CN107885924B - Performance simulation method of vehicle-mounted hydraulic shock absorber - Google Patents

Performance simulation method of vehicle-mounted hydraulic shock absorber Download PDF

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CN107885924B
CN107885924B CN201711055141.3A CN201711055141A CN107885924B CN 107885924 B CN107885924 B CN 107885924B CN 201711055141 A CN201711055141 A CN 201711055141A CN 107885924 B CN107885924 B CN 107885924B
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valve
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shock absorber
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CN107885924A (en
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邹文斌
杨永泰
邹炎火
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Quanzhou Institute of Equipment Manufacturing
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Abstract

The invention relates to a performance simulation method of a vehicle-mounted hydraulic shock absorber, which is based on MATLAB software, aims at valves with different channel section types and sizes, establishes a disc valve opening model based on a fluid mechanics theory, obtains the opening degree of a piston valve through the disc valve opening model, then establishes a hydraulic transmission calculation model among cavities of the vehicle-mounted hydraulic shock absorber, calculates the pressure loss caused by friction between fluid and a channel, the pressure loss caused by narrowing of a fluid inflow channel, the pressure loss caused by widening of the fluid inflow channel and the pressure loss caused by turning of the channel, and then fits a hydraulic pressure-speed curve and a hydraulic pressure-displacement curve of the vehicle-mounted hydraulic shock absorber by combining the opening degree of the piston valve to realize the performance simulation of the vehicle-mounted hydraulic shock absorber.

Description

Performance simulation method of vehicle-mounted hydraulic shock absorber
Technical Field
The invention relates to the field of hydraulic shock absorbers, in particular to a performance simulation method of a vehicle-mounted hydraulic shock absorber.
Background
The product development process of the current vehicle-mounted shock absorber adopts a virtual prototype to control the product performance in the product development process based on the product characteristics, however, the adjustability of the virtual prototype of the shock absorber on the current market is too poor, the standard degree requirement on the size of a piston and a valve in the shock absorber is very high, the application field of the virtual prototype is limited, the simulation precision is limited by a few adjustable parameters, and particularly, the shock absorber using the piston with a special valve for achieving higher product performance does not have the simulation capability.
Disclosure of Invention
The invention aims to provide a performance simulation method of a vehicle-mounted hydraulic shock absorber, which is used for performing performance simulation on the vehicle-mounted hydraulic shock absorber with adjustable multiple parameters based on MATLAB software, so that the performance parameters obtained by simulation are closer to actual performance parameters, and the development of the vehicle-mounted hydraulic shock absorber is better performed.
The invention relates to a performance simulation method of a vehicle-mounted hydraulic shock absorber, wherein a valve in the vehicle-mounted hydraulic shock absorber is a piston with a disk valve plate and a choke, the whole valve channel comprises the choke and a channel after the valve is opened, a disk valve opening model is established based on MATLAB software and aiming at the valves with different channel section types and sizes based on the fluid mechanics theory, the valve opening degree of the piston valve is obtained through the disk valve opening model, a hydraulic transmission calculation model among all cavities of the vehicle-mounted hydraulic shock absorber is established, pressure loss caused by friction of fluid and the channel, pressure loss caused by narrowing of a fluid inflow channel, pressure loss caused by widening of the fluid inflow channel and pressure loss caused by turning of the channel are calculated, and then a hydraulic pressure-speed curve and a hydraulic pressure-displacement curve of the vehicle-mounted hydraulic shock absorber are fitted by combining the valve opening degree of the piston valve, so as to realize the performance simulation of the vehicle-mounted hydraulic shock absorber.
