CN111027149B - Method and device for calculating time-varying meshing stiffness of straight-tooth cylindrical gear pair - Google Patents
Method and device for calculating time-varying meshing stiffness of straight-tooth cylindrical gear pair Download PDFInfo
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Abstract
The invention relates to the field of gear dynamics, in particular to a method and a device for calculating time-varying meshing stiffness of a straight-tooth cylindrical gear pair. The calculation method comprises the following steps: step one, calculating the rigidity of each part of gears which changes along with the rotation angle of a driving gear in the process of meshing a single pair of gears; step two, setting a gear tooth error curve which changes along with the rotation angle of the driving wheel; and step three, calculating to obtain the deformation amount when the gear teeth are meshed by taking the shaft hole of the driven gear as a reference, solving to obtain a static transmission error based on the deformation amount when the gear teeth are meshed and the total acting force generated by the sum of all the acting forces of the teeth to the external static moment, and obtaining the time-varying meshing stiffness according to the static transmission error and the displacement excitation. The computing device is used for executing the computing method. The calculation method provided by the invention considers the influence of gear tooth errors and is beneficial to obtaining more accurate time-varying meshing stiffness.
Description
Technical Field
The invention relates to the field of gear dynamics, in particular to a method and a device for calculating time-varying meshing rigidity of a straight-tooth cylindrical gear pair.
Background
The gear transmission system is widely applied to various fields of rail locomotives, automobiles, ships, aerospace, wind power, engineering machinery and the like due to the characteristics of compact structure, constant transmission ratio, high transmission efficiency and the like. The gear errors generated by time-varying meshing rigidity, manufacturing assembly errors, tooth profile modification, tooth surface defects and the like caused by time-varying contact positions of gear teeth and logarithmic alternation of the gear teeth participating in meshing are the two most main excitation forms of the gear transmission system, and the efficient and accurate calculation of the time-varying meshing rigidity is the premise and the basis of the comprehensive analysis of the dynamic performance of the gear transmission system. Therefore, the method has important significance for designing a high-performance gear transmission system, estimating and controlling the vibration noise level of a gear system, monitoring the state of the gear transmission system and diagnosing faults by deeply discussing the properties and excitation mechanisms of internal excitation sources such as time-varying meshing rigidity, gear errors and the like of the gear transmission system.
The published data show that the calculation method of the time-varying meshing stiffness of the gear mainly comprises a material mechanics method, an elastic mechanics method and a numerical method, so that a plurality of calculation formulas such as a Weber-Banaschk formula and a Ishikawa formula are obtained, and when the calculation methods are used for processing the meshing stiffness of a multi-tooth zone, single teeth participating in meshing are directly superposed on the stiffness, and the influence of gear tooth errors is ignored.
The gear tooth error is the deviation between the actual tooth profile and the ideal tooth profile caused by the design or the machining manufacturing process, or the plastic deformation of the gear tooth or the defect of the gear tooth in the operation process. The method in the prior art ignores the influence of gear tooth errors, so that the accuracy of the calculation result is low, and the accuracy of the comprehensive analysis result of the dynamic performance of the gear is influenced.
Disclosure of Invention
The invention aims to: aiming at the problems in the prior art, a method and a device for calculating time-varying meshing stiffness of a straight-tooth cylindrical gear pair are provided.
In order to achieve the purpose, the invention adopts the technical scheme that:
on one hand, the invention provides a method for calculating time-varying meshing stiffness of a straight-tooth cylindrical gear pair, which comprises the following steps of:
step one, calculating the rigidity of each part of gears which changes along with the rotation angle of a driving gear in the process of meshing a single pair of gears;
step two, setting a gear tooth error curve which changes along with the rotation angle of the driving wheel;
calculating the deformation of the meshed gear teeth by taking the shaft hole of the driven gear as a reference;
then, based on the deformation amount of the gear teeth during meshing and the total acting force of all the gear teeth to the acting force equal to the total acting force generated by the external static moment, solving to obtain a static transmission error, and obtaining time-varying meshing rigidity according to the static transmission error and displacement excitation;
the displacement excitation is:
δNLTE＝min([ep1+eg1,...,epi+egi,...,epN+egN])
wherein, deltaNLTEFor displacement excitation, subscript p denotes the driving wheel, subscript g denotes the driven wheel, and e is the gear tooth error obtained in step two.
