CN115828649A - Method and device for determining gear tooth back side meshing rigidity - Google Patents
Method and device for determining gear tooth back side meshing rigidity Download PDFInfo
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Abstract
The disclosure belongs to the technical field of mechanical design, and particularly relates to a method and a device for determining meshing stiffness of the back side of a gear tooth. The method comprises the following steps: acquiring meshing position coordinates of the back side of the tooth; determining actual tooth top coordinates of the meshing teeth on the tooth back side according to the meshing position coordinates of the tooth back side and the tooth top circle pressure angle; determining the deformation angle of the gear on the back side of the tooth according to the actual tooth top coordinate on the back side of the tooth and the standard tooth top coordinate of the meshing tooth on the back side of the tooth; determining the tooth back side tooth pair separation distance according to the gear base circle radius and the deformation angle of the tooth back side gear; the tooth back side mesh stiffness is determined based on the tooth back side tooth pair separation distance. The implementation of the present disclosure is used for solving the problem that the tooth back side meshing stiffness calculated by the current calculation mode is inaccurate.
Description
Technical Field
The disclosure relates to the technical field of mechanical design, in particular to a method and a device for determining meshing stiffness of the back side of a gear tooth.
Background
In the gear meshing process, the meshing stiffness of the tooth back side is directly replaced by the meshing stiffness of the driving side under some conditions, or the meshing stiffness of the driving side is adjusted according to a certain meshing phase difference, and the phenomenon that the tooth back side is meshed outside the gear pair possibly under the influence of working conditions such as no load and the like is not considered, so that the meshing stiffness of the tooth back side is changed, and therefore the meshing stiffness of the tooth back side calculated by adopting the conventional calculation method is inaccurate.
Disclosure of Invention
In order to solve the above technical problem or at least partially solve the above technical problem, the present disclosure provides a method and an apparatus for determining a backside meshing stiffness of a gear tooth, by which a higher accuracy of the backside meshing stiffness calculated in this way can be achieved.
In order to achieve the above purpose, the technical solutions provided by the embodiments of the present disclosure are as follows:
in a first aspect, there is provided a method of determining gear tooth backside meshing stiffness, comprising:
acquiring meshing position coordinates of the back side of the tooth;
determining the actual tooth crest coordinate of the tooth back side meshing tooth according to the tooth back side meshing position coordinate and the tooth top circle pressure angle;
determining a deformation angle of the tooth back side gear according to the actual tooth top coordinate of the tooth back side meshing tooth and the standard tooth top coordinate of the tooth back side meshing tooth;
determining the tooth back side tooth pair separation distance according to the gear base circle radius and the deformation angle of the tooth back side gear;
the tooth back side meshing stiffness is determined based on the tooth back side tooth pair separation distance.
In a second aspect, there is provided a device for determining the back-flank mesh stiffness, comprising:
the acquisition module is used for acquiring the meshing position coordinates of the back side of the tooth;
the determining module is used for determining the actual tooth crest coordinate of the tooth back side meshing tooth according to the tooth back side meshing position coordinate and the tooth top circle pressure angle;
determining the deformation angle of the gear on the tooth back side according to the actual tooth top coordinate of the meshing tooth on the tooth back side and the standard tooth top coordinate of the meshing tooth on the tooth back side;
determining the tooth back side tooth pair separation distance according to the gear base circle radius and the deformation angle of the tooth back side gear;
the tooth back side mesh stiffness is determined based on the tooth back side tooth pair separation distance.
In a third aspect, an electronic device is provided, including: a processor, a memory and a computer program stored on the memory and executable on the processor, the computer program, when executed by the processor, implementing a method of determining a gear tooth flank meshing stiffness as set forth in the first aspect or any one of its alternative embodiments.
In a fourth aspect, a computer-readable storage medium is provided, comprising: the computer-readable storage medium has stored thereon a computer program which, when executed by a processor, implements a method of determining a gear tooth back-side mesh stiffness as set forth in the first aspect or any one of its alternative embodiments.
In a fifth aspect, there is provided a computer program product comprising: when the computer program product is run on a computer, the computer is caused to implement the method of determining gear tooth back side mesh stiffness as set forth in the first aspect or any one of its alternative embodiments.
According to the method for determining the meshing stiffness of the back side of the gear, the actual tooth top coordinate of the meshing tooth of the back side of the gear is determined according to the meshing position coordinate of the back side of the gear and the circular pressure angle of the top of the gear, the deformation angle of the gear of the back side of the gear is determined according to the actual tooth top coordinate of the back side of the gear and the standard tooth top coordinate of the meshing tooth of the back side of the gear, the tooth-to-tooth separation distance of the back side of the gear is determined according to the radius of the gear base circle and the deformation angle of the gear of the back side of the gear, and the meshing stiffness of the back side of the gear is determined based on the tooth-to-tooth separation distance of the back side of the gear. Through the scheme, in the process of calculating the meshing stiffness of the back side of the tooth, the situation that the meshing stiffness of the back side of the tooth is changed due to the fact that the gear pair is likely to have external meshing of the back side of the tooth is considered, the separation distance of the back side of the tooth pair is determined by calculating the deformation angle of the back side gear, and the meshing stiffness of the back side of the tooth is further calculated.
Drawings
The accompanying drawings, which are incorporated in and constitute a part of this specification, illustrate embodiments consistent with the present disclosure and together with the description, serve to explain the principles of the disclosure.
In order to more clearly illustrate the embodiments or technical solutions in the prior art of the present disclosure, the drawings used in the description of the embodiments or prior art will be briefly described below, and it is obvious for those skilled in the art that other drawings can be obtained according to the drawings without inventive exercise.
