Fast calculation method and system for diesel engine shafting vibration response

Abstract

The application provides a quick calculation method and system for diesel engine shaft vibration response, comprising: simplifying a crankshaft system and stress of a diesel engine to obtain a simplified model of the diesel engine; establishing a transverse vibration transfer matrix, a longitudinal vibration transfer matrix and a torsional vibration transfer matrix of a straight beam respectively based on a straight beam unit, and calculating a spatial continuum transfer matrix of the straight beam; establishing a point transfer matrix of coordinate transformation at a connecting point of each straight beam through force balance conditions and displacement coordination conditions; splicing a transfer matrix of a single crank to a transfer matrix of the entire crankshaft system according to the spatial continuum transfer matrix of the straight beam and the point transfer matrix of coordinate transformation; constructing a dynamic equation according to the transfer matrix of the single crank to the entire crankshaft system; calculating inherent frequencies of the crankshaft system according to the dynamic equation; loading a map of excitation force on a crankpin of the crankshaft system, and solving forced vibration responses of any point on the crankshaft by using a Newmark-beta method.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of diesel engine shafting vibration response calculation and design, and particularly relates to a rapid calculation method and system for diesel engine shafting vibration response. BACKGROUND

[0002] The ship power device (diesel engine, gas engine, steam turbine and motor) refers to the entire device for transmitting the energy of a prime mover to a load, and is the entire transmission and support system starting from the prime mover, passing through a gearbox, a transmission shaft section and other devices and reaching the load. The ship power device has increasingly complex composition, more compact structure and layout, continuously improved power density, increasingly harsh operating environment and frequently changed operating conditions, and these characteristics have relatively high requirements for the quietness, safety, reliability and intelligent control of the ship power device.

[0003] In actual engineering, the diesel engine is a main excitation source of ship body vibration and noise, and the vibration condition of the diesel engine directly affects the smooth operation of the ship. The diesel engine shafting is prone to fracture due to the action of time-varying excitation, and once the shafting is fractured, the ship loses power, which will cause unbearable loss. Most of the existing theories are to calculate after discretizing the shafting, and it is difficult to meet the calculation accuracy of the shafting with complex structure and large size.

[0004] The crankshaft system in the diesel engine is a space structure with three-dimensional vibration form, and the existing shafting calculation method is mainly to calculate and design the shafting according to the existing empirical formula and the finite element method.

[0005] The research based on the empirical formula is mostly based on a large amount of experimental data of a mature engine type that has been built, and this method is suitable for a specific type of diesel engine and cannot be used as a general calculation method. The finite element method needs to build a three-dimensional finite element model of the diesel engine and perform simulation calculation, which is complex and time-consuming, and the three-dimensional coupling vibration mechanism of the diesel engine crankshaft transverse (bending) direction, longitudinal direction and torsional direction is not truly mastered. SUMMARY

[0006] Therefore, the present application aims to provide a rapid calculation method and system for diesel engine shafting vibration response, which increases the simulation calculation accuracy by substantially existing three-dimensional coupling vibration of shaft vibration, ensures the completeness of calculation by extracting the forced vibration response time domain signal of any part of the crankshaft based on the continuum vibration theory, has short calculation time, controllable calculation accuracy, good universality and engineering applicability by directly simplifying the state parameters such as the geometric size of the crankshaft.

[0007] In a first aspect, the present application provides a rapid calculation method for diesel engine shafting vibration response, which comprises the following steps:

[0008] simplify the crankshaft system and force of the diesel engine to obtain a simplified model of the diesel engine; wherein the simplified model of the diesel engine comprises an excitation force;

[0009] Based on the straight beam element, a transverse vibration transfer matrix, a longitudinal vibration transfer matrix and a torsional vibration transfer matrix of the straight beam are respectively established;

[0010] According to the transverse vibration transfer matrix, the longitudinal vibration transfer matrix and the torsional vibration transfer matrix, a spatial continuum transfer matrix of the straight beam is calculated;

[0011] A point transfer matrix of coordinate transformation at a connecting point of each section of the straight beam is established through force balance conditions and displacement coordination conditions;

[0012] According to the spatial continuum transfer matrix of the straight beam and the point transfer matrix of coordinate transformation, a transfer matrix of a single crank to the entire crankshaft system is spliced;

[0013] According to the transfer matrix of the single crank to the entire crankshaft system, a dynamic equation is constructed;

[0014] According to the dynamic equation, the natural frequency of the crankshaft system is calculated;

[0015] A map of the excitation force is loaded on the crankpin of the crankshaft system, and the forced vibration response of any point on the crankshaft is solved by using the Newmark-β method.

[0016] In the second aspect, the embodiments of the present application provide a fast calculation system of diesel engine shaft system vibration response, the system comprises:

[0017] A simplification module is configured to simplify the crankshaft system and force of the diesel engine to obtain a simplified model of the diesel engine; wherein the simplified model of the diesel engine comprises an excitation force;

[0018] A first establishment module is configured to establish a transverse vibration transfer matrix, a longitudinal vibration transfer matrix and a torsional vibration transfer matrix of the straight beam based on the straight beam element;

[0019] A first calculation module is configured to calculate a spatial continuum transfer matrix of the straight beam according to the transverse vibration transfer matrix, the longitudinal vibration transfer matrix and the torsional vibration transfer matrix;

[0020] A second establishment module is configured to establish a point transfer matrix of coordinate transformation at a connecting point of each section of the straight beam through force balance conditions and displacement coordination conditions;

[0021] A splicing module is configured to splice a transfer matrix of a single crank to the entire crankshaft system according to the spatial continuum transfer matrix of the straight beam and the point transfer matrix of coordinate transformation;

[0022] a construction module configured to construct a dynamic equation according to a transfer matrix of the single crank to the entire crankshaft system;

[0023] a second calculation module configured to calculate the natural frequency of the crankshaft system according to the dynamic equation;

[0024] a solution module configured to load the map of the excitation force on the crankpin of the crankshaft system, and solve the forced vibration response of any point on the crankshaft by using the Newmark-β method.

[0025] In a third aspect, an electronic device is provided, which includes a memory and a processor, and the memory stores a computer program capable of running on the processor, and the processor implements the method as described above when executing the computer program.

[0026] The embodiment of the present application provides a fast calculation method and system for diesel engine shaft vibration response, including: simplifying a crankshaft system and stress of a diesel engine to obtain a simplified model of the diesel engine; wherein the simplified model of the diesel engine includes an excitation force; based on a straight beam element, a transverse vibration transfer matrix, a longitudinal vibration transfer matrix and a torsional vibration transfer matrix of the straight beam are respectively established; the spatial continuum transfer matrix of the straight beam is calculated according to the transverse vibration transfer matrix, the longitudinal vibration transfer matrix and the torsional vibration transfer matrix; the point transfer matrix of coordinate transformation at the connecting point of each straight beam is established through force balance conditions and displacement coordination conditions; the transfer matrix of the single crank to the entire crankshaft system is spliced according to the spatial continuum transfer matrix of the straight beam and the point transfer matrix of coordinate transformation; the dynamic equation is constructed according to the transfer matrix of the single crank to the entire crankshaft system; the natural frequency of the crankshaft system is calculated according to the dynamic equation; the map of the excitation force is loaded on the crankpin of the crankshaft system, and the forced vibration response of any point on the crankshaft is solved by using the Newmark-β method; through the three-dimensional coupled vibration of the shaft vibration, the simulation calculation precision is increased; based on the continuum vibration theory, the forced vibration response time domain signal of the crankshaft at any position can be extracted, and the completeness of the calculation is ensured; the state parameters such as the geometric size of the crankshaft are directly simplified, the calculation time is short, the calculation precision can be controlled, and the method has good universality and engineering applicability.

