CN107451359B - Gear meshing characteristic finite element analysis method considering matrix crack influence - Google Patents
Gear meshing characteristic finite element analysis method considering matrix crack influence Download PDFInfo
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Abstract
The invention relates to a finite element analysis method for gear meshing characteristics considering influence of matrix cracks, which comprises the following steps of: acquiring basic parameters of a gear pair of a driving wheel and a driven wheel and crack parameters of a gear with matrix cracks; establishing a three-dimensional finite element model of the healthy gear according to basic parameters of the gear pair, and cutting a gear matrix to generate a gear finite element model containing matrix cracks; performing grid refinement on the crack surfaces, and establishing surface-surface contact units Conta174 and Targe170 on the crack surfaces according to the interaction between the crack surfaces; and calculating the gear meshing characteristic according to the crack parameters, and calculating the difference of whether the contact is established on the crack surface or not to the calculation result. The method enables the calculation results of the meshing rigidity of the cracked gear and the tooth root strain to be more accurate, is beneficial to understanding the meshing characteristics of the cracked gear containing the non-penetrating matrix and the interaction between crack surfaces, and research results can provide certain reference for gear design.
Description
Technical Field
The invention belongs to the technical field of mechanical dynamics, and particularly relates to a finite element analysis method for gear meshing characteristics by considering matrix cracks.
Background
The gear is an important mechanical transmission part, but cracks can occur on the gear due to manufacturing errors, poor lubrication, overload, stress concentration and the like. Cracks propagate not only along the gear teeth, but also along the gear matrix. In the prior art, a great deal of research is carried out on the meshing characteristics of the crack gear by adopting an analytic method and a finite element method. However, the following disadvantages exist: (1) the analysis method mainly aims at the tooth root cracks to be researched, and due to the complexity of non-penetrating matrix cracks, the analysis method cannot effectively calculate the damage of the matrix cracks to the gear matrix; (2) similarly, finite element methods are mainly studied for root cracks, with little concern for non-penetrating matrix cracks and no consideration for the effects of interactions between crack faces, which will produce errors and are not practical; (3) in the prior art, only the strain of a healthy gear is researched, the influence of matrix cracks on the strain of the gear is ignored, and the calculation is inaccurate.
Disclosure of Invention
Technical problem to be solved
In order to solve the problems in the prior art, the invention provides a finite element analysis method for the gear meshing characteristics considering the influence of matrix cracks, which is characterized in that a finite element model of a gear containing non-penetrating matrix cracks is established through ANSYS software, the meshing characteristics of the gear containing the non-penetrating matrix cracks are researched, and meanwhile, the interaction between crack surfaces is also considered, so that the contact is established on the crack surfaces, the calculation accuracy is improved, and the method is more practical.
(II) technical scheme
In order to achieve the purpose, the invention adopts the main technical scheme that:
a finite element analysis method for gear meshing characteristics considering influence of matrix cracks comprises the following steps:
s1, acquiring basic parameters of a gear pair of the driving wheel and the driven wheel and crack parameters of the gear with the matrix cracks;
s2, establishing a gear three-dimensional finite element model containing a parabolic non-penetrating matrix crack, and comprising the following steps:
s201, according to the basic parameters of the gear pair, simulating a gear entity by using a Solid185 unit by using an APDL language programming function of ANSYS software, and establishing a three-dimensional finite element model of the healthy gear;
s202, on the basis of the three-dimensional finite element model of the healthy gear, cutting a gear matrix to generate a gear finite element model containing matrix cracks;
s203, carrying out grid refinement on crack surfaces of the gear finite element model containing the matrix cracks, and establishing surface-surface contact units Conta174 and target 170 on the crack surfaces according to interaction between the crack surfaces;
s3, calculating the gear meshing characteristics according to the crack parameters, and calculating the difference of whether contact is established on the crack surface to the calculation result; wherein the crack parameters comprise crack depth and crack width, and the gear meshing characteristics comprise meshing rigidity and strain.