Wherein, the static transfer error is: under the action of static moment, the gear pair is subjected to load deformation, gear tooth contact deformation and gear body load deformation to cause displacement on meshing lines corresponding to the relative rotation angles of the two meshed gears.
As a preferred aspect of the present invention, in step one, the bending stiffness, the shearing stiffness, the compression stiffness, the contact deformation of the gear teeth, the stiffness of the gear body of the gear, and the stiffness corresponding to the deflection of the adjacent teeth caused by the deformation of the gear body when the gear teeth are loaded during the meshing of the single pair of teeth are calculated.
According to the potential energy principle, the bending rigidity, the shearing rigidity and the compression rigidity of the gear tooth part are calculated as the preferable scheme of the invention:
in the formula, KbRepresenting the bending stiffness of the teeth, KsRepresents the shear stiffness; kaRepresents the compression stiffness; h represents half of the tooth thickness at the action position of the meshing force; alpha is alpha1The included angle between the meshing force and the tooth thickness direction is shown; d represents an effective acting length, i.e., a distance from an engaging force acting position to a root circle fixing portion; dx represents the width of the micro-section from the force application position of the engaging force by x, E represents the elastic modulus of the material, G is the shear modulus of the material, wherein:
v is the Poisson's ratio of the material; ix and Ax represent the moment of inertia and the cross-sectional area, respectively, of the section at x from the point of application of the meshing force, i.e.
Ax＝2hxW, wherein the symbol W is the tooth width, hx represents half the length of the micro section from the meshing force application position as x.
As a preferred scheme of the invention, the contact deformation of the gear teeth is calculated by adopting the following method:
δh＝ChFk
wherein, deltahDeforming the gear teeth in a contact manner;
when only the linear deformation of the tooth contact is considered,
when considering non-linear deformation of the tooth contact,
as a preferred scheme of the invention, the rigidity of the gear wheel body is calculated by adopting the following method:
wherein u represents the distance from the intersection point of the meshing line and the gear tooth symmetry line to the tooth root circle, and S is the arc length on the tooth root circle between the two intersection points of the single gear tooth profile curve and the tooth root circle; l, M, P, Q are coefficients related to gear design parameters. The calculation of the parameter L, M, P, Q is well known in the art and is readily available. For example, the paper "tooth shape distortion analysis formula of straight-tooth cylindrical gear pair" ("Analytical for use in gear body-induced tooth deflection of tooth contact coupling structure effect", Chongyang Xie et al, International Journal of Mechanical Sciences 148(2018), pp.174 and 190, formula B.1-formula B.4) gives the calculation formula of the parameter L, M, P, Q.
As a preferred embodiment of the present invention, the stiffness K of adjacent tooth deformations caused by tooth loading is calculated in the following mannerfij：
Wherein u represents the distance from the intersection point of the meshing line and the symmetric line of the gear teeth to the root circle, Li、Mi、Pi、Qi、 Ri、Si、Ti、Ui、ViIs a coefficient related to the gear design parameter and the subscript i is the gear tooth number participating in the meshing.
With respect to the parameter Li、Mi、Pi、Qi、Ri、Si、Ti、Ui、ViThe calculation of (c) is well known in the art and is readily calculated. For example, the paper "tooth shape distortion analysis formula of straight-tooth cylindrical gear pair" (Analytical for use in tooth body-induced tooth deflection of tooth contact coupling structure, Chongyang Xie et al, International Journal of Mechanical Sciences 148(2018), pp.174 and 190, formula C.1-C.9) gives the parameter Li、 Mi、Pi、Qi、Ri、Si、Ti、Ui、ViThe calculation formula of (2). According to the scheme, the complex multi-tooth meshing interaction power action of the gear tooth error and the loaded gear tooth under the combined action of adjacent tooth deviation caused by the deformation of the gear body is comprehensively considered.