[0027] Additional features and advantages of the application will be set forth in the descriptions that follow, and in part will be apparent from the description or can be learned by practice of the application. The objectives and other advantages of the application will be realized and attained by the structure particularly pointed out in the description and claims.

[0028] In order to make the above-mentioned objectives, characteristics and advantages of the present application more obvious and easy to understand, the following preferred embodiments are specifically described below, and the accompanying drawings are described as follows. BRIEF DESCRIPTION OF DRAWINGS

[0029] In order to more clearly illustrate the technical solutions of the specific embodiments or prior art of the present application, the drawings required to be used in the description of the specific embodiments or prior art will be briefly introduced. Obviously, the drawings in the following description are some embodiments of the present application, and other drawings can be obtained by those skilled in the art without creative effort on the basis of these drawings.

[0030] Figure 1 The flow chart of the rapid calculation method of the diesel engine shaft vibration response provided by the embodiment one of the present application is shown in the figure.

[0031] Figure 2(a) is a schematic diagram of the crank model provided by the embodiment one of the present application.

[0032] Figure 2(b) is a schematic diagram of the single crank simplified model provided by the embodiment one of the present application.

[0033] Figure 2(c) is a schematic diagram of the overall simplified crank provided by the embodiment one of the present application.

[0034] Figure 3 The schematic diagram of the crank-connecting rod mechanism and its force provided by the embodiment one of the present application is shown in the figure.

[0035] Figure 4 The time domain diagram of the decomposed pressure curve provided by the embodiment one of the present application is shown in the figure.

[0036] Figure 5(a) is a schematic diagram of the force and deformation of the xoy plane of the Timoshenko beam microelement provided by the embodiment one of the present application.

[0037] Figure 5(b) is a schematic diagram of the force and deformation of the xoz plane of the Timoshenko beam microelement provided by the embodiment one of the present application.

[0038] Figure 6 The schematic diagram of the longitudinal force and deformation of the Timoshenko beam provided by the embodiment one of the present application is shown in the figure.

[0039] Figure 7 The schematic diagram of the torsional force and deformation of the Timoshenko beam provided by the embodiment one of the present application is shown in the figure.

[0040] Figure 8 The schematic diagram of the spring support provided by the embodiment one of the present application is shown in the figure.

[0041] Figure 9 The schematic diagram of the lumped mass element provided by the embodiment one of the present application is shown in the figure.

[0042] Figure 10 The schematic diagram of the local coordinates of the crank provided by the embodiment one of the present application is shown in the figure.

[0043] Figure 11A schematic diagram of adjacent crank phases provided for the first embodiment of the present application;

[0044] Figure 12 A schematic diagram of coordinate transformation around the x-axis provided for the first embodiment of the present application;

[0045] Figure 13 A schematic diagram of a general position crank local coordinate provided for the first embodiment of the present application;

[0046] Figure 14 A schematic diagram of a double crank model provided for the first embodiment of the present application;

[0047] Fig. 15(a) is a schematic diagram of a response point position provided for the first embodiment of the present application;

[0048] Fig. 15(b) is a schematic diagram of a response point axial displacement time domain curve provided for the first embodiment of the present application;

[0049] Figure 16 A schematic diagram of a diesel engine shaft system vibration response fast calculation system provided for the second embodiment of the present application. DETAILED DESCRIPTION

[0050] In order to make the purpose, technical scheme and advantages of the embodiments of the present application clearer, the technical scheme of the present application will be described in detail below with reference to the drawings. Obviously, the described embodiments are some but not all of the embodiments of the present application. Based on the embodiments in the present application, all other embodiments obtained by those of ordinary skill in the art without creative work fall within the protection scope of the present application.

[0051] In order to make the purpose, technical scheme and advantages of the embodiments of the present application clearer, the technical scheme of the present application will be described in detail below with reference to the drawings. Obviously, the described embodiments are some but not all of the embodiments of the present application. Based on the embodiments in the present application, all other embodiments obtained by those of ordinary skill in the art without creative work fall within the protection scope of the present application.

[0052] Embodiment one:

[0053] Figure 1 A flow chart of a diesel engine shaft system vibration response fast calculation method provided for the first embodiment of the present application.

[0054] With reference to Figure 1 , the method comprises the following steps:

[0055] Step S101, the crankshaft system and stress of the diesel engine are simplified to obtain a simplified model of the diesel engine; wherein the simplified model of the diesel engine comprises an excitation force;

[0056] Step S102, based on a straight beam element, a transverse vibration transfer matrix, a longitudinal vibration transfer matrix and a torsional vibration transfer matrix of the straight beam are respectively established;

[0057] Step S103, according to the transverse vibration transfer matrix, the longitudinal vibration transfer matrix and the torsional vibration transfer matrix, the spatial continuum transfer matrix of the straight beam is calculated;

[0058] Step S104, the point transfer matrix of the coordinate transformation at the connecting point of each segment of the straight beam is established by the force balance condition and the displacement coordination condition;

[0059] Step S105, the transfer matrix of the single crank to the whole crankshaft system is spliced according to the spatial continuum transfer matrix of the straight beam and the point transfer matrix of the coordinate transformation;

[0060] Step S106, the dynamic equation is constructed according to the transfer matrix of the single crank to the whole crankshaft system;

[0061] Step S107, the natural frequency of the crankshaft system is calculated according to the dynamic equation;

[0062] Step S108, the excitation force map is loaded on the crankpin of the crankshaft system, and the forced vibration response of any point on the crankshaft is solved by using the Newmark-β method.

[0063] Further, referring to the crank model schematic diagram as shown in Figure 2(a); Figure 2(b) is a single crank simplified model schematic diagram; Figure 2(c) is a whole crank simplified schematic diagram; step S101 includes the following steps:

[0064] Step S201, the crankshaft is simplified as a spatial structure of multiple straight beams connected to each other;

[0065] Step S202, the crank connecting rod and the piston are simplified as excitation forces:

[0066] Step S203, the crank arm, the crankpin and the main journal are simplified as uniform beam structures with equal cross sections;

[0067] Here, according to the crank diagram of a certain five-cylinder diesel engine, the crank arm, the crankpin and the main journal are simplified as uniform beam structures with equal cross sections.

[0068] Step S204, the bearing is simplified as a three-direction spring structure;

[0069] Step S205, the flywheel is simplified as a lumped mass structure;

[0070] Among them, the excitation force includes: the force F 气 generated by the gas pressure of the cylinder acting on the upper surface of the piston, the reciprocating inertia force F 往 generated by the reciprocating motion of the piston group, the side thrust F 侧 exerted by the inner wall of the cylinder when the piston moves, and the centrifugal inertia force F 离 generated when the crankshaft rotates and acting on the crankpin.