As a preferable mode of the method, the basic parameters of the gear pair include the number of teeth, the modulus of elasticity, the poisson's ratio, the radius of an inner hole, the radius of a base circle, the modulus, the tooth width, the pressure angle, the coefficient of the crest height, the coefficient of the crest clearance, and the coefficient of friction; the crack parameters comprise a crack starting position angle, a crack width, a crack depth and a crack propagation direction angle.
As a preferable scheme of the method as described above, the step S201 includes the steps of: s20101: generating the tooth profile of a single gear by using ANSYS software according to the elastic modulus, the Poisson's ratio, the inner hole radius, the base circle radius, the modulus, the pressure angle, the addendum coefficient, the tip clearance coefficient and the friction coefficient of the gear in the basic parameters of the gear pair, wherein the tooth profile comprises an involute and a transition curve;
s20102, carrying out rotary replication on the single gear tooth to generate a two-dimensional finite element model of the healthy gear;
s20103, stretching the generated two-dimensional finite element model of the gear along the central axis of the gear, wherein the stretching length is equal to the tooth width value, and generating a three-dimensional finite element model of the healthy gear;
s20104, carrying out mesh thinning on the tooth surface near the meshing line.
As a preferable solution of the method described above, the step S202 includes the steps of:
s20201, selecting a gear matrix part with cracks in the three-dimensional finite element model of the healthy gear according to the initial position and the crack propagation direction of the matrix cracks;
s20202, dividing the selected gear matrix part into two parts according to the crack starting position and the crack propagation direction by using a VSBL command in ANSYS;
s20203, establishing a coordinate system on the division surfaces of the two parts of entities, and generating a non-penetrating matrix crack according to a crack parabolic curve equation, wherein the crack parabolic curve equation is as follows:
wherein q (x) is the crack depth at any position x, q0To initial crack depth, LcFor crack width, L is gear width.
As a preferable scheme of the method, the step S203 of grid refining the crack surface includes that three boundary curves forming the crack surface are equally divided by using the "LESIZE" command, and then the crack surface is refined by using the "VMESH" command.
As a preferable mode of the method described above, the step S3 includes:
s301, calculating the gear meshing characteristic according to the crack depth of the matrix, and the method comprises the following steps:
s30101, constraining the gear on the gear three-dimensional finite element model established in the step S2, wherein the constraining mode comprises coupling the inner ring nodes of the driving wheel and the driven wheel with the respective geometric centers, completely constraining the central point of the driven wheel, and constraining the central point of the driving wheel to enable the driving wheel to only rotate around the central shaft; the load applying mode comprises applying torque to the geometric center of the driving wheel to obtain the angular displacement of the driving wheel; according to a calculation formula of the meshing stiffness, the meshing stiffness of the gear under different matrix crack depths when contact is established on a crack surface and contact is not established is obtained, wherein the calculation formula of the meshing stiffness is as follows:
where K denotes a meshing rigidity, T denotes a torque applied to the primary pulley, Delta theta denotes an angular displacement of the primary pulley, and rbThe radius of the base circle of the driving wheel;
calculating to obtain a percentage error of the mesh rigidity reduction amount under the conditions of contact establishment and non-contact establishment on the crack surface, wherein the percentage error of the mesh rigidity reduction amount is [ (the rigidity reduction amount under the condition of no contact unit on the crack surface-the rigidity reduction amount under the condition of contact unit on the crack surface)/the rigidity reduction amount under the condition of no contact unit on the crack surface ] × 100%;
meanwhile, the contact pressure distribution on the crack surface under different crack depths is obtained by utilizing the post-processing function of ANSYS software;
s30102, calculating the strain of the tooth root according to the crack depths of different matrixes: selecting a point Q of a crack gear tooth close to a tooth root as a strain extraction point, and extracting the strain of the point Q at each meshing position of the gear by utilizing the post-processing function of ANSYS software; obtaining a percentage error of strain according to the strain drop of a point Q when no contact unit exists on a crack surface, which is equal to the strain drop of a point Q of a healthy gear Q-point strain-no-contact unit crack gear Q on the crack surface, and the strain drop of the point Q when a contact unit exists on the crack surface, which is equal to the strain drop of a point Q of the healthy gear Q-point strain-contact unit crack gear Q on the crack surface, wherein the percentage error of strain of the point Q is equal to the percentage error of strain [ (the strain drop of the point Q when no contact unit exists on the crack surface-the strain drop of the point Q when a contact unit exists on the crack surface)/the strain drop of the point Q when no contact unit exists on the crack surface ] × 100%; s302, calculating the gear meshing characteristics according to the crack width of the matrix, wherein the gear meshing characteristics comprise:
s30201, calculating the gear meshing stiffness according to the crack width of the matrix: the gear constraint method and the load applying mode are the same as those of S30101, and the gear meshing rigidity formula under the condition of different matrix crack widths is the same as that of S30101;
meanwhile, obtaining displacement cloud pictures of the crack gear and contact pressure distribution on a crack surface under different crack width conditions by utilizing the post-processing function of ANSYS software;
s30202, calculating the gear tooth root strain according to the matrix crack width: the calculation method is the same as that in step S30102.