FIG. 1 is a schematic flow chart diagram illustrating a method for determining gear tooth backside mesh stiffness provided by an embodiment of the present disclosure;
FIG. 2 is a schematic flow chart illustrating a process for obtaining gear tooth backside meshing position coordinates according to an embodiment of the present disclosure;
FIG. 3 is a schematic diagram of a driving side engagement of a gear pair provided in an embodiment of the present disclosure;
FIG. 4 is a model diagram of a load angle calculation for a gear tooth of a gear engagement provided in an embodiment of the present disclosure;
FIG. 5 is a diagram of an external meshing analysis model of a gear pair line according to an embodiment of the present disclosure;
FIG. 6 is a diagram of method steps for determining gear tooth backside meshing stiffness based on tooth backside tooth-to-tooth separation distance provided by an embodiment of the present disclosure;
FIG. 7 is a graph of the number of pairs of meshing teeth on the drive side and the back side of a gear pair over time according to an embodiment of the present disclosure;
FIG. 8 is a schematic diagram illustrating a variation of a deflection angle of a driving side tooth of a gear pair corresponding to a separation distance with time according to an embodiment of the present disclosure;
fig. 9 is a schematic diagram illustrating a variation of a deformation angle of a back tooth pair separation distance of a gear pair according to time according to an embodiment of the present disclosure;
FIG. 10 is a graph of gear tooth back side mesh stiffness for a straight circular cylinder gear provided by an embodiment of the present disclosure;
FIG. 11 is a device for determining the stiffness of the backside engagement of teeth provided by embodiments of the present disclosure;
fig. 12 is a schematic diagram of a hardware structure of an electronic device according to an embodiment of the present disclosure.
Detailed Description
In order that the above objects, features and advantages of the present disclosure may be more clearly understood, aspects of the present disclosure will be further described below. It should be noted that the embodiments and features of the embodiments of the present disclosure may be combined with each other without conflict.
In the following description, numerous specific details are set forth in order to provide a thorough understanding of the present disclosure, but the present disclosure may be practiced in other ways than those described herein; it is to be understood that the embodiments disclosed in the specification are only a few embodiments of the present disclosure, and not all embodiments.
At present, the meshing stiffness of the tooth back side is directly replaced by the meshing stiffness of the driving side under some conditions, or the meshing stiffness of the driving side is adjusted according to a certain meshing phase difference. The calculation method ignores the difference between the meshing position and the off-line meshing of the tooth back side and the driving side, so that the calculation accuracy of the meshing rigidity of the tooth back side is not high, and the application range of the existing meshing rigidity calculation model is limited.
In order to solve the above problems, the embodiments of the present disclosure provide a method and apparatus for determining gear tooth backside meshing stiffness. The actual tooth top coordinate of the tooth back side meshing tooth is determined by acquiring the tooth back side meshing position, according to the tooth back side meshing position coordinate and the tooth top circle pressure angle, the deformation angle of the tooth back side gear is determined according to the actual tooth top coordinate of the tooth back side and the standard tooth top coordinate of the tooth back side meshing tooth, the tooth back side tooth pair separation distance is determined according to the gear base circle radius and the deformation angle of the tooth back side gear, and the tooth back side meshing rigidity is automatically determined based on the tooth back side tooth pair separation distance. According to the scheme, the situation that the meshing stiffness of the tooth back side is changed due to the fact that the gear pair is likely to have tooth back side line external meshing is considered in the process of calculating the meshing stiffness of the tooth back side, the tooth back side tooth pair separation distance is determined and the meshing stiffness of the tooth back side is further calculated by calculating the deformation angle of the tooth back side gear, and compared with the prior art that the meshing stiffness of the tooth back side is determined only through the driving side meshing stiffness and the phase relation between the driving side and the tooth back side, the accuracy of calculating the meshing stiffness of the tooth back side can be improved.
FIG. 1 is a schematic flow chart illustrating a method for determining gear tooth backside meshing stiffness provided by an embodiment of the present disclosure.
As shown in FIG. 1, the method of determining gear tooth backside meshing stiffness includes, but is not limited to, the steps of:
101. tooth back side mesh position coordinates are acquired.
In some embodiments, the tooth back side mesh position coordinates may be determined by first calculating the tooth back side and drive side forward mesh phase difference and then determining the tooth back side mesh point coordinates from the mesh phase difference and the tooth back side mesh point coordinates. Wherein the engagement point on the back side of the tooth is the engagement position at the time of initial engagement of the back side of the gear tooth.
FIG. 2 is a schematic flow chart illustrating gear tooth backside meshing position coordinates provided in accordance with the disclosed embodiments.
As shown in FIG. 2, the tooth flank engagement position coordinate determination method includes, but is not limited to, the following steps
201. A meshing phase difference between the tooth back side and the drive side is determined.
In some embodiments, the phase difference of the meshing before the back side and the drive side of the tooth is calculated by the time the gear pair tooth symmetry line coincides with the tooth center line. The gear tooth symmetry line refers to the symmetry line of each meshing gear tooth, and the gear tooth center line is a central point connecting line between the driving wheel and the driven wheel.
Exemplarily, fig. 3 is a schematic diagram of a driving-side engagement of a gear pair provided by an embodiment of the present disclosure.
As shown in fig. 3, the symmetry line of the wheel set teethO s O p Line of the center of the toothO s O p When they coincide, the notation is made
In the case of the graph of FIG. 3,O s is the tooth center of the driving wheel (namely the driving side),O p is the tooth center of the driven wheel (i.e. the tooth back side) so as toO s Establishing global sit for originMarker systemx-O s -yTo do so byO p Establishing a local coordinate system for an originx 2 -O p -y 2 The drive side meshing line isA 1 B 1 The direction of movement of the meshing point isA 1 ToB 1 . The tooth flank meshing line isB 2 A 2 The direction of movement of the meshing point isB 2 ToA 2 . According to the principle of gear engagement, the drive side engagement pointS 1 And the flank engagement pointS 2 The two-dimensional mirror is symmetrical to each other,C 2 in order to drive the side out-of-engagement point,D 1 is the point of the back side of the tooth which is engaged,C 1 in order to drive the point of engagement on the side,D 2 is the engagement point of the back side of the tooth,Pis a gear pair node. At the moment, the driving side and the back side of the gear pair have the same number of meshing teeth and the same meshing rigidity amplitude.
