cam profile is constructed according to the performance requirements of the fuel injection system. A system load model is established based on the kinematic and dynamic responses provided by the cam profile, and the initial matching and verification of spring parameters are completed using the key constraint that "spring clamping force ≥ system inertial force". A multi-objective genetic algorithm is used to collaboratively optimize the cam and spring parameters, generating a Pareto optimal solution set. The optimal matching parameters with the best overall performance are selected through a multi-attribute decision-making method. This forms a systematic closed-loop design process from cam profile design and initial spring matching verification to parameter collaborative optimization. It achieves collaborative optimization matching of the cam and spring, constructs a multi-dimensional performance verification system, improves design efficiency and the reliability and safety of the system under complex operating conditions, and ensures high-quality service of the marine injection system in fields such as methanol fuel.

Description

Technical Field

[0001] This invention belongs to the technical field of internal combustion engine fuel injection systems, and relates to a design of the cam profile of a plunger pump in a marine injection system and a method for selecting springs. Background Technology

[0002] With the increasing demands on power systems from fields such as shipping and construction machinery, diesel engines are rapidly developing towards higher speeds, higher power densities, and higher reliability. This places more stringent requirements on the operational stability, fuel injection accuracy, and reliability of fuel injection systems. As the core driving component of the fuel injection system, the fuel injection cam's profile directly determines the movement pattern of the fuel injection pump plunger, thus affecting key performance parameters such as fuel injection rate, injection pressure, and injection duration, ultimately impacting the diesel engine's power output, fuel economy, and emissions.

[0003] Under complex operating conditions (such as high speed, high load, variable speed, and variable load), the motion characteristics and stress state of the cam-roller pair become extremely complex. On the one hand, the contact frequency between the cam and the roller increases significantly, and the contact stress increases sharply, easily leading to failure problems such as surface wear and fatigue pitting. On the other hand, the inertial force of the piston movement increases significantly, placing extremely high demands on the buffering and reset performance of the spring. The rationality of the matching between the spring parameters and the cam profile directly determines whether the system will experience faults such as spring fly-out, increased vibration, and response lag. In addition, the rationality of geometric parameters such as pressure angle and radius of curvature under complex operating conditions has a more prominent impact on system energy loss, transmission efficiency, and service life.

[0004] However, existing cam designs and spring selection technologies have many shortcomings and are difficult to meet the needs of complex working conditions:

[0005] 1) Disconnection between cam and spring selection: Existing technologies often design the cam profile and select spring parameters separately without establishing a collaborative optimization mechanism between the two. This results in poor system matching after the design is completed, and problems such as insufficient limit speed and excessive contact stress are likely to occur.

[0006] 2) Incomplete performance verification system: There is a lack of systematic verification methods covering multiple dimensions such as radius of curvature, pressure angle, contact stress, and limiting speed. The constraints on key parameters during the design process are insufficient, making it difficult to guarantee reliability under complex working conditions.

[0007] 3) Insufficient design efficiency and optimality: The trial-and-error method relies on the professional experience of designers, requires repeated modification and verification, has a long design cycle, poor repeatability, and is difficult to find the optimal design solution under multiple constraints.

[0008] 4) Difficult to adapt to the complex constraints of extreme marine operating conditions: Marine jet systems operate under harsh conditions, and traditional design methods cannot simultaneously incorporate complex constraints such as contact stress and limiting speed into the optimization model.

[0009] Therefore, developing a systematic and automated method for selecting cam profiles and springs under complex working conditions, and realizing the design, comprehensive verification, and intelligent matching of spring parameters for cam profiles, has become the key to solving the above-mentioned technical bottlenecks. Summary of the Invention

[0010] In view of this, in order to solve the problem that the current design of the cam and spring of the plunger pump in the marine injection system has not been fully verified and intelligently matched, resulting in difficulty in meeting the reliability and safety requirements under complex working conditions, the present invention provides a cam profile design and spring selection method for the plunger pump in the marine injection system.

