CN110990931B - Modeling method for nonlinear spring unit of lathe bed-foundation joint surface - Google Patents
Modeling method for nonlinear spring unit of lathe bed-foundation joint surface Download PDFInfo
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- 239000004567 concrete Substances 0.000 claims abstract description 34
- 230000005489 elastic deformation Effects 0.000 claims abstract description 21
- 239000000463 material Substances 0.000 claims abstract description 14
- 238000004513 sizing Methods 0.000 claims abstract description 7
- 238000004088 simulation Methods 0.000 claims abstract description 4
- 238000010606 normalization Methods 0.000 claims description 10
- 238000006073 displacement reaction Methods 0.000 claims description 4
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- 238000010998 test method Methods 0.000 claims description 3
- 238000002474 experimental method Methods 0.000 claims description 2
- 239000007779 soft material Substances 0.000 claims description 2
- 230000003746 surface roughness Effects 0.000 claims description 2
- 238000012876 topography Methods 0.000 claims description 2
- 238000003754 machining Methods 0.000 description 2
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Abstract
The invention discloses a modeling method of a nonlinear spring unit of a lathe bed-foundation junction surface, aiming at the junction surface contact characteristic between the lathe bed and the foundation, the method considers the stress softening stage of a foundation concrete material, and obtains critical contact areas of elastic deformation and plastic deformation and crushing by introducing a uniaxial compressive stress-strain curve equation of the concrete material, and the surface contact microprotrusions are divided into three types of elastic deformation, plastic deformation and crushing. Obtaining the contact stiffness of each microprotrusion body which elastically deforms based on a statistical theory, and regarding the contact stiffness of the whole bolting junction surface as a parallel connection result of the contact stiffness of each microprotrusion body; and establishing nonlinear spring unit models of the positions of the sizing blocks between the machine tool and the foundation through the obtained nonlinear relation between the applied load and the distance between the two planes. The method solves the contact problem of finite element simulation in actual engineering, and verifies the correctness of a theoretical model by comparing a theoretical result with an experimental result.
Description
Technical Field
The invention belongs to the field of junction surface dynamics, and relates to a modeling method of a nonlinear spring unit of a lathe bed-foundation junction surface.
Background
The foundation is usually made of concrete materials and is connected with the machine tool body through foundation bolts, and the connection characteristic of the joint surface of the machine tool body and the foundation has very important influence on the machining precision and the service life of the whole machine tool. The heavy machine tool has the characteristics of large size, large deformation, large torque and the like, so that the contact characteristic of the combined surface of the machine tool body and the foundation is considered to have very important influence on improving the processing performance of the whole machine tool. At present, the research on the joint surfaces at home and abroad mostly adopts an experimental test method to identify the parameters of the joint surfaces, so that the influence rule of each parameter on the result cannot be qualitatively and quantitatively analyzed, and the modeling of the contact characteristics of the joint surfaces of the bed body and the foundation is necessary by considering the crushing stage of the concrete material.
Disclosure of Invention
Aiming at the contact characteristic of the joint surface between the lathe bed and the foundation, the method considers the stress softening stage of the foundation concrete material, obtains the critical contact areas of elastic deformation and plastic deformation and crushing by introducing a uniaxial compressive stress-strain curve equation of the concrete material, and divides the surface contact microprotrusions into three types of elastic deformation, plastic deformation and crushing. Obtaining the contact stiffness of each microprotrusion body which elastically deforms based on a statistical theory, and regarding the contact stiffness of the whole bolting junction surface as a parallel connection result of the contact stiffness of each microprotrusion body; and establishing nonlinear spring unit models of the positions of the sizing blocks between the machine tool and the foundation through the obtained nonlinear relation between the applied load and the distance between the two planes. The method provides a new method for solving the contact problem of finite element simulation in actual engineering.
The invention is realized by adopting the following technical means: a method of modeling a bed-foundation interface nonlinear spring unit, the method comprising the steps of:
s1, obtaining critical deformation delta from elastic deformation to plastic deformation through stress-strain curve equation and Hertz contact theory obtained through concrete material uniaxial experiment 1 Critical deformation delta from plastic deformation to fracture 2 。
S2, obtaining the contact load F of elastic deformation and plastic deformation through the distribution density function of the micro-convex body on the nominal area e 、F p And the contact stiffness K of the elastically deformable microprotrusions.
