CN113158479B - Cylindrical gear transmission efficiency calculation method, computer device and readable storage medium - Google Patents
Cylindrical gear transmission efficiency calculation method, computer device and readable storage medium Download PDFInfo
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Abstract
The invention relates to a cylindrical gear transmission efficiency calculation method, a computer device and a readable storage medium. The method comprises the following steps: step A: establishing a cylindrical gear loading contact analysis model considering friction influence, setting the friction coefficient of a gear pair as mu, and calculating tooth surface deformation of the gear pair under the theoretical meshing condition; and (B) step (B): calculating a gear engagement area after considering the out-of-line engagement effect according to the tooth surface deformation; step C: the gear pair load distribution and transmission efficiency taking into account the effect of out-of-line meshing are calculated. The invention provides a transmission efficiency calculation method considering the influence of external wire engagement, which can calculate the load distribution and transmission efficiency of gears under actual working conditions more accurately by considering the influence of external wire engagement, friction and other factors, and provides guidance for the design of cylindrical gears.
Description
Technical Field
The invention relates to the technical field of gears, in particular to a calculation method of cylindrical gear transmission efficiency, a computer device and a readable storage medium.
Background
With the rapid development of society, energy safety and environmental protection are widely paid attention to. The transmission efficiency is one of key performance indexes of an automobile transmission system, and the improvement of the transmission efficiency can effectively reduce automobile emission and reduce pollution. The cylindrical gear is one of common parts in an automobile transmission system, and the key for calculating the overall efficiency of the transmission system is to accurately calculate the transmission efficiency of a pair of cylindrical gears.
At present, a relatively widely used method for calculating the tooth surface load distribution is load contact analysis (LTCA) based on a Hertz contact method, and the method has the defect that the friction force is not considered and is inconsistent with the actual gear working condition.
At present, an empirical formula is mostly adopted for calculating the transmission efficiency of the cylindrical gear, and the out-of-line meshing phenomenon caused by tooth surface deformation in the actual meshing process of the gear cannot be considered. The instantaneous gear engagement efficiency is increased at the engagement and disengagement timings after the influence of the out-of-line engagement is considered.
Disclosure of Invention
In view of the above, the present invention aims to provide a method for calculating the transmission efficiency of a cylindrical gear, a computer device and a readable storage medium, so as to calculate the load distribution and the transmission efficiency of the gear under the actual working conditions more accurately, and provide more accurate guidance for the design of the cylindrical gear.
The invention firstly provides a method for calculating gear transmission efficiency, which comprises the following steps:
step A: establishing a cylindrical gear loading contact analysis model considering friction influence, setting the friction coefficient of a gear pair as mu, and calculating tooth surface deformation of the gear pair under the theoretical meshing condition;
and (B) step (B): calculating the actual meshing area of the gear after considering the external meshing effect of the line according to the tooth surface deformation;
step C: the gear pair load distribution and transmission efficiency taking into account the effect of out-of-line meshing are calculated.
According to one embodiment of the invention, the friction coefficient μ of the gear pair is a constant friction coefficient or a time-varying friction coefficient.
According to one embodiment of the present invention, the step a, taking into account the friction influence, of the loaded contact calculation analysis model equally divides the meshing process of the gear pair into N calculation steps, and the calculation process for each calculation step includes:
step A1: calculating a theoretical meshing line and a corresponding theoretical meshing point of the gear according to the basic parameters of the gear;
step A2: calculating a tooth surface reduction stiffness matrix of the gear;
step A3: the deformation coordination equation is satisfied at each meshing point of each calculation step;
step A4: each meshing line of each calculation step satisfies a load balancing equation;
step A5: satisfying a contact pressure convergence equation at each engagement point of each calculation step;
step A6: and (3) carrying out iterative solution on the steps A3 to A5 by utilizing a Newton-Laporthelson method until three equations in the steps A3 to A5 are converged, and reading the tooth surface deformation delta of each calculation step.