[0071] Specifically, the state parameter table of the diesel engine simplified model is shown in Table 1.

[0072] Table 1

[0073]

[0074]

[0075] The sources of various exciting forces of the diesel engine are determined, so as to Figure 3 The crank-connecting rod mechanism is taken as a frame to analyze the excitation of the crankshaft during the operation of the diesel engine.

[0076] After the above exciting forces are synthesized and decomposed along the tangential direction and the normal direction, the tangential and normal pressure curves under the rated working condition (74 rpm) of the first cylinder (the pressure curves of the remaining cylinders are obtained by sequentially recursively calculating the firing sequence 1-4-3-2-5 and the firing interval angle 0.0-216.0-144.0-72.0-288.0) are obtained as shown in Figure 4

[0077] Further, the step S102 comprises the following steps.

[0078] In step S301, the inertia force and the inertia moment acting on the beam microelement are obtained.

[0079] In step S302, the dynamic balance equation of the beam microelement is obtained according to theoretical mechanics.

[0080] In step S303, the bending moment acting on the beam microelement and the shear force acting on the beam microelement are obtained according to material mechanics.

[0081] In step S304, the bending moment acting on the beam microelement and the shear force acting on the beam microelement are substituted into the dynamic balance equation to obtain the transverse vibration differential equation of the beam.

[0082] In step S305, the variables in the transverse vibration differential equation of the beam are separated to obtain a first equation group; wherein the variables include the rotation angle generated when the beam is bent and the transverse deformation of the beam microelement.

[0083] In step S306, the excitation is substituted into the first equation group to obtain a general solution; wherein the general solution comprises a plurality of first undetermined constants.

[0084] In step S307, the solution of the cross-section rotation angle is obtained; wherein the solution of the cross-section rotation angle comprises a plurality of second undetermined constants.

[0085] In step S308, the general solution and the solution of the cross-section rotation angle are substituted into the transverse vibration differential equation of the beam to obtain the relationship between the plurality of first undetermined constants and the plurality of second undetermined constants.

[0086] ​Step S309, obtaining the bending moment formula and the shear force formula according to material mechanics;

[0087] Step S310, substituting the general solution and the solution of the cross-section rotation angle into the bending moment formula and the shear force formula respectively to obtain an expression between the shear force and the bending moment;

[0088] Step S311, establishing a second equation group according to the general solution, the solution of the cross-section rotation angle, and the expression between the shear force and the bending moment;

[0089] Step S312, transforming the second equation group into a first matrix according to the relationship between the plurality of first undetermined constants and the plurality of second undetermined constants;

[0090] Step S313, calculating the first transfer relationship of the state quantity at both ends of the straight beam according to the first matrix;

[0091] Step S314, calculating the transverse vibration transfer matrix of the straight beam in the xoy plane according to the first transfer relationship of the state quantity at both ends of the straight beam.

[0092] Specifically, FIG. 5(a) shows the force and deformation state of the beam microelement dx when the beam microelement dx vibrates transversely in the xoy plane, where Q y is the shear force on the beam microelement, M z is the bending moment on the beam microelement, I q is the inertial force on the beam microelement, I0 is the inertial moment on the beam microelement, γ is the shear angle generated on the neutral axis of the beam due to shear deformation, φ represents the rotation angle generated when the beam is bent, and y is the transverse deformation of the beam microelement.

[0093] In order to unify the direction of physical quantities, the positive direction convention of general mechanics is adopted: when the cross section of the microelement with the same direction as the x-axis produces deformation with the same direction as the y-axis, and the cross section with the opposite direction as the x-axis produces deformation with the opposite direction as the y-axis, the shear force Q y is positive, and vice versa; when the cross section of the microelement with the same direction as the x-axis produces rotation with the same direction as the z-axis, and the cross section with the opposite direction as the x-axis produces rotation with the opposite direction as the z-axis, the bending moment M z is positive, and vice versa; the sign of the bending-induced rotation angle φ is consistent with the slope .

[0094] According to Newtonian mechanics, the inertial force I q and the inertial moment I0 on the beam microelement are shown in formulas (1) and (2) respectively:

[0095]

[0096] As can be seen from the above, μ s represents the linear density of the beam, I zrepresents the moment of inertia of the beam microelement cross section, and p represents the body density of the beam itself.

[0097] According to the knowledge of theoretical mechanics, the dynamic balance equation of the beam microelement is shown in formulas (3) and (4):

[0098]

[0099] According to the knowledge of material mechanics:

[0100]

[0101] Substitute formulas (5) and (6) into formulas (3) and (4), and after rearrangement, the transverse vibration differential equation of the beam is obtained:

[0102]

[0103] In the above formula, E represents the Young's modulus of the beam, G represents the shear Young's modulus of the beam, A represents the cross-sectional area of the beam, and k represents the shear correction coefficient. Separate the variables y and φ in formulas (7) and (8) to obtain the first equation group.

[0104]

[0105] Assume that the system performs the same frequency harmonic vibration, and set y(x, t) = y(x) sin ωt, wherein the symbol ω represents the free vibration circular frequency of the entire beam structure. Next, substitute the excitation y(x, t) into formula (9) to obtain:

[0106] y IV (x)+g 2 y″(x)-a 4 y(x) = 0 (11)

[0107] In the formula, g and a are intermediate variables:

[0108]

[0109] Assume that y(x) = Ce Sx , and substitute it into formula (11) to obtain:

[0110] S 4 +g 2 S 2 -a 4 = 0 (14)

[0111] The roots of equation (14) are respectively For convenience, λ1 / l and λ2 / l are respectively represented, and l represents the total length of the beam.

[0112]

[0113] For consistency with the following text, λ1, λ2 are simplified as:

[0114]

[0115] In the formula:

[0116]

[0117] The general solution obtained by substituting the simultaneous solution into formula (14) is:

[0118]

[0119] In the formula C1-C4 are undetermined constants. The differential equation (10) satisfied by the cross-section rotation angle φ(x, t) is completely consistent in form with the differential equation (9) satisfied by the transverse displacement y(x, t), so the solution of the cross-section rotation angle φ(x, t) can be assumed to be in the form shown in (23) as follows:

[0120]

[0121] In formula (23), B1-B4 represent undetermined constants. Formula (22) and formula (23) are not completely independent. By substituting formula (22) and formula (23) into formula (8) and using the condition that the coefficients of each term on both sides of the equation correspond to each other, the relationship between the coefficients B1-B4 in the solution of the cross-section rotation angle φ(x, t) and the coefficients C1-C4 in the solution of the transverse displacement φ(x, t) can be obtained as shown in formulas (24)-(27).