(III) advantageous effects
The invention has the beneficial effects that: according to the finite element analysis method for the gear meshing characteristics considering the influence of the matrix cracks, the damage of the matrix cracks on the gear matrix is effectively considered by utilizing the gear three-dimensional finite element model which is established by ANSYS software and contains the parabolic non-penetrating matrix cracks; in the actual working process, cracks can not only expand along gear teeth of the gear, but also expand towards a gear matrix, and the problem is solved by establishing a gear three-dimensional finite element model containing matrix cracks through ANSYS software because the damage of the matrix cracks to the gear matrix cannot be effectively considered by an analytic method.
The finite element model considers the interaction between crack surfaces, and establishes a surface-surface contact element Conta174 and a Targe170 on the crack surfaces to simulate the interaction between the crack surfaces, so that the calculation results of the meshing rigidity and the tooth root strain of the crack gear are more accurate, and the establishment of the contact element on the crack surfaces is more practical. Because the gear meshing position is changed continuously, the crack surfaces can contact with each other or separate from each other, the interaction between the crack surfaces is not considered in the previous research, the crack surfaces are not restricted, the phenomenon is obviously not practical, and the calculation result is in error. The surface-surface contact unit is established on the crack surface, so that the error can be effectively reduced, and the method is close to the reality. Meanwhile, errors generated by establishing contact and not establishing on the crack surface are quantified, and the influence of a contact unit on the crack surface on a calculation result is analyzed, so that people can know the meshing characteristics of the gear with the crack of the non-penetrating matrix and the interaction between the crack surfaces. The method analyzes the influence of the matrix crack parameters on the strain, is helpful for deepening people to comprehensively understand the gear containing the matrix crack, and provides help for fatigue analysis of the crack gear.
According to the invention, the influence of the matrix cracks on the gear meshing characteristics is researched by establishing the three-dimensional finite element model containing the non-penetrating matrix cracks, and the research result can provide certain reference for the gear design, such as: at the position with larger strain, measures are taken to reduce the strain magnitude and the strain concentration phenomenon. Meanwhile, the damage degree of the crack gear is measured according to the rigidity and the strain change of the crack gear, and the gear fault diagnosis is facilitated.
Drawings
FIG. 1 is a flow chart of a finite element method for analyzing the effect of a crack in a gear matrix on the meshing characteristics in an embodiment of the present invention;
FIG. 2 is a finite element model of a gear with matrix cracks according to an embodiment of the present invention;
FIG. 3 is a schematic view of a parabolic non-penetrating substrate crack in accordance with an embodiment of the present invention;
FIG. 4 shows healthy gear mesh stiffness and crack depth q in an embodiment of the present invention0When the diameter is 5mm, 15mm and 25mm, the contact is established on the crack surface and the meshing rigidity of the crack gear is realized under the condition that the contact is not established;
FIG. 5 is a displacement cloud and contact pressure distribution across the crack face for various crack depths corresponding to time A in FIG. 4 for mesh stiffness in accordance with an embodiment of the present invention;
FIG. 6 healthy gear and crack depth q in an embodiment of the invention05mm, 15mm, 25mm crack gear establishes contact on the crack face and no strain is established at the root portion Q point;
FIG. 7 shows healthy gear mesh stiffness and crack width L in an embodiment of the inventioncWhen the diameter is 5mm, 15mm and 25mm, the contact is established on the crack surface and the meshing rigidity of the crack gear is realized under the condition that the contact is not established;
FIG. 8 is a graph of the contact pressure distribution at various crack widths corresponding to time A in FIG. 7 for mesh stiffness in accordance with an embodiment of the present invention;
FIG. 9 shows a healthy gear and crack width L in an embodiment of the present inventioncA 5mm, 15mm, 25mm crack gear establishes contact on the crack face and no strain at the root location Q point.