According to the gear meshing principle and the gear geometric theory, the method can obtain
Comprises the following steps:
in the above-mentioned (1), the resin composition,θ C1 is shown in FIG. 3O s A 1 AndO s C 1 the included angle between the two parts is included,α sp is the meshing angle of the gear pair, and the gear pair is a gear pair,w s the rotating speed of the driving wheel,R bs Is the radius of a base circle,αIn order to index the circular pressure angle,x s m is the gear modulus.
According to the gear meshing principle, according to the theoretical analysis process,t≤t s tooth flank mesh stiffness of the toothk b (t) Is equal tot≥t s Drive side engagement stiffness ofk(t) At this time:
in the above-mentioned (2), the first step,
the time consumed after the gear rotates a certain angle is shown, and the simplification of (2) can obtain:
in the above (3)
Is the phase difference.
202. And determining the meshing position coordinate of the back side of the tooth according to the meshing phase difference between the back side of the tooth and the driving side and the meshing point coordinate of the back side of the tooth.
In some embodiments, the tooth back side engagement position coordinates are coordinates in a local coordinate system corresponding to the tooth back side, or the tooth back side engagement position coordinates are coordinates in a global coordinate system corresponding to the drive side.
The phase difference of the meshing between the back and drive sides calculated in step 201 and the point of engagement of the back of the tooth corresponding to the meshing time in fig. 3D 2 Where the back-side meshing point is the point of gear contact at the time of initial back-side meshing of the gear teeth, the back-side meshing position at that time of meshing in fig. 3 can be obtainedS 2 The coordinates of (a).
Since the back side engagement position is not at other engagement timesS 2 For the sake of no loss of generality, the drive side mesh point and the tooth back side mesh point are named asX 1 AndX 2 local coordinate system at any time of engagementx 2 -O p -y 2 Lower tooth back side engagement positionX 2 Coordinates of points (
,
) Comprises the following steps:
in the above-mentioned (4), the first step,T=P b1 /w s the meshing period of the gear pair is set as the period,w p for the rotational speed of the driven wheel,P b1 the pitch of the gear base circle is the pitch of the gear base circle,R bp is the driven wheel base radius. From the above (4), the coordinates of the meshing position on the tooth back side
Based on the phase difference of the meshing between the back side and the driving side and the meshing point of the back side of the tooth corresponding to the meshing timeD 2 Is calculated from the coordinates of (a).
The tooth back side meshing position alone obtained in the above (4)X 2 In a local coordinate systemx 2 -O p -y 2 Coordinates of the teeth, the back side engagement position of which can be obtained by derivationX 2 In a global coordinate systemx-O s -yIs marked by (x X2 ,y X2 ) Of) and (4) coordinates. The specific derivation is as follows:
a local coordinate system can be obtained according to the geometric relationship of the driving wheel and the driven wheel and the spatial coordinate transformation theory shown in figure 3x 2 -O p -y 2 Lower partX 2 The homogeneous coordinate corresponding to the point is
=(
,
1, 1) and global coordinate systemx-O s -yLower partX 2 Homogeneous coordinate C corresponding to point X2 =(x X2 , y X2 1, 1) conversion betweenThe relationship is as follows:
in the above-mentioned (5), the first step,
the space coordinate transformation matrix represents the change condition of the coordinates of any point from a local coordinate system to a global coordinate system. The several matrices are derived according to the theory of spatial coordinate transformation. The concrete expression is as follows:
in the above items (6), (7) and (8),θ 1 is composed ofO p B 1 Andy 2 the included angle of the positive half shaft,athe center distance of the gear pair.
The back-tooth engagement position in the global coordinate system can be determined according to the above equation (5)x-O s -yThe coordinates of the following.
102. And determining the actual tooth crest coordinate of the back side meshing tooth according to the back side meshing position coordinate and the tooth crest circle pressure angle.
In some embodiments, the actual addendum coordinates of the back-side tooth are determined by modeling a gear tooth load angle calculation. Since the actual tooth tip coordinate position of the gear tooth back-side engaging tooth changes at any engaging time in the case of gear rotation. Therefore, the actual tooth tip coordinates of the tooth flank meshing teeth are calculated.
Exemplarily, fig. 4 shows a model diagram for calculating a load angle of a gear tooth meshing according to an embodiment of the present disclosure.
As shown in fig. 4, S is the mesh point,His the tooth top of the tooth, and the tooth top,Lis the middle point of the tooth top,Mis the point where the meshing point is perpendicular to the symmetry line of the gear teeth,ASto mesh the line (denoted as LOA),F、FaandFbrespectively the tooth pair engagement force, the vertical direction and the horizontal direction components of the engagement force. Angle of erectionAOHFor gear tooth top circle pressure angleα H ，∠AOSIs the pressure angle at the point of engagementα S 。θ S In order to engage the tooth load angle,Rbis the radius of the base circle, wherein the pressure angle at the point of engagementα S The included angle between the perpendicular line of the meshing line LOA of the meshing point S and the connecting line of the meshing point S and the tooth profile is set.
In some embodiments, the pressure angle is based on gear tooth tip circleα H And pressure angle at the point of engagementα S A coordinate system can be determinedx-O-yLower tooth topHCoordinates (A)
) The concrete expression is as follows:
in the above-mentioned (9), the first step,R a the gear tooth crest radius.
