WO2014081399A1 - Apparatus and method for determining and verifying of strength of a mechanically loaded machine part - Google Patents
Apparatus and method for determining and verifying of strength of a mechanically loaded machine part Download PDFInfo
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- WO2014081399A1 WO2014081399A1 PCT/SI2013/000065 SI2013000065W WO2014081399A1 WO 2014081399 A1 WO2014081399 A1 WO 2014081399A1 SI 2013000065 W SI2013000065 W SI 2013000065W WO 2014081399 A1 WO2014081399 A1 WO 2014081399A1
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- machine part
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- increment
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- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F30/00—Computer-aided design [CAD]
- G06F30/20—Design optimisation, verification or simulation
- G06F30/23—Design optimisation, verification or simulation using finite element methods [FEM] or finite difference methods [FDM]
Abstract
Apparatus for determining and verifying of strength of a mechanically loaded machine part, comprising a digital calculating unit, which is adapted for calculating of stresses and deformations in each pre-determined zones on said mechanically loaded part on the basis of each disposable software and in accordance to Finite Element Method (FEM) on the basis of data concerning geometry, mechanical loads to which each part is exposed, as well as the material, of which each mechanically loaded part is made. In addition to said digital calculating unit, said apparatus also comprises an apparatus for mechanically testing of mechanical properties of each desired material of each mechanically loaded machine part, by which appropriate testing of the material is performed both during elastic and plastic deforming, and the retrieved data is then forwarded to said digital calculating unit.
Description
Apparatus and method for determining and verifying of strength of a mechanically loaded machine part
The present invention refers to an apparatus as well as to a method for determining and verifying of strength of a mechanically loaded machine part, in particular of a non-standardized statically and/or dynamically loaded metallic bearing component of a vehicle or a machine, or of any other appliance, wherein during the use thereof in addition to elastic deformations also controlled i.e. pre-determined plastic deformations are allowed, and wherein however each excessive deformation or damage of said mechanical part, due to which said part could become unable to withstand each expected mechanical loadings, must be prevented with sufficiently high probability.
According to the International Patent Classification, such inventions belong to physics, namely to digital computing or data processing equipment or methods, specially adapted for specific functions, namely to computer-aided design.
The purpose of the invention is to enable determining and verifying of a bearing capability of each mechanically loaded machine part having pre-determined geometric features, namely a shape and dimensions, and consisting of a predetermined material, so that dimensions of such part could be essentially reduced with respect to dimensions of parts designed according to the state of the art, while the part would despite to reduced dimensions and weight still be able to withstand mechanical loadings, to which it is exposed during the use thereof.
In addition to functionality, vehicle components must also fulfil high security requirements. In certain loading conditions like in a vehicle crash, such parts shall not be destroyed, e.g. broken or cracked. During a virtual testing of each product, plastic deformations indicate vicinity to destroying in critical zones of certain part. Analysis is usually used to this aim, which are based on engineering stress- deformation curves, and which usually results in over-dimensioned constructions.
A usual approach in engineering, concerning the bearing capability of each mechanically loaded machine part, is based on a presumption that the machine part is capable to withstand to loadings in particular below the limit of the proportionality defining area of plastic deformations, by which such part is elastically deformed, but after releasing, deformations are practically eliminated and the initial state of the part is re-established. Depending on each loading, which can be static or dynamic, either pulsing (just compression or just tension) or alternative (i.e. alternating compression and tension), the machine part is then dimensioned by introducing a safeguard coefficient, which enables the part to withstand either occasional or permanent static loadings, or occasional or permanent dynamic loadings.
Such approach is among others described in US 2009/0192766, wherein a behavior of two mutually interconnected parts is monitored according to a Finite Element Method. Such method is based on a simulation of each machine part by means of a mathematical model, by which the shape of such part is defined. The simulated part consists of a finite number of geometrically regular elements, which are linked with each other in their corner points. When presuming that such simulating part is exposed to certain mechanical loadings, stresses and deformations in each desired in each desired points, by which the conditions in particular critical zones of said part are determined, or also deformations of the part as such. Deformations depend on the material, which is defined by the module of elasticity, which is used in calculation, verification can be achieved by means of amending the number and/or dimensions and/or the shape of said elements of the mathematical model of the geometry of the part.
A bearing capability of such mechanically loaded machine part as declared by such engineering approach, is directly depending both on the module of elasticity of each used material and on admissible stresses, by which said part is still capable to withstand the loadings by maintaining just plastic deformations and by avoiding entering the area of plastic deformations above the limit of proportionality.