[0122]

[0123] For the sake of simplicity, assume that the coefficients α and β are:

[0124]

[0125] The relationship between B1-B4 and C1-C4 can be simplified as formula (30):

[0126] B1=-αC1, B2=αC2, B3=βC3, B4=βC4 (30)

[0127] According to the calculation formula of bending moment and shear force in material mechanics:

[0128]

[0129] By substituting (22) and (23) into the bending moment formula (31) and the shear force formula (32) of material mechanics, the expressions of the shear force M z and the bending moment Q y are shown in (33) and (34) as follows:

[0130]

[0131] The formula (22), (23), (33) and (34) are combined to establish the second equation group (35):

[0132]

[0133] The relationship (30) between the coefficients B1-B4 and C1-C4 is used to eliminate the coefficients B1-B4, and the equation group (35) is written into the first matrix form shown in the following (36):

[0134]

[0135] Wherein:

[0136]

[0137] For a straight beam with a length of l, the coordinates (x=0 and x=l) at the left and right ends are respectively substituted into the formula (36), and the unknown constants C1-C4 are eliminated, so that the transfer relationship of the state quantities at the two ends of the straight beam is obtained as shown in the formula (37):

[0138]

[0139] Take T xoy =M xoy (l)M xoy (0) -1 , which is the lateral vibration transfer matrix of the straight beam in the xoy plane.

[0140] Further, the step S102 comprises the following steps:

[0141] Step S401, constructing a third equation group;

[0142] Step S402, transforming the third equation group into a second matrix according to the relationship between the plurality of first undetermined constants and the plurality of second undetermined constants;

[0143] Step S403, calculating a second transfer relationship of the state quantities at the two ends of the straight beam according to the second matrix;

[0144] Step S404, calculating the lateral vibration transfer matrix of the straight beam in the xoz plane according to the second transfer relationship of the state quantities at the two ends of the straight beam.

[0145] Specifically, Fig. 5(b) shows the force and deformation state of the beam microelement dx when it vibrates laterally in the xoz plane, wherein Q z is the shear force on the beam microelement, M y is the bending moment on the beam microelement, and I qis the inertial force of the micro-element of the beam, I0is the inertial moment of the micro-element of the beam, β is the shear angle generated by the shear deformation at the neutral axis of the beam, represents the rotation angle generated by the bending of the beam, and z is the lateral deformation of the micro-element of the beam.

[0146] For the lateral vibration of the straight beam in the xoz plane, the positive direction is still defined according to the general mechanics: when the outer normal direction of the micro-element is the same as the x axis, the deformation of the cross section in the same direction as the z axis is generated, and the deformation of the cross section in the opposite direction as the z axis is generated when the outer normal direction of the micro-element is opposite to the x axis, the shear force Q z is positive, and vice versa; when the outer normal direction of the micro-element is the same as the x axis, the rotation angle of the cross section in the same direction as the y axis is generated, and the rotation angle of the cross section in the opposite direction as the y axis is generated when the outer normal direction of the micro-element is opposite to the x axis, the bending moment M y is positive, and vice versa; the rotation angle generated by the bending has the same sign as the slope . It should be noted that according to Fig. 5(b), since the direction of the rotation angle is exactly opposite to the y axis, the rotation angle y will be negative when the bending moment M is positive, so when considering the lateral vibration of the Timoshenko beam in the xoz plane, the relationship between the rotation angle and the bending moment is different from the formula (5) for the lateral vibration in the xoy plane, and should be as shown in formula (38):

[0147]

[0148] where Iy is the moment of inertia of the cross section of the straight beam about the y axis.

[0149] Similarly, based on the Timoshenko beam theory and its related assumptions, according to the same derivation method as the lateral vibration in the xoy plane, a third equation group similar to formula (35) can be obtained, as shown in formula (39):

[0150]

[0151] According to the relationship (30), the equation group (39) can be written in the second matrix form as shown in formula (40):

[0152]

[0153] wherein:

[0154]

[0155] For a straight beam of length l, the coordinates of its two axial ends (x = 0 and x = l) can be substituted into (41) respectively, and the unknown constants C1 to C4 can be eliminated to obtain the relationship between the state quantities at both ends of the straight beam, as shown in formula (42):

[0156]

[0157] Let T xoz =M xoz (l)M xoz (0) -1 , which is the transfer matrix of the lateral vibration of the straight beam in the xoz plane.

[0158] Furthermore, step S102 includes the following steps:

[0159] Step S501, obtaining the longitudinal vibration equation of the straight beam element;

[0160] Step S502, using the separation of variables method to separate the variables of the longitudinal vibration equation and calculate the expression of the axial force;

[0161] Step S503, converting the expression of the axial force into a third matrix;

[0162] Step S504: Calculate the longitudinal vibration transfer matrix of the straight beam according to the third matrix.

[0163] Specifically, according to Figure 6 The longitudinal force and deformation diagram of the Timoshenko beam shown in the figure is based on a microelement of length dx taken from the axis at a distance x from the origin. The force state of this microelement is analyzed: let the unit volume mass of the microelement be ρ, the cross-sectional area be A, the longitudinal displacement (displacement in the x-direction) at the cross section be u, and the axial force be N. According to the general mechanics convention for the positive and negative directions of axial forces, the axial force acting on the microelement is considered positive if it is in the same direction as the normal to the cross-section.

[0164] The longitudinal vibration equation of the straight beam element is:

[0165]

[0166] Where E is the elastic modulus, ρ is the density, and u is the longitudinal displacement. The separation of variables method is used to separate u:

[0167] u(x,t)=U(x)sin(ωt) (44)

[0168] You can get:

[0169] U(x)=Ccos(βx)+Dsin(βx) (45)

[0170]

[0171] Find the expression for the axial force N:

[0172] N(x)=EAU'(x)=EA(-βsin(βx)+βcos(βx)) (47)

[0173] Expressed in the third matrix form:

[0174]

[0175] For the left end point of a straight beam when x=0:

[0176]

[0177] For the right end point of a straight beam when x=l:

[0178]

[0179] According to formulas (49) and (50), eliminating constants C and D, we obtain:

[0180]

[0181] The longitudinal vibration transfer matrix is ​​obtained as:

[0182]

[0183] Furthermore, step S102 includes the following steps:

[0184] Step S601, obtaining the torsional vibration equation of the straight beam element;

[0185] Step S602, using the separation of variables method to separate the variables of the torsional vibration equation and calculate the torque of the torsional vibration;

[0186] Step S603, converting the torque of the torsional vibration into a fourth matrix;

[0187] Step S604: Calculate the torsional vibration transfer matrix of the straight beam according to the fourth matrix.

[0188] Specifically, according to Figure 7 The torsional force and deformation diagram of the Timoshenko beam is shown in the figure. Assume that the polar moment of inertia of the cross section of the shaft segment is I p The symbols for other material and dimensional parameters are the same as those specified in the longitudinal vibration section. The torsion angle around the axis of the cross section, that is, the x-direction, is θ, and the torque is T. According to the general mechanics sign convention: According to the right-hand screw rule, the torque vector has a positive sign when it is in the same direction as the cross section's external normal.