The method specifically comprises the following steps:
step 1, establishing a disc valve opening model and obtaining the opening degree of the valve
The disc valve opening module calculates the opening degree of the valve by using a thin plate theory and an equivalent stiffness attenuation model based on the pressure difference and the size of the valve on two sides of the valve, so that input information of the disc valve opening model comprises the pressure difference and the size of the valve on two sides of the valve, and output information is the opening degree of a valve plate corresponding to the pressure difference, namely the lifting height of the valve plate, and the specific calculation comprises the following contents:
the valve plate of the disc valve in the vehicle-mounted hydraulic shock absorber is formed by overlapping a plurality of disc plates, the valve plate is split into n units through finite elements, wherein the rigidity D of the ith unitiThe sum of the stiffness of the stacked discs at the cell, wherein the stiffness D of any disc is calculated by the formula:
Figure BDA0001453537550000021
wherein E is the elastic modulus of the material, h is the disc steel plate height, and mu is the Poisson's ratio;
the valve plate is split into a plurality of annular finite element units along the radial direction, and the stress condition of the ith unit is calculated as follows:
(1) total force F to be applied to the toroidiConverted into line load QFi：
Figure BDA0001453537550000031
Wherein Q isFiIs a line load, FiIs the total force, RiIs the inner radius of the ith cell;
(2) calculating the total stress F when the pressure p acts on the ith unit of the valvep,i:
Fp,i＝pπ(Re 2-Ri 2) (3)
Wherein p is pressure, ReAnd RiThe inner radius and the outer radius of the ith unit respectively;
(3) will be subjected to a total force Fp,iCalculating the line load Q according to the formula (2)p,i：
Figure BDA0001453537550000032
Wherein Q isp,iIs a line load, Fp,iIs the total force, R, of the ith cell at pressure piIs the inner radius of the ith cell;
(4) calculating the total stress Q on the ith unit of the valve platei：
Qi＝QF,i+Qp,i (5)
Wherein Q isF,iIs a linear load, Q, converted from a concentrated load force F borne by the upper end of the valve platep,iThe linear load is converted from the pressure p applied to the lower end of the valve plate;
(5) according to the deformation condition of the annular unit calculated by the thin plate theory, the deformation W of the ith unit of the valve plate is calculatedi：
Figure BDA0001453537550000033
Wherein, C1,i、C2,i、C3,iAre the three unknown parameters of equation (6), FiIs the force, p, exerted on the upper end of the i-th unit of the valve plateiThe pressure intensity born by the lower end of the ith unit of the valve plate;
(6) deformation W of ith unit of valve plateiDerivation of radius r:
Figure BDA0001453537550000034
(7) calculating the bending moment M of the ith unit of the valve platei：
Figure BDA0001453537550000041
Equations (6), (7) and (8) have three unknown parameters C for the ith cell1,i、C2,i、C3,iIn the above formula FiAnd PiThe values of (A) have the following relations:
Figure BDA0001453537550000042
Figure BDA0001453537550000043
wherein D ispDenotes the diameter of a circle with an applied pressure P, DFA circle diameter representing a concentration force F;
equations (6) to (8) can be solved in conjunction with the following boundary conditions:
1. the inner ring displacement is 0:
Figure BDA0001453537550000044
2. the inner ring displacement derivative is also 0:
Figure BDA0001453537550000045
3. the outermost unit belongs to the free end, the torque is 0:
Figure BDA0001453537550000046
4. due to the continuity of two adjacent cells:
wi(R)＝wi+1(R)
Figure BDA0001453537550000047
Mi(R)＝Mi+1(R)
combining the above equations, the relationship between the valve opening degree of the valve plate and the radius of the valve plate can be obtained, a group of pressure differences and the valve opening height values of the corresponding group of valve plates can be obtained, and the obtained data is input into the hydraulic transmission calculation model in the step 2;
step 2, establishing a hydraulic transmission calculation model to obtain the pressure loss in the fluid channel
(1) Pressure loss due to fluid friction with the channel:
Figure BDA0001453537550000051
where λ is the coefficient of friction, l is the channel length, ρ is the fluid density, v is the fluid velocity, deIs the equivalent diameter of the channel;
(2) pressure loss due to narrowing of the fluid inflow passage:
Figure BDA0001453537550000052
wherein k isinInflow coefficient for channel size, ρ is fluid density, v is fluid velocity;
(3) pressure loss due to widening of the fluid outflow channel:
Figure BDA0001453537550000053
wherein k isoutThe outflow coefficient is the channel size, ρ is the fluid density, v is the fluid velocity;
(4) pressure loss due to passage turning:
Figure BDA0001453537550000054
wherein,
Figure BDA0001453537550000055
is the bending coefficient of the channel, ρ is the fluid density, v is the fluid velocity, θ is the angle at which the channel bends;
