CN112287478A - Spline fatigue life distribution determining method and device - Google Patents

Spline fatigue life distribution determining method and device Download PDF

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CN112287478A
CN112287478A CN202011122065.5A CN202011122065A CN112287478A CN 112287478 A CN112287478 A CN 112287478A CN 202011122065 A CN202011122065 A CN 202011122065A CN 112287478 A CN112287478 A CN 112287478A
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spline
tooth
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CN112287478B (en
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赵庆岩
喻天翔
庄新臣
宋笔锋
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Northwestern Polytechnical University
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Abstract

The embodiment of the invention discloses a spline fatigue life distribution determining method and a spline fatigue life distribution determining device, wherein the tooth flank clearance of each spline is determined by utilizing the spline tooth groove width, the spline tooth thickness and the indexing error which are obtained by sampling, then the maximum nominal tangential force on the spline tooth of each spline is obtained, and the stress distribution corresponding to a plurality of splines is obtained based on the maximum nominal tangential force; and then, obtaining the equivalent stress by determining a life calculation formula of the spline and correcting a stress distribution result, and calculating the fatigue life distribution of the spline by using the equivalent stress and life calculation formula. That is, when the fatigue life distribution of the spline is obtained, the spline tooth groove width, the spline tooth thickness and the indexing error are fully considered; thereby facilitating random sampling of spline backlash. And further, the practical situation of the engineering can be better reduced, and the fatigue life of the obtained spline is more reasonable and accurate.

Description

Spline fatigue life distribution determining method and device
Technical Field
The disclosure relates to the technical field of mechanical design, in particular to a spline fatigue life distribution determining method and device.
Background
The involute spline has the advantages of high bearing capacity, good centering performance and the like, and is widely applied to the fields of automobiles, aviation, aerospace and the like.
However, the spline is often broken along the tooth root during load transfer, which in turn affects the spline performance and even renders it unusable. The occurrence of a spline fracture along the root is generally caused by the alternating loading of the spline teeth, which in turn results in large alternating stresses at the root stress concentrations. However, because the spline is generally processed and formed, a processing error exists, so that the size of the tooth side clearance between the spline matching surfaces is not consistent, and then, the tooth side clearance is non-uniform, so that the load distributed on the spline teeth is different. And the teeth carrying the larger must first be destroyed.
That is, in the actual use process, because the load that each spline tooth receives is different, and bear the weight of bigger spline tooth and certainly compare and bear the weight of less spline tooth and damage in advance, consequently, it is the key of analysis spline fatigue life to confirm the maximum load pair of spline tooth.
The reason for causing the uneven distribution of spline tooth load and stress is that the tooth flank clearance of spline tooth is uneven, therefore, in the prior art, through the influence of analysis graduation error or tooth pitch accumulated error to the tooth flank clearance of spline tooth, and then the fatigue life of analysis spline, the result that this kind of mode obtained has great difference with the true condition.
Disclosure of Invention
This disclosure is provided to introduce concepts in a simplified form that are further described below in the detailed description. This disclosure is not intended to identify key features or essential features of the claimed subject matter, nor is it intended to be used to limit the scope of the claimed subject matter.
The embodiment of the disclosure provides a spline fatigue life distribution determining method and device, which can enable the obtained spline fatigue life to be more reasonable and accurate.
In a first aspect, an embodiment of the present disclosure provides a spline fatigue life distribution determining method, including: acquiring parameters of each spline in a plurality of splines, wherein the parameters comprise spline tooth groove width, spline tooth thickness and indexing error, and the values of the parameters are within a preset error range; determining a spline flank clearance for each spline based on the parameters; obtaining a maximum nominal tangential force on the spline teeth of each spline based on the spline tooth flank clearance; obtaining stress distributions corresponding to the plurality of splines based on the maximum nominal tangential force; determining a life calculation formula of the spline; performing equivalent correction on the stress distribution to obtain equivalent stress when the average stress is a preset value; and calculating to obtain the fatigue life distribution of the spline based on the equivalent stress and the life calculation formula.
With reference to embodiments of the first aspect, in some embodiments, the determining the spline flank clearance of each spline based on the parameters includes: based on the formula:
Figure BDA0002732331720000021
determining a spline flank clearance of each spline; wherein a is the spline flank clearance, ErIs the spline tooth groove width, SrIs the spline tooth thickness, deltaSZFor the indexing error, δ, of the external spline teethEZAnd the indexing error of the internal spline tooth groove is obtained.
In combination with an embodiment of the first aspect, in some embodiments, the obtaining a maximum nominal tangential force on the spline teeth of each spline based on the spline flank clearance is described above; the method comprises the following steps: acquiring a torsional load applied to each spline and the rigidity of a single pair of spline teeth of each spline; determining the number of meshing teeth pairs of each spline according to the torsional load, the tooth flank clearance of each spline and the rigidity of the single pair of spline teeth; and calculating to obtain the maximum nominal tangential force on the key teeth of each spline according to the torsional load, the side clearance of each spline, the rigidity of the single pair of key teeth and the number of the meshing teeth.
With reference to the embodiments of the first aspect, in some embodiments, the obtaining the stress distribution corresponding to the plurality of splines based on the maximum nominal tangential force includes: determining the distribution relation of the load on the spline teeth and the external load; wherein, the distribution relationship includes: the calculation rule corresponding to the maximum nominal tangential force; determining a stress formula at a fatigue danger point on the spline tooth; and obtaining stress distribution corresponding to the plurality of splines based on the distribution relation and the stress formula.
