CN104807432A - Soft measuring method of axial deformation quantity of rectangular rubber sealing ring based on flexible screwing assembly - Google Patents

Abstract

The invention relates to a soft measuring method of axial deformation quantity of a rectangular rubber sealing ring based on flexible screwing assembly. The method comprises the following steps that (1) a Mooney-Rivlin constitutive relation model of rubber materials is built; (2) a rubber material strain invariant and engineering stress relation model is built according to the constitutive relation; (3) a single-axis stretching model of rubber materials is built, and the strain invariant expressed by the axial decoration rate is worked out; (4) the strain invariant expressed by the axial decoration rate is substituted into the strain invariant and engineering stress relation model to obtain an axial engineering stress strain relation model; (5) a penalty function is adopted to convert the axial strain rate of the rectangular rubber ring and an engineering stress value model into a rectangular rubber ring axial strain rate and engineering rotation friction value model; (6) the rectangular rubber ring axial strain rate and engineering rotation friction value model is converted into a rectangular rubber ring axial strain rate and screwing torque value model. The method has the advantages that the soft detection of the rectangular rubber sealing ring axial deformation quantity in the flexible screwing assembly is realized.

Description

The flexible measurement method of the rubber rectangular ring axial deformation amount of assembling is tightened based on flexibility

Technical field

The invention belongs to elastomeric material mechanical technology field, relate to a kind of flexible measurement method tightening the rubber rectangular ring axial deformation amount of assembling based on flexibility.

Background technology

Along with the fast development of science and technology, tighten in assembly technology in flexibility, Automated assembly instead of traditional manual general assembly gradually, and the efficiency of assembling and consistance are improved.Namely flexibility tightens mounting technology is that moment of torsion---controlling angle carries out a control technology of automatic tightening to bolt member and nut part in employing, and wherein very important technical indicator is exactly the impermeability ensureing Assembly interface.

As the critical piece of hermetically-sealed construction, in the seal groove of silicon rubber rectangular seal between upper and lower metal flange, by the tools for bolts ' pretension effect of upper and lower flange, crush seal circle makes its deformation thus reaches seal operation state.And tighten for general assembly for robotization, if pretightning force is excessive in rundown process, ring structure can be destroyed and cause seal failure; If pretightning force is too small, accessory surface can be caused again to contact with O-ring seal insufficient, thus do not reach sealing effectiveness.Therefore the axial deformation amount of O-ring seal becomes the important control objectives of of Automated assembly.But due in automatic tightening process, rubber seal is often positioned at assembly parts inside, does not possess again the condition of additional measuring equipment under most operating mode, therefore directly measure O-ring seal deformation quantity very difficult.And adopting moment of torsion---the automatic assembling of Research on Slew Control Strategy mainly judges the contact condition with O-ring seal by the moment of torsion fed back to, due to the elastomeric material that silicone rubber O-ring is high extensibility and the low modulus had, there is the features such as material, geometry Double Nonlinear and incompressibility, these characteristics judge to bring very large difficulty to the contact of rectangular seal, have a strong impact on the precision thus the reliability affecting robotization general assembly that contact judgement.

Domestic and international little for detecting flexible method of tightening the rubber rectangular loop axial deformation amount in assembling process at present, and present stage mainly relies on test and experience to judge by the method for moment of torsion indirect inspection rubber rectangular loop axial deformation amount, this judgment mode all also exists deficiency in reliability and precision, has augmented no small hidden danger to the security of producing simultaneously.

Summary of the invention

In view of this, the object of the present invention is to provide a kind of flexible measurement method tightening the rubber rectangular ring axial deformation amount of assembling based on flexibility, the method adopts Mooney-Rivlin model, rubber single shaft stretch model and penalty function method, and pass through finite element analysis, have studied the relation of moment of torsion in the axial deformation amount of O-ring seal and assembling process, thus realize the flexible hard measurement tightening rubber rectangular ring axial deformation amount in assembling.