step 3, calculating a stress-speed curve and a stress-displacement curve of the hydraulic shock absorber to evaluate the performance of the hydraulic shock absorber
The hydraulic damper comprises a first cavity return cavity, a second cavity compression cavity and a third cavity compensation cavity, wherein the three cavities of the first cavity return cavity, the second cavity compression cavity and the third cavity compensation cavity are arranged inside the hydraulic damper, and the pressure of the three cavities inside the hydraulic damper is respectively obtained according to the valve opening height value of a valve plate obtained by the disc valve opening model in the step 1 and the pressure loss in a fluid channel obtained by the hydraulic transmission calculation model in the step 2:
in order to simulate the force curve of the whole process, firstly a sinusoidal motion state is input to the piston: asin (2 pi ft)
Wherein, A is amplitude, f is frequency, t is time, can be adjusted according to the working condition of the piston;
pressure p of the compensation chamber3It can be calculated from the adiabatic process equation for ideal air:
Figure BDA0001453537550000061
wherein p is0Is the initial pressure of the gas inside the compensation chamber, ArodIs the cross-sectional area, v, of the piston rod0Is the initial volume of gas, S is the initial position of the piston, and is normally set to 0;
pressure p of the compression chamber2Calculated from the following formula:
p2＝p3+Δp32
wherein, Δ p32The pressure difference between the two sides of the lower piston;
pressure p of the return chamber1Calculated from the following formula:
p1＝p2+Δp21
wherein, Δ p21Is the pressure difference at both sides of the upper piston;
the piston force-displacement relationship is represented by the following equation:
F＝p1Areb-p2Acom+p3Arod
wherein F is the pressure on one side of the disc valve, ArebIs the cross-sectional area of the return chamber, AcomIs the cross-sectional area of the compression chamber, ArodIs the sectional area of the piston rod, the pressure p in the return cavity1Pressure p in the compression chamber2Compensating the pressure p in the chamber3；
Each frequency in the piston stress-displacement relationship corresponds to a stress-displacement curve, the stress-displacement curve is a closed circle, a stress value is formed by mapping the peak value of the circle to a stress-speed curve, a speed value is obtained by derivation of an input condition of S-Asin (2 pi ft), namely the corresponding speed value is A2 pi f, and the corresponding relationship of the two is the stress-speed relationship of the piston.
According to the invention, a disc valve opening model is established based on the theory of hydrodynamics according to the types and sizes of the channel sections of different valves, the performance parameters of the vehicle-mounted hydraulic damper are obtained through the disc valve opening model and the hydraulic transmission calculation model, and the pressure loss in a hydraulic channel system is considered in the hydraulic transmission calculation model, so that the performance parameters obtained through simulation are closer to the actual performance parameters, the development of the vehicle-mounted hydraulic damper is better carried out, and finally, a set of virtual prototype with strong universality and high simulation precision is realized. The method has the advantages that the calculation of the valve channel hydraulic model is different from the traditional thought, the simulation precision is greatly improved, the system universality is stronger, the calculation time is slightly increased, the secondary development of the system is stronger, the operation is simple, and the method is also suitable for non-professionals.
Drawings
FIG. 1 is a schematic flow diagram of the present invention;
FIG. 2 is an equivalent model of a valve plate in the vehicle hydraulic shock absorber of the present invention;
FIG. 3 is a schematic force diagram of the valve plate split into annular finite element units along the radial direction in the invention;
FIG. 4 is a stress analysis diagram of the ith unit of the vehicle-mounted hydraulic shock absorber in which a valve plate is split by a finite element;
FIG. 5 shows a force F applied to the upper end of the i-th unit of the valve plate in the hydraulic shock absorber of the present inventioniThe pressure p borne by the lower end of the ith unit of the valve plateiA relationship diagram of (1);
FIG. 6 is a diagram showing a relationship between a valve opening degree of a valve plate and a radius of the valve plate in the vehicle-mounted hydraulic shock absorber;
FIG. 7 is a schematic view showing a pressure loss of a valve passage in the on-vehicle hydraulic shock absorber according to the present invention;
FIG. 8 is a schematic view of the pressure distribution in the on-board hydraulic shock absorber of the present invention;
FIG. 9 is a schematic view of the valve stress relationship in the vehicle hydraulic shock absorber of the present invention;
FIG. 10 is a force-displacement curve according to the present invention;
FIG. 11 is a force-velocity curve of the present invention;
FIG. 12 is a force-velocity curve versus force-displacement curve for the present invention.