S3, carrying out dimension normalization processing on the relation of the obtained distribution density function to obtain a nonlinear relation between the contact load and the distance between the two planes and a nonlinear relation between the rigidity and the distance between the two planes.
S4, adding a nonlinear spring contact unit to the sizing block position between the bed body and the foundation by drawing a force-displacement curve between planes.
The method is characterized in that the crushing stage of the foundation concrete material is considered, and the deformation critical parameter is obtained through the stress-strain curve of the uniaxial compression of the concrete material. And obtaining the nonlinear relation between the contact load and the distance between the two contact planes through dimension normalization. The nonlinear spring unit is added at the position of the sizing block to provide a new solution to the contact problem in actual engineering. Provides theoretical reference for improving the integral rigidity and the machining precision of the machine tool. The following figures and tables illustrate the present invention more clearly.
Drawings
Fig. 1 is a uniaxial compressive stress-strain graph of a concrete material.
Fig. 2 is a flow chart of an implementation of the present invention.
Detailed Description
The invention discloses a modeling method of a nonlinear spring unit of a lathe bed-foundation combined surface. The method is specifically described below with reference to the accompanying drawings:
step 1. Contact Critical deformation of individual microprotrusions
Because Popovics' formula considers E/E 0 (E is the initial elastic modulus, E 0 Is the limit stress sigma 0 Secant modulus) reflects the change of the stress-strain curve with the concrete grade to a certain extent. This curve was used for the calculation. (for concrete materials with complex components, in the practical engineering problem, stress and strain data of different concretes can be obtained through a test method, and a curve equation suitable for specific concrete labels can be found through fitting the data with different curve equations).
Wherein:
n＝5.7×10 -3 σ 0 +1；
α＝n+β；
beta curve camber adjustment constant; sigma (sigma) 0 -concrete compressive strength; epsilon 0 -peak strain;
as can be seen from the study of the stress-strain curve of concrete, when the concrete is under uniaxial compression, the stress is mainly applied to failureThe three stages of elastic deformation, plastic deformation and crushing deformation of the concrete are performed. Peak point C stress value, i.e. compressive strength, sigma 0 The following steps are:
1) Elastic deformation stage of concrete, maximum stress value sigma of said stage c Referred to as the proportion limit, the proportion limit of common concrete is sigma c ＝(0.3～0.5)σ 0 Concrete with C60 mark number sigma c ＝0.408σ 0 ，
2) The microprotrusions plastically deform when exceeding the critical stress sigma of fracture u ＝(0.88～0.97)σ 0 When the microprotrusions are deformed, the microprotrusions yield and break, and the concrete marked by C60 takes a value sigma u ＝0.902σ 0 ，
3) The stress value is larger than 0.9020, so that the broken microprotrusions cannot continuously bear load, and the stress-strain curve is sharply reduced.
The elastic deformation stage contact load and the contact area obtained by the Hertz contact theory are respectively as follows:
a e ＝πRδ
f e -elastically deforming the individual microprotrusions by an elastic contact force;
a e -elastically deforming the true contact area of the individual microprotrusions;
E * the equivalent modulus of elasticity and,E 1 、E 2 、v 1 、v 2 the elastic modulus and the poisson ratio of the two surfaces contacted are respectively;
radius of curvature of R-microprotrusions;
delta-microprotrusion deformation;
the critical deformation amount of the microprotrusions from elastic deformation to plastic deformation can be obtained by the method:
δ 1 -a critical deformation amount from elastic deformation to plastic deformation;
k-average contact pressure coefficient;
hardness of H-soft material.
Contact load and contact area at plastic deformation stage:
a p ＝2πRδ
f p ＝Ha p
f p -plastically deforming the individual microprotrusions to a resilient contact force;
a p true contact area of plastically deformed individual microprotrusions
Obtaining critical deformation epsilon of the crushing stage according to the stress-strain curve of the concrete material when being uniaxially pressed s The critical deformation amount from plastic deformation to crushing is:
δ 2 ＝ε s R
δ 2 -plastic deformation to a critical deformation of fracture;
ε s -critical deformation of plasticity to crushing stage.
When delta<δ 1 The micro-convex body is elastically deformed when in use,
when delta 2 >δ>δ 1 The micro-convex body is subjected to plastic deformation,
when delta>δ 2 The microprotrusions are broken.