Detailed Description
For the purpose of better explaining the present invention and to facilitate understanding, the present invention will be described in detail by way of specific embodiments with reference to the accompanying drawings.
Example 1
A finite element analysis method of gear mesh characteristics considering the influence of matrix cracks, as shown in fig. 1, comprising the steps of:
step 1: acquiring basic parameters of a gear pair of a driving wheel and a driven wheel and crack parameters of a gear with matrix cracks; the basic parameters of the gear pair and the crack parameters of the gear with matrix cracks are obtained in the embodiment as shown in table 1:
TABLE 1 basic parameters of gear pairs and crack parameters of gears with matrix cracks
In the present embodiment, the crack initiation position angle ψ and the crack width LcRemaining unchanged, crack depth q0The crack width L varies from 5mm to 25mmcVarying between 5mm and 25 mm;
step 2: establishing a gear finite element model containing matrix cracks, wherein the cracks are parabolic non-penetrating matrix cracks;
step 2.1: the APDL function of ANSYS software is used for establishing a healthy gear finite element model containing 5 gear teeth. The method comprises the following steps: firstly, the method comprises the following steps: generating a tooth profile curve of a single gear by using ANSYS software according to the elastic modulus, the Poisson ratio, the inner hole radius, the base circle radius, the modulus, the pressure angle, the tooth crest height coefficient, the top clearance coefficient and the friction coefficient of the gear in basic parameters of the gear pair, wherein the tooth profile curve comprises an involute and a transition curve; secondly, the method comprises the following steps: carrying out rotary replication on the single gear teeth to generate a two-dimensional finite element model of the healthy gear; thirdly, the method comprises the following steps: stretching the generated two-dimensional finite element model of the gear along the central axis of the gear, wherein the stretching length is the tooth width value, and thus, generating a three-dimensional finite element model of the healthy gear; fourthly: and carrying out mesh thinning on the tooth surface near the meshing line.
Step 2.2: and generating a gear finite element model containing matrix cracks on the basis of the healthy gear model. The method specifically comprises the following steps: firstly, the method comprises the following steps: in the three-dimensional finite element model of the healthy gear, selecting a gear matrix part with cracks according to the initial position and the crack propagation direction of matrix cracks; secondly, the method comprises the following steps: dividing the selected gear matrix part into two parts of entities according to the crack starting position and the crack propagation direction by using a 'VSBL' command (using a working plane cutting body) in ANSYS; thirdly, the method comprises the following steps: establishing a coordinate system on the division surface of the two parts of entities, and generating the non-penetrating matrix crack according to a crack parabolic curve equation, wherein the crack parabolic curve equation is as follows:
wherein q (x) is the crack depth at any position x, q0To initial crack depth, LcFor crack width, L is gear width.
The finite element model of the matrix crack gear is established as shown in FIG. 2, wherein O1Is the central point of the driven wheel gear, O2From the center of the circle of the main wheel gear, a1 is indicated as a cracked cog, fig. 2b) is an enlarged view of fig. 2a) at a, and fig. 2c) is an enlarged view of fig. 2b) at a2, A3, indicates a matrix crack. The parabolic non-penetrating matrix crack is schematically shown in FIG. 3, wherein (B) is a cross-sectional view at B-B in (a), P1Expressed as starting point, P2Denoted as endpoint, 1 as path, A4 as crack plane, LcExpressed as crack width, q0Expressed as crack depth.