With reference to the embodiments of the first aspect, in some embodiments, the determining a life calculation formula of the spline includes: obtaining parameters corresponding to the spline and material properties corresponding to the spline; determining a stress concentration coefficient based on a finite element calculation spline theory; and fitting and obtaining the service life calculation formula based on the parameters corresponding to the spline, the material performance corresponding to the spline and the stress concentration coefficient.
In a second aspect, an embodiment of the present disclosure provides a spline fatigue life distribution determining apparatus, including: the device comprises an acquisition unit, a calculation unit and a calculation unit, wherein the acquisition unit is used for acquiring parameters of each spline in a plurality of splines, the parameters comprise spline tooth groove width, spline tooth thickness and indexing error, and the values of the parameters are within a preset error range; a spline backlash determining unit for determining a spline backlash of each spline based on the parameters; a maximum nominal tangential force obtaining unit for obtaining a maximum nominal tangential force on the spline teeth of each spline based on the spline tooth flank clearance; a stress distribution obtaining unit, configured to obtain stress distributions corresponding to the plurality of splines based on the maximum nominal tangential force; the service life calculation formula determining unit is used for determining the service life calculation formula of the spline; an equivalent stress obtaining unit, configured to perform equivalent correction on the stress distribution to obtain an equivalent stress when the average stress is a preset value; and the calculating unit is used for calculating and obtaining the fatigue life distribution of the spline based on the equivalent stress and the life calculation formula.
Embodiments incorporating the second aspectIn some embodiments, the spline backlash determining unit is specifically configured to determine the spline backlash based on the formula:
Figure BDA0002732331720000031
determining a spline flank clearance of each spline; wherein a is the spline flank clearance, ErIs the spline tooth groove width, SrIs the spline tooth thickness, deltaSZFor the indexing error, δ, of the external spline teethEZAnd the indexing error of the internal spline tooth groove is obtained.
In combination with an embodiment of the second aspect, in some embodiments, the maximum nominal tangential force obtaining unit is specifically configured to obtain a torsional load applied to each spline, a single pair of spline tooth stiffness of each spline; determining the number of meshing teeth pairs of each spline according to the torsional load, the tooth flank clearance of each spline and the rigidity of the single pair of spline teeth; and calculating to obtain the maximum nominal tangential force on the key teeth of each spline according to the torsional load, the side clearance of each spline, the rigidity of the single pair of key teeth and the number of the meshing teeth.
With reference to the embodiments of the second aspect, in some embodiments, the stress distribution obtaining unit is specifically configured to determine a distribution relationship between a load on the spline tooth and an external load; wherein, the distribution relationship includes: the calculation rule corresponding to the maximum nominal tangential force; determining a stress formula at a fatigue danger point on the spline tooth; and obtaining stress distribution corresponding to the plurality of splines based on the distribution relation and the stress formula.
With reference to the embodiment of the second aspect, in some embodiments, the life calculation formula determining unit is specifically configured to obtain parameters corresponding to the spline and material properties corresponding to the spline; determining a stress concentration coefficient based on a finite element calculation spline theory; and fitting and obtaining the service life calculation formula based on the parameters corresponding to the spline, the material performance corresponding to the spline and the stress concentration coefficient.
In a third aspect, an embodiment of the present disclosure provides an electronic device, including: one or more processors; a storage device, configured to store one or more programs, which when executed by the one or more processors, cause the one or more processors to implement the spline fatigue life distribution determination method according to the first aspect.
In a fourth aspect, the disclosed embodiments provide a computer readable medium, on which a computer program is stored, which when executed by a processor, implements the steps of the spline fatigue life distribution determination method as described above in the first aspect.
According to the spline fatigue life distribution determining method and device provided by the embodiment of the disclosure, the spline tooth groove width, the spline tooth thickness and the indexing error are obtained by utilizing random sampling; determining the spline tooth side clearance of each spline, then obtaining the maximum nominal tangential force on the spline tooth of each spline, and obtaining the stress distribution corresponding to a plurality of splines on the basis of the maximum nominal tangential force; and finally, calculating and obtaining the fatigue life distribution of the spline by using the equivalent stress and life calculation formula. That is, when the fatigue life distribution of the spline is obtained, the spline tooth groove width, the spline tooth thickness and the indexing error are fully considered; thereby facilitating random sampling of spline backlash. And further, the practical situation of the engineering can be better reduced, and the fatigue life of the obtained spline is more reasonable and accurate.
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The above and other features, advantages and aspects of various embodiments of the present disclosure will become more apparent by referring to the following detailed description when taken in conjunction with the accompanying drawings. Throughout the drawings, the same or similar reference numbers refer to the same or similar elements. It should be understood that the drawings are schematic and that elements and features are not necessarily drawn to scale.
FIG. 1 is a flow chart of one embodiment of a spline fatigue life distribution determination method according to the present disclosure;
FIG. 2A is a schematic view of a clearance-containing spline tooth and spline groove fit according to the present disclosure;
FIG. 2B is a schematic view of another clearance-containing spline tooth and spline groove fit according to the present disclosure;
FIG. 3 is a spline indexing error schematic according to the present disclosure;
FIG. 4 is a spline pitch cumulative error schematic according to the present disclosure;
FIG. 5A is a spline root bending stress distribution according to the present disclosure;
FIG. 5B is a spline root bending stress distribution according to the present disclosure;
FIG. 6 is a spline equivalent stress profile according to the present disclosure;
FIG. 7 is a spline fatigue life profile according to the present disclosure;
FIG. 8 is a schematic structural view of a spline fatigue life distribution determining apparatus of the present disclosure;
fig. 9 is a schematic diagram of a basic structure of an electronic device provided according to an embodiment of the present disclosure.