[0189] The torsional vibration equation of the straight beam element is:

[0190]

[0191] Where G is the shear Young's modulus of the material, ρ is the density, θ is the torsion angle, and I p is the equivalent polar moment of inertia of the cross section, I y , I z are the moments of inertia of the cross section about the y-axis and the z-axis respectively, and the separation of variables method is used to separate the variables of θ:

[0192] θ(x,t)=Θ(x)sin(ωt) (54)

[0193] You can get:

[0194] Θ(x)=A s cos(αx)+B s sin(αx) (55)

[0195]

[0196] Find the expression for the torque T of torsional vibration:

[0197]

[0198] Expressed in the fourth matrix form:

[0199]

[0200] For the left end point of a straight beam when x=0:

[0201]

[0202] For the right end point of a straight beam when x=l:

[0203]

[0204] According to formulas (60), (61), the constant A is eliminated. s 、B s ,get:

[0205]

[0206] The torsional vibration transfer matrix is ​​obtained as:

[0207]

[0208] It is worth noting that the polar moment of inertia I of the circular cross-section beam is P =π(D 4 -d 4 ) / 32,I y =I z =π(D 4 -d4 ) / 64, meet I P = I y + I z For rectangular cross-section beam, its torsion after cross-section no longer remains as a plane, but warping, polar moment of inertia and the relationship between the moment of inertia I P = I y + I z No longer established, should be revised as I P = β n hb 3 (h and b represent the long side and short side of the rectangular cross-section respectively), the coefficient β n Related to the cross-sectional side length ratio h / b, its value is shown in Table 2 Coefficient β of rectangular cross-section rod when torsion n .

[0209] Table 2

[0210]

[0211] The motion of the straight beam unit includes axial motion, torsion motion, xoz lateral motion and xoy lateral motion, according to the variables set in the above lateral, longitudinal, torsion stress and deformation state analysis, the overall state variable of the straight beam unit is:

[0212]

[0213] Further, step S103 comprises:

[0214] According to formula (64), the spatial continuum transfer matrix of the straight beam is calculated:

[0215]

[0216] Wherein, G is the spatial continuum transfer matrix of the straight beam, T xoy is the lateral vibration transfer matrix of the straight beam in the xoy plane, T xoz is the lateral vibration transfer matrix of the straight beam in the xoz plane, T x is the longitudinal vibration transfer matrix of the straight beam, T tor is the torsion vibration transfer matrix of the straight beam.

[0217] The transfer relationship of the left and right sides of the straight beam can be expressed as:

[0218] S i+1 = G i S i (65)

[0219] In the crankshaft system, the common elements also include the flywheel, the axial damper and the bearing support. When the flywheel rotates at high speed, it can store and release energy to make the engine run smoothly. The diesel engine axial damper can reduce the longitudinal displacement of the crankshaft. The diesel engine main bearing can support the crankshaft to ensure the normal operation and power output of the crankshaft. The axial damper and the bearing support can be equivalent to an elastic support, and the flywheel can be equivalent to a concentrated mass without considering its shape and motion state. The axial damper is equivalent to a single degree of freedom axial spring, and the bearing support is equivalent to a three-dimensional spring. According to the force balance condition in material mechanics, the transfer matrix of the elastic support and the concentrated mass is obtained.

[0220] The simplified schematic diagram of the elastic support is shown in Figure 8 . The spring stiffness in x, y and z directions is k x ,k y ,k z , respectively. The force balance equation of the left and right sides of the spring can be expressed as:

[0221] N R -N L -k x u=0 (66)

[0222]

[0223] The matrix form is:

[0224]

[0225] The schematic diagram of the concentrated mass element is shown in Figure 9 . The mass of the concentrated mass is m, and the force balance equation of the left and right sides of the concentrated mass is:

[0226] N R -N L +mω 2 u=0 (70)

[0227]

[0228] The matrix form is:

[0229]

[0230] Since the local coordinate system is defined on the straight beam element of the crankshaft, and the transfer matrix of each element is derived based on the local coordinate system, the local coordinates of different beams need to be converted. The method adopts the classical Euler angle coordinate transformation method, and the transfer matrix obtained by coordinate transformation is called the point transfer matrix of coordinate transformation.

[0231] In each local coordinate system, the x axis is consistent with the center line of the straight beam. Figure 10 The transformation of the local coordinate system of the single crank is shown in the figure. The single crank is simplified into five beam structures, and the local coordinates of each beam are shown in the figure. In the coordinate transformation of the single crank, the local coordinates are mainly rotated around the z axis by a certain angle to achieve the transformation effect.

[0232] Figure 10 In the case of 1 and 4, the coordinate transformation relationship is:

[0233] x 2(5) →y 1(4) , y 2(5) →-x 1(4) , z 2(5) →z 1(4) (74)

[0235] The transformation relationship of the state vector is:

[0236]

[0237] N 2(5) →Q y1(4) , Q y2(5) →-N 1(4) , T 2(5) →M z1(4) , M z2(5) →-T 1(4) (76)

[0238] Therefore, the coordinate transformation transfer matrix in the case of 1 and 4 can be derived as:

[0239]

[0240] In the case of 2 and 3, the coordinate transformation relationship is:

[0241] x 3(4) →-y 2(3) , y 3(4) →x 2(3) , z 2(3) →z 3(4) (78)

[0242] The transformation relationship of the state vector is:

[0243] u 3(4) →-y 2(3) , y 3(4) →u 2(3) , θ 3(4) →φ 2(3) , φ 3(4) →θ 2(3) (79)

[0244] N3(4) → -Q y2(3) , Q y3(4) → N 2(3) , T 3(4) → -M z2(3) , M z3(4) → T 2(3) (80)

[0245] Thus, the point transfer matrix of the phase transformation of the adjacent cranks can be derived as follows:

[0246]

[0247] In the coordinate transformation of the adjacent cranks, the included angle of the two adjacent cranks is β, and the x axis is unchanged because the center lines of the cranks of the crankshaft are the same. The local coordinate system of the right crank is formed by rotating the local coordinate system of the left crank about the x axis by an angle β. The transformation relationship of the coordinate systems is shown in Figure 11 and Figure 12 .

[0248] The coordinate transformation relationship is:

[0249] y' = z sin β + y cos β (82)

[0251] z' = z cos β - y sin β

[0252] (83)The transformation relationship of the state vectors is:

[0253]

[0254] Thus, the point transfer matrix of the phase transformation of the adjacent cranks can be derived as follows: the point transfer matrix of the coordinate transformation of the local coordinate system rotating by an arbitrary angle β about the x axis is shown in (86).

[0255]

[0256] The method uses the straight beam element, the basic element of the crankshaft and the transfer matrix of the coordinate transformation of the spatial structure to splice the transfer matrix of the single crank, and further splice the transfer matrix of the entire crankshaft system. The detailed steps are as follows:

[0257] (1) Splicing of the transfer matrix of the single crank

[0258] The selection mode of the local coordinate system of the single crank is as follows: the x axis is always in the length direction of the straight beam element, the y axis on the main shaft neck is always vertically upward, the y axis on the crank arm and the crank pin is along the direction of the vibration in the crank face, and finally the z axis direction is selected according to the right-hand rule. The directions of the local coordinate systems on the main shaft necks of the cranks in different relative positions are completely consistent, but the directions of the local coordinate systems on the crank arms and the crank pins are different.