Step 2.3: contact is established. Firstly, further grid refinement is carried out on the crack surface according to the solving precision and efficiency, namely, three boundary curves forming the crack surface are equidistantly divided according to the interval of 1mm by using a 'LESIZE' command (for equidistantly dividing lines). The fracture surface is then refined using the "VMESH" command (for meshing). Finally, crack faces are individually selected and the surface-to-surface contact cells Conta174 and Targe170 are established on the crack faces of the refined grid, taking into account the contact and relative slippage that may occur between the crack faces; the Conta174 attribute is set by "KEYOPT", i.e., the gap between crack faces is automatically adjusted.
And step 3: analyzing the influence of the depth and the width of the crack on the meshing characteristics of the gear, and comparing the influence of whether contact is established on the crack surface on the calculation result;
step 3.1: the influence of the crack depth of the matrix on the meshing characteristics of the gear is analyzed.
Step 3.1.1: and calculating the meshing stiffness of the gear under the conditions of different matrix crack depths when contact is established on the crack surface and when contact is not established on the crack surface. After the gear finite element model is established, when finite element solution is carried out, the inner ring nodes of the driving wheel and the driven wheel are coupled together with respective geometric centers, the central point of the driven wheel is completely restrained, the central point of the driving wheel (the gear where the crack is located) is restrained so that the driving wheel can only rotate around the central shaft, torque of 500Nm in the clockwise direction is applied to the geometric center of the driving wheel, the angular displacement of the driving wheel is obtained, and a corresponding meshing rigidity value is obtained according to a meshing rigidity solution formula. The crack parameters were: depth of crack q05mm, 15mm, 25mm, crack initiation position angle psi 35 °, crack width Lc25mm and a crack propagation direction angle υ of 45 °. The calculation formula according to the meshing stiffness is as follows:
By utilizing the post-processing function of ANSYS software, displacement cloud charts of the crack gear under different crack depths and contact pressure distribution on a crack surface are respectively obtained, so that the reason for error generation is further explained, and the method is shown in FIG. 5. Wherein (a), (b) and (c) in FIG. 5 are crack depths q when no contact is established on the crack surface0Displacement cloud pictures corresponding to 5mm, 15mm and 25 mm; it can be seen from the figure that the crack faces are intrusive and do not match reality. In FIG. 5, (d), (e), (f) show the crack depth q when contact is established on the crack surface0Displacement cloud pictures corresponding to 5mm, 15mm and 25 mm; it can be seen from the figure that the crack planes are not mutually intrusive and have relative slippage and are consistent with reality. In FIG. 5, (g), (h), (i) show the crack depth q after contact has been established on the crack surface0Contact pressure distribution on crack faces of 5mm, 15mm, 25 mm.
As can be seen from fig. 4 and table 2: (1) whether contact is established on the crack surface or not, the meshing rigidity of the gear is gradually reduced along with the increase of the depth of the crack; (2) the percentage error is progressively less when the cracked gear teeth are not entering mesh (see region 1). However, when the cracked teeth enter into mesh (see region 2), the percentage error tends to 0, i.e., the contact elements on the crack face have no effect on the time-varying mesh stiffness; the reason is as shown in fig. 5: (1) with the increase of the crack depth, the ratio of the actual contact area on the crack surface to the area of the whole crack surface is gradually smaller; (2) the contact pressure on the crack face becomes progressively smaller as the crack depth increases. Therefore, the effect of the actually contacted portion on the crack surface becomes smaller, and the percentage error becomes smaller.
TABLE 2 percent error in mesh stiffness at different crack depths
Step 3.1.2: the effect of matrix crack depth on gear root strain was analyzed. Since the gear tooth root portion is most severely stretched or squeezed and the effect of the crack on strain is to be investigated, a point Q on the left side tooth root portion of the cracked gear tooth is selected as a strain extraction point (the cracked gear tooth is close to the tooth root portion), the position of the point Q is shown in fig. 3, and the distance of the point Q from the gear end face is 27 mm. At each meshing position of the gear, the strain at the Q point is extracted using the post-processing function of ANSYS software. And drawing a curve of the strain of the point Q along with the change of the meshing period by taking the meshing period as an abscissa and the strain of the point Q at the corresponding position as an ordinate. The Q point strain extraction mode when no contact unit exists on the crack surface is the same as the Q point strain extraction mode when a contact unit exists on the crack surface.