Step 2, calculating the contact load and the contact rigidity of the joint surface
Single microprotrusion contact stiffness:
two macroscopically roughened surfaces are in contact, microscopically representing the contact of the microprotrusions, if the nominal contact area A n The elastic contact force and the plastic are the total contact load of the two surfaces according to the three deformation mechanisms of the above microprotrusionsThe sum of the sexual contact force and the rough rigidity are combined as a result of the parallel connection of the elastically deformed microprotrusion contact rigidity. Meanwhile, a great deal of researches show that the height distribution of the microprotrusions on the engineering surface is compliant with Gaussian distribution, and the surface is in nominal contact area A n With N asperities, the desired number of contact asperities is:
n-number of microprotrusions;
A n -a nominal contact area;
η -microprotrusion area density;
-probability density function of microprotrusion height distribution.
Contact load of the whole joint surface:
d-distance of contact surface;
f-total contact load;
F e -total elastic contact force;
F p total plastic contact force.
Contact stiffness
Step 3, dimension normalization
In order to make the comparison result have wider practicability than that of special cases, it is necessary to dimension normalize the model to be compared, and use sigma and A for all length, contact area and contact load respectively n 、EA n Sigma is subjected to dimension normalization, and the contact load and the contact rigidity after dimension normalizationThe method comprises the following steps:
wherein:
β -surface topography parameter, β=σrη;
d * the dimension normalized surface distance,
-critical deformation amount of elastic deformation to plastic deformation after dimension normalization, +.>
z * Dimension normalized microprotrusion height,
-a probability density function of the dimension normalized microprotrusion height distribution;
sigma-mean variance of roughened surface height;
σ s -mean variance of microprotrusion height;
the surface roughness parameter can be beta,To describe, the following table gives values for two parameters of different roughened surfaces, which are tested by NURI on a typical engineered surfaceThe resulting contact state of a surface can also be more fully characterized by a plasticity index ψ, which is defined as:
see the attached table-rough surface parameter table.
Step 4, adding a nonlinear spring unit
And describing a force-displacement curve of the nonlinear spring through the obtained relation between the contact load of the joint surface and the plane distance, and adding a nonlinear spring unit at the position of the sizing block in the finite element simulation process of the bed body-foundation joint surface.
TABLE 1 roughened surface parameter table
Claims (4)
1. A modeling method of a nonlinear spring unit of a lathe bed-foundation joint surface is characterized by comprising the following steps of: the method comprises the steps of,
s1, obtaining critical deformation delta from elastic deformation to plastic deformation through stress-strain curve equation and Hertz contact theory obtained through concrete material uniaxial experiment 1 Critical deformation delta from plastic deformation to fracture 2 ；
S2, obtaining the contact load F of elastic deformation and plastic deformation through the distribution density function of the micro-convex body on the nominal area e 、F p And the contact stiffness K of the elastically deformable microprotrusions;
s3, carrying out dimension normalization processing on the relation of the obtained distribution density function to obtain a nonlinear relation between the contact load and the distance between two planes and a nonlinear relation between rigidity and the distance between two planes;
s4, adding a nonlinear spring contact unit to the sizing block position between the bed body and the foundation by drawing a force-displacement curve between planes;
popovics' formula considers E/E 0 E is the initial modulus of elasticity, E 0 Is the limit stress sigma 0 Secant modulus at time; the characteristic that the stress-strain curve changes along with the concrete label is reflected to a certain extent; calculating by adopting the curve; stress and strain data of different concrete are obtained through a test method, and a curve equation suitable for specific concrete labels is found through fitting of the data and different curve equations;
wherein:
n＝5.7×10 -3 σ 0 +1；
α＝n+β；
beta curve camber adjustment constant; sigma (sigma) 0 -extreme stress; epsilon 0 -peak strain;
when the concrete is under uniaxial compression, the concrete is subjected to three stages of elastic deformation, plastic deformation of the microprotrusions and crushing deformation from the beginning of loading to failure; peak point C stress value, i.e. limit stress is sigma 0 The following steps are:
1) Elastic deformation stage of concrete, maximum stress value sigma of said stage c Is called a proportion limit, and the proportion limit of common concrete is sigma c ＝(0.3～0.5)σ 0 Concrete with C60 mark number sigma c ＝0.408σ 0 ，