Detailed Description
Embodiments of the present disclosure will be described in more detail below with reference to the accompanying drawings. While certain embodiments of the present disclosure are shown in the drawings, it is to be understood that the present disclosure may be embodied in various forms and should not be construed as limited to the embodiments set forth herein, but rather are provided for a more thorough and complete understanding of the present disclosure. It should be understood that the drawings and embodiments of the disclosure are for illustration purposes only and are not intended to limit the scope of the disclosure.
It should be understood that the various steps recited in the method embodiments of the present disclosure may be performed in a different order, and/or performed in parallel. Moreover, method embodiments may include additional steps and/or omit performing the illustrated steps. The scope of the present disclosure is not limited in this respect.
The term "include" and variations thereof as used herein are open-ended, i.e., "including but not limited to". The term "based on" is "based, at least in part, on". The term "one embodiment" means "at least one embodiment"; the term "another embodiment" means "at least one additional embodiment"; the term "some embodiments" means "at least some embodiments". Relevant definitions for other terms will be given in the following description.
It should be noted that the terms "first", "second", and the like in the present disclosure are only used for distinguishing different devices, modules or units, and are not used for limiting the order or interdependence relationship of the functions performed by the devices, modules or units.
It is noted that references to "a", "an", and "the" modifications in this disclosure are intended to be illustrative rather than limiting, and that those skilled in the art will recognize that "one or more" may be used unless the context clearly dictates otherwise.
The names of messages or information exchanged between devices in the embodiments of the present disclosure are for illustrative purposes only, and are not intended to limit the scope of the messages or information.
Referring to fig. 1, a flow of one embodiment of a spline fatigue life distribution determination method according to the present disclosure is shown. The spline fatigue life distribution determination method can be applied to a cylindrical straight tooth involute spline, but is not limited. As shown in fig. 1, the spline fatigue life distribution determining method includes the steps of:
step 101, obtaining parameters of each spline of a plurality of splines.
Here, the above parameters may include: the spline tooth groove width, the spline tooth thickness and the indexing error, and the values of the parameters are within a preset error range.
Step 102, determining a spline flank clearance of each spline based on the parameters.
It can be seen that in some embodiments of the present application, the spline flank clearance can be obtained based on the spline tooth groove width, the spline tooth thickness, and the indexing error of the spline teeth. In the process of obtaining the spline tooth side clearance in the prior art, the indexing error of the spline teeth is only utilized, and the influence of the spline tooth groove width error and the spline tooth thickness error on the spline tooth side clearance is not considered, so that the calculated spline tooth side clearance is not accurate enough. And the influence of the spline tooth groove width, the spline tooth thickness and the indexing error of the spline teeth on the spline tooth side clearance is comprehensively considered, so that the obtained spline tooth side clearance is more accurate.
In some alternative embodiments, the following may be based on the formula:
Figure BDA0002732331720000071
Figure BDA0002732331720000072
a spline flank clearance is determined for each spline.
Here, a in the above formula may be a spline flank clearance, ErMay be the spline tooth groove width, SrMay be the spline tooth thickness, deltaSZMay be the indexing error of the external spline teeth, deltaEZThe indexing error of the internal spline tooth groove can be used.
To facilitate a better understanding of the above formula:
Figure BDA0002732331720000073
this is explained in detail below with reference to fig. 2A and 2B.
It can be assumed that the indexing error of the external spline is deltaSZThe indexing error of the internal spline is deltaEZThe width of the spline tooth groove is ErThe key tooth thickness is SrThe spline single tooth backlash is deltaC＝Er-Sr. When the influence of the indexing error on the spline is not considered, the clearance between the spline mating surface side and the spline non-mating surface side is 1/2 Δ at a certain mating typeCAs shown in fig. 2A.
The following is a description of the method of calculating the clearance between the two sides of the spline teeth when there is an indexing error in the spline. The direction of the indexing error pointing to the spline fitting surface side along the tooth thickness symmetry center line can be defined as a positive direction, and then the indexing error delta of the external spline in fig. 2BSZPositive value, internal spline indexing error deltaEZThe value is negative. For any involute spline containing n pairs of spline teeth, the influence of spline fit type and indexing error on spline clearance is comprehensively considered, and the indexing errors of the external spline tooth and the internal spline tooth groove of the ith pair of spline teeth are respectively set to be deltaSZ，iAnd deltaEZ，iThe width of the spline tooth groove is Er，iTooth thickness of Sr，iThe sum of the clearances at both sides of the spline is deltaC，i＝Er，i-Sr，i. Then for the ith pair of spline teeth, the clearance between the outer spline teeth and the mating surface side of the tooth socket can be:
Figure BDA0002732331720000081
it should be noted that, unless otherwise specified in the present application, the backlash refers to the clearance on the spline mating surface side.
The indexing error delta of the external spline teeth can be setSZInternal spline tooth groove indexing error deltaEZSpline tooth groove width ErAnd tooth thickness SrBeing a random variable, the spline flank clearance a can then be expressed as:
Figure BDA0002732331720000082
in some alternative embodiments, the value of the parameter within the preset error range may be understood as: the preset error corresponding to the spline tooth groove width, the preset error corresponding to the spline tooth thickness and the preset error mean value corresponding to the indexing error are within a preset range. The specific preset error range may be set reasonably according to the actual application scenario and the type of the specific spline, and is not limited herein.