[0011] To achieve the above objectives, the present invention provides the following technical solution:

[0012] A method for designing the cam profile and selecting springs for a marine injection system plunger pump includes the following steps:

[0013] S1. Cam profile design under complex service conditions

[0014] Based on a polynomial piecewise function, a smooth and controllable cam profile is constructed according to the performance requirements of the fuel injection system.

[0015] Specifically, based on the performance requirements of the fuel injection system, such as the plunger pump's fuel supply rate and injection advance angle, a suitable motion law for the cam follower is designed, the basic design parameters of the cam are determined, and a mathematical model of the cam profile is constructed using polynomial combination. The entire working cycle is divided into multiple segments, and each segment selects a polynomial function of different orders according to the motion characteristics required. By setting boundary condition equations, a system of linear equations is established to solve the polynomial coefficients, ensuring that the profile meets specific process requirements while achieving controllable and smooth motion without abrupt changes.

[0016] S2. Spring Design and Selection Based on Cam Profile

[0017] Based on the kinematic and dynamic response provided by the cam profile in step S1, a system load model is established, and the spring parameters are initially matched and checked using "spring clamping force ≥ system inertial force" as the key constraint.

[0018] Specifically, based on the follower displacement-velocity-acceleration curves provided by the obtained cam profile, especially the magnitude and location of the maximum lift and maximum negative acceleration, and combined with system parameters (mass of moving parts, pump chamber pressure, etc.), the composite variation curves of hydraulic pressure, inertial force, and frictional force acting on the follower within one working cycle are calculated. A system dynamic model is established, and the dynamic load that the spring needs to overcome is defined. A set of initial spring parameters is selected, and the mathematical expression for "spring clamping force ≥ system inertial force" at the key point (at the maximum negative acceleration) is determined as the design red line. System-level performance indicators such as actual contact stress, actual spring shear stress, and minimum limiting speed are calculated. The dynamic performance indicators are directly incorporated into the cam profile evaluation system, and a multi-dimensional verification model including geometric and dynamic characteristics is established to verify whether the selected spring meets the allowable performance indicators.

[0019] S3. Determine the boundary of the cam-spring matching parameters.

[0020] A multi-objective genetic algorithm is used to jointly optimize the parameters of the cam and the spring in step S2, generating a Pareto optimal solution set, and a multi-attribute decision method is used to select the matching parameters with the best overall performance.

[0021] Specifically, a multi-objective genetic algorithm is used as a multi-objective optimization algorithm to perform collaborative evolution optimization of cam and spring parameters. By defining a search space with spring stiffness, preload, spring mean diameter, and spring wire diameter as decision variables, and setting constraints including contact stress, spring shear stress, and limiting speed, the algorithm aims to minimize contact stress, minimize spring shear stress, maximize limiting speed margin, and minimize spring flyoff risk. These objectives are integrated through weighting coefficients. Population size, number of iterations, crossover and mutation probability parameters are configured. The algorithm is run to output a Pareto optimal solution set, and a multi-attribute decision method is used to identify the safety boundary of parameters and the optimal range of comprehensive performance from the solution set.

[0022] S4. Cam profile design and spring selection method

[0023] Integrating steps S1 to S3 forms a systematic closed-loop design process from cam profile design and initial spring matching verification to parameter co-optimization. It outputs verified and optimized cam profile data, spring parameter set, and system matching performance report, completing the entire closed-loop process from design to verification.

[0024] Furthermore, the basic design parameters of the cam in step S1 include the cam base circle radius, roller radius, plunger diameter, cam maximum lift, pre-stroke, effective stroke, cam offset, cam rated speed, equivalent mass of moving parts, elastic modulus and friction coefficient of cam and roller materials, and effective contact width of roller.

[0025] Furthermore, in step S1, the polynomial piecewise function is a 5-segment polynomial, which divides one working cycle segment of the cam into the following segments based on the motion characteristics of starting, accelerating, constant speed, deceleration, and returning to position: the first segment is the pre-lift segment, which uses a 6th-order polynomial; the second segment is the effective stroke segment, which uses a 3rd-order polynomial; the third segment is the transition segment, which uses a 1st-order polynomial; the fourth segment is the return segment, which uses a 3rd-order polynomial; and the fifth segment is the end-point buffer segment, which uses a 6th-order polynomial.