2) The microprotrusions plastically deform when exceeding the critical stress sigma of fracture u ＝(0.88～0.97)σ 0 When the microprotrusions are deformed, the microprotrusions yield and break, and the concrete marked by C60 takes a value sigma u ＝0.902σ 0 ，
3) The stress value is larger than 0.9020, so that the broken microprotrusions cannot continuously bear load, and the stress-strain curve is sharply reduced;
the elastic deformation stage contact load and the contact area obtained by the Hertz contact theory are respectively as follows:
a e ＝πRδ
f e -elastically deforming the individual microprotrusions by an elastic contact force;
a e -elastically deforming the true contact area of the individual microprotrusions;
E * the equivalent modulus of elasticity and,E 1 、E 2 、v 1 、v 2 the elastic modulus and the poisson ratio of the two surfaces contacted are respectively;
radius of curvature of R-microprotrusions;
delta-microprotrusion deformation;
the critical deformation amount of the microprotrusions from elastic deformation to plastic deformation can be obtained by the method:
δ 1 -a critical deformation amount from elastic deformation to plastic deformation;
k-average contact pressure coefficient;
hardness of H-soft material;
contact load and contact area at plastic deformation stage:
a p ＝2πRδ
f p ＝Ha p
f p -plastically deforming the individual microprotrusions to a resilient contact force;
a p true contact area of plastically deformed individual microprotrusions
Obtaining critical deformation epsilon of the crushing stage according to the stress-strain curve of the concrete material when being uniaxially pressed s The critical deformation amount from plastic deformation to crushing is:
δ 2 ＝ε s R
δ 2 -plastic deformation to a critical deformation of fracture;
ε s -critical deformation of plasticity to crushing stage;
when delta is less than delta 1 The micro-convex body is elastically deformed when in use,
when delta 2 ＞δ＞δ 1 The micro-convex body is subjected to plastic deformation,
when delta > delta 2 The microprotrusions are broken.
2. A method of modeling a bed-foundation interface nonlinear spring unit in accordance with claim 1, wherein: the joint face contact load and the contact stiffness are calculated as follows,
single microprotrusion contact stiffness:
two macroscopically roughened surfaces are in contact, microscopically representing the contact of the microprotrusions, if the nominal contact area A n The elastic contact force and the plastic contact force are added according to the total contact load of the two surfaces, and the combination of the rough rigidity and the parallel connection of the elastic deformation microprotrusions is realized; meanwhile, a great deal of researches show that the height distribution of the microprotrusions on the engineering surface is compliant with Gaussian distribution, and the surface is in nominal contact area A n With N asperities, the desired number of contact asperities is:
m-number of microprotrusions;
A n -a nominal contact area;
η -microprotrusion area density;
-a probability density function of the microprotrusion height distribution;
contact load of the whole joint surface:
d-distance of contact surface;
f-total contact load;
F e -total elastic contact force;
F p -total plastic contact force;
contact stiffness
3. A method of modeling a bed-foundation interface nonlinear spring unit in accordance with claim 1, wherein: the dimension normalization process is as follows,
all length, contact area and contact load are respectively omega and A n 、EA n Omega is subjected to dimension normalization, and the contact load and the contact rigidity after dimension normalization are as follows:
wherein:
μ -surface topography parameter, μ=ωrη;
d * the dimension normalized surface distance,
-critical deformation amount of elastic deformation to plastic deformation after dimension normalization, +.>
z * Dimension normalized microprotrusion height,
-a probability density function of the dimension normalized microprotrusion height distribution;
omega-roughened surface height average variance;
ω s -mean variance of microprotrusion height;
the surface roughness parameter is mu,To describe, the values of two parameters, given for different roughened surfaces, the parameters being determined experimentally for a typical engineered surface by NURI, the contact state of the surface being characterized by a plasticity index ψ, which is defined as:
4. a method of modeling a bed-foundation interface nonlinear spring unit in accordance with claim 1, wherein: the process of adding the nonlinear spring unit is as follows,
and describing a force-displacement curve of the nonlinear spring through the obtained relation between the contact load of the joint surface and the plane distance, and adding a nonlinear spring contact unit at the position of the sizing block in the finite element simulation process of the bed body-foundation joint surface.
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| 杨红平等.机械结合面基础特性参数的理论计算与实验研究.西南交通大学出版社,2016,第96-101页. * |
| 结合面卸载法向接触刚度统计模型;安冉等;太原科技大学学报;全文 * |
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