For example, in some application scenarios, the preset error range corresponding to the spline tooth slot width may be: [ E + Lambda, E + Lambda + T](ii) a The preset error range corresponding to the spline tooth thickness may be: [ S + esV-(T+λ)，S+esV-λ]. Here, E and S are the basic dimensions of the spline tooth groove width and the tooth thickness, respectively, λ is the comprehensive tolerance of the spline, T is the machining tolerance, and esvThe outer spline is acted on by the upper deviation of the tooth thickness.
The preset error range corresponding to the indexing error can be set reasonably by calculating the indexing tolerance of the spline teeth and then calculating the value according to the indexing tolerance.
And the indexing tolerance can be calculated as follows.
In some optional embodiments, the spline tooth groove width tolerance and the spline tooth thickness tolerance may be obtained based on the preset error range corresponding to the spline tooth groove width and the preset error range corresponding to the spline tooth thickness. Spline tooth groove width tolerance deltaEMay be ΔE＝Emax-EminT; the spline tooth thickness tolerance ΔSMay be ΔS＝Smax-Smin＝T。
Further, according to the definition: spline indexing error deltaZComprises the following steps: on the reference circle, the symmetrical center line of the tooth thickness (the tooth groove width) of the external spline deviates from the maximum error value of the theoretical position. DeltaZTake | deltaZmax| and | δZminThe larger of | is shown in fig. 3. While in practical application, the indexing tolerance ΔZI.e. can be a tolerance range for the indexing error. Involute spline pitch cumulative error deltapIs defined as: on the pitch circle, the maximum absolute value of the difference between the actual arc length and the theoretical arc length between any two same-side tooth surfaces is shown in fig. 4. Cumulative pitch tolerance ΔPI.e. the allowable variation range of the accumulated error of the tooth pitch.
In some alternative embodiments, the above definition may also be understood as: on the reference circle, the sum of two absolute values of the maximum positive arc length error and the maximum negative arc length error of the tooth form deviation from the theoretical position on the same side.
Therefore, the accumulated tolerance Δ of the spline pitch is not considered in consideration of the influence of the variation in the spline tooth thickness on the position of the spline center line of symmetryP，1To the indexing tolerance deltaZThe relationship of (1) is:
ΔP，1＝2ΔZ
when only the spline tooth thickness tolerance delta is consideredP，2Cumulative tolerance delta to spline pitchP，2The effect of (c) may then be:
Figure BDA0002732331720000091
therefore, the cumulative tolerance for the spline pitch taking into account the effects of the indexing tolerance and the tooth thickness tolerance may be:
Figure BDA0002732331720000101
the indexing tolerance may be:
Figure BDA0002732331720000102
then, accumulated tolerance and machining tolerance value of the pitch of the spline can be found through GB/T3478.1-2008 and substituted into the formula
Figure BDA0002732331720000103
The spline indexing tolerance is known.
And 103, acquiring the maximum nominal tangential force on the spline tooth of each spline based on the spline tooth side clearance.
In some alternative embodiments, the maximum nominal tangential force on the spline teeth of each of the above-described splines may be obtained through steps a, b and c.
And a step a of acquiring the torsional load applied to each spline and the rigidity of a single pair of key teeth of each spline.
In the prior art, there are many ways to obtain the torsional load applied to the spline teeth on the spline, and for the sake of brevity of the description, the description is not repeated here.
In some alternative embodiments, the single pair of spline teeth stiffness of each spline may then be achieved by: acquiring a rigidity parameter of the internal spline and a rigidity parameter of the external spline, wherein the rigidity parameters can comprise: the standard pressure angle, the distance from the point of application of the load to the tooth root, the tooth width, the tooth thickness, and the modulus of elasticity, shear modulus and poisson's ratio of the spline material; the single key rigidity of the inner spline and the single key rigidity of the outer spline can be respectively calculated according to the rigidity parameters; and the rigidity of the single pair of key teeth of the spline can be calculated according to the single key rigidity of the inner spline and the single key rigidity of the outer spline.
And b, determining the number of meshing teeth pairs of each spline according to the torsional load, the tooth side clearance of each spline and the rigidity of the single pair of spline teeth.
In some alternative embodiments, since determining the number of pairs of meshing teeth of each spline through the torsional load, the backlash of each spline and the stiffness of a single pair of spline teeth is a relatively conventional technical means in the prior art, and therefore, the details are not repeated herein.
And c, calculating to obtain the maximum nominal tangential force on the key teeth of each spline according to the torsional load, the tooth side clearance of each spline, the rigidity of the single pair of key teeth and the number of the meshing teeth.
And 104, acquiring stress distribution corresponding to the plurality of splines based on the maximum nominal tangential force.
In some alternative embodiments, the distribution relationship between the load on the spline teeth and the external load may be determined; here, the assignment relationship includes: the above calculation rule for the maximum nominal tangential force. And the maximum nominal tangential force can be obtained through the calculation rule corresponding to the maximum nominal tangential force. Then, a stress formula at a fatigue danger point on the spline tooth can be determined; and finally, obtaining stress distribution corresponding to the splines based on the distribution relation and the stress formula. In other words, the nominal tangential force on the tooth with the smallest spline backlash can be extracted based on the relationship of the external load to the load distribution on the spline teeth; and then, calculating by using a stress formula, and counting the stress distribution of the fatigue danger points on the spline. Here, the fatigue risk points are understood to be: the splines are at points where the splines are susceptible to failure, such as by breaking at the roots of the teeth.
In some optional embodiments, reference may also be made to the calculation method regarding spline root stress in the document GB/T17855-; after obtaining the stress results corresponding to each of the plurality of splines, the stress distribution can be obtained.
And step 105, determining a life calculation formula of the spline.