[0026] Furthermore, the matrix inversion method used in step S1 to solve for the polynomial coefficients involves transforming the boundary conditions and constraints into the form of... The system of linear equations, where A is the coefficient matrix, X is the coefficient vector of the polynomial to be solved, and B is the vector of constant terms, is obtained by calculating... Solve for the coefficients of all polynomials.

[0027] Furthermore, the contact stress verification step in step S2 includes: calculating the normal force of the cam-roller pair, calculating the equivalent radius of curvature, and calculating the maximum contact stress according to Hertzian contact theory. The verification condition is that the maximum contact stress is less than the allowable contact stress of the material.

[0028] Furthermore, in step S3, when selecting the final solution from the Pareto optimal solution set, the Top-Ideal Solution Ranking Method (TOPSIS) is used for multi-objective decision-making. The relative closeness of each solution to the ideal solution and the anti-ideal solution is calculated, and the solution with the highest closeness is selected as the optimal spring parameters to determine the final spring stiffness K and spring preload Ft.

[0029] The beneficial effects of this invention are as follows:

[0030] 1. The cam profile design and spring selection method for marine injection system plunger pumps disclosed in this invention first constructs a smooth and precisely controllable cam profile based on the performance indicators of the fuel injection system using polynomial piecewise modeling technology. On this basis, a system load model is established based on the kinematic and dynamic responses determined by the profile, and the initial matching and verification of spring parameters are completed using the key constraint that "the spring clamping force is not less than the inertial force". Next, a multi-objective collaborative optimization mechanism is introduced to jointly optimize the cam and spring parameters, generating a Pareto solution set characterizing the performance trade-off. Using multi-attribute decision-making methods, parameter matching boundaries that combine safety and superior overall performance are identified, thus achieving a leap from local parameter design to optimal global system performance. Finally, the verified and optimized cam profile data, spring parameter set, and system matching performance report are output, completing the entire closed-loop process from design to verification, forming a systematic design-matching-optimization closed-loop process.

[0031] 2. The cam profile design and spring selection method for marine injection system plunger pumps disclosed in this invention establishes a linkage mechanism of "cam profile design - performance verification - spring parameter optimization - system integration verification". The dynamic characteristics of the cam profile and spring parameters (stiffness, preload, etc.) are taken as the overall optimization objects. The method uses a multi-objective genetic algorithm to intelligently match and collaboratively optimize the two, which fundamentally solves the problem of cam and spring matching disconnect in traditional design. This effectively avoids system failures such as insufficient limit speed and excessive contact stress caused by poor matching, and significantly improves the overall matching and working stability of the system under complex working conditions.

[0032] 3. The cam profile design and spring selection method for marine injection system plunger pumps disclosed in this invention establish a comprehensive multi-dimensional performance verification system. This system fully covers key performance indicators such as radius of curvature, pressure angle, contact stress, limiting speed, spring non-disengagement, and allowable pump chamber pressure, and clarifies the quantitative constraint standards and precise calculation methods for each parameter. This systematic verification process greatly alleviates the shortcomings of traditional technology verification items being singular and lacking sufficient constraints, providing a solid guarantee for the reliability of the cam-spring system under harsh marine operating conditions such as high pressure and high speed.

[0033] 4. The cam profile design and spring selection method for marine injection system plunger pumps disclosed in this invention achieves a high degree of automation and reproducibility in the design process through mathematical modeling, matrix solving, and intelligent optimization algorithms. This significantly reduces reliance on human experience and effectively shortens the design cycle. The multi-objective genetic algorithm can quickly search and generate Pareto optimal solution sets representing different performance trade-offs under multiple constraints. Combined with multi-attribute decision-making methods such as TOPSIS, the optimal solution with the best overall performance is selected, thus solving the problems of low efficiency and difficulty in obtaining globally optimal solutions in traditional trial-and-error methods. More importantly, the optimization algorithm explicitly sets hard engineering constraints such as contact stress, spring shear stress, and limiting speed, ensuring that each candidate solution generated by the algorithm automatically meets these core safety requirements. This gives the final design the potential to adapt to extreme marine operating conditions, greatly improving the reliability and engineering practicality of the design.