As a preferred aspect of the present invention, in step two, the gear tooth error curve is expressed as:
wherein A represents the harmonic amplitude, θmaxIn order to engage the corresponding gear drive angle with the gear teeth,
is the phase angle, NeRepresenting the total harmonic order contained in the error curve. Namely: the gear tooth error curve is expressed by a fourier series.
As a preferable aspect of the present invention, in the third step, the i-th pair of teeth are engaged with each other with the deformation obtained:
from the fact that the sum of all tooth pair forces equals the total force generated by the external static moment, one can obtain:
the calculation method of the time-varying meshing stiffness comprises the following steps:
wherein, in the formula, Z represents an integer set, RbRepresenting the gear base radius, subscript p representing the drive wheel, downThe symbol g denotes the driven wheel, deltaSTEFor static transfer error, δNLTEFor displacement excitation, KmeshBecomes a time-varying meshing stiffness.
As a preferable scheme of the present invention, after the step three is finished, the method further comprises the following steps:
and step four, continuously rotating the angular positions of the gears to change the meshing positions of the wheel pairs, and calculating corresponding time-varying meshing rigidity and displacement excitation for each angular position to obtain a gear pair dynamic excitation curve of the whole meshing period.
On the other hand, the invention also provides a device for calculating the time-varying meshing stiffness of the straight-tooth cylindrical gear pair, which comprises a processor and a memory, wherein the memory is in communication connection with the processor; the memory stores instructions executable by the processor to cause the processor to perform the method described above.
In summary, due to the adoption of the technical scheme, the invention has the beneficial effects that:
compared with the traditional analytic algorithm, the method and the device have the advantages that the influence of gear errors and adjacent tooth deviation caused by loaded teeth generated by wheel body structure coupling effect is considered at the same time, the precision is higher, and accurate calculation of gear time-varying meshing rigidity under the influence of the gear errors is realized. The gear tooth error curve given in the second step of the invention not only comprises the situation of errors caused by machining precision or assembly limitation in the gear manufacturing process, abrasion and failure in the operation process and the like, but also comprises the situation of artificial tooth profile modification.
Drawings
FIG. 1 is a schematic diagram of a gear tooth force deformation calculation.
Fig. 2 is a schematic diagram of the calculation of the deformation of the gear wheel body under stress.
FIG. 3 is a schematic diagram of the calculation of the deformation of the adjacent teeth of the gear under force.
Fig. 4 is a comparison of the time-varying meshing stiffness of the gear obtained by the calculation method provided by the embodiment of the present invention and an analytic calculation method in the prior art.
FIG. 5 is a comparison of time varying meshing stiffness before and after modification of the tooth tops of the driving and driven gears obtained by the calculation method provided by the embodiment of the invention.
FIG. 6 is a comparison of tooth space load distribution coefficients before and after the modification of the tooth tops of the driving and driven gears obtained by the calculation method provided by the embodiment of the invention.
FIG. 7 is a comparison of tooth transfer errors before and after modification of the tooth tops of the driving and driven gear teeth obtained by the calculation method provided by the embodiment of the invention.
FIG. 8 is a comparison of time varying mesh stiffness obtained when tooth error is considered and when tooth error is not considered by the calculation method provided by embodiments of the present invention.
FIG. 9 is a comparison of tooth to tooth load distribution coefficients obtained with and without consideration of tooth error, obtained by the calculation method provided by embodiments of the present invention.
FIG. 10 is a graphical comparison of displacement excitation and single tooth to tooth error obtained by the calculation provided by embodiments of the present invention.
Detailed Description
The present invention will be described in detail below with reference to the accompanying drawings.
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention will be described in further detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention.