[0259] Figure 13The selection of the local coordinate system for the general position crank is given. For the crank in general position (relative angle β), if the transfer matrix of the five straight beam elements contained in the crank is calculated as T i (i = 1,..5), the transfer matrix between the head and tail state vectors is:

[0260] T 单曲拐 (β) = T5H x (-β)H S T4H N T3H N T2H S H x (β)T1 (87)

[0261] (2) Transfer matrix splicing of multi-crank system

[0262] The actual crankshaft system is composed of multiple cranks. The general multi-crank (here, the double crank is taken as an example to demonstrate the matrix splicing formula) model is shown in Figure 14 In the actual crankshaft model, there is often an elastic support at the main journal connecting different cranks. In this case, the two sides are divided into different cranks, respectively. In the double crank model, if the transfer matrices of the two cranks are T1 and T2, respectively, and the transfer matrix of the elastic support in the middle is T k , the transfer matrix of the head and tail state vectors of the double crank system should be:

[0263] T 双曲拐 = T2T k T1 (88)

[0264] Using the above transfer matrix, the dynamic equation of the system is constructed by multiplying it. The space transfer matrix of the beam element is called the field transfer matrix, the coordinate transformation transfer matrix is called the point transfer matrix, the transfer matrix of the bearing is called the spring point transfer matrix, and the transfer matrix of the flywheel is called the lumped mass point transfer matrix. Let the overall state variable of the crankshaft be:

[0265]

[0266] Starting from the crankpin, the field transfer matrix of the first beam is constructed, then multiplied by the first spring point transfer matrix, and then multiplied by the field transfer matrix of the second beam, and so on. In this way, the state vector transfer equation of the entire crankshaft is constructed, as shown in the following formula:

[0267] S 右 = [T] 左-右 S 左 (90)

[0268] The parameters of the simplified model of the crankshaft system obtained in step one are input into the constructed dynamic equation for numerical analysis by programming means.

[0269] Further, step S107 comprises the following steps:

[0270] In step S701, the boundary conditions at the left end and the boundary conditions at the right end are substituted into the dynamic equation, and a homogeneous linear equation set is extracted;

[0271] In step S702, based on the necessary and sufficient condition of non-zero solution in the homogeneous linear equation set, the natural frequency of the crankshaft system is obtained.

[0272] The necessary and sufficient condition of non-zero solution is that the value of the coefficient determinant is zero.

[0273] Specifically, the boundary conditions at the left end and the right end are substituted into the system dynamic equation, and a homogeneous equation set is extracted to form a new equation set. Based on the necessary and sufficient condition that the homogeneous linear equation set has a non-zero solution, the value of the coefficient determinant is zero, and the natural frequency of the crankshaft system can be obtained:

[0274] For the basic boundary conditions at the left end and the right end, among the 12 components of the state vectors at the left end and the right end, 6 components will be zero, and the remaining 6 components will not be zero, for example:

[0275]

[0276] F = [NT M y Q z M z Q y ] T = 0, free boundary

[0277] The boundary conditions at the left end and the right end are substituted into the system dynamic equation, and a homogeneous equation set is extracted to form a new equation set. According to the knowledge of linear algebra, the necessary and sufficient condition for the homogeneous linear equation set to have a non-zero solution is that the value of the coefficient determinant is zero. Therefore, the natural frequency of the system can be obtained, for example, for the boundary condition of the left end fixed and the right end free: the left end boundary has X = 0 F ≠ 0 and the right end boundary has X ≠ 0 F = 0. The original equation can be processed to obtain the following homogeneous linear equation:

[0278] 0 = F 右 = [T] 子式 F 左 (92)

[0279] Where, [T] 子式is a minor expression formed by extracting some rows and columns from the state vector transfer matrix on the left and right sides of the original system. For the boundary conditions of the fixed left end and the free right end in this example, it is obvious that the 2nd, 4th, 7th, 8th, 11th, and 12th rows and the 2nd, 4th, 7th, 8th, 11th, and 12th columns should be extracted. According to linear algebra, the necessary and sufficient condition for a homogeneous linear system of equations to have a non-zero solution is that the determinant of the coefficient matrix is ​​0, and [T] 子式 The determinant of is a single-valued function assuming the same frequency resonant vibration frequency ω, so the natural frequency of the system is such that [T] 子式 The value of ω for which the determinant is 0.

[0280] And fill the non-zero solution of the equation into the state vector S on the left 左 In the non-zero terms of , combined with the multiplication of the transfer matrix, the state vector value of any point on the crankshaft can be determined by the continuous multiplication of the transfer matrix. The state vectors of all points on the crankshaft can be extracted, and the vibration modes of each order of the system can be further obtained. n (x).

[0281] According to the exciting force spectrum loaded on the crank pin, the Newmark-β method is used to solve the forced vibration response of any point on the crankshaft.

[0282] This method uses generalized coordinates to describe the dynamic equations of the crankshaft system by the second-kind Lagrangian equation, and decomposes the true displacement of each point into the superposition of modal vibration shapes of various orders, as shown in the following formula:

[0283]

[0284] Among them, q n (t) is the value corresponding to the nth mode X n The generalized coordinates of (x) are also called modal coordinates. Solving the generalized coordinates yields the time-domain displacement response of any point in the crankshaft system. The Lagrange equation for the crankshaft system in generalized coordinates is as follows:

[0285]

[0286] To solve equation (94), we need to first calculate the kinetic energy T and potential energy V of the system, as well as the generalized forces Q of each order. n expression.

[0287] Assume that the vibration mode functions of each order of the crankshaft system have been obtained in the free vibration link, and their specific expressions are: The longitudinal vibration mode function is U n (x), the torsional vibration function is Θ n (x), is the xz lateral vibration displacement mode function is Z n (x), the bending angle vibration mode function is The xy lateral vibration displacement mode function is Y n (x), the bending angle vibration mode function is φn (x) The kinetic energy T and potential energy V of the system can be listed as follows:

[0288]

[0289] The kinetic energy and potential energy equations of the system are substituted into the second Lagrange equation, and the modal mass and modal stiffness of each order are defined as follows:

[0290]

[0291] Substituting the expressions of modal mass and modal stiffness (97) into the Lagrange equation (94), the equation can be simplified as:

[0292]

[0293] According to the knowledge of analytical mechanics, it is assumed that there are points p i in the system that are subjected to spatial forces F ix , F iy , F iz and spatial moments M ix , M iy , M iz , respectively. The generalized force expression of the system corresponding to the generalized coordinate q n (t) is shown in equation (99):

[0294]

[0295] According to the relationship between the real displacement and the generalized coordinate, equation (100) is obtained:

[0296]

[0297] Therefore, under the premise of knowing the real external excitation of the system, the generalized force can be expressed as equation (101):

[0298]

[0299] The crankshaft system is a continuous system with infinite natural frequencies and modes. In actual solving, the modal truncation method is used. After selecting enough but limited natural frequencies and modes, the modal mass, modal stiffness, and generalized force of each order are obtained according to the above method, and then the second-order linear differential equation (102) about the generalized coordinate q n (t) is obtained, which can be solved by the Newmark-β method.

[0300]

[0301] where N is the maximum order of the selected natural frequencies and modes.

[0302] The natural frequencies of the longitudinal and torsional vibration modes obtained by the continuum method are compared with the results of the lumped mass method, and the results are shown in Table 3.

[0303] Table 3

[0304]

[0305] The first five natural frequencies of the longitudinal and torsional vibration modes are calculated by the lumped mass method, and the first five (the results are shown as the first, fourth, seventh, ninth and tenth orders) of the longitudinal and torsional vibration modes in the results of the method are compared, and it can be seen from the comparison results that the natural frequency calculation results of the continuum method are relatively small compared with the lumped mass method, and the natural frequencies of the transverse vibration not considered in the report of the MAN are calculated, so that the completeness of the free vibration calculation is improved.