As a consequence of such approach, machine parts are over-dimensioned and bulky machine parts having a corresponding weight, which is in particular in manufacturing of vehicles not really desired, since such bulky parts during the use of each vehicle lead to additional loadings of correlated machine parts and correspondingly higher fuel consumption and environment pollution.
W
4
A known apparatus for determining and verifying of strength of a mechanically loaded machine part, comprising a digital calculating unit, which is adapted for calculating of stresses and deformations in each pre-determined zones on said mechanically loaded part on the basis of each disposable software and in accordance to Finite Element Method (FEM) on the basis of data concerning
- geometry, namely a shape and dimensions of said machine part, expressed by means of a mathematical model, consisting of a finite number of geometrically regular bodies i.e. finite elements, which are defined by means of a plurality of corners, namely points defined by means of each pre-determined spatial coordinates, which define geometry, namely a geometric matrix B having a volume V, AV;
- mechanical loadings, to which each machine part is exposed and which are expressed e.g. by forces or continuous loadings in certain zones of the machine part, or also by torque; and
- material, which is defined by means of the module of the elasticity E and determines an elasticity matrix as a property of each used material, as well as with a real deformation curve i.e. the curve of elongation;
wherein the calculating by means of said digital calculating unit is performed on the basis of iterations, in which a non-balanced force is calculated, which is then entered into each subsequent calculating step, wherein the steps are performed in the following sequence:
i) generating a deformation matrix B on the basis of each geometry of the machine part:
ii) calculating of increment of deformations;
iii) calculating of increment of stresses;
and wherein each obtained results comprise on the one hand the data related to loadings in at least certain points of said loaded part, and on the other hand the data concerning deformations in at least certain points of said machine part, which
depend on geometry, mechanical loadings and each disposable material of the machine part.
The initially exposed technical problem is solved by means of an apparatus as well as by means of a method according to independent and dependent claims.
In accordance with the present invention, such apparatus in addition to said digital calculating unit also comprises an apparatus for mechanically testing of mechanical properties of each desired material of each mechanically loaded machine part.
Said apparatus for testing of mechanical properties is adapted to cooperate with said digital calculating unit, is adapted to generate data about functional dependency of stresses within a mechanically loaded part and within the material thereof the on the basis of a standardized specimen consisting of the same material as said machine part, starting from initiation of loading both during the stage of elastic deformation thereof and also along the stage of plastic deformation up to the final rupture of the material of said specimen.
To this aim, a specimen is used in said apparatus for testing of mechanical properties, said specimen having initial length (10) and initial cross-section (A0) and consisting of each desired material which is identical to the material of each mechanically loaded machine part, wherein said specimen is loaded by means of simultaneously step-like tensioning thereof, by which at the same time the loading force (F) is measured together with contraction of the cross-section between said initial cross-section (Ao) and each actual cross-section (A) i.e. together with specific deformations (ε) just prior to rupture of the part.
Behavior during said step-like extending (of the length or any other corresponding dimension) is shown in the attached diagrams (Figs 1 and 2). In general, the relationship between each actual stresses and deformations as well as stresses and deformations calculated by means of classic engineering methods can also be mathematically presented, wherein the ratio between each actual stress and said engineering stress is the following
wherein
F is a force, by which the specimen is loaded;
σ is a stress within a cross-section of the specimen as calculated on the basis of usual engineering method;
A is each actual cross-section of a deformed specimen;
Ao is each actual cross-section of a non-deformed specimen;
while the actual deformations relative to deformations calculated by means of engineering method are the following:
Attached are also appropriate stress - strain diagrams (Figs 3 and 4), which present output data retrieved from the apparatus for testing of mechanical properties and which also enable comparing relationships between each actual stresses and deformations as well as stresses and deformations calculated by means of engineering methods.