In some alternative embodiments, the finite element can be used to calculate the theoretical stress concentration coefficient of the spline, the spline parameters and the material performance, and a life formula at the fatigue risk point of the spline can be fitted. The specific fitting method can be referred to the following specific embodiments, and is not limited herein.
And 106, performing equivalent correction on the stress distribution to obtain the equivalent stress when the average stress is a preset value.
In some optional embodiments, the average stress may be 0 at a preset value.
And step 107, calculating and obtaining the fatigue life distribution of the spline based on the equivalent stress and the life calculation formula.
In some optional embodiments, in order to make the obtained fatigue life distribution of the spline more accurate, Goodman equivalent correction may be performed on the obtained spline stress distribution, so as to obtain the spline equivalent stress under the action of an external load, and further, the fatigue life distribution of the spline may be obtained according to the obtained spline equivalent stress and a life formula at a spline fatigue risk point fitted out.
It can be seen that in the embodiment of the present application, the spline tooth groove width, the spline tooth thickness and the indexing error can be obtained by using random sampling; determining the spline tooth side clearance of each spline, then obtaining the maximum nominal tangential force on the spline tooth of each spline, and obtaining the stress distribution corresponding to a plurality of splines on the basis of the maximum nominal tangential force; and finally, calculating and obtaining the fatigue life distribution of the spline by using the equivalent stress and life calculation formula. That is, when the fatigue life distribution of the spline is obtained, the spline tooth groove width, the spline tooth thickness and the indexing error are fully considered; thereby facilitating random sampling of spline backlash. And further, the practical situation of the engineering can be better reduced, and the fatigue life of the obtained spline is more reasonable and accurate.
The following description is presented in connection with specific examples to aid in understanding the inventive concepts disclosed herein and is not intended to be limiting.
Such as: taking the bending fatigue life of the spline tooth root as an example, the fatigue life distribution condition of the spline is calculated. The specific parameters and properties of the involute splines are selected as shown in tables 1 and 2.
Conventional mechanical Properties of Table 140 CrNiMoA
Figure BDA0002732331720000121
TABLE 2 spline model parameters
Figure BDA0002732331720000122
For the H/H matched 30-tooth spline, the tooth groove width value range (unit: mm) can be as follows: [1.981495408493621,2.001495408493621 ]; the range of values of the tooth thickness (unit: mm) can be as follows: [1.925495408493621,1.945495408493621 ]; the indexing error range (unit: mm) of the spline teeth and the tooth grooves can be [ -0.0075,0.0075 ].
It can be assumed that each error of the spline is normally distributed, and Matlab is used to randomly extract 100 ten thousand sets of the tooth groove width error, the tooth thickness error and the indexing error within the error range, however, in the specific implementation, how many sets of data are specifically extracted is not limited, and only needs to be reasonably set according to the actual situation. The spline flank clearance value may then be calculated using the following equation:
Figure BDA0002732331720000131
and it can be assumed that the average value of the torsional load on the active spline is 350Nm, the load amplitude is 150Nm and the period is t. And the maximum nominal tangential force F corresponding to each selected spline backlash can be calculated by referring to the calculation method for calculating the spline meshing tooth pair number and the load distribution on the spline tooth in the patent CN201810561153.1max。
Reference may then be made to the calculation of the spline load capacity of GB/T17855-maxAnd calculating the bending stress distribution at the tooth root of the spline.
And the formula for calculating the bending stress of the spline tooth root can be as follows:
Figure BDA0002732331720000132
wherein h is the full tooth height of the spline, SFnThe thickness of the chord tooth on the involute circle of the spline is L, and the axial matching length of the spline is L.
The spline root bending stress distribution obtained by calculation is shown in fig. 5A and 5B, wherein fig. 5A is a probability distribution of spline root bending stress when M is 200 Nm; and fig. 5B shows the probability distribution of spline root bending stress when M is 500 Nm.
The theoretical stress concentration coefficient of the spline of this example can then be calculated by means of finite elements to be KT2.3, combining spline parameters and material performance, fitting an S-N curve at a spline fatigue dangerous point, wherein a specific life formula can be as follows:
lgN＝38.5484-15.2096·lgS
then, Goodman equivalent correction can be carried out on the obtained spline fatigue stress amplitude distribution to obtain spline equivalent stress S under the action of external loadeqvThen applying the equivalent stress SeqvSubstituting the life fitting formula, calculating the spline probability fatigue life under each group of backlash, and specifically, the method can be shown in fig. 6 and 7. FIG. 6 is a spline equivalent stress distribution diagram, and FIG. 7 is a spline fatigue life distribution diagram.
It can be seen that in this embodiment, the influence of the uncertainty of the backlash on the fatigue life of the spline is fully considered, and the value tolerance of the backlash of the spline is calculated through the accumulated tolerance of the tooth pitch and the width/thickness tolerance of the tooth groove, so that the backlash of the spline can be randomly sampled conveniently. And by means of a calculation method for calculating load distribution on the spline teeth in patent CN201810561153.1, a load stress spectrum on the spline teeth bearing the maximum load is counted, and the fatigue life distribution of the spline is counted by fitting an S-N curve of the spline. Compared with the journal ' Harbin university of Industrial university ' journal ' 2016 volume 48 No. 1 ' fretting wear fatigue life estimation ', the method calculates the load stress spectrum on the spline teeth by means of a numerical method, and is more efficient than a finite element method. In addition, the spline backlash sampling model established by the method fully considers the coupling effect among all errors, and the size of the spline backlash is completely calculated, so that the established spline model containing the uncertain backlash is closer to the actual engineering situation, and the calculated spline fatigue life is more reasonable.