[0306] A point at the front end of the crankshaft is taken as a response point to extract the forced vibration response, and the time domain signal from 0 to 15s is shown in Figure 15.

[0307] Compared with the prior art, the present application has the following advantages:

[0308] 1) For engineering calculation, the shaft vibration is previously calculated separately in the form of bending, longitudinal and torsional vibration without affecting each other, and the method considers the three-dimensional coupled vibration of the crankshaft vibration, which increases the simulation calculation precision.

[0309] 2) The discrete method for calculating the overall crankshaft system of the diesel engine is to simplify each part of the crankshaft as a lumped mass for calculation, and cannot completely reflect the overall structure of the crankshaft, and the method based on the continuum vibration theory can extract the forced vibration response time domain signal of any part of the crankshaft, and emphasizes the calculation completeness.

[0310] 3) The diesel engine crankshaft vibration calculation using the finite element method needs complex and time-consuming model building and mesh division, the method directly simplifies the geometric size and other state parameters, inputs the program compiled by matlab, has short calculation time, controllable calculation precision, and has good universality and engineering applicability.

[0311] Example 2

[0312] Figure 16 The diesel engine shaft vibration response rapid calculation system provided for the second embodiment of the present application is shown in the schematic diagram.

[0313] Referring to Figure 16 The system comprises:

[0314] The simplification module is used for simplifying the crankshaft system and stress of the diesel engine to obtain a simplified model of the diesel engine, wherein the simplified model of the diesel engine comprises an excitation force;

[0315] The first establishing module is configured to establish a transverse vibration transfer matrix, a longitudinal vibration transfer matrix and a torsional vibration transfer matrix of the straight beam based on the straight beam element;

[0316] The first calculating module is configured to calculate the spatial continuum transfer matrix of the straight beam according to the transverse vibration transfer matrix, the longitudinal vibration transfer matrix and the torsional vibration transfer matrix;

[0317] The second establishing module is configured to establish a point transfer matrix of coordinate transformation at a connecting point of each segment of the straight beam through force balance conditions and displacement coordination conditions;

[0318] The splicing module is configured to splice the transfer matrix of the single crank to the whole crankshaft system according to the spatial continuum transfer matrix of the straight beam and the point transfer matrix of coordinate transformation;

[0319] The constructing module is configured to construct a dynamic equation according to the transfer matrix of the single crank to the whole crankshaft system;

[0320] The second calculating module is configured to calculate the natural frequency of the crankshaft system according to the dynamic equation;

[0321] The solving module is configured to load a map of excitation force on the crankpin of the crankshaft system, and solve forced vibration responses of any point on the crankshaft by using the Newmark-β method.

[0322] The embodiment of the present application further provides an electronic device, including a memory, a processor and a computer program stored in the memory and executable on the processor, and the processor executes the computer program to realize the steps of the fast calculation method of the diesel engine shaft vibration response provided by the above embodiment.

[0323] The embodiment of the present application further provides a computer readable medium with non-volatile program code executable by a processor, and the computer readable medium stores a computer program, and the computer program is executed by the processor to execute the steps of the fast calculation method of the diesel engine shaft vibration response of the above embodiment.

[0324] The computer program product provided by the embodiment of the present application includes a computer readable storage medium storing program codes, and the instructions included in the program codes can be used to execute the method described in the foregoing method embodiment, and the specific implementation can be referred to the method embodiment, and will not be repeated here.

[0325] Those skilled in the art can clearly understand that, for the convenience and brevity of description, the specific working process of the system and device described above can refer to the corresponding process in the foregoing method embodiment, and will not be repeated here.

[0326] In addition, in the description of the embodiments of the present application, unless otherwise explicitly specified and limited, the terms "mounting", "connection", "connecting" should be understood in a broad sense, for example, can be fixed connection, can also be detachable connection, or integral connection; can be mechanical connection, can also be electrical connection; can be direct connection, can also be indirect connection through intervening medium, can be internal communication of two elements. For those skilled in the art, the specific meaning of the above terms in the present application can be understood according to the specific circumstances.

[0327] If the functions are realized in the form of software function units and sold or used as independent products, they can be stored in a computer readable storage medium. Based on such understanding, the technical solutions of the present application or the part of the present application which essentially contributes to the prior art or the part of the technical solutions can be embodied in the form of software products. The computer software product is stored in a storage medium and includes a plurality of instructions for causing a computer device (which can be a personal computer, a server, or a network device, etc.) to execute all or part of the steps of the method described in the various embodiments of the present application. The aforementioned storage medium includes: a U disk, a mobile hard disk, a read-only memory (ROM, Read-Only Memory), a random access memory (RAM, Random Access Memory), a magnetic disk or an optical disk, and various program code storage media.

[0328] In the description of the present application, it should be noted that the terms "center", "upper", "lower", "left", "right", "vertical", "horizontal", "inner", "outer" and the like indicate the orientation or positional relationship based on the orientation or positional relationship shown in the drawings, and are only for the convenience of describing the present application and simplifying the description, and do not indicate or imply that the devices or elements referred to must have a particular orientation, be constructed and operated in a particular orientation, and therefore cannot be understood as a limitation on the present application. In addition, the terms "first", "second", "third" are only for the purpose of description, and cannot be understood as indicating or implying relative importance.

[0329] Finally, it should be noted that the above-described embodiments are merely specific embodiments of the present application, which are used to illustrate the technical solutions of the present application, but not to limit the same. The protection scope of the present application is not limited thereto. Although the present application has been described in detail with reference to the foregoing embodiments, it should be understood by those skilled in the art that any person skilled in the art can still modify or easily think of changes to the technical solutions recorded in the foregoing embodiments, or make equivalent replacements to some of the technical features, within the technical scope disclosed by the present application. The modifications, changes or replacements do not cause the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present application, and should be covered within the protection scope of the present application. Therefore, the protection scope of the present application should be subject to the protection scope of the claims.

Claims

1. A fast calculation method for diesel engine shaft vibration response, characterized in that: The method comprises: Simplifying the crankshaft system and forces of the diesel engine to obtain a simplified model of the diesel engine; wherein the simplified model of the diesel engine includes an excitation force; Based on the straight beam element, the transverse vibration transfer matrix, longitudinal vibration transfer matrix and torsional vibration transfer matrix of the straight beam are established respectively; Calculating a spatial continuum transfer matrix of the straight beam according to the lateral vibration transfer matrix, the longitudinal vibration transfer matrix, and the torsional vibration transfer matrix; Establishing a point transfer matrix for coordinate transformation at the connection points of each straight beam section through force balance conditions and displacement coordination conditions; Laying the transfer matrix of a single crank to the entire crankshaft system according to the spatial continuum transfer matrix of the straight beam and the point transfer matrix of the coordinate transformation; Constructing dynamic equations based on the transfer matrix from the single crank to the entire crankshaft system; Calculating the natural frequency of the crankshaft system according to the dynamic equation; The spectrum of the excitation force is loaded on the crank pin of the crankshaft system, and the forced vibration response of any point on the crankshaft is solved using the Newmark-β method.