The tooth root strain curves at Q-point for the case of contact and non-contact elements on the crack plane are shown in FIG. 6, where (i) contact is established on the crack plane
Denotes q0＝5mm、
Denotes q0＝15mm、
Denotes q025mm, (ii) no contact is established on the crack face
Denotes q0＝5mm、
Denotes q0＝15mm、
Denotes q0The strain drop amounts corresponding to 3 meshing timings, i.e., a to C in fig. 6, are shown in table 3, where the strain drop amount at the Q point when there is no contact element on the crack surface is defined as the strain at the Q point of the healthy gear-the strain at the Q point of the crack gear without contact element on the crack surface, and the strain drop amount when there is a contact element on the crack surface is defined as the strain at the Q point of the healthy gear-the strain at the Q point of the crack surface with contact element. Percent error of strain [ (amount of strain decrease without contact unit on crack surface-amount of strain decrease with contact unit on crack surface)/amount of strain decrease without contact unit on crack surface]×100％。
The following conclusions are drawn from fig. 6 and table 3: (1) the trend of the change of the percentage error of the strain at the point Q and the reason for the trend in the areas 1 and 2 are the same as in step 3.1.1; (2) it is to be noted that in region 1, when no contact is established on the crack faces of the crack, i.e., the interaction between the crack faces is not considered, the strain at the point Q tends to 0; considering the interaction between the crack faces, the Q point is subjected to compressive strain. This is because when no contact is established on the crack surface, the crack surface is not restrained, the substrate load-bearing capacity on both sides of the crack surface is much reduced, and therefore the Q-point strain is almost 0, but this is not practical. (3) As can be seen from fig. 6, the Q point is alternately subjected to compressive strain and tensile strain, and the strain gradually decreases as the crack depth increases.
TABLE 3 percent error in root strain for different crack depths
Step 3.2: the influence of the matrix crack width on the gear mesh characteristics was analyzed.
Step 3.2.1: and (3) researching the influence of different matrix crack widths on the gear meshing rigidity, wherein the gear constraint mode, the load applying mode and the meshing rigidity solving mode are the same as the step 3.1.1 when finite element solving is carried out. The crack parameters were: crack width Lc5mm, 15mm, 25mm, crack initiation position angle psi 35 °, crack depth q025mm and a crack propagation direction angle υ of 45 °. The meshing stiffness curves for the case of contact and no contact elements at the crack plane are shown in FIG. 7, where (i) contact is established at the crack plane
Denotes q0＝5mm、
Denotes q0＝15mm、
Denotes q025mm, (ii) no contact is established on the crack face
Denotes q0＝5mm、
Denotes q0＝15mm、
Denotes q025mm, which represents health, and the amounts of decrease in rigidity corresponding to 5 engagement times, E to a, are shown in table 4. It can be seen from fig. 7 and table 4 that in region 1, the percent meshing stiffness error gradually increases as the crack width increases, but in region 2, the percent meshing stiffness error approaches 0. In FIG. 8, (a), (b), and (c) are the respective crack widths LcContact pressure on the crack surface at 5mm, 15mm, 25 mm. As can be seen from fig. 8, the contact pressure on the crack face gradually increases with the increase of the column width, indicating that the interaction between the crack faces is larger and larger, so the engagement percentage error gradually increases with the increase of the crack width.
TABLE 4 percent error of mesh stiffness under different crack widths
Step 3.2.2: study of the influence of different matrix crack widths on the gear root strain, crack width LcStrain extraction at point Q is performed in the same manner as in step 3.1.2 at 5mm, 15mm, 25mm, and the strain curve at point Q is shown in fig. 9, where contact is established at (i) the fracture plane
Denotes q0＝5mm、
Denotes q0＝15mm、
Denotes q025mm, (ii) no contact is established on the crack face
Denotes q0＝5mm、
Denotes q0＝15mm、
Denotes q025mm, healthy, the root strain reduction at meshing time A, B, C is shown in table 5. As can be seen from fig. 9 and table 5, in region 1, the strain gradually decreased as the crack width increased. However, the strain percentage error gradually increases with increasing crack width. In region 2, the strain percentage error is close to 0.