Examples
The embodiment of the invention provides a method for calculating time-varying meshing stiffness of a straight-tooth cylindrical gear pair, which comprises the following steps of:
step one, calculating the rigidity of each part of gears which changes along with the rotation angle of a driving gear in the process of meshing a single pair of gears;
specifically, according to the potential energy principle, the bending rigidity K of the tooth part of the gear tooth is calculatedbThe calculation method comprises the following steps:
calculating the tooth shear stiffness K of the gear teethsWhich calculatesThe method comprises the following steps:
calculating the tooth compression stiffness K of the gear teethaThe calculation method comprises the following steps:
in the above formulas, h represents a half of the tooth thickness at the position where the meshing force acts; alpha is alpha1The included angle between the meshing force and the tooth thickness direction is shown; d represents the effective acting length, i.e. the distance from the meshing force acting position to the root circle fixing part; dx represents the width of the micro section from the position of application of the engaging force by x, E represents the modulus of elasticity of the material, G is the modulus of shear of the material, wherein:
v is the Poisson's ratio of the material; ix and Ax represent the moment of inertia and the cross-sectional area, respectively, of the section at x from the point of application of the meshing force, i.e.
Ax＝2hxW, wherein the symbol W is the tooth width, hxRepresenting half the length of the micro-section at x from the location of the engagement force.
Calculating tooth contact variation deltah. The calculation principle is as follows: when a single gear tooth is contacted to transmit power, the contact part can generate contact deformation under the action of force F, so that the contact rigidity of the gear tooth can be calculated. The calculation method for calculating the contact stiffness of the gear teeth comprises a Hertz contact algorithm, a finite element method, an empirical formula and the like. In this embodiment, the following formula is used to calculate the tooth contact deformation:
δh＝ChFk (4)
when only the linear deformation of the tooth contact is considered,
when considering non-linear deformation of the tooth contact,
calculating the rigidity K of the gear bodyf：
Wherein u represents the distance from the intersection point of the meshing line and the gear tooth symmetry line to the tooth root circle, and S is the arc length on the tooth root circle between the two intersection points of the single gear tooth profile curve and the tooth root circle; l, M, P, Q is a coefficient related to a gear design parameter.
Calculating the stiffness K of the deformation of adjacent teeth caused by the loading of the teethfijIn particular, the stiffness KfijAnd the action force required to be exerted along the action line direction at the intersection point of the ith gear tooth profile and the gear pair action line to generate unit displacement along the action line is defined as the magnitude of the action force required to be exerted along the action line direction at the intersection point of the jth gear tooth profile and the gear pair action line. In this embodiment, the rigidity K is obtained by an analytic calculation methodfijThe calculation method comprises the following steps:
wherein u represents the distance from the intersection point of the meshing line and the symmetric line of the gear teeth to the root circle, Li、Mi、Pi、Qi、 Ri、Si、Ti、Ui、ViIs a coefficient related to the gear design parameter and the subscript i is the gear tooth number participating in the meshing. With respect to the parameter Li、Mi、Pi、Qi、Ri、Si、Ti、Ui、ViThe calculation of (b) is well known in the art and is readily available.
For example, please refer to FIG. 3, Kf21The acting force F which is required to be exerted along the acting line direction at the intersection point of the gear tooth profile of the gear tooth 1 and the gear pair acting line and is required to generate unit displacement along the acting line at the intersection point of the gear tooth profile of the gear tooth 2 and the gear pair acting line1The size of (2).
Kf12The acting force F which is required to be exerted along the acting line direction at the intersection point of the gear tooth profile of the gear tooth 2 and the gear pair acting line and is required to generate unit displacement along the acting line at the intersection point of the gear tooth profile of the gear tooth 1 and the gear pair acting line2The size of (2).
In other embodiments of the invention, the stiffness K can also be obtained by means of finite elementsfij。
Setting a gear error curve which changes along with the rotation angle of the driving wheel;
the gear error curve is a gear error expressed in a curve form in which a circumferential angle is used as an abscissa and an error amount corresponding to the circumferential angle is used as an ordinate. For any curve, the expression can be carried out through Fourier transform and in the form of sine function and cosine function. The above-mentioned gear error curve that changes with the action wheel corner that gives means that expresses the gear error curve through the form of fourier series, specifically is:
step three, obtaining a deformation calculation formula when the gear is meshed by taking the shaft hole of the driven gear as a reference, solving to obtain a static transmission error according to the total acting force generated by the sum of acting forces of all the teeth to the external static moment and the deformation calculation formula, and obtaining time-varying meshing rigidity according to the static transmission error and displacement excitation;
in particular, for a determined angular position of the gear, the joint in the shaft hole of the driven gear is engagedPoint fixed, driving gear external static moment T0Under the action of the force, the gear teeth and the wheel body are slightly rotated due to the load deformation, when N (N is more than or equal to 1, N belongs to Z) pairs of teeth are in meshing contact and bear, the deformation displacement generated on a meshing line by each pair of teeth by taking the shaft hole as reference is equal, namely the deformation of the ith pair of gear teeth during meshing is as follows:
at the same time, the sum of all tooth pair forces should equal the total force generated by the external static moment, i.e.:
in the formula, Z represents an integer set, RbRepresenting the gear base radius, subscript p representing the primary wheel, subscript g representing the secondary wheel, δSTEFor static transfer error, δNLTEFor displacement excitation, KmeshFor time-varying meshing stiffness, T0Representing the external static moment.