With further reference to fig. 8, as an implementation of the methods shown in the above-mentioned figures, the present disclosure provides a spline fatigue life distribution determining apparatus, an embodiment of which corresponds to the embodiment of the method shown in fig. 1, and the apparatus may be specifically applied to various electronic devices.
As shown in fig. 8, the spline fatigue life distribution determining apparatus of the present embodiment includes: the acquiring unit 801 is configured to acquire parameters of each spline of the plurality of splines, where the parameters include a spline tooth groove width, a spline tooth thickness, and an indexing error, and values of the parameters are within a preset error range; a spline backlash determining unit 802 for determining a spline backlash of each spline based on the above parameters; a maximum nominal tangential force obtaining unit 803 for obtaining a maximum nominal tangential force on the spline tooth of each spline based on the above spline tooth flank clearance; a stress distribution obtaining unit 804, configured to obtain stress distributions corresponding to the plurality of splines based on the maximum nominal tangential force; a life calculation formula determination unit 805 configured to determine a life calculation formula of the spline; an equivalent stress obtaining unit 806, configured to perform equivalent correction on the stress distribution to obtain an equivalent stress when the average stress is a preset value; a calculating unit 807 for calculating and obtaining the fatigue life distribution of the spline based on the equivalent stress and the life calculation formula.
In some alternative embodiments, the spline backlash determination unit 802 is specifically configured to determine the backlash based on the formula:
Figure BDA0002732331720000151
determining a spline flank clearance of each spline; wherein a is the spline flank clearance, ErIs the spline tooth groove width, SrIs the spline tooth thickness, deltaSZFor the indexing error, δ, of the external spline teethEZAnd the indexing error of the internal spline tooth groove is obtained.
In some alternative embodiments, the maximum nominal tangential force obtaining unit 803 is specifically configured to obtain a torsional load applied to each spline, a single pair of spline tooth stiffness for each spline; determining the number of meshing teeth pairs of each spline according to the torsional load, the tooth flank clearance of each spline and the rigidity of the single pair of spline teeth; and calculating to obtain the maximum nominal tangential force on the key teeth of each spline according to the torsional load, the side clearance of each spline, the rigidity of the single pair of key teeth and the number of the meshing teeth.
In some optional embodiments, the stress distribution obtaining unit 804 is specifically configured to determine a distribution relationship between the load on the spline tooth and the external load; wherein, the distribution relationship includes: the calculation rule corresponding to the maximum nominal tangential force; determining a stress formula at a fatigue danger point on the spline tooth; and obtaining stress distribution corresponding to the plurality of splines based on the distribution relation and the stress formula.
In some optional embodiments, the life calculation formula determining unit 805 is specifically configured to obtain parameters corresponding to the spline and material properties corresponding to the spline; determining a stress concentration coefficient based on a finite element calculation spline theory; and fitting and obtaining the service life calculation formula based on the parameters corresponding to the spline, the material performance corresponding to the spline and the stress concentration coefficient.
Referring now to FIG. 9, shown is a schematic diagram of an electronic device suitable for use in implementing embodiments of the present disclosure. The electronic devices in the embodiments of the present disclosure may include, but are not limited to, mobile terminals such as mobile phones, notebook computers, digital broadcast receivers, PDAs (personal digital assistants), PADs (tablet computers), PMPs (portable multimedia players), in-vehicle terminals (e.g., car navigation terminals), and the like, and fixed terminals such as digital TVs, desktop computers, and the like. The electronic device shown in fig. 9 is only an example, and should not bring any limitation to the functions and the scope of use of the embodiments of the present disclosure.
As shown in fig. 9, the electronic device may include a processing means (e.g., a central processing unit, a graphic processor, etc.) 901, which may perform various appropriate actions and processes according to a program stored in a Read Only Memory (ROM)902 or a program loaded from a storage means 908 into a Random Access Memory (RAM) 903. In the RAM903, various programs and data necessary for the operation of the electronic apparatus 900 are also stored. The processing apparatus 901, the ROM 902, and the RAM903 are connected to each other through a bus 904. An input/output (I/O) interface 905 is also connected to bus 904.
Generally, the following devices may be connected to the I/O interface 905: input devices 906 including, for example, a touch screen, touch pad, keyboard, mouse, camera, microphone, accelerometer, gyroscope, etc.; an output device 907 including, for example, a Liquid Crystal Display (LCD), a speaker, a vibrator, and the like; storage 908 including, for example, magnetic tape, hard disk, etc.; and a communication device 909. The communication means 909 may allow the electronic device to perform wireless or wired communication with other devices to exchange data. While fig. 9 illustrates an electronic device having various means, it is to be understood that not all illustrated means are required to be implemented or provided. More or fewer devices may alternatively be implemented or provided.
In particular, according to an embodiment of the present disclosure, the processes described above with reference to the flowcharts may be implemented as computer software programs. For example, embodiments of the present disclosure include a computer program product comprising a computer program carried on a non-transitory computer readable medium, the computer program containing program code for performing the method illustrated by the flow chart. In such an embodiment, the computer program may be downloaded and installed from a network through the communication device 909, or installed from the storage device 908, or installed from the ROM 6902. The computer program performs the above-described functions defined in the methods of the embodiments of the present disclosure when executed by the processing apparatus 901.