TABLE 5 percent error in root strain for different crack widths
And 4, step 4: meshing stiffness and strain curves were analyzed. From steps 3.1 and 3.2 it can be seen that:
(1) as the depth and width of the matrix crack increase, the mesh stiffness and strain gradually decrease. (2) The meshing stiffness and strain of a cracked gear are different, with and without consideration of the interaction between the crack faces. It is noted that the meshing stiffness and the strain percentage error gradually decrease with the increase of the crack depth, because the area ratio of the actual contact portion between the crack surfaces to the entire crack surface gradually decreases with the increase of the crack depth, and the contact pressure on the crack surfaces gradually decreases with the increase of the crack depth, and the contact portion on the crack surfaces gradually decreases in function. In contrast, as the crack width increases, the contact pressure on the crack surface gradually increases, and the contact portion on the crack surface gradually increases in play, so that the meshing rigidity and the strain percentage error gradually increase with the crack width. In summary, for a non-through-the-matrix cracked gear, consideration of the interaction between the crack faces makes the meshing stiffness and strain results more accurate. Since the percentage error is greater with smaller substrate crack depths and larger substrate crack widths, the interaction between the crack faces is considered at this time.
While the invention has been described with reference to a preferred embodiment, it will be understood by those skilled in the art that various changes may be made and equivalents may be substituted for elements thereof without departing from the scope of the invention. However, any simple modification, equivalent change and modification of the above embodiments according to the technical essence of the present invention are within the protection scope of the technical solution of the present invention.
Claims (5)
1. A finite element analysis method for gear meshing characteristics considering influence of matrix cracks is characterized by comprising the following steps of:
s1, acquiring basic parameters of a gear pair of the driving wheel and the driven wheel and crack parameters of the gear with the matrix cracks;
s2, establishing a gear three-dimensional finite element model containing parabolic non-penetrating matrix cracks, including
S201, according to the basic parameters of the gear pair, simulating a gear entity by using a Solid185 unit by using an APDL language programming function of ANSYS software, and establishing a three-dimensional finite element model of the healthy gear;
s202, on the basis of the three-dimensional finite element model of the healthy gear, cutting a gear matrix to generate a gear finite element model containing matrix cracks;
s203, carrying out grid refinement on crack surfaces of the gear finite element model containing the matrix cracks, and establishing surface-surface contact units Conta174 and target 170 on the crack surfaces according to interaction between the crack surfaces;
s3, calculating the gear meshing characteristics according to the crack parameters, and calculating the difference of whether contact is established on the crack surface to the calculation result; wherein the crack parameters comprise crack depth and crack width, and the gear meshing characteristics comprise meshing rigidity and strain;
the step S3 includes:
s301, calculating the gear meshing characteristic according to the crack depth of the matrix, and the method comprises the following steps:
s30101, constraining the gear on the gear three-dimensional finite element model established in the step S2, wherein the constraining mode comprises coupling the inner ring nodes of the driving wheel and the driven wheel with the respective geometric centers, completely constraining the central point of the driven wheel, and constraining the central point of the driving wheel to enable the driving wheel to only rotate around the central shaft; the load applying mode comprises applying torque to the geometric center of the driving wheel to obtain the angular displacement of the driving wheel; according to a calculation formula of the meshing stiffness, the meshing stiffness of the gear under different matrix crack depths when contact is established on a crack surface and contact is not established is obtained, wherein the calculation formula of the meshing stiffness is as follows:
where K denotes a meshing rigidity, T denotes a torque applied to the primary pulley, Delta theta denotes an angular displacement of the primary pulley, and rbThe radius of the base circle of the driving wheel;
calculating to obtain a percentage error of the mesh rigidity reduction amount under the conditions of contact establishment and non-contact establishment on the crack surface, wherein the percentage error of the mesh rigidity reduction amount is [ (the rigidity reduction amount under the condition of no contact unit on the crack surface-the rigidity reduction amount under the condition of contact unit on the crack surface)/the rigidity reduction amount under the condition of no contact unit on the crack surface ] × 100%;