According to one embodiment of the invention, the deformation coordination equation satisfied at each engagement point is:
δ b +δ s +δ c -(Z-d 0 )＜ε 1
wherein Z is the rigid body rotation of the gear, d 0 Is the initial clearance of the gear, epsilon 1 Is a convergence tolerance;
δ b is tooth surface bending deformation:
δ b ＝([R 1 ]+[R 2 ])·({F N }+{F f })·n p
R 1 and R is 2 To calculate a compliance matrix from the reduced stiffness matrix, n p As normal vector at tooth-surface engagement point, F N F is the tooth surface normal contact force f Is tooth surface friction force delta c For tooth-surface contact deformation, delta s Is the shear deformation of the tooth surface.
In E 1 And E is 2 Is the elastic modulus of the driving gear and the driven gear, v 1 And v 2 Poisson ratio, h, of the driving and driven gears 1 And h 2 Is the main partDistance between contact point of moving gear and driven gear and gear center line, b f Is the hertz contact half width and l is the contact line length.
According to one embodiment of the invention, the load balancing equation satisfied by each meshing line is:
where m is the number of contact lines per calculation step, n is the number of aliquoting contact points on each contact line, r is the position vector of the contact points, p is the axial vector of the drive gear, T load Is the load torque, epsilon, on the driven gear determined by the load condition 2 Is a convergence tolerance;
the contact pressure convergence equation satisfied at each meshing point is:
Ph k -Ph k-1 ＜ε 3
wherein Ph is k Is the maximum contact pressure of the tooth surface on the kth contact line, ph k-1 For maximum contact pressure on the (k-1) th contact line, ε 3 To converge tolerances.
According to one embodiment of the present invention, the step B includes the steps of:
step B1: reading tooth surface deformations at theoretical engagement start and end points, i.e. deformation of engagement section line external engagement end point and engagement section line external engagement start point, from the calculation result of step A, which are respectively denoted as delta 1 And delta 2 ；
Step B2: calculating the actual engagement start point and engagement end point after considering the line external engagement phenomenon, and dividing the line external engagement area of the engagement section into N 1 The outside line engagement area of the engagement section is divided into N 2 And (3) step (c).
According to one embodiment of the present invention, the calculation process for each calculation step includes:
step C1: calculating the meshing point of the two-section line external meshing area;
step C2: the deformation coordination equation after the out-of-line engagement factors are considered is satisfied at each engagement point of each calculation step;
step C3: the meshing line of each calculation step meets a load balance equation;
step C4: satisfying a contact pressure convergence equation at each meshing line of each calculation step;
step C5: and (3) carrying out iterative solution on the steps C2 to C4 by utilizing a Newton-Laporthelson method until three equations in the steps C2 to C4 are converged, and obtaining the load distribution and the transmission efficiency of the complete meshing process.
According to one embodiment of the invention, the deformation coordination equation after the consideration of the out-of-line engagement factor satisfied at each engagement point is:
δ b +δ s +δ c +δ sd -(Z-d 0 )＜ε 1
according to one embodiment of the invention, the load balancing equation satisfied at each line of engagement is:
the contact pressure convergence equation satisfied at each meshing line is:
Ph k -Ph k-1 ＜ε 3
wherein Z is the rigid body rotation of the gear, d 0 Is the initial gear play, delta b Is the bending deformation of tooth surface delta s Is the tooth surface shear deformation, delta c For tooth-surface contact deformation, delta sd Is the tooth surface deformation of the engaging and the engaging section epsilon 1 To converge the tolerance, m is the number of contact lines per calculation step, n is the number of aliquoting contact points on each contact line, r is the position vector of the contact points, p is the axial vector of the driving gear, T load For load torque, ε, on driven gear determined by load conditions 2 To converge tolerance, ph k For maximum contact pressure of tooth surface on kth contact line, ph k-1 For maximum contact pressure on the (k-1) th contact line, ε 3 To converge tolerances.
The invention also provides a computer device, which comprises a memory and a processor; the memory is used for storing a computer program; the processor is configured to implement the gear transmission efficiency calculation method when executing the computer program.
The invention also proposes a computer storage medium having a computer program stored thereon, which, when executed by a processor, implements the method of calculating gear transmission efficiency.