[0034] Other advantages, objectives, and features of the invention will be set forth in part in the description which follows, and in part will be apparent to those skilled in the art from the following examination, or may be learned from practice of the invention. The objectives and other advantages of the invention can be realized and obtained through the following description. Attached Figure Description

[0035] To make the objectives, technical solutions, and advantages of the present invention clearer, the preferred embodiments of the present invention will be described in detail below with reference to the accompanying drawings, wherein:

[0036] Figure 1 This is a flowchart illustrating the cam profile design and spring selection method of the present invention.

[0037] Figure 2 This is a schematic diagram of the polynomial segmentation design of the cam profile of the present invention; Figure 2 (a) is a graph showing the relationship between piston displacement and cam rotation angle. Figure 2 (b) is a graph showing the relationship between the piston's speed and the cam's rotation angle. Figure 2 (c) is a graph showing the relationship between the piston's acceleration and the cam's rotation angle;

[0038] Figure 3 This is a diagram defining the cam profile and geometric parameters of the present invention;

[0039] Figure 4 This is a diagram of the cam-roller contact stress calculation model for this invention;

[0040] Figure 5 This is a flowchart of the multi-objective optimization algorithm for spring parameters (NSGA-II) of this invention;

[0041] Figure 6 This is a schematic diagram illustrating the Pareto front and optimal solution selection for multi-objective optimization in this invention. Detailed Implementation

[0042] The following specific examples illustrate the implementation of the present invention. Those skilled in the art can easily understand other advantages and effects of the present invention from the content disclosed in this specification. The present invention can also be implemented or applied through other different specific embodiments, and various details in this specification can also be modified or changed based on different viewpoints and applications without departing from the spirit of the present invention.

[0043] like Figure 1 The illustrated design of the cam profile and spring selection method for the marine injection system plunger pump includes the following steps:

[0044] S1. Cam profile design method for complex service conditions;

[0045] Based on the performance requirements of the fuel injection system, such as the plunger pump's fuel supply rate and injection advance angle, a suitable motion law for the cam follower is designed, and the following is determined: Figure 3 The basic design parameters of the cam shown include the cam base circle radius. Roller radius plunger diameter cam maximum lift Pre-trip Effective itinerary Cam offset e=0, cam rated speed Equivalent mass of moving parts The elastic modulus of the cam and roller materials The friction coefficient The effective contact width of the roller B = 51 mm;

[0046] A mathematical model of the cam profile is constructed by polynomial combination. A working cycle of the cam from 0° to 45° (the lift segment) is divided into 5 sections. Different-order polynomial functions are selected for each section according to the motion characteristic requirements to achieve smooth motion from start, acceleration, constant speed, deceleration to return. The piecewise polynomial function is a 5-piece polynomial, and a working cycle of the cam is divided into: the first pre-travel section, using a 6th-order polynomial; the second effective-travel section, using a 3rd-order polynomial; the third transition section, using a 1st-order polynomial; the fourth return section, using a 3rd-order polynomial; the fifth base circle section, using a 6th-order polynomial. The polynomials for each section are selected as follows ( is the cam rotation angle):

[0047] The first section (0° ≤ x ≤ 17°): pre-lift section, using a 6th-order polynomial combination:

[0048]

[0049] The second section (17° < x ≤ 19°): effective-travel section, using a 3rd-order polynomial:

[0050]

[0051] The third section (19° < x ≤ 27°): transition section, using a linear function:

[0052]

[0053] The fourth section (27° < x ≤ 30°): return section, using a 3rd-order polynomial:

[0054]

[0055] The fifth section (30° < x ≤ 45°): end buffer section, using a 6th-order polynomial:

[0056]

[0057] where is the order of the th polynomial segment, are the polynomial coefficients to be determined,

[0058] Furthermore, by setting boundary condition equations, including the starting zero-value condition, the ending extreme-value condition, the constraints of process special control points, and the continuity conditions of displacement, velocity, and acceleration at each segmentation point, the following 20 boundary condition equations are established:

[0059] Set the starting zero value condition : , , ;