In some embodiments, the tooth top coordinates of the driven wheel in the local coordinate system are only calculated in the above equation (9), and the tooth top coordinates of the driving wheel in the global coordinate system can be obtained through the conversion of equation (5).
In the embodiment, the tooth crest coordinate of the tooth back side of the actual driving wheel and the tooth pressure angle of the actual meshing point at the meshing moment are analyzed by establishing the gear meshing gear tooth load angle calculation model, and more accurate parameters are provided for the subsequent calculation of the actual meshing stiffness of the tooth back side.
103. And determining the deformation angle of the gear on the tooth back side according to the actual tooth top coordinate on the tooth back side and the standard tooth top coordinate of the meshing tooth on the tooth back side.
In some embodiments, the angle of deformation of the gear back-side gear is determined by modeling an out-of-gear mesh analysis of the gear pair.
Exemplarily, fig. 5 is a diagram of an analysis model for external meshing of a gear pair line provided in the embodiment of the present disclosure.
As shown in figure 5 of the drawings,H is andH ip (i =1,2, 3) are respectively tooth crests of gear teeth 1,2 and 3 of the driving wheel and the driven wheel, under the working conditions of high speed or/and heavy load, the elastic deformation of the gear meshing tooth pair can lead the tooth pair 1 which does not participate in the meshing process in theory to enter into meshing in advance, namely the phenomenon of line external meshing, at the moment, the driven wheel rotates a certain angle through deformation and is recorded as angleH 1p O P I. As shown in fig. 5θ 0 Is a deformed rotation angle, I is a meshing point corresponding to the deformed driven wheel,θ p the tooth top center and the tooth center of the driven wheel 2 and the driven wheel 3O P The included angle of (a).
In the above embodiment, the online external meshing condition and the tooth-to-tooth separation distance at the tooth back meshing time in the actual meshing process are analyzed by the gear pair online external meshing analysis model, and the difference and relationship between the actual meshing process and the theoretical meshing process can be known by the analysis model, so that an actual calculation parameter is provided for calculating the tooth back stiffness, and the accuracy of the tooth back meshing stiffness calculated subsequently is higher.
104. And determining the tooth pair separation distance of the tooth back side according to the radius of the gear base circle and the deformation angle of the tooth back side gear.
In some embodiments, before determining the back-side tooth pair separation distance based on the gear base radius and the deformation angle of the back-side gear, further comprising: calculating a load angle of the meshing gear according to the number of the gear teeth, a reference circle pressure angle at the back side of the gear and a meshing position pressure angle;
illustratively, the meshing tooth load angle of FIG. 4 can be calculated based on the number of gear teeth, the pitch circle pressure angle on the tooth back side, and the meshing position pressure angle
Tool for measuringThe body expression is:
in the above (10)z、αRespectively the number of teeth of the gear and the pressure angle of the reference circle. If it is usedR s <RThe formula (10) is given with a plus sign ifR s ≥RThe formula (10) is represented by the symbol "-".R s AndRrespectively the tooth center distance and the reference circle radius at the meshing point S.
In some embodiments, based on the deformation angle of the tooth back side gear and the base radius of the driven wheel determined in step 103, the separation distance of the current deformed tooth pair 1 can be found as:R bp *∠H 1p O P I. WhereinR bp The base radius of the driven wheel. The separation distance of a particular deformed tooth pair 1 is calculated as follows:
local coordinate system, see FIG. 5x 2 -O j -y 2 Lower partH ij (i=1，2，3，j=s，p) The coordinates of (a) are:
in the above-mentioned (11), the first step,
expressed as the tooth crest coordinates of the meshing gear teeth in an arbitrary local coordinate system,
the matrix can be calculated from the following equation:
in the above-mentioned (12), the first step of the method,θ j =2(2-i)π/z j is the included angle of the symmetric line of adjacent gear teeth of the gear.z j The number of teeth of the main driving wheel and the driven wheel of any gear is provided.
Local coordinate system of driving wheelx 2 -O s -y 2 And local coordinate system of driven wheelx 2 -O p -y 2 The coordinate transformation relationship between the two is as follows:
wherein the content of the first and second substances,
representing coordinates in a local coordinate system of the driven wheel,
the coordinate in the local coordinate system of the driving wheel is represented, and each matrix in the formula (13) can be calculated by the following formula:
in the above-mentioned formula (14),α 0 is the pitch circle pressure angle of the gear pair.
Using the theory of gear geometry in conjunction with FIG. 5H ij (i=1，2，3，j=s，p)、O s 、O p Coordinate system of equal points in localx 2 -O j -y 2 The following coordinates may be obtained when the tooth pair 1 enters the meshing moment in advance, and the separation distance of the tooth pair 1 is:
in the above formula (15)α H s1 Andα H p1 respectively at the driven wheelH s1 And pointH p1 The pressure angle of (d).
Similarly, with reference to the above calculation process, the separation distances of other tooth pairs can be obtained.
105. The tooth back side mesh stiffness is determined based on the tooth back side tooth pair separation distance.
In some embodiments, determining the tooth back side mesh stiffness based on the tooth back side tooth pair separation distance comprises: the tooth back mesh stiffness is determined based on the tooth back tooth-to-tooth separation distance and the meshing tooth load angle. That is, the tooth back side mesh stiffness can be calculated from the tooth back side tooth pair separation distance calculated in equation (15) and the meshing tooth load angle calculated in equation (10) in step 104.
FIG. 6 is a diagram of method steps for determining gear tooth backside meshing stiffness based on tooth backside tooth-to-tooth separation distance provided by an embodiment of the present disclosure.
As shown in fig. 6, the method for determining gear tooth backside meshing stiffness based on tooth backside tooth to separation distance includes, but is not limited to, the steps of:
601. a mesh stiffness component corresponding to a target potential energy stored on the back-of-tooth engaging tooth is determined based on the engaging tooth load angle.