The invention provides a calculation method of the cylindrical gear transmission efficiency, which can consider the influence of external engagement, can calculate the load distribution and the transmission efficiency of the gear under the actual working condition more accurately, provides more accurate guidance for the design of the cylindrical gear, and further improves the transmission efficiency. The method is applied to design the automobile transmission system in practical application, can effectively improve the transmission efficiency index of the product, reduce the automobile emission and reduce pollution.
Drawings
FIG. 1 is a schematic diagram of a theoretical meshing line according to an embodiment of the present invention;
FIG. 2 is a graph showing the contact line calculation results according to an embodiment of the present invention;
FIG. 3 is a graph showing the calculation result of the load distribution of the tooth surface according to an embodiment of the present invention;
FIG. 4 is a graph showing the tooth surface deformation calculation result according to an embodiment of the present invention;
FIG. 5 is a schematic view of an external engagement area of an engagement line according to an embodiment of the present invention;
FIG. 6 is a schematic view of an external engagement area of an engaged wire according to an embodiment of the present invention;
FIG. 7 is a diagram illustrating the calculation results of the instant engagement efficiency according to an embodiment of the present invention.
Detailed Description
The preferred embodiments of the present invention will be described in detail below with reference to the attached drawings, so that the objects, features and advantages of the present invention will be more clearly understood. It should be understood that the embodiments shown in the drawings are not intended to limit the scope of the invention, but rather are merely illustrative of the true spirit of the invention.
Aiming at the defect that the conventional cylindrical gear transmission efficiency calculation method cannot consider the influence of external wire meshing, the invention provides a calculation method of the cylindrical gear transmission efficiency, which can consider the influence of external wire meshing so as to guide the design of gears, further improve the transmission efficiency, and effectively reduce the emission of automobiles and reduce pollution in practical application.
In consideration of the friction force effect between two mutually meshed tooth surfaces in the actual running process of the gear, when the cylindrical gear transmission efficiency is calculated, the tooth surface load distribution is obtained through the gear tooth loading contact analysis (Frictional Loaded Tooth Contact Analysis, FLTCA) considering the friction force, and the cylindrical gear transmission efficiency considering the influence of the out-of-line meshing phenomenon is calculated.
In order to achieve the above purpose, the invention adopts the following technical scheme that a calculation method for influencing the transmission efficiency of a cylindrical gear by considering the out-of-line meshing phenomenon mainly comprises the following three steps:
step A: and establishing a friction-considered cylindrical gear loading contact analysis model, setting the friction coefficient of the gear pair as mu (which can be a constant friction coefficient or a time-varying friction coefficient), and calculating the tooth surface deformation of the gear pair under the condition of not considering out-of-line engagement.
And (B) step (B): the actual meshing area of the gears after considering the influence of the out-of-line meshing is calculated.
Step C: the gear pair load distribution and transmission efficiency taking into account the effect of out-of-line meshing are calculated.
Further, in step a, the loaded contact calculation analysis model taking into consideration friction equally divides the meshing process of the gear pair into N calculation steps, and the calculation process for each calculation step is as follows:
step A1: calculating a theoretical meshing line and a corresponding theoretical meshing point of the gear according to the basic parameters of the gear;
step A2: calculating a gear tooth surface reduction stiffness matrix:
where K is the stiffness matrix of the gear established, K r A reduced stiffness matrix after polycondensation for tooth surfaces;
step A3: the deformation coordination equation should be satisfied at each engagement point of each calculation step:
δ b +δ s +δ c -(Z-d 0 )＜ε 1 (2)
wherein Z is the rigid body rotation of the gear, d 0 Is the initial clearance of the gear epsilon 1 Is a very small positive number, delta, for convergence tolerance b Is tooth surface bending deformation:
δ b ＝([R 1 ]+[R 2 ])·({F N }+{F f })·n p (3)
R 1 and R is 2 To reduce the rigidity matrix K r Calculated compliance matrix, n p Is the normal vector at the tooth flank engagement point. F (F) N F is the tooth surface normal contact force f The tooth surface friction force is obtained by the following relation:
F f ＝μF N (4)
δ c for tooth-surface contact deformation, delta s For tooth surface shear deformation, the calculation formula is:
in E 1 And E is 2 Is the elastic modulus of the driving gear and the driven gear, v 1 And v 2 Poisson ratio, h, of the driving and driven gears 1 And h 2 Is the distance between the contact point of the driving gear and the driven gear and the center line of the gear, b f Is the hertz contact half width and l is the contact line length.