[0060] Set the endpoint extreme value condition : , , ;

[0061] Set the continuity condition for the segmentation points: for i = 1, 2, ..., 4, satisfy... ,

[0062] ;

[0063] Set special control point constraints: Pre-travel point Valid travel points Maximum lift point ;

[0064] The above boundary conditions and constraints can be rearranged into a system of linear equations: Where A is a 20×20 coefficient matrix, Let B be the coefficient vector of the polynomial to be determined, and let B be the constant term vector. The coefficients are calculated using the matrix inversion method. Solve for all polynomial coefficients. Ensure that the profile meets specific process requirements while achieving controllable, smooth, and abrupt motion.

[0065] S2. Spring design and selection technology based on cam profile;

[0066] Based on the follower displacement-velocity-acceleration curve provided by the obtained cam profile, such as Figure 2 As shown, from left to right, the graphs depict the piston displacement as a function of the cam angle, the piston speed as a function of the cam angle, and the piston acceleration as a function of the cam angle. Based on the magnitude and position of the maximum lift and maximum negative acceleration, combined with system parameters (mass of moving parts, pump chamber pressure, etc.), the combined curves of hydraulic pressure, inertial force, and friction force acting on the driven part within one working cycle are calculated. A system dynamic model is then established, and the dynamic load that the spring needs to overcome is defined.

[0067] Select a set of initial spring parameters, spring preload... Spring stiffness The mathematical expression for "spring clamping force ≥ system inertial force" at the key point (at the maximum negative acceleration) is determined as the design red line. System-level performance indicators such as actual contact stress, actual spring shear stress, and minimum limit speed are calculated. The dynamic performance indicators are directly incorporated into the cam profile evaluation system. A multi-dimensional verification model including geometric and dynamic characteristics is established to verify whether the selected initial spring meets the allowable performance indicators.

[0068] The steps for contact stress verification include: calculating the normal force of the cam-roller pair, calculating the equivalent radius of curvature, and calculating the maximum contact stress based on Hertzian contact theory. The verification condition is that the maximum contact stress is less than the allowable contact stress of the material.

[0069] Curvature radius verification: Calculate the theoretical profile curvature radius:

[0070]

[0071] in Actual contour radius of curvature The verification criteria are: ≥ , The minimum permissible radius of curvature is set.

[0072] Pressure angle check: Calculate the pressure angle

[0073] ,

[0074] Verification criteria are (Pushing segment) The maximum allowable pressure angle set;

[0075] Limit speed verification: Calculate cam speed

[0076] ,

[0077] Verification criteria are ;

[0078] Contact stress check: Calculate Hertzian contact stress

[0079] ,

[0080] Among them, such as Figure 4 As shown, calculate the normal force. The hydraulic pressure on the driven component Inertial force Spring clamping force Calculate the equivalent radius of curvature Iterative calculation of friction force: ,in , The set pump chamber pressure, For cam linear acceleration, , where is the angular velocity of the cam;

[0081] Verification criteria are , The maximum allowable contact stress is set.

[0082] Spring non-flyout check: at the point of maximum negative acceleration ( , The verification criteria are: ;

[0083] S3. Determine the boundary of the cam-spring matching parameters based on multi-objective cooperative evolution and dynamic decision-making;

[0084] A multi-objective genetic algorithm is used as a multi-objective optimization algorithm to perform collaborative evolution optimization of cam and spring parameters. The search space is defined with spring stiffness, preload, pitch diameter, and wire diameter as decision variables, including: setting spring stiffness K: range [20, 500] N / mm, preload Ft: range [300, 1500] N, spring pitch diameter D: range [30, 80] mm, and spring wire diameter d: range [10, 20] mm;

[0085] The objective function is defined by setting constraints including contact stress, spring shear stress, and limiting speed, with the goals of minimizing contact stress, minimizing spring shear stress, maximizing the limiting speed margin, and minimizing the risk of spring flyoff, and combining these with weighting coefficients.