It should be noted that the computer readable medium of the present disclosure can be a computer readable signal medium or a computer readable storage medium or any combination of the two. A computer readable storage medium may be, for example, but not limited to, an electronic, magnetic, optical, electromagnetic, infrared, or semiconductor system, apparatus, or device, or any combination of the foregoing. More specific examples of the computer readable storage medium may include, but are not limited to: an electrical connection having one or more wires, a portable computer diskette, a hard disk, a Random Access Memory (RAM), a read-only memory (ROM), an erasable programmable read-only memory (EPROM or flash memory), an optical fiber, a portable compact disc read-only memory (CD-ROM), an optical storage device, a magnetic storage device, or any suitable combination of the foregoing. In the present disclosure, a computer readable storage medium may be any tangible medium that can contain, or store a program for use by or in connection with an instruction execution system, apparatus, or device. In contrast, in the present disclosure, a computer readable signal medium may comprise a propagated data signal with computer readable program code embodied therein, either in baseband or as part of a carrier wave. Such a propagated data signal may take many forms, including, but not limited to, electro-magnetic, optical, or any suitable combination thereof. A computer readable signal medium may also be any computer readable medium that is not a computer readable storage medium and that can communicate, propagate, or transport a program for use by or in connection with an instruction execution system, apparatus, or device. Program code embodied on a computer readable medium may be transmitted using any appropriate medium, including but not limited to: electrical wires, optical cables, RF (radio frequency), etc., or any suitable combination of the foregoing.
In some embodiments, the clients, servers may communicate using any currently known or future developed network Protocol, such as HTTP (HyperText Transfer Protocol), and may interconnect with any form or medium of digital data communication (e.g., a communications network). Examples of communication networks include a local area network ("LAN"), a wide area network ("WAN"), the Internet (e.g., the Internet), and peer-to-peer networks (e.g., ad hoc peer-to-peer networks), as well as any currently known or future developed network.
The computer readable medium may be embodied in the electronic device; or may exist separately without being assembled into the electronic device.
The computer readable medium carries one or more programs which, when executed by the electronic device, cause the electronic device to: acquiring parameters of each spline in a plurality of splines, wherein the parameters comprise spline tooth groove width, spline tooth thickness and indexing error, the values of the parameters are within a preset error range, and the splines comprise at least one spline with uneven tooth side clearance; determining a spline flank clearance for each spline based on the parameters; obtaining a maximum nominal tangential force on the spline teeth of each spline based on the spline tooth flank clearance; obtaining stress distribution of fatigue danger points on each spline based on the calculated spline bearing capacity and the maximum nominal tangential force; determining a life calculation formula of the fatigue danger point; performing equivalent correction on the stress distribution to obtain equivalent stress when the average stress is a preset value; and calculating to obtain the fatigue life distribution of the spline based on the equivalent stress and the life calculation formula.
Computer program code for carrying out operations for the present disclosure may be written in any combination of one or more programming languages, including but not limited to an object oriented programming language such as Java, Smalltalk, C + +, and conventional procedural programming languages, such as the "C" programming language or similar programming languages. The program code may execute entirely on the user's computer, partly on the user's computer, as a stand-alone software package, partly on the user's computer and partly on a remote computer or entirely on the remote computer or server. In the case of a remote computer, the remote computer may be connected to the user's computer through any type of network, including a Local Area Network (LAN) or a Wide Area Network (WAN), or the connection may be made to an external computer (for example, through the Internet using an Internet service provider).
The flowchart and block diagrams in the figures illustrate the architecture, functionality, and operation of possible implementations of systems, methods and computer program products according to various embodiments of the present disclosure. In this regard, each block in the flowchart or block diagrams may represent a module, segment, or portion of code, which comprises one or more executable instructions for implementing the specified logical function(s). It should also be noted that, in some alternative implementations, the functions noted in the block may occur out of the order noted in the figures. For example, two blocks shown in succession may, in fact, be executed substantially concurrently, or the blocks may sometimes be executed in the reverse order, depending upon the functionality involved. It will also be noted that each block of the block diagrams and/or flowchart illustration, and combinations of blocks in the block diagrams and/or flowchart illustration, can be implemented by special purpose hardware-based systems which perform the specified functions or acts, or combinations of special purpose hardware and computer instructions.
The units described in the embodiments of the present disclosure may be implemented by software or hardware. The name of the unit does not in some cases constitute a limitation of the unit itself, and for example, the acquiring unit may also be described as a "unit that acquires parameters of each spline in a plurality of sets".
The functions described herein above may be performed, at least in part, by one or more hardware logic components. For example, without limitation, exemplary types of hardware logic components that may be used include: field Programmable Gate Arrays (FPGAs), Application Specific Integrated Circuits (ASICs), Application Specific Standard Products (ASSPs), systems on a chip (SOCs), Complex Programmable Logic Devices (CPLDs), and the like.
In the context of this disclosure, a machine-readable medium may be a tangible medium that can contain, or store a program for use by or in connection with an instruction execution system, apparatus, or device. The machine-readable medium may be a machine-readable signal medium or a machine-readable storage medium. A machine-readable medium may include, but is not limited to, an electronic, magnetic, optical, electromagnetic, infrared, or semiconductor system, apparatus, or device, or any suitable combination of the foregoing. More specific examples of a machine-readable storage medium would include an electrical connection based on one or more wires, a portable computer diskette, a hard disk, a Random Access Memory (RAM), a read-only memory (ROM), an erasable programmable read-only memory (EPROM or flash memory), an optical fiber, a portable compact disc read-only memory (CD-ROM), an optical storage device, a magnetic storage device, or any suitable combination of the foregoing.
The foregoing description is only exemplary of the preferred embodiments of the disclosure and is illustrative of the principles of the technology employed. It will be appreciated by those skilled in the art that the scope of the disclosure herein is not limited to the particular combination of features described above, but also encompasses other embodiments in which any combination of the features described above or their equivalents does not depart from the spirit of the disclosure. For example, the above features and (but not limited to) the features disclosed in this disclosure having similar functions are replaced with each other to form the technical solution.