Step A4: each meshing line of each calculation step should satisfy the load balancing equation:
where m is the number of contact lines per calculation step, n is the number of aliquoting contact points on each contact line, r is the position vector of the contact points, p is the axial vector of the drive gear, T load Is the load torque, epsilon, on the driven gear determined by the load condition 2 Is a very small positive number, which is the convergence tolerance.
Step A5: the contact pressure convergence equation should be satisfied at each engagement point of each calculation step:
Ph k -Ph k-1 ＜ε 3 (7)
wherein Ph is k Is the maximum contact pressure of the tooth surface on the kth contact line, ph k-1 For maximum contact pressure on the (k-1) th contact line, ε 3 Is a very small positive number, which is the convergence tolerance.
Step A6: and (3) carrying out iterative solution on the steps A3 to A5 by utilizing a Newton-Laporthelson method until three equations are converged, and reading the tooth surface deformation delta of each calculation step.
After the influence of the external meshing factor is considered, the meshing line of the gear is not a theoretical meshing line any more, and the meshing line is prolonged in the meshing in area and the meshing out area. In order to accurately calculate the external engagement area of the engaged and engaged two-section line, the step B comprises the following steps:
step B1: and C, reading tooth surface deformation at the theoretical meshing starting point and the theoretical meshing end point from the calculation result of the step A, namely, deformation of the meshing section line external meshing end point and the meshing section line external meshing starting point. The deformations are denoted as delta respectively 1 And delta 2 。
Step B2: and calculating an actual engagement start point and an engagement end point after the out-of-line engagement phenomenon is considered. And dividing the line external engagement area of the engagement section into N 1 The outside line engagement area of the engagement section is divided into N 2 And (3) step (c).
After calculating the out-of-line engagement area, a complete engagement process is divided into N+N 1 +N 2 A calculation step for which load distribution and transmission efficiency are available for the complete engagement process, the calculation process for each calculation step comprising:
step C1: calculating a theoretical meshing point on a theoretical meshing lineThe engagement point is calculated in step A1, where it is necessary to calculate the engagement point of the two-wire outer engagement region, N 1 And N 2 A corresponding theoretical meshing point.
Step C2: the deformation coordination equation after considering the out-of-line engagement factor should be satisfied at each engagement point of each calculation step:
δ b +δ s +δ c +δ sd -(Z-d 0 )＜ε 1 (8)
wherein delta sd The tooth surface deformation of the meshing section and the tooth surface deformation of the meshing section are obtained through interpolation calculation according to the deformation of the theoretical meshing point and the theoretical meshing point, and the tooth surface deformation of the meshing section is obtained in the meshing section:
and (3) meshing out:
step C3: the load balancing equation should be satisfied at each line of engagement for each calculation step:
step C4: the contact pressure convergence equation should be satisfied at each meshing line of each calculation step:
Ph k -Ph k-1 ＜ε 3 (12)
step C5: and (3) carrying out iterative solution on the steps C2 to C4 by utilizing a Newton-Laporthelson method until all three equations are converged, and obtaining the load distribution and the transmission efficiency of the complete meshing process.
In the invention, the cylindrical gear comprises a straight-tooth cylindrical gear and a helical-tooth cylindrical gear, and the method is applicable to the gears in two forms.
The invention also provides a computer device, which comprises a memory and a processor; the memory is used for storing a computer program; the processor is configured to implement the gear transmission efficiency calculation method when executing the computer program.
The invention also proposes a computer storage medium having a computer program stored thereon, which, when executed by a processor, implements the method of calculating gear transmission efficiency.