For achieving the above object, the invention provides following technical scheme:

Tighten a flexible measurement method for the rubber rectangular ring axial deformation amount of assembling based on flexibility, comprise the following steps: the Mooney-Rivlin constitutive relation model 1) building elastomeric material; 2) according to step 1) in constitutive relation set up the relational model of elastomeric material strain invariant and engineering stress; 3) build the uniaxial tension model of elastomeric material, calculate the strain invariant represented by axial deformation rate; 4) by step 3) in the strain invariant that represents of axial deformation rate that calculates be brought into step 2) in strain invariant and engineering stress relational model in, draw the axial engineering stress strain stress relation model represented by rubber rectangular loop axial deformation rate; 5) adopt penalty function by step 4) in the numerical model of the rubber rectangular loop axial strain rate that obtains and engineering stress change into the numerical model of rubber rectangular loop axial strain rate and engineering rotation friction; 6) finally by adding moment and contact area by step 5) numerical model of the rubber rectangular loop axial strain rate derived and engineering rotation friction changes into the numerical model of rubber rectangular loop axial strain rate and screw-down torque, thus realizes the soft detection of tightening Rubber Rectangular Rings axial deformation amount in assembling in flexibility.

Further, step 1) described in Mooney-Rivlin constitutive relation model be:

W＝C ₁₀(I ₁-3)+C ₀₁(I ₂-3)

$I_1={\mathrm{\λ}}_1^2+{\mathrm{\λ}}_2^2+{\mathrm{\λ}}_3^2$

$I_2={\mathrm{\λ}}_1^2{\mathrm{\λ}}_2^2+{\mathrm{\λ}}_2^2{\mathrm{\λ}}_3^2+{\mathrm{\λ}}_3^2{\mathrm{\λ}}_1^2$

$I_3={\mathrm{\λ}}_1^2{\mathrm{\λ}}_2^2{\mathrm{\λ}}_3^2$

Wherein, W is strain energy function; C ₁₀, C ₀₁for Mooney constant; I ₁, I ₂, I ₃for strain invariant; λ ₁for X axis rate of strain (%); λ ₂for Y-axis rate of strain (%); λ ₃for Z-axis direction rate of strain (%).

Further, step 2) described in strain invariant and engineering stress relational model be:

$t_{ij}=\frac{\∂W}{\∂E_{ij}}=\frac{\∂W}{\∂I_1}\frac{\∂I_1}{\∂E_{ij}}+\frac{\∂W}{\∂I_2}\frac{\∂I_2}{\∂E_{ij}}+\frac{\∂W}{\∂I_3}\frac{\∂I_3}{\∂E_{ij}}$

Wherein, t _ijfor engineering stress (MPa); E _ijfor Green strain tensor; I ₁, I ₂, I ₃for strain invariant.

Further, step 3) described in the strain invariant relational expression that represents of axial deformation rate be:

λ ₁＝λ

${\mathrm{\λ}}_2={\mathrm{\λ}}_3=\sqrt{{\mathrm{\λ}}^{-1}}$

$I_1={\mathrm{\λ}}^2+\frac{2}{\mathrm{\λ}};I_2=2\mathrm{\λ}+\frac{1}{{\mathrm{\λ}}^2}$

Wherein, λ is rectangular loop axial deformation rate (%), and rectangular loop is axially set as X-axis; λ ₁for X axis rate of strain (%); λ ₂for Y-axis rate of strain (%); λ ₃for Z-axis direction rate of strain (%); I ₁, I ₂for strain invariant.

Further, step 4) described in the axial engineering stress strain stress relation formula that represents of rubber rectangular loop axial deformation rate be:

$t_{11}=C_{10}(2\mathrm{\λ}-\frac{2}{{\mathrm{\λ}}^2})+C_{01}(2-\frac{2}{{\mathrm{\λ}}^3})$

Wherein, t ₁₁for the axial engineering stress (MPa) of rectangular loop; λ is rectangular loop axial deformation rate (%); I ₁, I ₂for strain invariant; C ₁₀, C ₀₁for Mooney constant.

Further, step 5) described in the numerical model relational expression of rubber rectangular loop axial strain rate and engineering rotation friction be:

f _t＝μt ₁₁

Wherein, t ₁₁for the axial engineering stress (MPa) of rectangular loop; f _tfor engineering rotation friction (MPa); μ is friction factor.