Combining formula (9) and formula (10) can be solved to obtain FiAnd static transfer error deltaSTESo as to excite delta according to the displacement of the gear pairNLTECalculating to obtain time-varying meshing stiffness KmeshThe following were used:
δNLTE＝min([ep1+eg1,...,epi+egi,...,epN+egN]) (11)
and step four, continuously rotating the angle positions of the gear, and obtaining corresponding time-varying meshing rigidity and displacement excitation at each angle position, thereby obtaining a gear pair dynamic excitation curve of the whole meshing period.
The embodiment of the invention also provides a device for calculating the variable meshing stiffness of the straight-tooth cylindrical gear pair, which comprises a processor and a memory in communication connection with the processor. The memory stores instructions executable by the processor to enable the processor to perform the method for calculating the time-varying meshing stiffness and displacement excitation of the spur gear pair.
The method and the device for calculating the time-varying meshing stiffness of the straight-tooth cylindrical gear pair have the advantages that:
the method for calculating the time-varying meshing stiffness of the straight-tooth cylindrical gear pair can realize calculation of the time-varying meshing stiffness of the gear under the influence of gear tooth errors. The gear tooth error comprises an error caused by the limitation of the machining precision of the gear and an error caused by the artificial modification of the tooth profile;
the method for calculating the time-varying meshing stiffness of the straight-tooth cylindrical gear pair comprehensively considers the influences of various factors of gear tooth bending, compression and shearing deformation, gear tooth contact deformation and gear tooth and adjacent tooth displacement caused by gear body deformation, and provides a simple and feasible gear transmission system dynamic excitation calculation method.
The method for calculating the time-varying meshing stiffness of the straight-tooth cylindrical gear pair provided by the embodiment of the invention is further described by an example as follows:
the gear parameters selected for this example are shown in table 1.
TABLE 1 Gear design parameters
| Parameter name | Driving gear | Driven gear |
| Modulus (mm) | 2 | 2 |
| Number of teeth | 25 | 41 |
| Angle of pressure (°) | 20 | 20 |
| Coefficient of |
1 | 1 |
| Coefficient of head space | 0.25 | 0.25 |
| Modulus of elasticity (GPa) | 206.8 | 206.8 |
| Density (kg/m)3) | 7800 | 7800 |
| Poisson ratio | 0.3 | 0.3 |
| Tooth width (mm) | 20 | 20 |
| Diameter of axle hole (mm) | 4 | 6 |
The calculation results of the time-varying meshing stiffness for the gears of the design parameters shown in table 1 are shown in fig. 4. The dotted line in fig. 4 is the operation result of the analytic algorithm in the prior art without considering the influence of deformation and displacement of the adjacent teeth, and the solid line shows the calculation result of the algorithm provided by the present invention. Therefore, in the traditional algorithm, the calculated result deviates about 58% from the real result due to neglecting the deformation displacement influence of the gear tooth acting force on the adjacent tooth.