The beneficial effects of the invention are as follows: compared with the existing calculation method, the method can calculate the load distribution and the transmission efficiency of the gear under the actual working condition more accurately by considering the influence of factors such as external wire engagement and friction, and provides guidance for the design of the cylindrical gear.
Examples
The gear parameters and load conditions used in this example are shown in table 1.
TABLE 1 gear design and operating parameters
The transmission efficiency calculation considering the external gear engagement of the gear pair specifically comprises the following steps:
step A: establishing a friction-considered cylindrical gear loading contact analysis model, dividing the complete meshing process into multiple steps, such as N=41 steps, wherein the friction coefficient of a gear pair is as follows:
table 2 table of coefficient of friction parameters
| b 1 | -8.916465 | b 2 | -0.354068 | b 3 | 0.752755 |
| b 4 | 1.03303 | b 5 | 2.812084 | b 6 | -0.390958 |
| b 7 | 1.036077 | b 8 | -0.100601 | b 9 | 0.620305 |
R is the relative curvature radius of tooth surface, V e Is the entrainment speed, SR is the slip ratio, ph is the maximum contact pressure of the tooth surface, v 0 Is the viscosity of the lubricating oil, and S is the average roughness of the tooth surface.
Step A1: the theoretical meshing line and the theoretical meshing point without taking the out-of-line meshing into consideration are calculated from the gear pair basic parameters of table 1. As shown in fig. 1, taking a theoretical meshing line corresponding to a tooth top E of the driving wheel as an example, the following calculation steps are taken:
can be found in ΔO by cosine law 1 O 2 E countCalculating to obtain r 2 Length of (2):
after the radial coordinates of each group of contact wires are calculated, each group of contact wires can be obtained, as shown in fig. 2.
Step A2: dividing the tooth surface into 2X 2 units and 9 nodes to obtain a tooth surface reduction stiffness matrix of the driving wheel and the driven wheel:
rigidity matrix K for reducing tooth surface of driving wheel r1 ＝[K r1a ,K r1b ,K r1c ]Wherein:
driven wheel tooth face reduced stiffness matrix K r2 ＝[K r2a ,K r2b ,K r2c ]Wherein:
step A3: taking the first iterative calculation of the first contact line as an example, an initial load F is set N ＝1N，F f =0.05n, tooth surface normal vector N p = (0,0.5105, -0.8599), the bending deformation can be calculated by:
the contact and shear deformation are calculated by the following formula:
wherein:
brings in the deformation coordination equation:
step A4: calculating the total load of the tooth surface at the moment:
step A5: calculating the contact pressure difference between the first step and the second step:
step A6: let the convergence tolerances of equations A3, A4, A5 be: epsilon 1 ＝0.0001，ε 2 ＝0.001，ε 3 =0.001, subject to iterative divisionSolving each contact line separately results in a tooth surface load distribution (shown by the broken line in fig. 3) without taking the out-of-line engagement into account, and a contact deformation (shown in fig. 4):
and (B) step (B): as shown in fig. 5 and 6, the actual gear is not on the theoretical meshing line during the meshing process, and the phenomenon of advance meshing or delay meshing occurs due to deformation of the tooth surface during the meshing and the meshing process. The calculation of the actual meshing line comprises the following steps:
step B1: the tooth surface deformation after the line external meshing phenomenon is not considered is calculated in the step A, and since the line external meshing phenomenon occurs in the two processes of gear meshing and gear meshing, the tooth surface deformation δ1=0.0217 mm and δ2= 0.02114mm at the theoretical meshing and gear meshing points can be read from fig. 4.
Step B2: and calculating an engagement start point and an engagement end point after the out-of-line engagement phenomenon is considered.