In some embodiments, the meshing stiffness component corresponding to the target potential energy stored on the back of the tooth engaging tooth is determined based on the meshing cog load angle calculated by equation (10) above in step 104.
In some embodiments, the step of calculating the tooth back side mesh stiffness based specifically on the tooth back side separation distance and the meshing tooth load angle may comprise: determining a mesh stiffness component corresponding to a target potential energy stored on the back-of-tooth engaging tooth based on the engaging tooth load angle; the target potential energy includes: hertzian contact potential energy, bending potential energy, radial compression potential energy, and shear potential energy;
illustratively, during engagement, the potential energy stored on the primary and secondary drive wheel engagement teeth includes four components: hertzian contact potential energy
Bending potential energy
Radial compression potential energy
And shear potential energy
. The four parts of potential energy respectively correspond to the Hertz contact rigidity
Bending stiffness
Radial compression stiffness
And shear stiffness
The following can be obtained by material mechanics:
in the above-mentioned (16) to (19),E、lrespectively the elastic modulus and the tooth width of the gear,α 1 in order to provide a gear tooth load angle,α 2 the included angle between the tooth profile starting point-tooth center connecting line and the tooth center line is formed. Whereinα 1 Representative is the load angle of the meshing teeth calculated by equation (10) above.
602. The base body deformation stiffness of the tooth back side is determined based on the meshing tooth load angle.
In some embodiments, the base deformation stiffness of the tooth back side comprises: the product of the coefficient of deformation correction at the tooth back side and the base stiffness corresponding to the base deformation portion at the tooth back side, or the base stiffness corresponding to the base deformation portion.
In some embodiments, during the meshing process of the gears, the gear base body also deforms to a certain degree, and the rigidity corresponding to the deformation of the gear base body is the rigidity of the gear base body
This can be obtained by the following equation:
in the above-mentioned (20), the first step,
the distance from the meshing line and the focus of the symmetric line of the gear teeth to the root circle,α 1 in order to provide a gear tooth load angle,
is a base circular arc corresponding to the whole tooth profile of the gear.L*、M*、P*AndQ*for coefficients, the following polynomial equation can be used:
in the above-mentioned (21), the first step,
means that:L*、M*、P*andQ*，A、B、C、D、EandFthe values are detailed in table 1,h f =r f /r int ，r f the radius of the tooth root circle is the radius of the tooth root circle,r int is the radius of the gear shaft hole,
is the central angle of the tooth profile of the gear.
TABLE 1
603. And determining the meshing rigidity of the meshing tooth pair based on the meshing rigidity component corresponding to the target potential energy.
In some embodiments, the meshing stiffness of the meshing tooth pair is determined based on the meshing stiffness component corresponding to the target potential energy, that is, the meshing stiffness of the meshing tooth pair can be determined by the meshing stiffness component corresponding to the target potential energy on the tooth back side meshing tooth obtained by equations (16) to (19) in step 601, and the specific expression is:
in the above-mentioned (22), the first step,
representing the stiffness of the meshing of the tooth pair i,
representing the radial compression stiffness of the driving and driven wheels,
representing the bending rigidity of the driving and driven wheels,
Representing the shear stiffness of the driving and driven wheels.
604. The meshing load of each meshing tooth pair is determined based on the tooth back side tooth pair separation distance, the meshing stiffness of the meshing tooth pair, and the gear torque.
In some embodiments, determining the backside meshing stiffness based on the backside tooth pair separation distance, the meshing stiffness of the meshing tooth pair, and the gear torque comprises: determining the meshing load of each meshing tooth pair based on the tooth back side tooth pair separation distance, the meshing rigidity of the meshing tooth pair and the gear torque; wherein the meshing load of each meshing tooth pair refers to the meshing load distributed by the respective tooth pair of the gear pair.
In some embodiments, when the elastic deformation of the gear is greater than the separation distance of the tooth pair, the gear pair may actually engage the tooth pair that is not engaged in theory, that is, the gear pair may be engaged out of line. At this time, the tooth pair separation distance of the plurality of pairs of meshing teeth is obtained from the above equation (10), and the meshing stiffness of the meshing tooth pair calculated by the above equation (22) is obtained by obtaining the meshing load distributed to each tooth pair of the gear pair by the following equation (23):
in the above (23)R bs The radius of the base circle of the driving wheel,F i is a firstiThe meshing load distributed to the pair of teeth,i=1，2，，，n，nis an integer greater than or equal to 1,
is the torque of the rotation of the driving wheel.
Is formed by a pair of teeth 1,2,nthe separation distance of (a).
605. The actual pair of meshing teeth is determined from the pair of meshing teeth based on the meshing load of each pair of meshing teeth.
In some embodiments, the actual pair of engaging teeth is determined from the pair of engaging teeth based on the engaging load of each pair of engaging teeth; that is, the tooth back side tooth pair separation distance and the tooth pair meshing rigidity calculated by the expressions (15) and (22) are substituted into the expression (23) in step 604, and the meshing load assigned to each tooth pair can be obtained when the second step is executediLoad of engagement distributed to tooth pairsF i When the number is less than or equal to 0, the corresponding parameter is removed in the formula (23), and the calculation is carried out again until the tooth pair number which finally participates in the meshing is determined.
606. And determining the meshing stiffness of the tooth back side based on the meshing stiffness of the actual meshing tooth pair and the base deformation stiffness of the tooth back side.