[0086] Contact stress difference:

[0087] Difference in spring shear stress: ,in

[0088] Difference in limiting speed margin:

[0089] Differences in the risk of spring detachment:

[0090] Set the final objective function based on the weights:

[0091]

[0092] Set the algorithm parameters: population size, number of iterations, crossover probability, mutation probability; configure the parameters of population size, number of iterations, crossover and mutation probability, run the algorithm to output the Pareto optimal solution set, and use the multi-attribute decision method to identify the safe boundary of parameters and the optimal range of comprehensive performance from the solution set.

[0093] like Figure 5 As shown, the specific steps are as follows:

[0094] S31. Population initialization:

[0095] Set population size Maximum number of iterations Crossover probability Probability of mutation 100 individuals (100 sets of spring parameters) are randomly generated according to the constraints, ensuring that the initial parameters are all within the defined spring parameter range. An initial population is randomly generated, with each individual being... .

[0096] S32. Fitness Assessment: For each individual, the dynamic model is invoked to calculate... A higher fitness value indicates better spring parameters. If a constraint is violated (such as stress exceeding the allowable value or parameter exceeding the range), the fitness value will drop sharply through a "penalty term" to ensure that GA will not select individuals that violate the constraints.

[0097] S33. Non-dominated sorting and crowding calculation:

[0098] Based on the required engineering design requirements, set the weight coefficients for each objective function. , , , Prioritize ensuring rotational speed margin and contact stress, and perform non-dominated sorting based on target values ​​to classify Pareto front levels. Calculate the crowding degree of individuals within the same front layer to maintain the distribution of the solution set.

[0099] S34. Selection, Crossover, and Mutation:

[0100] Selection: Tournament selection is adopted, and three individuals are randomly selected for comparison. The individual with the lowest fitness is selected as the parent, which preserves a certain degree of diversity and crossover while avoiding premature convergence.

[0101] Crossover: A single-point crossover method is adopted, randomly selecting a crossover point and swapping the parameters of the two parent individuals after the crossover point. After the crossover, it is checked whether the parameters exceed the constraint range; if they do, they are truncated to the boundary.

[0102] Mutation: Gaussian mutation method is used to add Gaussian noise (mean 0, standard deviation 0.1 of the parameter range) to each parameter of an individual, which ensures population diversity and avoids excessive parameter mutation;

[0103] Repair: Perform boundary repair on the offspring generated by crossover and mutation to ensure that all parameters are within the allowable range.

[0104] S35, Elite Preservation and Population Renewal:

[0105] Sort the current generation (parent generation) by fitness and select the top 5 elite individuals. After calculating the fitness of the offspring, replace the corresponding number of the worst-fitting offspring individuals with the elite parent individuals. Then, completely replace the parent generation with the updated offspring to update the population and avoid losing the optimal solution during iteration.

[0106] S36. Termination judgment: If the set number of iterations is reached or the Pareto front converges (front change <1% for 10 consecutive generations), then stop; otherwise, return to S32.

[0107] S37. Optimal Solution Decision:

[0108] When selecting the final solution from the Pareto optimal solution set, the Top-Ideal Solution Ranking Method (TOPSIS) is used for multi-objective decision-making. The relative closeness of each solution to the ideal solution and the anti-ideal solution is calculated, and the solution with the highest closeness is selected as the optimal spring parameter.

[0109] Normalize the objective value of each solution in the Pareto front, and define the ideal solution and the anti-ideal solution respectively:

[0110] ;

[0111] ;

[0112] Calculate each solution to and Euclidean distance , Calculate the closeness ,choose The largest solution is used as the final spring parameters to determine the final spring stiffness K and spring preload Ft.

[0113] S4. Forming a design method for the cam profile of the plunger pump in a marine injection system and a method for selecting springs;

[0114] Integrating steps S1 to S3 forms a systematic closed-loop design process from cam profile design and initial spring matching verification to parameter co-optimization. It outputs verified and optimized cam profile data, spring parameter set, and system matching performance report, completing the entire closed-loop process from design to verification.