Further, while operations are depicted in a particular order, this should not be understood as requiring that such operations be performed in the particular order shown or in sequential order. Under certain circumstances, multitasking and parallel processing may be advantageous. Likewise, while several specific implementation details are included in the above discussion, these should not be construed as limitations on the scope of the disclosure. Certain features that are described in the context of separate embodiments can also be implemented in combination in a single embodiment. Conversely, various features that are described in the context of a single embodiment can also be implemented in multiple embodiments separately or in any suitable subcombination.
Although the subject matter has been described in language specific to structural features and/or methodological acts, it is to be understood that the subject matter defined in the appended claims is not necessarily limited to the specific features or acts described above. Rather, the specific features and acts described above are disclosed as example forms of implementing the claims.

Claims (10)

1. A spline fatigue life distribution determining method, characterized by comprising:
acquiring parameters of each spline in a plurality of splines, wherein the parameters comprise spline tooth groove width, spline tooth thickness and indexing error, and the values of the parameters are within a preset error range;
determining a spline flank clearance for each spline based on the parameters;
obtaining a maximum nominal tangential force on a spline tooth of each spline based on the spline tooth flank clearance;
obtaining stress distributions corresponding to the plurality of splines based on the maximum nominal tangential force;
determining a life calculation formula of the spline;
performing equivalent correction on the stress distribution to obtain equivalent stress when the average stress is a preset value;
and calculating to obtain the fatigue life distribution of the spline based on the equivalent stress and the life calculation formula.
2. The method of claim 1, wherein the determining a spline flank clearance for each spline based on the parameter comprises:
based on the formula:
Figure FDA0002732331710000011
determining a spline flank clearance of each spline;
wherein a is the spline flank clearance, ErIs the spline tooth groove width, SrIs the spline tooth thickness, deltaSZFor the indexing error, δ, of the external spline teethEZAnd the indexing error of the internal spline tooth groove is obtained.
3. The method of claim 1, wherein the maximum nominal tangential force on the spline teeth of each spline is obtained based on the spline flank clearance; the method comprises the following steps:
acquiring a torsional load applied to each spline and the rigidity of a single pair of spline teeth of each spline;
determining the number of meshing teeth pairs of each spline according to the torsional load, the tooth side clearance of each spline and the rigidity of the single pair of spline teeth;
and calculating to obtain the maximum nominal tangential force on the key teeth of each spline according to the torsional load, the spline tooth side clearance, the single pair of key tooth rigidity and the meshing tooth pairs.
4. The method of claim 1, wherein obtaining the stress profile corresponding to the plurality of splines based on the maximum nominal tangential force comprises:
determining the distribution relation of the load on the spline teeth and the external load; wherein, the allocation relationship comprises: a calculation rule corresponding to the maximum nominal tangential force;
determining a stress formula at a fatigue danger point on the spline tooth;
and obtaining stress distribution corresponding to the plurality of splines based on the distribution relation and the stress formula.
5. The method of claim 1, wherein the determining a life calculation formula for the spline comprises:
obtaining parameters corresponding to the spline and material properties corresponding to the spline;
determining a stress concentration coefficient based on a finite element calculation spline theory;
and fitting and obtaining the service life calculation formula based on the parameters corresponding to the spline, the material performance corresponding to the spline and the stress concentration coefficient.
6. A spline fatigue life distribution determining apparatus, characterized in that the apparatus comprises:
the device comprises an acquisition unit, a calculation unit and a control unit, wherein the acquisition unit is used for acquiring parameters of each spline in a plurality of splines, the parameters comprise spline tooth groove width, spline tooth thickness and errors, and the values of the parameters are within a preset error range;
a spline backlash determining unit for determining a spline backlash of each spline based on the parameter;
a maximum nominal tangential force obtaining unit for obtaining a maximum nominal tangential force on the spline teeth of each spline based on the spline tooth flank clearance;
the stress distribution obtaining unit is used for obtaining stress distributions corresponding to the plurality of splines based on the maximum nominal tangential force;
the service life calculation formula determining unit is used for determining a service life calculation formula of the spline;
the equivalent stress obtaining unit is used for carrying out equivalent correction on the stress distribution to obtain equivalent stress when the average stress is a preset value;
and the calculating unit is used for calculating and obtaining the fatigue life distribution of the spline based on the equivalent stress and the life calculation formula.
7. The device according to claim 6, wherein the spline flank clearance determination unit is specifically configured to determine the clearance based on the formula:
Figure FDA0002732331710000031
determining a spline flank clearance of each spline;
wherein a is the spline flank clearance, ErIs the spline tooth groove width, SrIs the spline tooth thickness, deltaSZFor the indexing error, δ, of the external spline teethEZAnd the indexing error of the internal spline tooth groove is obtained.
8. The device according to claim 6, characterized in that the maximum nominal tangential force obtaining unit is specifically adapted to obtain the torsional load exerted on the splines on each spline, a single pair of spline stiffness of each spline;
determining the number of meshing teeth pairs of each spline according to the torsional load, the tooth side clearance of each spline and the rigidity of the single pair of spline teeth;
and calculating to obtain the maximum nominal tangential force on the key teeth of each spline according to the torsional load, the spline tooth side clearance, the single pair of key tooth rigidity and the meshing tooth pairs.
9. An electronic device, comprising:
one or more processors;
a storage device for storing one or more programs,
when executed by the one or more processors, cause the one or more processors to implement the method of any one of claims 1-5.
10. A computer-readable medium, on which a computer program is stored which, when being executed by a processor, carries out the method according to any one of claims 1-5.
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