2. The rapid calculation method of diesel engine shaft vibration response according to claim 1 is characterized in that: The crankshaft system and forces of the diesel engine are simplified to obtain a simplified model of the diesel engine, including: The crankshaft is simplified into a spatial structure with multiple straight beams overlapping each other; Simplify the crank connecting rod and piston to the excitation force: Simplify the crank arm, crank pin and main journal into uniform beam structures with equal cross-section; Simplify the bearing into a three-way spring structure; Simplify the flywheel into a centralized mass structure; Among them, the excitation force includes: the force generated by the gas pressure generated by the ignition of the cylinder acting on the upper surface of the piston, the reciprocating inertia force generated by the reciprocating motion of the piston group and acting on the piston, the lateral thrust given by the inner wall of the cylinder when the piston moves, and the centrifugal inertia force generated when the crankshaft rotates and acts on the crank pin.

3. The rapid calculation method of diesel engine shaft vibration response according to claim 1 is characterized in that: Based on the straight beam element, the lateral vibration transfer matrix, longitudinal vibration transfer matrix, and torsional vibration transfer matrix of the straight beam are established respectively, including: Obtain the inertial force and inertial moment acting on the beam element; Obtaining the dynamic equilibrium equation of the beam element according to theoretical mechanics; Obtaining the bending moment and shear force of the beam element according to material mechanics; Substituting the bending moment and the shear force of the beam element into the dynamic equilibrium equation to obtain the lateral vibration differential equation of the beam; Separating the variables in the differential equation of the lateral vibration of the beam to obtain a first set of equations; wherein the variables include the rotation angle generated when the beam is bent and the lateral deformation of the beam element; Substituting the excitation into the first set of equations for calculation to obtain a general solution; wherein the general solution includes a plurality of first undetermined constants; Obtaining a solution for a cross-sectional rotation angle; wherein the solution for the cross-sectional rotation angle includes a plurality of second undetermined constants; Substituting the general solution and the solution of the cross-sectional rotation angle into the lateral vibration differential equation of the beam to obtain the relationship between the plurality of first undetermined constants and the plurality of second undetermined constants; Obtain bending moment formula and shear force formula based on material mechanics; Substituting the general solution and the solution of the cross-sectional rotation into the bending moment formula and the shear force formula respectively, to obtain an expression between shear force and bending moment; Establishing a second set of equations based on the general solution, the solution of the cross-sectional rotation, and the expressions between the shear force and the bending moment; Converting the second set of equations into a first matrix according to a relationship between the plurality of first undetermined constants and the plurality of second undetermined constants; Calculate a first transfer relationship of state quantities at both ends of the straight beam according to the first matrix; The transverse vibration transfer matrix of the straight beam in the xoy plane is calculated according to the first transfer relationship of the state quantities at both ends of the straight beam.

4. The rapid calculation method for diesel engine shaft vibration response according to claim 1, characterized in that: Based on the straight beam element, the lateral vibration transfer matrix, longitudinal vibration transfer matrix, and torsional vibration transfer matrix of the straight beam are established respectively, including: Build a third-party program group; converting the third equation group into a second matrix according to a relationship between a plurality of first undetermined constants and a plurality of second undetermined constants; Calculate the second transfer relationship of the state quantities at both ends of the straight beam according to the second matrix; The lateral vibration transfer matrix of the straight beam in the xoz plane is calculated according to the second transfer relationship of the state quantities at both ends of the straight beam.

5. The rapid calculation method of diesel engine shaft vibration response according to claim 1 is characterized in that: Based on the straight beam element, the lateral vibration transfer matrix, longitudinal vibration transfer matrix, and torsional vibration transfer matrix of the straight beam are established respectively, including: Obtaining the longitudinal vibration equation of the straight beam element; The longitudinal vibration equation is separated by the separation of variables method to calculate the expression of the axial force; Convert the expression of the axial force into a third matrix; The longitudinal vibration transfer matrix of the straight beam is calculated according to the third matrix.

6. The rapid calculation method of diesel engine shaft vibration response according to claim 1, characterized in that: Based on the straight beam element, the lateral vibration transfer matrix, longitudinal vibration transfer matrix, and torsional vibration transfer matrix of the straight beam are established respectively, including: Obtaining a torsional vibration equation of the straight beam element; Separating variables from the torsional vibration equation using a separation of variables method to calculate the torque of the torsional vibration; converting the torque of the torsional vibration into a fourth matrix; The torsional vibration transfer matrix of the straight beam is calculated according to the fourth matrix.

7. The rapid calculation method for diesel engine shaft vibration response according to claim 1, characterized in that: Calculating the spatial continuum transfer matrix of the straight beam according to the lateral vibration transfer matrix, the longitudinal vibration transfer matrix, and the torsional vibration transfer matrix includes: The spatial continuum transfer matrix of the straight beam is calculated according to the following formula: Where G is the spatial continuum transfer matrix of the straight beam, T xoy is the lateral vibration transfer matrix of the straight beam in the xoy plane, T xoz is the lateral vibration transfer matrix of the straight beam in the xoz plane, T x is the longitudinal vibration transfer matrix of the straight beam, T tor is the torsional vibration transfer matrix of the straight beam.

8. The rapid calculation method for diesel engine shaft vibration response according to claim 1 is characterized in that: Calculating the natural frequency of the crankshaft system according to the dynamic equation includes: Substituting the boundary conditions on the left and the boundary conditions on the right into the dynamic equations, and extracting a homogeneous linear equation system; Based on the necessary and sufficient conditions for non-zero solutions in the homogeneous linear equations, obtaining the natural frequency of the crankshaft system; The necessary and sufficient condition for the non-zero solution is that the value of the coefficient determinant is zero.

9. A fast calculation system for diesel engine shaft vibration response, characterized in that: The system comprises: A simplification module, configured to simplify the crankshaft system and forces of the diesel engine to obtain a simplified model of the diesel engine; wherein the simplified model of the diesel engine includes an excitation force; The first establishment module is used to establish the lateral vibration transfer matrix, the longitudinal vibration transfer matrix and the torsional vibration transfer matrix of the straight beam based on the straight beam unit; a first calculation module, configured to calculate a spatial continuum transfer matrix of the straight beam based on the lateral vibration transfer matrix, the longitudinal vibration transfer matrix, and the torsional vibration transfer matrix; The second establishing module is used to establish a point transfer matrix of coordinate transformation at the connection points of each section of the straight beam through force balance conditions and displacement coordination conditions; A connection module, for connecting a single crank to the transfer matrix of the entire crankshaft system according to the spatial continuum transfer matrix of the straight beam and the point transfer matrix of the coordinate transformation; A construction module, configured to construct a dynamic equation based on a transfer matrix from the single crank to the entire crankshaft system; A second calculation module, configured to calculate the natural frequency of the crankshaft system according to the dynamic equation; A solution module is used to load the spectrum of the excitation force on the crank pin of the crankshaft system and solve the forced vibration response of any point on the crankshaft using the Newmark-β method.

10. An electronic device comprising a memory and a processor, wherein the memory stores a computer program that can be run on the processor, wherein: When the processor executes the computer program, the method according to any one of claims 1 to 8 is implemented.

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