In some embodiments, the meshing stiffness expression of the back side meshing stiffness of the pinion is obtained from the meshing stiffness component corresponding to the target potential energy calculated in step 601, the base deformation stiffness of the back side of the tooth calculated in step 602, the meshing stiffness of the meshing tooth pair calculated in step 603, and the actual meshing tooth pair calculated in step 605:
in the above-mentioned formula (24),nis the number of pairs of teeth that are engaged,ε j (j=s，p) The base deformation correction coefficient, which is generally 1.1,k i (t) Is a pair of teethiThe rigidity of the meshing is improved,
the rigidity of the base body corresponding to the deformed part of the driving wheel,
the rigidity of the base body corresponding to the deformed part of the driven wheel.
In the above embodiment, not only the condition of gear meshing deformation is analyzed, but also parameters such as tooth back side tooth pair separation distance, meshing stiffness of a meshing tooth pair and actual meshing tooth pair equivalent in the actual meshing process, which correspond to the target potential energy in the driving traction wheel, are calculated through the analysis process, and the back side meshing stiffness of the secondary gear tooth in the actual meshing process is calculated based on the parameters, so that the calculated back side meshing stiffness of the gear is more accurate.
Illustratively, based on the method for determining meshing stiffness of the back side of a spur gear according to the present application, an example of calculating the meshing stiffness of the back side of a secondary spur gear of a single-stage spur gear is shown in table 2.
TABLE 2
After gear parameters and materials are selected based on the table 2, an algorithm program is written through matlab, and a result is obtained.
As shown in fig. 7, which is a simulation diagram showing the change of the pairs of the meshing teeth on the driving side and the back side of the gear pair of the single-stage spur gear with time, fig. 7 (a) shows the pairs of the meshing teeth on the driving side of the gear pair of the single-stage spur gearAs a function of time, (b) in fig. 7 shows a change of the number of pairs of back-side meshing teeth of the pinion spur gear of the single-stage spur gear with time. In fig. 7 (a) and 7 (b), the abscissa represents time in T, and the ordinate represents the number of meshing teeth in pairs. The number of meshing tooth pairs is 2 pairs each time the double teeth are meshed, and the meshing area of the double teeth on the driving side is [0 ]T，0.5T]，[1T，1.5T]，[2T，2.5T]Because of the influence of the meshing phase difference between the driving side and the tooth back side, the number of meshing teeth on the tooth back side has a delay compared with that on the driving side, and the meshing intervals of the double teeth are respectively [0.6 ]T，1.1T]，[1.6T，2.1T]，[1.6T，3.1T]。
As shown in fig. 8, the time-dependent change of the deformation angle corresponding to the separation distance of the driving side tooth pair of the gear pair is illustrated in fig. 8, (a) of fig. 8 shows the time-dependent change of the deformation angle corresponding to the separation distance of the driving side approach stage tooth pair of the gear pair, and (b) of fig. 8 shows the time-dependent change of the deformation angle corresponding to the separation distance of the driving side separation stage tooth pair of the gear pair. In fig. 8 (a) and 8 (b), the abscissa is time, the unit is T, the ordinate is the deformation angle, the unit is °, and in fig. 8 (a) the approach phase, the deformation angle corresponding to the drive side tooth separation distance is gradually changed from 0.04 ° to 0 °, and this is repeated in order. In the disengagement stage (b) of fig. 8, the deformation angle of the drive-side teeth with respect to the disengagement distance gradually changes from 0.01 ° to 0.04 °, and then gradually changes from 0 ° to 0.04 ° in this order.
As shown in fig. 9, a schematic diagram of a change over time of a deformation angle corresponding to a tooth pair separation distance of a gear pair back side, where (a) in fig. 9 shows a change over time of a deformation angle corresponding to a tooth pair separation distance in a tooth approaching stage of the gear pair back side, and (b) in fig. 9 shows a change over time of a deformation angle corresponding to a tooth pair separation distance in a tooth back side separating stage of the gear pair back side, where (a) in fig. 9 and (b) in fig. 9, an abscissa is time, an ordinate is a deformation angle, and an abscissa is a deformation angle, and an approximation stage (a) in fig. 9, and a deformation angle corresponding to a tooth pair separation distance in the tooth back side gradually changes from 0.008 ° to 0 ° and then sequentially changes from 0.04 ° to 0 °. In the separation stage (b) of fig. 9, the deformation angle of the back teeth with respect to the separation distance gradually changes from 0 ° to 0.04 °.
As can be seen from a comparison of the simulation results of fig. 8 and 9, the deformation angle of the back teeth with respect to the separation distance is different from the deformation angle change of the driving teeth with respect to the separation distance due to the influence of the meshing phase difference between the driving side and the back teeth, thereby indicating the rationality of considering the influence of the back teeth line external meshing.
As shown in FIG. 10, which is a simulation diagram of the meshing stiffness of the back side of the tooth in the actual gear meshing process obtained by the invention, as shown in FIG. 10, the abscissa is time and the unit is T, the ordinate is the meshing stiffness and the unit is N/m, and in FIG. 10, the actual double-tooth meshing zone of the back side of the secondary gear is [0.4 ]T，1.2T]，[1.4T，2.2T]，[2.4T，3.2T]And the theoretical double-tooth meshing zone at the back side of the secondary gear teeth shown in figure 7 is 0.6T，1.1T]，[1.6T，2.1T]，[1.6T，3.1T]。
Comparing fig. 7 and fig. 10, the results show that the actual double-tooth meshing area of the tooth back side under the influence of the off-line meshing is larger than the theoretical double-tooth meshing area by 60%. Thus, the line out-of-line mesh has no negligible effect on the gear tooth back-side mesh, especially under load or/and high speed conditions.
In the embodiment, the meshing rigidity of the tooth back side under the actual meshing condition of a single-stage spur gear is calculated based on the scheme of the application, and the rationality of the application is verified by analyzing the difference between the actual gear meshing result and the theoretical result.