The invention is described in further detail below with reference to the figures and specific examples.
Detailed Description
The invention discloses a performance simulation method of a vehicle-mounted hydraulic shock absorber, wherein a valve in the vehicle-mounted hydraulic shock absorber is a piston with a disk valve plate and a choke, namely the whole valve channel comprises the choke and a channel after the valve is opened, as shown in figure 1, a disk valve opening model is established based on the fluid mechanics theory aiming at the valves with different channel section types and sizes based on MATLAB software, the valve opening degree of a piston valve is obtained through the disk valve opening model, a hydraulic transmission calculation model among all cavities of the vehicle-mounted hydraulic shock absorber is established, the pressure loss caused by the friction of fluid and the channel, the pressure loss caused by the narrowing of a fluid inflow channel, the pressure loss caused by the widening of the fluid inflow channel and the pressure loss caused by the turning of the channel are calculated, and then a hydraulic pressure-speed curve and a hydraulic pressure-displacement curve of the vehicle-mounted hydraulic shock absorber are fitted by combining the valve opening degree of the piston valve, the method is used for realizing the performance simulation of the vehicle-mounted hydraulic shock absorber and specifically comprises the following steps:
step 1, establishing a disc valve opening model, and obtaining the opening degree of a valve:
the disc valve opening module is mainly used for calculating the opening degree of the valve by utilizing a thin plate theory and an equivalent stiffness attenuation model based on the pressure difference and the valve size of two sides of the valve, the input information of the disc valve opening model comprises the pressure difference and the valve size of the two sides of the valve, and the output information is the opening degree of the valve plate (the lifting height of the valve plate) corresponding to the pressure difference;
the valve plate of the disc-shaped valve in the vehicle-mounted hydraulic shock absorber is formed by overlapping a plurality of disc sheets, the valve plate is split into n units through finite elements, wherein the rigidity D of the ith unitiThe sum of the stiffness of the stacked discs at the cell, see fig. 2, where the stiffness D of any disc is calculated as:
Figure BDA0001453537550000091
wherein E is the elastic modulus of the material, h is the disc steel plate height, and mu is the Poisson's ratio;
as shown in fig. 2, the stress condition of the valve plate is split into a plurality of annular finite element units along with the radial direction is shown in fig. 3, and the stress condition of the ith unit is shown in fig. 4;
(1) total force F to be applied to the toroidiConverted into line load QFi：
Figure BDA0001453537550000092
Wherein Q isFiIs the line load (uniform pressure), FiIs the total force (concentration force), RiIs the inner radius of the ith cell;
(2) calculating the total stress F when the pressure p acts on the ith unit of the valvep,i:
Fp,i＝pπ(Re 2-Ri 2) (3)
Wherein p is pressure, ReAnd RiThe inner radius and the outer radius of the ith unit respectively;
(3) will be subjected to a total force Fp,iCalculating the line load Q according to the formula (2)p,i：
Figure BDA0001453537550000093
Wherein Q isp,iIs a line load, Fp,iIs the total force, R, of the ith cell at pressure piIs the inner radius of the ith cell;
(4) calculating the total stress Q on the ith unit of the valve platei：
Qi＝QF,i+Qp,i (5)
Wherein Q isF,iIs a linear load, Q, converted from a concentrated load force F borne by the upper end of the valve platep,iThe linear load is converted from the pressure p applied to the lower end of the valve plate;
(5) according to the deformation condition of the annular unit calculated by the thin plate theory, the deformation W of the ith unit of the valve plate is calculatedi：
Figure BDA0001453537550000101
Wherein, C1,i、C2,i、C3,iAre the three unknown parameters of equation (6), FiIs the force, p, exerted on the upper end of the i-th unit of the valve plateiThe pressure intensity born by the lower end of the ith unit of the valve plate;
(6) deformation W of ith unit of valve plateiDerivation of radius r:
Figure BDA0001453537550000102
(7) calculating the bending moment M of the ith unit of the valve platei：
Figure BDA0001453537550000103
Equations (6), (7) and (8) have three unknown parameters C for the ith cell1,i、C2,i、C3,iIn the above formula FiAnd PiThe values of (A) have the following relationship (see FIG. 5):
Figure BDA0001453537550000104
Figure BDA0001453537550000111