The algorithm provided by the embodiment of the invention can also be used for gear meshing parameters under the influence of the modified tooth profile. The modification of the tooth profile is one of errors of gear teeth and is the deviation of the tooth profile which is designed by people intentionally, so that the modification of the tooth profile is used for reducing or eliminating the engagement and the engagement impact of gears, and the modification of the tooth profile has obvious effects on vibration reduction and noise reduction of a gear transmission system. The analytic algorithm in the prior art cannot calculate gear meshing parameters under the influence of tooth profile modification. Please refer to fig. 5-7. FIG. 5 shows the time-varying meshing stiffness of the driving and driven gear tooth tops after the profile modification (the profile modification amount is 10um, and the profile modification length is 0.32mm) calculated by the method provided by the invention; FIG. 6 is the interdental load distribution coefficient before and after the modification of the gear tooth tops of the driving and driven gears (the modification amount is 10um, and the modification length is 0.32mm) calculated by using the method provided by the invention; FIG. 7 shows the static transmission error delta before and after the addendum modification (modification amount is 10um, modification length is 0.32mm) of the driving and driven gears calculated by the method provided by the inventionSTEAnd (5) waiting for gear meshing parameter results.
The interdental load distribution coefficient is a ratio of the meshing force borne by a pair of teeth participating in meshing to the total force, and the calculation mode is as follows:
wherein, LSRiThe interdental load distribution coefficient of the ith pair of teeth, and the meanings of the other parameters are described in the foregoing, and are not described herein again.
As can be seen from the figure, the tooth profile modification has obvious influence on the gear meshing parameters, and the method provided by the embodiment of the invention can accurately reflect the influence.
In addition, errors exist in gear machining and manufacturing, so that gear tooth errors cannot be avoided, and the errors also greatly change the amplitude and the shape of a gear meshing parameter curve, so that the dynamic performance of a gear transmission system is influenced. On the basis of the above tooth profile modification, a gear tooth error is further added, and a curve of the added single-tooth-to-gear tooth error is shown as a solid line in fig. 10. As can be seen from fig. 8-10, the micron-sized tooth error has a significant effect on both the time-varying meshing stiffness and the interdental load distribution coefficient.
Meanwhile, the displacement excitation is shown by a dotted line in fig. 10, and is greatly different from the error of a single tooth to a pair of gear teeth, so that in the dynamic simulation process of the gear transmission system, the error of the single tooth to the gear teeth does not completely coincide with the curve of the displacement excitation, and the misalignment is the root cause of large fluctuation of the meshing stiffness and the inter-tooth load distribution coefficient in the error-free state compared with the meshing stiffness and the inter-tooth load distribution coefficient in the error-free state (see fig. 8 and fig. 9). The influence of the non-overlapping portions of the two curves shown in fig. 10 is not considered in the prior art, resulting in inaccuracy of the calculation results in the prior art.
It should be noted that: in other embodiments of the invention, the tooth contact deformation δhIt can also be calculated by other methods, such as finite element, Hertz contact algorithm, etc.;
in other embodiments of the invention, the stiffness KfijIt can also be calculated by other embodiments, such as: fitting numerical values;
in other embodiments of the present invention, L, M, P, Q can also be obtained by numerical fitting.
The above description is only for the purpose of illustrating the preferred embodiments of the present invention and is not to be construed as limiting the invention, and any modifications, equivalents and improvements made within the spirit and principle of the present invention are intended to be included within the scope of the present invention.
Claims (9)
1. The method for calculating the time-varying meshing stiffness of the straight-tooth cylindrical gear pair is characterized by comprising the following steps of:
step one, calculating the rigidity and deformation of each part of gears which change along with the rotation angle of the driving gear in the single-pair gear meshing process;
step two, setting a gear tooth error curve which changes along with the rotation angle of the driving wheel;
calculating the deformation of the meshed gear teeth by taking the shaft hole of the driven gear as a reference;
then, based on the deformation amount of the gear teeth during meshing and the total acting force of all the gear teeth to the acting force equal to the total acting force generated by the external static moment, solving to obtain a static transmission error, and obtaining time-varying meshing rigidity according to the static transmission error and displacement excitation;
the displacement stimulus is:
δNLTE＝min([ep1+eg1,...,epi+egi,...,epN+egN])
wherein, deltaNLTEFor displacement excitation, subscript p represents a driving wheel, subscript g represents a driven wheel, and e represents the gear tooth error obtained in the second step;
in the third step, the obtained deformation of the i-th pair of wheel teeth when engaged is:
from the fact that the sum of all tooth pair forces equals the total force generated by the external static moment, one can obtain:
the calculation method of the time-varying meshing stiffness comprises the following steps:
wherein, in the formula, Z represents an integer set, RbRepresenting the gear base radius, subscript p representing the primary wheel, subscript g representing the secondary wheel, δSTEFor static transfer error, δNLTEFor displacement excitation, KmeshFor time-varying meshing stiffness, T0Representing external static moment, FiIndicating the force of the ith pair of gears.