Further, step 6) described in the relational expression of rubber rectangular loop axial strain rate and screw-down torque be:

T＝SLf _t

Wherein, T is screw-down torque (N.m); f _tfor engineering rotation friction (MPa); S is contact area (m ²); L is the arm of force (m).

Beneficial effect of the present invention is:

1, easy to detect, reliability is high, and accuracy of detection is high, uses moment of torsion to detect flexible Rubber Rectangular Rings axial deformation amount of tightening in assembling, without the need at devices such as the inner sensor installations of assembly parts;

2, by Mooney-Rivlin constitutive model, adopt strain energy function to describe the axial stress that Rubber Rectangular Rings axial strain causes, reduce the difficulty of the stress-strain analysis caused due to the nonlinear characteristic of rubber own, improve the precision of analysis simultaneously;

3, described the change of Rubber Rectangular Rings configuration in axially loaded deformation process by rubber single shaft stretch model, make force analysis more comprehensive, more reliably.

Accompanying drawing explanation

In order to make object of the present invention, technical scheme and beneficial effect clearly, the invention provides following accompanying drawing and being described:

Fig. 1 is the schematic flow sheet of the method for the invention;

Fig. 2 is Rubber Rectangular Rings assembling sectional view;

Fig. 3 is the variation relation figure of rectangular loop axial deformation rate and screw-down torque under example situation.

Embodiment

Below in conjunction with accompanying drawing, the preferred embodiments of the present invention are described in detail.

First the present invention utilizes the Mooney-Rivlin constitutive relation model of elastomeric material, obtains the relational model of elastomeric material strain invariant and engineering stress.By the uniaxial tension model of elastomeric material, obtain the expression formula of strain invariant, the relational model of bound rubber material strain invariant and engineering stress obtains the axial strain rate of rubber rectangular ring and the expression formula of axial engineering stress, thus reflects the axial stress strain stress relation of rubber rectangular ring.By employing penalty function, axial strain rate and engineering stress relational model are changed into the relational model of axial strain rate and engineering rotation friction simultaneously, finally add moment and contact area, obtain the expression formula of Rubber Rectangular Rings axial strain rate and screw-down torque, finally realize the soft detection of tightening Rubber Rectangular Rings axial deformation amount in assembling in flexibility.

Fig. 1 is the schematic flow sheet of the method for the invention, and as shown in the figure, this method specifically comprises the following steps:

1) the Mooney-Rivlin constitutive relation model of elastomeric material is built;

2) according to step 1) in constitutive relation set up the relational model of elastomeric material strain invariant and engineering stress;

3) build the uniaxial tension model of elastomeric material, calculate the strain invariant represented by axial deformation rate;

4) by step 3) in the strain invariant that represents of axial deformation rate that calculates be brought into step 2) in strain invariant and engineering stress relational model in, draw the axial engineering stress strain stress relation model represented by rubber rectangular loop axial deformation rate;

5) adopt penalty function by step 4) in the numerical model of the rubber rectangular loop axial strain rate that obtains and engineering stress change into the numerical model of rubber rectangular loop axial strain rate and engineering rotation friction;

6) finally by adding moment and contact area by step 5) numerical model of the rubber rectangular loop axial strain rate derived and engineering rotation friction changes into the numerical model of rubber rectangular loop axial strain rate and screw-down torque, thus realizes the soft detection of tightening Rubber Rectangular Rings axial deformation amount in assembling in flexibility.

Wherein, step 1) described in Mooney-Rivlin constitutive relationship be:

W＝C ₁₀(I ₁-3)+C ₀₁(I ₂-3)

$I_1={\mathrm{\λ}}_1^2+{\mathrm{\λ}}_2^2+{\mathrm{\λ}}_3^2$

$I_2={\mathrm{\λ}}_1^2{\mathrm{\λ}}_2^2+{\mathrm{\λ}}_2^2{\mathrm{\λ}}_3^2+{\mathrm{\λ}}_3^2{\mathrm{\λ}}_1^2$

$I_3={\mathrm{\λ}}_1^2{\mathrm{\λ}}_2^2{\mathrm{\λ}}_3^2$

Wherein, W---strain energy function;

C ₁₀, C ₀₁---Mooney constant;

I ₁, I ₂, I ₃---strain invariant;

λ ₁---X axis rate of strain (%);

λ ₂---Y-axis rate of strain (%);

λ ₃---Z-axis direction rate of strain (%);

Wherein C ₁₀and C ₀₁for the intrinsic parameter of rubber, record by rubber uniaxial tensile test.