Fig. 11 is a device for determining the meshing stiffness of the back side of a tooth according to an embodiment of the present disclosure, as shown in fig. 11, the device including:
an obtaining module 1101, configured to obtain a tooth back side meshing position coordinate;
the determining module 1102 is configured to determine an actual tooth crest coordinate of the tooth back side meshing tooth according to the tooth back side meshing position coordinate and the tooth top circle pressure angle. And determining the deformation angle of the gear on the tooth back side according to the actual tooth top coordinate on the tooth back side and the standard tooth top coordinate of the meshing tooth on the tooth back side. And determining the tooth back side tooth pair separation distance according to the gear base circle radius and the deformation angle of the tooth back side gear, and determining the tooth back side meshing rigidity based on the tooth back side tooth pair separation distance.
In some embodiments, the obtaining module 1101 is specifically configured to: calculating a meshing phase difference between the tooth back side and the drive side; determining the meshing position coordinate of the tooth back side according to the meshing phase difference and the meshing point coordinate of the tooth back side; the tooth back side meshing position coordinate is a coordinate in a local coordinate system corresponding to the tooth back side, or the tooth back side meshing position coordinate is a coordinate in a global coordinate system corresponding to the driving side.
In some embodiments, the determining module 1102 is specifically configured to: according to tooth back side meshing position coordinates and a gear tooth top circle pressure angle, actual tooth top coordinates of the tooth back side meshing teeth are determined, and the method comprises the following steps: determining a perpendicular line passing through an engagement line of the tooth back side engagement position coordinates and a target connecting line of the tooth back side engagement position coordinates and the tooth center coordinates; determining an angle formed by the vertical line and the target connecting line as an engagement position pressure angle; and determining the actual tooth crest coordinate of the back side meshing tooth according to the meshing position pressure angle and the gear tooth crest circle pressure angle.
In some embodiments, before determining the back side tooth pair separation distance based on the gear base radius and the deformation angle of the back side gear, the determining module 1102 is further configured to: calculating a load angle of the meshing gear according to the number of the gears, the reference circle pressure angle on the back side of the gear and the meshing position pressure angle; the determining module 1102 is specifically configured to: determining the tooth back flank mesh stiffness based on a tooth back flank tooth-pair separation distance and the meshing gear tooth load angle.
In some embodiments, the determining module 1102 is specifically configured to: determining a mesh stiffness component corresponding to a target potential energy stored on a back-of-tooth engaging tooth based on the engaging tooth load angle; the target potential energy includes: hertzian contact potential energy, bending potential energy, radial compression potential energy, and shear potential energy; determining a base deformation stiffness of a tooth back side based on the meshing tooth load angle; determining the meshing rigidity of the meshing tooth pair based on the meshing rigidity component corresponding to the target potential energy; determining the tooth back side meshing stiffness based on a tooth back side tooth pair separation distance, a meshing stiffness of the meshing tooth pair, and a gear torque.
In some embodiments, the determining module 1102 is specifically configured to: determining a meshing load of each meshing tooth pair based on the tooth back side tooth pair separation distance, the meshing stiffness of the meshing tooth pair, and the gear torque; determining an actual pair of meshing teeth from said pair of meshing teeth based on the meshing load of each said pair of meshing teeth; and determining the meshing rigidity of the tooth back side based on the meshing rigidity of the actual meshing tooth pair and the deformation rigidity of the base body of the tooth back side.
In some embodiments, the base deformation stiffness of the tooth back side comprises: the product of the coefficient of deformation correction at the tooth back side and the base stiffness corresponding to the base deformation portion at the tooth back side, or the base stiffness corresponding to the base deformation portion.
Fig. 12 is a schematic diagram of a hardware structure of an electronic device according to an embodiment of the present disclosure, where the electronic device includes: a processor 1201, a memory 1202 and a computer program stored on the memory 1202 and executable on the processor 1201 realize the method of determining gear tooth backside meshing stiffness described in the above embodiments when the computer program is executed by the processor 1201.
A computer readable storage medium having a computer program stored thereon is also provided. The computer-readable storage medium may be included in the electronic device described in the above embodiment, or may exist separately. The computer program, when executed by a processor, implements the processes of the method for determining gear tooth backside meshing stiffness described above, and achieves the same technical effects, and is not described herein again to avoid repetition.
Based on the same inventive concept, the embodiment of the present application further provides a computer program product, when the computer program product runs on a computer, the computer program product enables the computing device to implement the method for determining the meshing stiffness of the gear tooth back side provided by the above embodiment.
As will be appreciated by one skilled in the art, embodiments of the present application may be provided as a method, system, or computer program product. Accordingly, the present application may take the form of an entirely hardware embodiment, an entirely software embodiment or an embodiment combining software and hardware aspects. Furthermore, the present application may take the form of a computer program product embodied on one or more computer-usable storage media having computer-usable program code embodied in the medium.
The Processor may be a Central Processing Unit (CPU), other general purpose Processor, a Digital Signal Processor (DSP), an Application Specific Integrated Circuit (ASIC), an off-the-shelf Programmable Gate Array (FPGA) or other Programmable logic device, discrete Gate or transistor logic, discrete hardware components, etc. A general purpose processor may be a microprocessor or the processor may be any conventional processor or the like.
The memory may include forms of volatile memory in a computer readable medium, random Access Memory (RAM) and/or non-volatile memory, such as Read Only Memory (ROM) or flash memory (flash RAM). The memory is an example of a computer-readable medium.
Computer readable media include both permanent and non-permanent, removable and non-removable storage media. Storage media may implement information storage by any method or technology, and the information may be computer-readable instructions, data structures, modules of a program, or other data. Examples of computer storage media include, but are not limited to, phase change memory (PRAM), static Random Access Memory (SRAM), dynamic Random Access Memory (DRAM), other types of Random Access Memory (RAM), read Only Memory (ROM), electrically Erasable Programmable Read Only Memory (EEPROM), flash memory or other memory technology, compact disc read only memory (CD-ROM), digital Versatile Discs (DVD) or other optical storage, magnetic cassettes, magnetic disk storage or other magnetic storage devices, or any other non-transmission medium that can be used to store information that can be accessed by a computing device. As defined herein, a computer readable medium does not include a transitory computer readable medium such as a modulated data signal and a carrier wave.