[0115] Figure 6The 3D scatter plot visually illustrates the complex trade-offs among multiple key performance indicators in the cam and spring co-optimization design. The three axes represent differences in rotational speed accuracy, contact stress, and spring stress, respectively. Each data point in the plot corresponds to a specific combination of design parameters, with colors grading from blue to yellow to reflect the overall performance level, with yellow indicating superior overall performance. The "Pareto front," outlined by a black line, identifies the best possible solution set where all objectives cannot be improved simultaneously under existing constraints, highlighting the inherent conflicts between design goals. Finally, the red star-shaped "optimal solution" selected from the Pareto front using multi-attribute decision-making methods (such as TOPSIS) provides specific optimization parameters (such as spring stiffness K, preload Ft, and diameter D) while balancing various indicators, offering designers a data-driven optimal design scheme and achieving a leap from empirical trial and error to scientific decision-making.

[0116] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit it. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can be made to the technical solutions of the present invention without departing from the spirit and scope of the present invention, and all such modifications or substitutions should be covered within the scope of the claims of the present invention.

Claims

1. A method for designing the cam profile and selecting springs for a marine injection system plunger pump, characterized in that, Includes the following steps: S1. Cam profile design under complex service conditions Based on the performance requirements of the fuel injection system, including plunger pump fuel supply rate, injection advance angle, cyclic fuel supply quantity, injection pressure and pressure build-up rate, and cam follower kinematic constraints, a reasonably matched cam follower motion law is designed, the basic design parameters of the cam are determined, and a mathematical model of the cam profile is constructed using polynomial combination. The entire working cycle is divided into multiple segments, and each segment selects a polynomial function of different orders according to the motion characteristics requirements. By setting boundary condition equations, a linear equation system is established to solve the polynomial coefficients, ensuring that the profile meets specific process requirements while achieving controllable and smooth motion without abrupt changes. S2. Spring Design and Selection Based on Cam Profile Based on the displacement-velocity-acceleration curve of the driven component provided by the obtained cam profile, especially the magnitude and position of the maximum lift and maximum negative acceleration, and combined with system parameters (including the mass of the moving part, the fuel pressure in the pump chamber, the plunger diameter, the plunger spring stiffness, the plunger spring preload, the coefficient of friction, and the engine speed), the composite change curve of the hydraulic pressure, inertial force, and friction force acting on the driven component within one working cycle is calculated, a system dynamic model is established, and the dynamic load that the spring needs to overcome is defined; Select a set of initial spring parameters, determine the mathematical expression for "spring clamping force ≥ system inertial force" at the key point (at the maximum negative acceleration), and use it as the design red line. Calculate the system-level performance indicators, including actual contact stress, actual spring shear stress, and minimum limit speed. Directly incorporate the dynamic performance indicators into the cam profile evaluation system, and establish a multi-dimensional verification model that includes geometric and dynamic characteristics to verify whether the selected spring meets the allowable performance indicators. S3. Determine the boundary of the cam-spring matching parameters. A multi-objective genetic algorithm is used as a multi-objective optimization algorithm to perform collaborative evolution optimization of cam and spring parameters. By defining a search space with spring stiffness, preload, spring mean diameter, and spring wire diameter as decision variables, and setting constraints including contact stress, spring shear stress, and limit speed, the algorithm aims to minimize contact stress, minimize spring shear stress, maximize limit speed margin, and minimize spring fly-off risk. The algorithm integrates these objectives with weight coefficients, configures parameters such as population size, number of iterations, and crossover and mutation probabilities, runs the algorithm to output Pareto optimal solution set, and uses a multi-attribute decision method to identify the safety boundary of parameters and the optimal range of comprehensive performance from the solution set. S4. Cam profile design and spring selection method Integrating steps S1 to S3 forms a systematic closed-loop design process from cam profile design and initial spring matching verification to parameter co-optimization. It outputs verified and optimized cam profile data, spring parameter set, and system matching performance report, completing the entire closed-loop process from design to verification.

2. The cam profile design and spring selection method as described in claim 1, characterized in that, The basic design parameters of the cam in step S1 include the cam base circle radius. Roller radius plunger diameter cam maximum lift Pre-trip Effective itinerary Cam offset e, cam rated speed Equivalent mass of moving parts Elastic modulus of cam and roller materials coefficient of friction , effective contact width of the roller B.