Wherein, step 2) described in strain invariant and engineering stress relational expression be:

$t_{ij}=\frac{\∂W}{\∂E_{ij}}=\frac{\∂W}{\∂I_1}\frac{\∂I_1}{\∂E_{ij}}+\frac{\∂W}{\∂I_2}\frac{\∂I_2}{\∂E_{ij}}+\frac{\∂W}{\∂I_3}\frac{\∂I_3}{\∂E_{ij}}$

Wherein, t _ij---engineering stress (MPa);

E _ij---Green strain tensor;

I ₁, I ₂, I ₃---strain invariant;

This formula is the stress-strain relation adopting Kirchhoff stress tensor and Green strain tensor to represent, is the intrinsic relational expression of ess-strain of being derived by strain energy function, can represent the Changing Pattern of elastomeric material engineering stress with strain by this formula.

Wherein, step 3) described in the strain invariant relational expression that represents of axial deformation rate be:

λ ₁＝λ

${\mathrm{\λ}}_2={\mathrm{\λ}}_3=\sqrt{{\mathrm{\λ}}^{-1}}$

$I_1={\mathrm{\λ}}^2+\frac{2}{\mathrm{\λ}};I_2=2\mathrm{\λ}+\frac{1}{{\mathrm{\λ}}^2}$

Wherein, λ---rectangular loop axial deformation rate (%), rectangular loop is axially set as X-axis;

λ ₁---X axis rate of strain (%);

λ ₂---Y-axis rate of strain (%);

λ ₃---Z-axis direction rate of strain (%);

I ₁, I ₂---strain invariant;

Wherein combine and tighten assembly technology, as shown in Figure 2, in fitting recess, rubber ring can free deformation, and therefore elastomeric material can be regarded as the material of volume invariability, the product of X, Y, Z triaxial strain rate is 1, I ₃it is a constant.The entirety that the finite element unit that to be regarded as by rubber rectangular ring by some shapes be regular hexahedron is formed, in the process being subject to axial stress, its Deformation Mechanisms is similar to rubber single shaft drawing process, therefore can think that all the other diaxon rate of strain vertical with axial stress direction are identical.

Wherein, step 4) described in the axial engineering stress strain stress relation formula that represents of rubber rectangular loop axial deformation rate be:

$t_{11}=C_{10}(2\mathrm{\λ}-\frac{2}{{\mathrm{\λ}}^2})+C_{01}(2-\frac{2}{{\mathrm{\λ}}^3})$

Wherein, t ₁₁---the axial engineering stress (MPa) of rectangular loop;

λ---rectangular loop axial deformation rate (%);

I ₁, I ₂---strain invariant;

C ₁₀, C ₀₁---Mooney constant;

Wherein step 2) middle I ₃it is a constant, by step 1) in strain energy function bring step 2 into) in, the axial engineering stress strain stress relation that rubber rectangular loop axial deformation rate represents can be obtained, the relation of the axial engineering stress of rectangular loop and rectangular loop axial deformation rate can be represented by this formula.

Wherein, step 5) described in the numerical model relational expression of rubber rectangular loop axial strain rate and engineering rotation friction be:

f _t＝μt ₁₁

Wherein, t ₁₁---the axial engineering stress (MPa) of rectangular loop;

F _t---engineering rotation friction (MPa);

μ---friction factor;

Wherein friction factor μ is the friction factor of rubber seal surface and bolt end face, can be recorded equally by friction test.

Wherein, step 6) described in the relational expression of rubber rectangular loop axial strain rate and screw-down torque be:

T＝SLf _t

Wherein, T---screw-down torque (N.m);

F _t---engineering rotation friction (MPa);

S---contact area (m ²);

L---the arm of force (m);

Wherein contact area S is the contact area of rubber rectangular loop and bolt end contact.