wherein D ispDenotes the diameter of a circle with an applied pressure P, DFA circle diameter representing a concentration force F;
equations (6) to (8) can be solved in conjunction with the following boundary conditions:
1. the inner ring displacement is 0:
Figure BDA0001453537550000112
2. the inner ring displacement derivative is also 0:
Figure BDA0001453537550000113
3. the outermost unit belongs to the free end, the torque is 0:
Figure BDA0001453537550000114
4. due to the continuity of two adjacent cells:
wi(R)＝wi+1(R)
Figure BDA0001453537550000115
Mi(R)＝Mi+1(R)
by combining the above equations, the relationship between the valve opening degree of the valve plate and the radius of the valve plate can be obtained;
at a certain pressure difference, the calculation results are shown in fig. 6;
through solving for many times, can try to get a set of pressure differentials and the open valve height of a set of valve block that corresponds, as follows:
Figure BDA0001453537550000116
Figure BDA0001453537550000121
Figure BDA0001453537550000131
inputting the obtained data into the hydraulic transmission calculation model in the step 2;
step 2, establishing a hydraulic transmission calculation model to obtain the pressure loss in the fluid channel;
as shown in fig. 7, the pressure loss in the fluid passage includes:
(1) pressure loss due to fluid friction with the channel:
Figure BDA0001453537550000132
where λ is the coefficient of friction, l is the channel length, ρ is the fluid density, v is the fluid velocity, deIs the equivalent diameter of the channel;
(2) pressure loss due to narrowing of the fluid inflow passage:
Figure BDA0001453537550000133
wherein k isinFor the inflow coefficient depending on the channel size, ρ is the fluid density and v is the fluid velocity;
(3) pressure loss due to widening of the fluid outflow channel:
Figure BDA0001453537550000141
wherein k isoutFor the outflow coefficient to be dependent on the channel dimensions, ρ is the fluid density and v is the fluid velocity;
(4) pressure loss due to passage turning:
Figure BDA0001453537550000142
wherein,
Figure BDA0001453537550000143
is the bending coefficient of the channel, ρ is the fluid density, v is the fluid velocity, θ is the angle at which the channel bends;
step 3, calculating a stress-speed curve and a stress-displacement curve of the hydraulic shock absorber to evaluate the performance of the hydraulic shock absorber:
as shown in fig. 8 and 9, the hydraulic damper is composed of three chambers, which are a first chamber return chamber, a second chamber compression chamber and a third chamber compensation chamber, and the pressures of the three chambers inside the hydraulic damper are respectively obtained according to the valve plate valve opening degree obtained by the disc valve opening model and the pressure loss in the fluid channel obtained by the hydraulic transmission calculation model:
in order to simulate the force curve of the whole process, firstly a sinusoidal motion state is input to the piston: asin (2 pi ft)
Wherein, A is amplitude, f is frequency, t is time, can be adjusted according to the working condition of the piston;
pressure p of the compensation chamber3It can be calculated from the adiabatic process equation for ideal air:
Figure BDA0001453537550000144
wherein p is0Is the initial pressure of the gas inside the compensation chamber, ArodIs the cross-sectional area of the piston rod; v. of0Is the initial volume of gas, S is the initial position of the piston, and is normally set to 0;
pressure p of the compression chamber2Calculated from the following formula:
p2＝p3+Δp32
wherein, Δ p32The pressure difference between the two sides of the lower piston;
pressure p of the return chamber1Calculated from the following formula:
p1＝p2+Δp21
wherein, Δ p21Is the pressure difference at both sides of the upper piston;
as shown in fig. 10, the force-displacement relationship of the piston is represented by the following formula:
F＝p1Areb-p2Acom+p3Arod
wherein F is the pressure on one side of the disc valve, ArebIs the cross-sectional area of the return chamber, AcomIs the cross-sectional area of the compression chamber, ArodIs the sectional area of the piston rod, the pressure p in the return cavity1Pressure p in the compression chamber2Compensating the pressure p in the chamber3；
Each frequency in fig. 10 corresponds to a force-displacement curve, which is a closed circle, and the peak value of the circle is mapped to a force-velocity curve (see fig. 11), so as to become a force value, and a velocity value is derived from the input condition of S ═ Asin (2 π ft), that is, the corresponding velocity value is a2 π f, and the corresponding relationship between the two is the force-velocity relationship of the piston, see fig. 12.