Thanks to the presence and use of said apparatus for testing of mechanical properties, and in particular to data experimentally retrieved there-from and related to actual stresses and deformations during both elastic and plastic deforming, namely the data about the real strength i.e. bearing capability of certain material during both elastic and plastic deforming thereof, the digital calculating unit is then able to calculate stresses and deformations in each disposable mechanically loaded part having each particular geometry and dimensions, wherein said calculation is performed with the following steps: i) determining of a rigidity matrix of the construction of each mechanically loaded machine part in accordance with formula (I)
K = V BTEBdV (I) wherein
K is a rigidity matrix of the construction;
B is a deformation matrix (geometry);
E is an elasticity matrix (material properties)
V, dV is a volume; ii) calculating of increment of deformations by means of resolving a global system of equations according to formula (II)
ΚΔιι = AF → Au = K 'AF (II) wherein
F, AF is a vector of forces, namely increment of forces i.e. loadings during each step i.e. during each iteration;
u, Διι is a vector of displacements, namely increment of displacements during each step i.e. during each iteration; iii) calculating each increment of stresses according to formula (III):
Δσ = ΕΒΔιι (III)
wherein
u = u + Au (IV)
and
σ = σ + Δσ (V) and wherein
σ, Λσ is a vector of stresses i.e. increment of stresses during each particular step i.e during each iteration; and then also iv) calculating of increment of plastic deformations according to formula (VI)
Δερ| = ΒΔιι - E"1 σ (VI)
where
ερ|, Δερ| is a vector of plastic part of specific deformations i.e. increment thereof; which is then followed by calculating of non-balanced force due to adding thereof to the loading before the next step of calculating within said iteration.
Claims
1. Apparatus for determining and verifying of strength of a mechanically loaded machine part, comprising a digital calculating unit, which is adapted for calculating of stresses and deformations in each pre-determined zones on said mechanically loaded part on the basis of each disposable software and in accordance to Finite Element Method (FEM) on the basis of data concerning
- geometry, namely a shape and dimensions of said machine part, expressed by means of a mathematical model, consisting of a finite number of geometrically regular bodies i.e. finite elements, which are defined by means of a plurality of corners, namely points defined by means of each pre-determined spatial coordinates, which define geometry, namely a geometric matrix (B) having a volume (V, AV);
- mechanical loadings, to which each machine part is exposed and which are expressed e.g. by forces or continuous loadings in certain zones of the machine part, or also by torque; and
- material, which is defined by means of the module of the elasticity (E) and determines an elasticity matrix as a property of each used material, as well as with a real deformation curve i.e. the curve of elongation;
wherein the calculating by means of said digital calculating unit is performed on the basis of iterations, in which a non-balanced force is calculated, which is then entered into each subsequent calculating step, wherein the steps are performed in the following sequence:
i) generating a deformation matrix (B) on the basis of each geometry of the machine part:
ii) calculating of increment (Δε) of deformations (ε);
iii) calculating of increment (Δσ) of stresses (σ);
and wherein each obtained results comprise on the one hand the data related to loadings in at least certain points of said loaded part, and on the other hand the data concerning deformations in at least certain points of said machine part, which depend on geometry, mechanical loadings and each disposable material of the machine part, characterized in that in addition to said digital calculating unit, said apparatus also comprises an apparatus for mechanically testing of mechanical properties of each desired material of each mechanically loaded machine part.
2. Apparatus according to Claim 1, characterized in that said apparatus for testing of mechanical properties according to Finite Element Method, which is adapted to cooperate with said digital calculating unit, is adapted to generate data about functional dependency of stresses (σ) within a mechanically loaded part and within the material thereof the on the basis of a standardized specimen consisting of the same material as said machine part, starting from initiation of loading both during the stage of elastic deformation thereof and also along the stage of plastic deformation up to the final rupture of the material of said specimen.
3. Apparatus according to Claim 1 or 2, characterized in that said apparatus for testing of mechanical properties of each specimen having initial length (10) and initial cross-section (A0) and consisting of each desired material which is identical to the material of each mechanically loaded machine part, is adapted for loading said specimen with simultaneously step-like tensioning thereof, by which at the same time the loading force (F) is measured together with contraction of the cross- section between said initial cross-section (A0) and each actual cross-section (A) i.e. together with specific deformations (ε) just prior to rupture of the part.