Finally, by integration step 1) to step 6) expression formula, step 6) described in the relational expression of rubber rectangular loop axial strain rate and screw-down torque can be expressed as again:

$T=\mathrm{\μ}\[C_{10}(2\mathrm{\λ}-\frac{2}{{\mathrm{\λ}}^2})+C_{01}(2-\frac{2}{{\mathrm{\λ}}^3})\]LS$

Wherein, T---screw-down torque (N.m);

μ---friction factor;

S---contact area (m ²);

L---the arm of force (m);

λ---rectangular loop axial deformation rate (%);

C ₁₀, C ₀₁---Mooney constant.

Tighten in assembling in flexibility, after between screw bolt and nut, threaded portion is engaged completely, namely after the torque levels produced by threaded portion, a segment distance is still had from bolt end contact rectangular loop surface, in the process continuing to tighten, record screw-down torque by moment of torsion to undergo mutation after screw thread torque levels, namely determine that initial contact occurs for bolt end face and rectangular loop surface, be set as rectangular loop deformation zero point.The moment of torsion recorded deducts the value that screw thread steady torque obtains, and namely thinks the torque value produced by Rubber Rectangular Rings axial deformation, i.e. the value of T in above formula.Bring T value into above formula, the value of Rubber Rectangular Rings axial deformation rate can have been calculated.

The specific embodiment of the present invention is illustrated by following instance:

The specific embodiment of the present invention is described for the assembly parts shown in Fig. 2.

1, the Mooney constant C of the rubber rectangular ring recorded is established ₁₀=2.1094, C ₀₁=1.0547; The friction factor recording rectangular loop and bolt end face is μ=2.0; The arm of force is L=0.1m.

2, the fitted position of rubber rectangular ring as shown in Figure 2, contact area S=407.6216e-6m ².

3, by device for screwing up, fitting recess is fixed, bolt member is at the uniform velocity tightened, record is carried out to screw-down torque simultaneously.

4, continue after torque levels to tighten, when screw-down torque is undergone mutation, record current torque value as moment of torsion zero point, and proceed to tighten.

5, in the process continuing to tighten, the changing value T of screw-down torque after moment of torsion zero point is recorded, as the torque value produced by rectangular loop axial deformation.

6, T value is brought into $T=2*\[2.1094*(2\mathrm{\λ}-\frac{2}{{\mathrm{\λ}}^2})+1.0547(2-\frac{2}{{\mathrm{\λ}}^3})\]*0.1*407.6216$ In, the value of rectangular loop axial deformation rate λ can be obtained.The variation relation of rectangular loop axial deformation rate λ and screw-down torque T as shown in Figure 3.

What finally illustrate is, above preferred embodiment is only in order to illustrate technical scheme of the present invention and unrestricted, although by above preferred embodiment to invention has been detailed description, but those skilled in the art are to be understood that, various change can be made to it in the form and details, and not depart from claims of the present invention limited range.

Claims (7)

1. tighten a flexible measurement method for the rubber rectangular ring axial deformation amount of assembling based on flexibility, it is characterized in that: comprise the following steps:

1) the Mooney-Rivlin constitutive relation model of elastomeric material is built;

2) according to step 1) in constitutive relation set up the relational model of elastomeric material strain invariant and engineering stress;

3) build the uniaxial tension model of elastomeric material, calculate the strain invariant represented by axial deformation rate;

4) by step 3) in the strain invariant that represents of axial deformation rate that calculates be brought into step 2) in strain invariant and engineering stress relational model in, draw the axial engineering stress strain stress relation model represented by rubber rectangular loop axial deformation rate;

5) adopt penalty function by step 4) in the numerical model of the rubber rectangular loop axial strain rate that obtains and engineering stress change into the numerical model of rubber rectangular loop axial strain rate and engineering rotation friction;

6) finally by adding moment and contact area by step 5) numerical model of the rubber rectangular loop axial strain rate derived and engineering rotation friction changes into the numerical model of rubber rectangular loop axial strain rate and screw-down torque, thus realizes the soft detection of tightening Rubber Rectangular Rings axial deformation amount in assembling in flexibility.