2. The method for calculating the time-varying meshing stiffness of a spur gear pair according to claim 1, wherein in the first step, bending stiffness, shearing stiffness, compression stiffness, gear contact deformation, gear body stiffness of a gear and stiffness of adjacent tooth deformation caused by loading of the gear body during meshing of a single pair of teeth are calculated.
3. The method for calculating the time-varying meshing stiffness of the spur gear pair according to claim 2, wherein the bending stiffness, the shearing stiffness and the compression stiffness of the tooth portion of the gear are calculated according to a potential energy principle:
in the formula，KbRepresenting the bending stiffness of the teeth, KsRepresents the shear stiffness; kaRepresents the compression stiffness; h represents half of the tooth thickness at the meshing force acting position; alpha is alpha1The included angle between the meshing force and the tooth thickness direction is shown; d represents the effective acting length, i.e. the distance from the meshing force acting position to the root circle fixing part; dx represents the width of the micro section from the position of application of the engaging force by x, E represents the modulus of elasticity of the material, G is the shear modulus of the material, wherein:
v is the Poisson's ratio of the material; ix and Ax represent the moment of inertia and the cross-sectional area, respectively, of the section at x from the point of application of the meshing force, i.e.
Ax＝2hxW, wherein the symbol W is the tooth width, hxRepresenting half the length of the micro-section from the engagement force application location, x.
4. The method for calculating the time-varying meshing stiffness of the spur gear pair according to claim 3, wherein the gear tooth contact deformation is calculated in the following manner:
δh＝ChFk
wherein, deltahDeforming the gear teeth in a contact manner;
when only the linear deformation of the tooth contact is considered,
when considering non-linear deformation of the tooth contact,
5. the method for calculating the time-varying meshing stiffness of the spur gear pair according to claim 4, wherein the stiffness of the gear body is calculated in the following manner:
wherein u represents the distance from the intersection point of the meshing line and the gear tooth symmetry line to the tooth root circle, and S is the arc length on the tooth root circle between the two intersection points of the single gear tooth profile curve and the tooth root circle;
l, M, P, Q are coefficients related to gear design parameters.
6. The method for calculating the time-varying meshing stiffness of a spur gear pair according to claim 5, wherein the stiffness K corresponding to the deflection of adjacent teeth caused by the deformation of a gear body when the gear teeth are loaded is calculated in the following mannerfij：
Wherein u represents the distance from the intersection point of the meshing line and the symmetric line of the gear teeth to the root circle, Li、Mi、Pi、Qi、Ri、Si、Ti、Ui、ViIs a coefficient related to the gear design parameter and the subscript i is the gear tooth number participating in the meshing.
7. The method for calculating the time-varying meshing stiffness of the spur gear pair according to claim 6, wherein in the second step, the gear tooth error curve is expressed by a fourier series:
wherein A represents the harmonic amplitude, θmaxIn order to engage the corresponding gear drive angle with the gear teeth,
is a phase angle, NeRepresenting the total harmonic order contained in the error curve.
8. The method for calculating the time-varying meshing stiffness of the spur gear pair according to claim 1, further comprising the following steps after the third step is finished:
and step four, continuously rotating the angular positions of the gears to change the meshing positions of the gear pairs, and calculating corresponding time-varying meshing stiffness and displacement excitation for each angular position to obtain a dynamic excitation curve of the gear pair in the whole meshing period.
9. The device for calculating the time-varying meshing stiffness of the straight-tooth cylindrical gear pair is characterized by comprising a processor and a memory, wherein the memory is in communication connection with the processor; the memory stores instructions executable by the processor to enable the processor to perform the method of any one of claims 1 to 8.
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