4. Apparatus according to anyone of Claims 1 to 3, characterized in that calculating of each actual status of stresses and deformations within each desired
machine part of each desired geometry and dimensions on the basis of data concerning each stress- and deformation characteristics of the specimen in both stages of elastic and plastic deformation retrieved from the apparatus for testing of mechanical properties is defined by following steps: i) determining of a rigidity matrix of the construction of each mechanically loaded machine part in accordance with formula (I)
wherein
K is a rigidity matrix of the construction;
B is a deformation matrix (geometry);
E is an elasticity matrix (material properties)
V, dV is a volume; ii) calculating of increment of deformations by means of resolving a global system of equations according to formula (II)
KAu = AF Au = K AF (II) wherein
F, AF is a vector of forces, namely increment of forces i.e. loadings during each step i.e. during each iteration;
u, Au is a vector of displacements, namely increment of displacements during each step i.e. during each iteration; calculating each increment of stresses according to formula (III):
Δσ = EBAu (III)
wherein
u = u + Au (IV)
and
σ = σ + Δσ (V) and wherein
σ, Δσ is a vector of stresses i.e. increment of stresses during each particular step i.e during each iteration; and then also iv) calculating of increment of plastic deformations according to formula (VI)
Δερ| = ΒΔιι - E-1 σ (VI)
where ερΙ, Δερ| is a vector of plastic part of specific deformations i.e. increment thereof; which is then followed by calculating of non-balanced force due to adding thereof to the loading before the next step of calculating within said iteration.
5. Apparatus according to anyone of Claims 1 to 3, characterized in that said apparatus for testing of mechanical properties is adapted for performing of static or dynamic tension testing by means of a standardized specimen consisting of each desired metallic material.
6. Method for determining and verifying of strength of a mechanically loaded machine part by means of a digital calculating unit, which is adapted for calculating of stresses and deformations in each pre-determined zones on said mechanically loaded part on the basis of each disposable software and in accordance to Finite Element Method (FEM) on the basis of data concerning
- geometry, namely a shape and dimensions of said machine part, expressed by means of a mathematical model, consisting of a finite number of geometrically regular bodies i.e. finite elements, which are defined by means of a plurality of corners, namely points defined by means of each pre-determined spatial coordinates, which define geometry, namely a geometric matrix (B) having a volume (V, AV);
- mechanical loadings, to which each machine part is exposed and which are expressed e.g. by forces or continuous loadings in certain zones of the machine part, or also by torque; and
- material, which is defined by means of its module of elasticity (E) and determines an elasticity matrix as a property of each used material, as well as with a real deformation curve i.e. the curve of elongation;
wherein the calculating by means of said digital calculating unit is performed by on the basis of iterations, in which a non-balanced force is calculated, which is then entered into each subsequent calculating step, wherein the steps are performed in the following sequence:
i) generating a deformation matrix (B) on the basis of each geometry of the machine part:
ii) calculation of increment (Δε) of deformations (ε);
iii) calculation of increment (Δσ) of stresses (σ);
and wherein each obtained results comprise on the one hand the data related to loadings in at least certain points of said loaded part, and on the other hand the data concerning deformations in at least certain points of said machine part, which
depend on geometry, mechanical loadings and each disposable material of the machine part, wherein said digital calculating unit is supplied with data retrieved from accompanied apparatus for mechanically testing of mechanical properties of each desired material of each mechanically loaded machine part.
7. Method according to Claim 6, in which the data, which is required by calculating in the digital calculating unit, is generated in the apparatus for testing of mechanical properties on the basis of a standardized specimen consisting of the same material as said machine part, by which a functional dependency of stresses (σ) within the mechanically loaded machine part and within the material thereof is determined, starting from the initiation of loading and then both along the stage of elastic deformation thereof and also along the stage of plastic deformation thereof up to the final rupture of the material of said specimen.
8. Method according to Claim 6 or 7, characterized in that in said apparatus for testing of mechanical properties of each specimen having initial length (I0) and initial cross-section (A0) and consisting of each desired material which is identical to the material of each mechanically loaded machine part, the data for submission into said digital calculating unit is obtained by means of loading said specimen with simultaneously step-like tensioning thereof, by which at the same time the loading force (F) is measured together with contraction of the cross-section between said initial cross-section (A0) and each actual cross-section (A) i.e. together with specific deformations (ε) just prior to rupture of the part.