2. a kind of flexible measurement method tightening the rubber rectangular ring axial deformation amount of assembling based on flexibility according to claim 1, is characterized in that: step 1) described in Mooney-Rivlin constitutive relation model be:

W＝C ₁₀(I ₁-3)+C ₀₁(I ₂-3)

$I_1={\mathrm{\λ}}_1^2+{\mathrm{\λ}}_2^2+{\mathrm{\λ}}_3^2$

$I_2={\mathrm{\λ}}_1^2{\mathrm{\λ}}_2^2+{\mathrm{\λ}}_2^2{\mathrm{\λ}}_3^2+{\mathrm{\λ}}_3^2{\mathrm{\λ}}_1^2$

$I_3={\mathrm{\λ}}_1^2{\mathrm{\λ}}_2^2{\mathrm{\λ}}_3^2$

Wherein, W is strain energy function; C ₁₀, C ₀₁for Mooney constant; I ₁, I ₂, I ₃for strain invariant; λ ₁for X axis rate of strain; λ ₂for Y-axis rate of strain; λ ₃for Z-axis direction rate of strain.

3. a kind of flexible measurement method tightening the rubber rectangular ring axial deformation amount of assembling based on flexibility according to claim 2, is characterized in that: step 2) described in strain invariant and engineering stress relational model be:

$t_{\mathrm{ij}}=\frac{\∂W}{\∂E_{\mathrm{ij}}}=\frac{\∂W}{\∂I_1}\frac{\∂I_1}{\∂E_{\mathrm{ij}}}+\frac{\∂W}{\∂I_2}\frac{\∂I_2}{\∂E_{\mathrm{ij}}}+\frac{\∂W}{\∂I_3}\frac{\∂I_3}{\∂E_{\mathrm{ij}}}$

Wherein, t _ijfor engineering stress; E _ijfor Green strain tensor; I ₁, I ₂, I ₃for strain invariant.

4. a kind of flexible measurement method tightening the rubber rectangular ring axial deformation amount of assembling based on flexibility according to claim 3, is characterized in that: step 3) described in the strain invariant relational expression that represents of axial deformation rate be:

λ ₁＝λ

${\mathrm{\λ}}_2={\mathrm{\λ}}_3=\sqrt{{\mathrm{\λ}}^{-1}}$

$I_1={\mathrm{\λ}}^2+\frac{2}{\mathrm{\λ}};I_2=2\mathrm{\λ}+\frac{1}{{\mathrm{\λ}}^2}$

Wherein, λ is rectangular loop axial deformation rate, and rectangular loop is axially set as X-axis; λ ₁for X axis rate of strain; λ ₂for Y-axis rate of strain; λ ₃for Z-axis direction rate of strain; I ₁, I ₂for strain invariant.

5. a kind of flexible measurement method tightening the rubber rectangular ring axial deformation amount of assembling based on flexibility according to claim 4, is characterized in that: step 4) described in the axial engineering stress strain stress relation formula that represents of rubber rectangular loop axial deformation rate be:

$t_{11}=c_{10}(2\mathrm{\λ}-\frac{2}{{\mathrm{\λ}}^2})+C_{01}(2-\frac{2}{{\mathrm{\λ}}^3})$

Wherein, t ₁₁for the axial engineering stress of rectangular loop; λ is rectangular loop axial deformation rate; I ₁, I ₂for strain invariant; C ₁₀, C ₀₁for Mooney constant.

6. a kind of flexible measurement method tightening the rubber rectangular ring axial deformation amount of assembling based on flexibility according to claim 5, is characterized in that: step 5) described in the numerical model relational expression of rubber rectangular loop axial strain rate and engineering rotation friction be:

f _t＝μt ₁₁

Wherein, t ₁₁for the axial engineering stress of rectangular loop; f _tfor engineering rotation friction; μ is friction factor.

7. a kind of flexible measurement method tightening the rubber rectangular ring axial deformation amount of assembling based on flexibility according to claim 6, is characterized in that: step 6) described in the relational expression of rubber rectangular loop axial strain rate and screw-down torque be:

T＝SLf _t

Wherein, T is screw-down torque; f _tfor engineering rotation friction; S is contact area; L is the arm of force.