CN106339604B - A kind of pressurized strut piston rod calculating method for stability - Google Patents
A kind of pressurized strut piston rod calculating method for stability Download PDFInfo
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- CN106339604B CN106339604B CN201610830013.0A CN201610830013A CN106339604B CN 106339604 B CN106339604 B CN 106339604B CN 201610830013 A CN201610830013 A CN 201610830013A CN 106339604 B CN106339604 B CN 106339604B
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Abstract
The present invention provides a kind of pressurized strut piston rod calculating method for stability, in suitable pressurized strut rigidity than in range, utilize binary stepped stem model hypothesis, that is the two units of pressurized strut outer cylinder, piston rod, according to stress criter ia and material properties, by the Instability load for calculating pressurized strut, and make it compared with suffered compressive load, more easily calculate more accurate pressurized strut piston rod engine sta bility margin, without consulting mechanical design handbook chart, error caused by human factor is reduced.
Description
Technical field
The present invention relates to a kind of pressurized strut piston rod calculating method for stability.
Background technique
Pressurized strut is the liquid of execution driving function common in Aeronautics and Astronautics, ship, weapons industry and civil engineering vehicle
Component is pressed, for example, the grapple mechanical movement driving unit of excavator, is to be served as by pressurized strut.As receiving compressive load
Rod piece, pressurized strut lose bearing capacity form, more show as unstability in practice in engineering.It is accurate to determine that pressurized strut is living
Stopper rod stability is the design difficulty of such component, need meticulously to study the material property of component, the geometrical property in section and
End condition establishes the calculation method for meeting the true loading conditions of structure.
It is many to pressure bar stabilization critical load derivation method in engineering mechanics or the mechanics of materials, such as static method, energy method
Deng.Divide several different constraint conditions, lists approximate, the cumbersome differential equation to solve, meanwhile, it needs to consult Machine Design
Handbook chart, human factor error is very big, and different designs person refers in application, different reading results would generally be obtained.
Summary of the invention
To overcome the problems of the above-mentioned prior art, the present invention provides a kind of pressurized strut piston rod stable calculation sides
Method, the pressurized strut include cylinder and piston rod, the calculation method the following steps are included:
Step 1 calculates the section inertia of the piston rod,
J in formula (1)2For the section inertia of piston rod, D2For the outer diameter of piston rod, d2For the internal diameter of piston rod；
Step 2 calculates the unstability max calculation length and overlap joint specific factor of the pressurized strut,
Lmax=a+b+c (2)；
A is the length of cylinder in formula (2), and c is the length of piston rod, and b is the overlap length of cylinder and piston rod, Lmax
For the unstability max calculation length of pressurized strut；K is overlap joint specific factor in formula (3), and ξ is the overlap joint ratio of cylinder, and ζ is piston rod
Overlap joint ratio；
Formula in above-mentioned steps one and step 2 is brought into and calculates the pressurized strut in following formula (4) by step 3
Instability load,
F in formula (4)crFor the Instability load of pressurized strut, E2For the elasticity modulus of materials of piston rod, π is pi,
μ is that coefficient is supported in effective end of pressurized strut；
The calculated result of above-mentioned steps three is brought into following formula (5), calculates the stability of the pressurized strut by step 4
Nargin,
η is the engine sta bility margin of pressurized strut, F in formula (5)comThe external axial compression load born for pressurized strut.
Preferably, the value range of the rigidity ratio Ψ of the pressurized strut is 3≤Ψ≤24, and the calculation method of rigidity ratio Ψ is such as
Shown in following formula (6) and formula (7):
J in formula (6)1For the section inertia of cylinder (1), D1For the outer diameter of cylinder (1), d1For the internal diameter of cylinder (1)；It is public
Ψ is the rigidity ratio of pressurized strut, E in formula (7)1For cylinder material elasticity modulus, E2For piston rod material elasticity modulus.When rigidity ratio
When the calculated result of Ψ is between 3≤Ψ≤24, the goodness of fit highest of stable calculation result and experimental result, therefore rigidity ratio
When Ψ is in above-mentioned interval range, the accuracy highest of stable calculation result.
Preferably, the effective end of pressurized strut supports that the value of coefficient μ is 1, and one end of pressurized strut at this time is fixed-hinged support, separately
One end is sliding hinged-support, that is, is hingedly supported using both ends.
A kind of pressurized strut piston rod calculating method for stability provided by the invention, using binary stepped stem model hypothesis, i.e.,
The two units of pressurized strut outer cylinder, piston rod more easily calculate more smart according to stress criter ia and material properties
True pressurized strut piston rod engine sta bility margin does not have to consult mechanical design handbook chart, reduces error caused by human factor.