Finally, it should be noted that: the above embodiments are only used for illustrating the technical solutions of the present application, and not for limiting the same; although the present application has been described in detail with reference to the foregoing embodiments, it should be understood by those of ordinary skill in the art that: the technical solutions described in the foregoing embodiments may still be modified, or some or all of the technical features may be equivalently replaced; and the modifications or the substitutions do not make the essence of the corresponding technical solutions depart from the technical solution scope of the embodiments of the present application.
Claims (10)
1. A method of determining gear tooth backside mesh stiffness, comprising:
acquiring meshing position coordinates of the back side of the tooth;
determining actual tooth top coordinates of the tooth back side meshing teeth according to the tooth back side meshing position coordinates and the tooth top circle pressure angle;
determining the deformation angle of the gear on the back side according to the actual tooth top coordinate of the meshing gear on the back side and the standard tooth top coordinate of the meshing gear on the back side;
determining the tooth back side tooth pair separation distance according to the gear base circle radius and the deformation angle of the tooth back side gear;
the tooth back side mesh stiffness is determined based on the tooth back side tooth pair separation distance.
2. The method of claim 1, wherein said acquiring tooth back side engagement position coordinates comprises:
calculating a meshing phase difference between the tooth back side and the drive side;
determining the meshing position coordinate of the tooth back side according to the meshing phase difference and the meshing point coordinate of the tooth back side;
the tooth back side meshing position coordinate is a coordinate in a local coordinate system corresponding to the tooth back side, and the tooth back side meshing position coordinate is a coordinate in a global coordinate system corresponding to the driving side.
3. The method of claim 1, wherein said determining actual addendum coordinates of a back-side engaging tooth based on the tooth back-side engagement position coordinates and a tooth tip circle pressure angle comprises:
determining a perpendicular line passing through an engagement line of the tooth back side engagement position coordinates and a target connecting line of the tooth back side engagement position coordinates and the tooth center coordinates;
determining an angle formed by the vertical line and the target connecting line as an engagement position pressure angle;
and determining the actual tooth crest coordinate of the back side meshing tooth according to the meshing position pressure angle and the gear tooth crest circle pressure angle.
4. The method of claim 1, wherein prior to determining the back side tooth pair separation distance based on the gear base radius and the deformation angle of the back side gear, further comprising:
calculating a load angle of the meshing gear according to the number of gear teeth, a reference circle pressure angle at the back side of the gear and a meshing position pressure angle;
said determining a tooth back side mesh stiffness based on a tooth back side tooth pair separation distance comprises:
determining the tooth back side mesh stiffness based on a tooth back side tooth-to-tooth separation distance and the meshing gear tooth load angle.
5. The method of claim 4, wherein said determining said back side tooth mesh stiffness based on a back side tooth pair separation distance and said meshing tooth load angle comprises:
determining a mesh stiffness component corresponding to a target potential energy stored on a back-of-tooth mesh tooth based on the mesh tooth load angle; the target potential energy comprises: hertzian contact potential energy, bending potential energy, radial compression potential energy, and shear potential energy;
determining a base deformation stiffness of a tooth back side based on the meshing tooth load angle;
determining the meshing rigidity of the meshing tooth pair based on the meshing rigidity component corresponding to the target potential energy;
determining the tooth back side mesh stiffness based on the tooth back side pair separation distance, the mesh stiffness of the mesh pair, and a gear torque.
6. The method of claim 5, wherein said determining said back-tooth meshing stiffness based on said back-tooth pair separation distance, said meshing stiffness of said meshing pair, and a gear torque comprises:
determining a meshing load of each meshing tooth pair based on the tooth back side tooth pair separation distance, the meshing stiffness of the meshing tooth pair, and the gear torque;
determining an actual pair of meshing teeth from said pair of meshing teeth based on the meshing load of each said pair of meshing teeth;
and determining the meshing stiffness of the tooth back side based on the meshing stiffness of the actual meshing tooth pair and the base deformation stiffness of the tooth back side.
7. The method of claim 6,
the tooth back side matrix deformation stiffness comprises: the product of the coefficient of deformation correction at the tooth back side and the base stiffness corresponding to the base deformation portion at the tooth back side, or the base stiffness corresponding to the base deformation portion.
8. An apparatus for determining gear tooth backside meshing stiffness, comprising:
the acquisition module is used for acquiring the meshing position coordinates of the back side of the tooth;
the determining module is used for determining the actual tooth crest coordinate of the tooth back side meshing tooth according to the tooth back side meshing position coordinate and the tooth top circle pressure angle;
determining the deformation angle of the gear on the tooth back side according to the actual tooth top coordinate of the meshing tooth on the tooth back side and the standard tooth top coordinate of the meshing tooth on the tooth back side;
determining the tooth back side tooth pair separation distance according to the gear base circle radius and the deformation angle of the tooth back side gear;
the tooth back side mesh stiffness is determined based on the tooth back side tooth pair separation distance.
9. An electronic device, comprising: a processor, a memory and a computer program stored on the memory and executable on the processor, the computer program, when executed by the processor, implementing a method of determining a gear tooth back side mesh stiffness as claimed in any one of claims 1 to 7.
10. A computer-readable storage medium, comprising: the computer-readable storage medium has stored thereon a computer program which, when being executed by a processor, carries out the method of determining a gear tooth flank meshing stiffness according to any one of claims 1 to 7.
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