meanwhile, obtaining displacement cloud pictures of the crack gear and contact pressure distribution on a crack surface under different crack depths by utilizing the post-processing function of ANSYS software;
s30102, calculating the strain of the tooth root according to the crack depths of different matrixes: selecting a point Q of a crack gear tooth close to a tooth root as a strain extraction point, and extracting the strain of the point Q at each meshing position of the gear by utilizing the post-processing function of ANSYS software; obtaining a percentage error of Q point strain according to Q point strain reduction when no contact unit exists on a crack surface, which is equal to Q point strain reduction of a healthy gear Q point-Q point strain of a crack surface without a contact unit, Q point strain reduction when a contact unit exists on the crack surface, which is equal to Q point strain reduction of the healthy gear Q point-Q point strain of the crack surface with the contact unit, and Q point strain reduction, which is equal to [ (Q point strain reduction when no contact unit exists on the crack surface-Q point strain reduction when a contact unit exists on the crack surface)/Q point strain reduction when no contact unit exists on the crack surface ] × 100%;
s302, calculating the gear meshing characteristics according to the crack width of the matrix, wherein the gear meshing characteristics comprise:
s30201, calculating the gear meshing stiffness according to the crack width of the matrix: the gear constraint method and the load applying mode are the same as those of S30101, and the gear meshing rigidity formula under the condition of different matrix crack widths is the same as that of S30101;
meanwhile, the contact pressure distribution on the crack surface under different crack width conditions is obtained by utilizing the post-processing function of ANSYS software;
s30202, calculating the gear tooth root strain according to the matrix crack width: the calculation method is the same as that in step S30102.
2. The method of claim 1, wherein the gear pair basic parameters include tooth number, modulus of elasticity, poisson's ratio, bore radius, base circle radius, modulus, tooth width, pressure angle, crest height coefficient, crest clearance coefficient, friction coefficient; the crack parameters comprise a crack starting position angle, a crack width, a crack depth and a crack propagation direction angle.
3. The method according to claim 2, wherein the step S201 comprises the steps of:
s20101, generating a tooth profile of a single gear by utilizing ANSYS software according to the elastic modulus, the Poisson ratio, the inner hole radius, the base circle radius, the modulus, the pressure angle, the tooth crest height coefficient, the top clearance coefficient and the friction coefficient of the gear in the basic parameters of the gear pair, wherein the tooth profile comprises an involute and a transition curve;
s20102, carrying out rotary replication on the single gear tooth to generate a two-dimensional finite element model of the healthy gear;
s20103, stretching the generated two-dimensional finite element model of the gear along the central axis of the gear, wherein the stretching length is equal to the tooth width value, and generating a three-dimensional finite element model of the healthy gear;
s20104, carrying out mesh thinning on the tooth surface near the meshing line.
4. The method of claim 3, wherein the step S202 comprises the steps of:
s20201, selecting a gear matrix part with cracks in the three-dimensional finite element model of the healthy gear according to the initial position and the crack propagation direction of the matrix cracks;
s20202, dividing the selected gear matrix part into two parts according to the crack starting position and the crack propagation direction by using a VSBL command in ANSYS;
s20203, establishing a coordinate system on the division surfaces of the two parts of entities, and generating a non-penetrating matrix crack according to a crack parabolic curve equation, wherein the crack parabolic curve equation is as follows:
wherein q (x) is the crack depth at any position x, q0To initial crack depth, LcFor crack width, L is gear width.
5. The method of claim 4, wherein the step S203 of mesh-refining the crack surface comprises the steps of dividing three boundary curves composing the crack surface into equal intervals by using a "LESIZE" command, and refining the crack surface by using a "VMESH" command.
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Application publication date: 20171208 Assignee: Beijing Xindian Hengyi Technology Co.,Ltd. Assignor: Northeastern University Contract record no.: X2022210000070 Denomination of invention: A Finite Element Analysis Method of Gear Meshing Characteristics Considering the Effect of Matrix Crack Granted publication date: 20200414 License type: Common License Record date: 20221213 |
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