3. The cam profile design and spring selection method as described in claim 2, characterized in that, In step S1, the piecewise polynomial function is a 5-segment polynomial. To adapt to the requirements of short stroke, low impact, and smooth buffering motion under marine high-pressure injection conditions, the cam's 0~45° working cycle segment is divided into five continuous angle intervals according to the functional characteristics of pre-lift, effective stroke, transition, return, and end-point buffering. A corresponding order polynomial is matched according to the motion control target of each segment. The first pre-lift segment (0° ≤ x ≤ 17°) uses a sixth-order polynomial ; the second effective stroke segment (17° < x ≤ 19°) uses a third-order polynomial ; the third transition segment (19° < x ≤ 27°) uses a first-order polynomial ; the fourth return stroke segment (27° < x ≤ 30°) uses a third-order polynomial ; the fifth end buffer segment (30° < x ≤ 45°) uses a sixth-order polynomial .

4. The cam profile design and spring selection method as described in claim 3, characterized in that, The matrix inversion method used in step S1 to solve for the polynomial coefficients is as follows: the 20 boundary conditions and constraints are transformed into the form of... A system of linear equations, where A is a 20×20 coefficient matrix. Let B be the coefficient vector of the polynomial to be solved, and let B be the constant term vector. This is achieved through calculation... Solve for the coefficients of all polynomials.

5. The cam profile design and spring selection method as described in claim 4, characterized in that, The boundary conditions in step S1 include the starting point zero value condition, the ending point extreme value condition, process-specific control point constraints, and the continuity conditions of displacement, velocity, and acceleration at each segment point, among which: the starting point zero value condition : , , Endpoint extreme value condition : , , Continuity condition for segmentation points: For i = 1, 2, ..., 4, the following condition is satisfied: , , Special control point constraints: pre-travel point Valid travel points Maximum lift point .

6. The cam profile design and spring selection method as described in claim 1, characterized in that, The contact stress verification steps in step S2 include: calculating the normal force of the cam-roller pair, calculating the equivalent radius of curvature, and calculating the maximum contact stress according to Hertz contact theory. The verification condition is that the maximum contact stress is less than the allowable contact stress of the material.

7. The cam profile design and spring selection method as described in claim 6, characterized in that, Step S2: Curvature radius verification: Calculate the theoretical profile curvature radius. in Actual contour radius of curvature The verification criteria are: ≥ , The minimum permissible radius of curvature is set. Pressure angle check: Calculate the pressure angle ， Verification criteria are (Pushing segment) The maximum allowable pressure angle set; Limiting speed verification: Calculate cam speed ， Verification criteria are ; Contact stress check: Calculate Hertzian contact stress , Among them, the calculation of normal force The hydraulic pressure on the driven component Inertial force Spring clamping force Calculate the equivalent radius of curvature Iterative calculation of friction force: ,in , The set pump chamber pressure, For cam linear acceleration, , where is the cam angular velocity; the verification condition is . , The maximum allowable contact stress is set. Spring non-flyout check: at the point of maximum negative acceleration ( , The verification criteria are: .

8. The cam profile design and spring selection method as described in claim 1, characterized in that, In step S3, when selecting the final solution from the Pareto optimal solution set, the Top-Ideal Solution Ranking Method (TOPSIS) is used for multi-objective decision-making. The relative closeness of each solution to the ideal solution and the anti-ideal solution is calculated, and the solution with the highest closeness is selected as the optimal spring parameters to determine the final spring stiffness K and spring preload Ft.

9. The cam profile design and spring selection method as described in claim 8, characterized in that, In step S3 Contact stress difference: Difference in spring shear stress: ,in Difference in limiting speed margin: Differences in the risk of spring detachment: Set the final objective function based on the weights: 。 10. The cam profile design and spring selection method as described in claim 9, characterized in that, In step S3, the objective value of each solution in the Pareto front is normalized, and the ideal solution and the anti-ideal solution are defined respectively: ； ； Calculate each solution to and Euclidean distance , Calculate the closeness ,choose The largest solution is used as the final spring parameters to determine the final spring stiffness K and spring preload Ft.

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