Detailed description of the invention
Fig. 1 is the structural schematic diagram of the pressurized strut；
Fig. 2 is the end boundaries constraint condition schematic diagram of the pressurized strut.
Appended drawing reference: cylinder 1, piston rod 2, cylinder external diameter D1, cylinder internal diameter d1, piston rod outer diameter D2, piston rod internal diameter
d2, barrel lenght a, piston pole length C, overlap length b, pressurized strut length Lmax。
Specific embodiment
To keep the purposes, technical schemes and advantages of the invention implemented clearer, below in conjunction in the embodiment of the present invention
Attached drawing, technical solution in the embodiment of the present invention is further described in more detail.In the accompanying drawings, identical from beginning to end or class
As label indicate same or similar element or element with the same or similar functions.Described embodiment is the present invention
A part of the embodiment, instead of all the embodiments.The embodiments described below with reference to the accompanying drawings are exemplary, it is intended to use
It is of the invention in explaining, and be not considered as limiting the invention.Based on the embodiments of the present invention, ordinary skill people
Member's every other embodiment obtained without creative efforts, shall fall within the protection scope of the present invention.Under
Face is described in detail the embodiment of the present invention in conjunction with attached drawing.
In the description of the present invention, it is to be understood that, term " center ", " longitudinal direction ", " transverse direction ", "front", "rear",
The orientation or positional relationship of the instructions such as "left", "right", "vertical", "horizontal", "top", "bottom", "inner", "outside" is based on attached drawing institute
The orientation or positional relationship shown, is merely for convenience of description of the present invention and simplification of the description, rather than the dress of indication or suggestion meaning
It sets or element must have a particular orientation, be constructed and operated in a specific orientation, therefore should not be understood as protecting the present invention
The limitation of range.
Below by specific embodiment to a kind of pressurized strut piston rod calculating method for stability provided by the invention make into
One step explanation.
Specific embodiment:
The stability of the pressurized strut piston rod is calculated by taking the hydraulic actuator of certain motor vehicles and machines as an example, wherein piston rod 2 exists
The maximum compression load that elongation state is born is 375kN, and the pressurized strut structural schematic diagram is as shown in Figure 1, pressurized strut includes
Cylinder 1 and piston rod 2, wherein D1For the outer diameter of cylinder 1, d1For the internal diameter of cylinder 1, D2For the outer diameter of piston rod 2, d2For piston
The internal diameter of bar 2, a are the length of cylinder 1, and C is the length of piston rod 2, and b is the overlap length of cylinder 1 and piston rod 2, LmaxTo make
The length of dynamic cylinder, and the end boundaries constraint condition schematic diagram of the pressurized strut is as shown in Fig. 2, pressurized strut described in figure uses two
End is hinged to be supported, and due to bearing external axial compression load FcomAnd it is in Failure Model.
The setting numerical value of basic parameter needed for calculating pressurized strut piston rod stability is as shown in table 1 below,
The setting numerical tabular of 1 pressurized strut basic parameter of table
| Pa-rameter symbols | Set numerical value | Dimension |
| a | 620 | mm |
| b | 185 | mm |
| C | 565 | mm |
| D1 | 85 | mm |
| d1 | 75 | mm |
| D2 | 55 | mm |
| d2 | 45 | mm |
| E1 | 195000 | MPa |
| E2 | 200000 | MPa |
| π | 3.1416 | |
| μ | 1.000 | |
| Fcom | 375000 | N |
In table 1, E1For the elasticity modulus of materials of cylinder 1, E2For the elasticity modulus of materials of piston rod 2, π is pi, and μ is
Support coefficient, F in effective end of pressurized strutcomThe external axial compression load born for pressurized strut.
The setting numerical value for going out pressurized strut basic parameter according to given in table 1, calculates the stability of the pressurized strut piston rod, makees
The calculation method for stability of dynamic cylinder piston bar includes the following steps:
Step 1 calculates the section inertia J of piston rod 22,
Step 2 calculates the unstability max calculation length L of the pressurized strutmaxWith overlap joint specific factor k,
Lmax=a+b+c=1370mm (2)；
ξ is the overlap joint ratio of cylinder 1 in formula (3), is the overlap joint of piston rod 2 its calculation formula is ξ=a/b ≈ 3.351, ζ
Than its calculation formula is ζ=c/b ≈ 3.054；
Step 3 brings the calculated result of formula in above-mentioned steps one and step 2 in following formula (4) into described in calculating
The Instability load F of pressurized strutcr, and in the present embodiment, pressurized strut is hingedly supported using both ends, and bears to be compressed axially
Load, therefore coefficient μ=1 is supported in effective end of pressurized strut,
E in formula (4)2For the elasticity modulus of materials of piston rod 2, the value of pi is π=3.1416；
Step 4, by Instability load F in above-mentioned steps threecrCalculated result bring into following formula (5), calculate institute
The engine sta bility margin η of pressurized strut is stated,
F in formula (5)comFor the external axial compression load that pressurized strut is born, calculated engine sta bility margin η is big at this time
In 0, illustrate that the hydraulic actuator meets stability requirement.