As described above, the technical scope of the present invention is not limited, and therefore, any minor modifications, equivalent changes and modifications made to the above embodiments according to the technical spirit of the present invention are within the scope of the technical solution of the present invention.

Claims (1)

1. A performance simulation method of a vehicle-mounted hydraulic shock absorber is characterized by comprising the following steps: wherein, the valve in the vehicle hydraulic shock absorber is a piston with a disk valve plate and a choke, the whole valve channel comprises the choke and a channel after the valve is opened, a disk valve opening model is established based on MATLAB software and aiming at the valves with different channel section types and sizes and based on the fluid mechanics theory, obtaining the valve opening degree of a piston valve through a disc valve opening model, then establishing a hydraulic transmission calculation model among all cavities of the vehicle-mounted hydraulic shock absorber, calculating pressure loss caused by friction between fluid and a channel, pressure loss caused by narrowing of a fluid inflow channel, pressure loss caused by widening of the fluid inflow channel and pressure loss caused by turning of the channel, then fitting a hydraulic pressure-speed curve and a hydraulic pressure-displacement curve of the vehicle-mounted hydraulic shock absorber by combining the opening degree of the piston valve so as to realize the performance simulation of the vehicle-mounted hydraulic shock absorber;
the method specifically comprises the following steps:
step 1, establishing a disc valve opening model and obtaining the opening degree of the valve
The disc valve opening module calculates the opening degree of the valve by using a thin plate theory and an equivalent stiffness attenuation model based on the pressure difference and the size of the valve on two sides of the valve, so that input information of the disc valve opening model comprises the pressure difference and the size of the valve on two sides of the valve, and output information is the opening degree of a valve plate corresponding to the pressure difference, namely the lifting height of the valve plate, and the specific calculation comprises the following contents:
the valve plate of the disc valve in the vehicle-mounted hydraulic shock absorber is formed by overlapping a plurality of disc plates, the valve plate is split into n units through finite elements, wherein the rigidity D of the ith unitiThe sum of the stiffness of the stacked discs at the cell, wherein the stiffness D of any disc is calculated by the formula:
Figure FDA0002765255800000011
wherein E is the elastic modulus of the material, h is the disc steel plate height, and mu is the Poisson's ratio;
the valve plate is split into a plurality of annular finite element units along the radial direction, and the stress condition of the ith unit is calculated as follows:
(1) total force F to be applied to the toroidiConverted into line load QFi：
Figure FDA0002765255800000021
Wherein Q isFiIs a line load, FiIs the total force, RiIs the inner radius of the ith cell;
(2) calculating the total stress F when the pressure p acts on the ith unit of the valvep，i：
Figure FDA0002765255800000022
Wherein p is pressure, RpAnd RiThe inner radius and the outer radius of the ith unit respectively;
(3) will be subjected to a total force Fp，iCalculating the line load Q according to the formula (2)p，i：
Figure FDA0002765255800000023
Wherein Q isp，iIs a line load, Fp，iIs the total force, R, of the ith cell at pressure piIs the inner radius of the ith cell;
(4) calculating the ith unit of valve plateTotal stress Q oni：
Qi＝QF，i+Qp，i (5)
Wherein Q isF，iIs a linear load, Q, converted from a concentrated load force F borne by the upper end of the valve platep，iThe linear load is converted from the pressure p applied to the lower end of the valve plate;
(5) according to the deformation condition of the annular unit calculated by the thin plate theory, the deformation W of the ith unit of the valve plate is calculatedi：
Figure FDA0002765255800000024
Wherein, C1，i、C2，i、C3，iAre the three unknown parameters of equation (6), FiIs the force, p, exerted on the upper end of the i-th unit of the valve plateiThe pressure intensity born by the lower end of the ith unit of the valve plate;
(6) deformation W of ith unit of valve plateiDerivation of radius r:
Figure FDA0002765255800000031
(7) calculating the bending moment M of the ith unit of the valve platei：
Figure FDA0002765255800000032
Equations (6), (7) and (8) have three unknown parameters C for the ith cell1，i、C2，i、C3，iIn the above formula FiAnd PiThe values of (A) have the following relations:
Figure FDA0002765255800000033
Figure FDA0002765255800000034
wherein D ispDenotes the diameter of a circle with an applied pressure P, DFA circle diameter representing a concentration force F;
equations (6) to (8) can be solved in conjunction with the following boundary conditions:
1. the inner ring displacement is 0:
Figure FDA0002765255800000035
2. the inner ring displacement derivative is also 0:
Figure FDA0002765255800000036
3. the outermost unit belongs to the free end, the torque is 0:
Figure FDA0002765255800000037
4. due to the continuity of two adjacent cells:
wi(R)＝wi+1(R)
Figure FDA0002765255800000041
Mi(R)＝Mi+1(R)
combining the above equations, the relationship between the valve opening degree of the valve plate and the radius of the valve plate can be obtained, a group of pressure differences and the valve opening height values of the corresponding group of valve plates can be obtained, and the obtained data is input into the hydraulic transmission calculation model in the step 2;
step 2, establishing a hydraulic transmission calculation model to obtain the pressure loss in the fluid channel
(1) Pressure loss due to fluid friction with the channel:
Figure FDA0002765255800000042
where λ is the coefficient of friction, l is the channel length, ρ is the fluid density, v is the fluid velocity, deIs the equivalent diameter of the channel;
(2) pressure loss due to narrowing of the fluid inflow passage:
Figure FDA0002765255800000043
wherein k isinInflow coefficient for channel size, ρ is fluid density, v is fluid velocity;
(3) pressure loss due to widening of the fluid outflow channel:
Figure FDA0002765255800000044
wherein k isoutThe outflow coefficient is the channel size, ρ is the fluid density, v is the fluid velocity;
(4) pressure loss due to passage turning:
Figure FDA0002765255800000045
wherein,
Figure FDA0002765255800000046
is the bending coefficient of the channel, ρ is the fluid density, v is the fluid velocity, θ is the angle at which the channel bends;
step 3, calculating a stress-speed curve and a stress-displacement curve of the hydraulic shock absorber to evaluate the performance of the hydraulic shock absorber
The hydraulic damper comprises a first cavity return cavity, a second cavity compression cavity and a third cavity compensation cavity, wherein the three cavities of the first cavity return cavity, the second cavity compression cavity and the third cavity compensation cavity are arranged inside the hydraulic damper, and the pressure of the three cavities inside the hydraulic damper is respectively obtained according to the valve opening height value of a valve plate obtained by the disc valve opening model in the step 1 and the pressure loss in a fluid channel obtained by the hydraulic transmission calculation model in the step 2:
in order to simulate the force curve of the whole process, firstly a sinusoidal motion state is input to the piston: asin (2 pi ft)
Wherein, A is amplitude, f is frequency, t is time, can be adjusted according to the working condition of the piston;
pressure p of the compensation chamber3It can be calculated from the adiabatic process equation for ideal air:
Figure FDA0002765255800000051
wherein p is0Is the initial pressure of the gas inside the compensation chamber, ArodIs the cross-sectional area, v, of the piston rod0Is the initial volume of gas, S is the initial position of the piston, and is normally set to 0;
pressure p of the compression chamber2Calculated from the following formula:
p2＝p3+Δp32
wherein, Δ p32The pressure difference between the two sides of the lower piston;
pressure p of the return chamber1Calculated from the following formula:
p1＝p2+Δp21
wherein, Δ p21Is the pressure difference at both sides of the upper piston;
the piston force-displacement relationship is represented by the following equation:
F＝p1Areb-p2Acom+p3Arod
wherein F is the pressure on one side of the disc valve, ArebIs the cross-sectional area of the return chamber, AcomIs the cross-sectional area of the compression chamber, ArodIs the sectional area of the piston rod, the pressure p in the return cavity1Pressure p in the compression chamber2Compensating the pressure p in the chamber3；
Each frequency in the piston stress-displacement relationship corresponds to a stress-displacement curve, the stress-displacement curve is a closed circle, a stress value is formed by mapping the peak value of the circle to a stress-speed curve, a speed value is obtained by derivation of an input condition of S-Asin (2 pi ft), namely the corresponding speed value is A2 pi f, and the corresponding relationship of the two is the stress-speed relationship of the piston.
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