9. Method according to anyone of Claims 6 to 8, characterized in that in the digital calculating unit, each calculating of each actual status of stresses and deformations within each desired machine part having each desired geometry and
dimensions is performed on the basis of data concerning each stress- and deformation characteristics of the specimen in both stages of elastic and plastic deformation which is retrieved from the apparatus for testing of mechanical properties, and is defined by following steps: i) determining of a rigidity matrix of the construction of each mechanically loaded machine part in accordance with formula (I)
wherein
K is a rigidity matrix of the construction;
B is a deformation matrix (geometry);
E is an elasticity matrix (material properties)
V, d V is a volume; ii) calculating of increment of deformations by means of resolving a global system of equations according to formula (II)
ΚΔιι = AF Διι = K AF (Π) wherein
F, AF is a vector of forces, namely increment of forces i.e. loadings during each step i.e. during each iteration;
u, Au is a vector of displacements, namely increment of displacements during each step i.e. during each iteration; calculating each increment of stresses according to formula (III):
Δσ = ΕΒΔιι (III)
wherein
u = u + Au (IV)
and
σ = σ + Δσ (V) and wherein
σ, Δσ is a vector of stresses i.e. increment of stresses during each particular step i.e during each iteration; and then also calculating of increment of plastic deformations according formula (VI)
Δερ1 = BAu - E'1 σ (VI)
is a vector of plastic part of specific deformations i.e. increment thereof; which is then followed by calculating of non-balanced force due to adding thereof to the loading before the next step of calculating within said iteration.
10. Method according to anyone of Claims 6 to 9, characterized in that said digital calculating unit is submitted with data retrieved from said apparatus for testing of mechanical properties which is adapted for performing of static or dynamic tension testing by means of a standardized specimen consisting of each desired metallic material.
Applications Claiming Priority (2)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| SI201200352A SI24244A (en) | 2012-11-21 | 2012-11-21 | Apparatus and method for determining and verifying of strength of a mechanically loaded machine part |
| SIP-201200352 | 2012-11-21 |
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| Publication Number | Publication Date |
|---|---|
| WO2014081399A1 true WO2014081399A1 (en) | 2014-05-30 |
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| PCT/SI2013/000065 WO2014081399A1 (en) | 2012-11-21 | 2013-11-11 | Apparatus and method for determining and verifying of strength of a mechanically loaded machine part |
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| SI (1) | SI24244A (en) |
| WO (1) | WO2014081399A1 (en) |
Cited By (1)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN111914358A (en) * | 2020-07-08 | 2020-11-10 | 中国第一汽车股份有限公司 | Method for forecasting limit bearing capacity of transmission shell under impact action of engine |
Citations (1)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US20090192766A1 (en) | 2008-01-30 | 2009-07-30 | Airbus Espana, S.L. | Method for simulating the behavior of a bonded joint of two parts |
-
2012
- 2012-11-21 SI SI201200352A patent/SI24244A/en not_active IP Right Cessation
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2013
- 2013-11-11 WO PCT/SI2013/000065 patent/WO2014081399A1/en active Application Filing
Patent Citations (1)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US20090192766A1 (en) | 2008-01-30 | 2009-07-30 | Airbus Espana, S.L. | Method for simulating the behavior of a bonded joint of two parts |
Non-Patent Citations (3)
| Title |
|---|
| "AutoFEM - Static Analysis", HTTP://WWW.AUTOFEMSOFT.COM/EN/AUTOFEM-PRODUCTS/AUTOFEM-STATIC-ANALYSIS.HTML, 26 September 2012 (2012-09-26), pages 1 - 10, XP055112304, Retrieved from the Internet <URL:http://web.archive.org/web/20120926020941/http://www.autofemsoft.com/en/autofem-products/autofem-static-analysis.html> [retrieved on 20140404] * |
| EHLERS S ET AL: "Strain and stress relation for non-linear finite element simulations", THIN-WALLED STRUCTURES, ELSEVIER, AMSTERDAM, NL, vol. 47, no. 11, 1 November 2009 (2009-11-01), pages 1203 - 1217, XP026495220, ISSN: 0263-8231, [retrieved on 20090520], DOI: 10.1016/J.TWS.2009.04.005 * |
| PINO KOC ET AL: "Usage of the Yield Curve in Numerical Simulations", JOURNAL OF MECHANICAL ENGINEERING, 2008, pages 821 - 829, XP055112940, Retrieved from the Internet <URL:http://www.sv-jme.eu/scripts/download.php?file=/data/upload/2008/SV-54-2008-12/1_Stok_zl.pdf> [retrieved on 20140408] * |
Cited By (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN111914358A (en) * | 2020-07-08 | 2020-11-10 | 中国第一汽车股份有限公司 | Method for forecasting limit bearing capacity of transmission shell under impact action of engine |
| CN111914358B (en) * | 2020-07-08 | 2022-07-19 | 中国第一汽车股份有限公司 | Method for forecasting limit bearing capacity of transmission shell under impact action of engine |
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| Publication number | Publication date |
|---|---|
| SI24244A (en) | 2014-05-30 |
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