FcrIt as the Instability load of pressurized strut, is consolidated according to what the preset parameter of the specific pressurized strut calculated
Definite value, as the critical value of pressurized strut collapsing load, FcomIt is the extraneous compressive load to pressurized strut, therefore in effective end branch
When holding coefficient μ=1, FcrNo less than Fcom, it is critical that the external axial compression load that otherwise pressurized strut is subject to is greater than collapsing load
Value, illustrate pressurized strut can unstability, therefore 0 foundation for meeting as pressurized strut stability is greater than using η, and no matter effective end branch
Hold what value coefficient μ takes, the foundation for judging whether pressurized strut meets stability is all that engine sta bility margin η is greater than 0.
Engine sta bility margin η has calculated that the pressurized strut is proved to meet stability requirement, at this time can be by calculating cylinder 1
It is whether accurate to verify the stable calculation result with the rigidity ratio Ψ of piston rod 2:
The section inertia J of cylinder 1 is calculated by formula (6)1,
The section inertia J that will be calculated in above-mentioned formula (6)1With section calculated in above-mentioned steps one inertia J2It brings into down
The rigidity ratio Ψ of cylinder 1 and piston rod 2 is calculated in face formula (7),
E in formula (7)1For cylinder material elasticity modulus, E2For piston rod material elasticity modulus；The calculating of rigidity ratio Ψ value
As a result in the range of 3≤Ψ≤24, therefore stable calculation is the result is that accurately.
Pressurized strut piston rod stable calculation process and rigidity than in calculating process, pass through what basic parameter calculated
Calculated result is as shown in Table 2 below:
2 pressurized strut Parameter Calculation result table of table
| Pa-rameter symbols | Calculated result | Dimension |
| Lmax | 1370 | mm |
| J1 | 1009237 | mm4 |
| J2 | 247891 | mm4 |
| ξ | 3.351 | |
| ζ | 3.054 | |
| k | 1.599 | |
| Fcr | 416869 | N |
| η | 0.11 | |
| Ψ | 3.970 |
The above description is merely a specific embodiment, but scope of protection of the present invention is not limited thereto, any
In the technical scope disclosed by the present invention, any changes or substitutions that can be easily thought of by those familiar with the art, all answers
It is included within the scope of the present invention.Therefore, protection scope of the present invention should be with the scope of protection of the claims
It is quasi-.
Claims (2)
1. a kind of pressurized strut piston rod calculating method for stability, the pressurized strut includes cylinder (1) and piston rod (2), feature
It is, comprising the following steps:
Step 1 calculates the section inertia of the piston rod (2),
J in formula (1)2For the section inertia of piston rod (2), D2For the outer diameter of piston rod (2), d2For the internal diameter of piston rod (2)；
Step 2 calculates the unstability max calculation length and overlap joint specific factor of the pressurized strut,
Lmax=a+b+c (2)；
A is the length of cylinder (1) in formula (2), and c is the length of piston rod (2), and b is that cylinder (1) is overlapping with piston rod (2)
Length, LmaxFor the unstability max calculation length of pressurized strut；K is overlap joint specific factor in formula (3), and ξ is the overlap joint ratio of cylinder (1),
ζ is the overlap joint ratio of piston rod (2)；
Formula in above-mentioned steps one and step 2 is brought into and calculates the critical of the pressurized strut in following formula (4) by step 3
Collapsing load,
F in formula (4)crFor the Instability load of pressurized strut, E2For the elasticity modulus of materials of piston rod (2), π is pi, μ
Coefficient is supported for effective end of pressurized strut；
Step 4 brings the calculated result of above-mentioned steps three in following formula (5) into, and the stability for calculating the pressurized strut is abundant
Degree,
η is the engine sta bility margin of pressurized strut, F in formula (5)comThe external axial compression load born for pressurized strut；
The value range of the rigidity ratio Ψ of the pressurized strut is 3≤Ψ≤24, and the calculation method of rigidity ratio Ψ is as follows:
J in formula (6)1For the section inertia of cylinder (1), D1For the outer diameter of cylinder (1), d1For the internal diameter of cylinder (1)；Formula (7)
Middle E1For cylinder material elasticity modulus, E2For piston rod material elasticity modulus.
2. pressurized strut piston rod calculating method for stability according to claim 1, which is characterized in that the effective end of pressurized strut
The value for supporting coefficient μ is 1.
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