E' is a point on the outer meshing of the meshing section line, and when the meshing section line is meshed, the tooth top of the driving wheel participates in meshing, and the meshing point of the driven wheel is near the tooth root. To calculate the increase in the rotational angle of the drive wheel due to the out-of-line engagement, an initial value θ is first given 2 =0.1 rad, then:
at DeltaO 1 O 2 E can be calculated to obtain O 2 Length of E:
by sine theorem:
so the included angle between the E' point and the connecting line of the center of the gear is as follows:
at DeltaO 1 O 2 O can be calculated in E 2 Length of E':
by sine theorem:
the amount of change in the pressure angle between the theoretical engagement point end point and the actual engagement end point is:
Δα＝∠E′O 2 O 1 -∠EO 2 O 1 -θ 2 ＝0.0043rad (28)
the variation of the pressure angle can also be calculated according to the following formula:
obviously, the pressure angle variation calculated by the equation (28) and the equation (29) is not equal, because θ 2 The initial value is improperly selected, thus changing theta 2 And (4) carrying out iterative solution on the initial value until the calculation results of the pressure angle change quantity are consistent. Through four iterative calculations, θ is obtained 2 ＝0.0306rad，θ 1 ＝0.0459rad。
Step C: the load distribution and the transmission efficiency after the out-of-line engagement factors are considered are calculated, and the calculation process is as follows:
step C1: and calculating an engagement point in the actual engagement process, wherein the engagement point comprises three parts: external engagement area N of engaged section line 1 External engagement area N of engaged section line 2 Theoretical meshing line area N. The meshing point calculation method of the theoretical meshing line area is similar to the step A1. The theoretical meshing point calculation process of the on-line outer meshing region is described below by taking the meshing section outer meshing region as an example, as shown in FIG. 5：
Let E1 be the midpoint of the line-out-of-engagement region, which can be found at ΔO by the cosine law 1 O 2 E 1 Calculated in (3) to obtain r 2 Length of (2):
E 1 the corresponding radial coordinate may be at ΔO 1 O 2 E 1 The following steps:
after the line external engagement area is obtained, the engagement point coordinates of the line external engagement area can be calculated according to the calculation method of the step A1. The schematic diagram of the calculation method for the engaged region is shown in fig. 6, and the specific calculation process is similar to that described herein and will not be repeated here.
Step C2: the deformation coordination equation after the line external engagement factors are considered is satisfied at the engagement point, the calculation of the deformation coordination equation on the theoretical engagement line is consistent with the step A3, and the influence of the initial deformation of the tooth surface is required to be considered for the line external engagement area. Taking external engagement of engaged segment lines as an example, N 2 ＝6：
Taking i=6 as an example, the calculation procedure:
setting an initial load F N ＝1N，F f =0.05n, tooth surface normal vector N p = (0,0.0127, -0.99992), the bending deformation is calculated by:
contact and shear deformation are:
brings in the deformation coordination equation:
step C3: calculating the total load of the tooth surface at the moment:
step C4: calculating the contact pressure difference between the first step and the second step:
step C5: and (3) carrying out iterative solution on each engagement moment of the complete engagement period according to the steps C2 to C4 until all three equations are converged, and obtaining the instantaneous transmission efficiency of the complete engagement process, as shown in fig. 7. It can be seen that the instantaneous transmission efficiency is close to 100% near the node, since the relative slip of the tooth flanks near the node is small.
Average transmission efficiency of the gears can be obtained by averaging the instantaneous engagement efficiency, and for the gear operation conditions in the embodiment, the average engagement efficiency is calculated as follows:
η i representing the instantaneous efficiency at each engagement instant.
After the transmission efficiency is obtained, the gear can be guided and designed. Taking a commercial electric drive axle as an example, wherein the commercial electric drive axle comprises a multi-stage cylindrical gear pair, the transmission efficiency of each stage of cylindrical gear pair can be calculated by using the calculation method provided by the invention, and the transmission efficiency of the system is further obtained. After the system transmission efficiency is obtained, the transmission efficiency of each stage of gear and the overall efficiency of the drive axle are improved by changing the design parameters of the gears, and the product economy is improved.
Finally, it should be noted that: the above embodiments are only for illustrating the technical scheme of the present invention and are not limited thereto; while the foregoing embodiments have described the calculation process of the present invention in more detail, those skilled in the art will appreciate that: the technical scheme of the embodiment can be modified or part of technical features can be replaced equally; and such simple modifications and substitutions do not depart from the spirit and scope of the corresponding technical solutions.
Claims (7)
1. A method of calculating gear transmission efficiency, the method comprising the steps of:
step A: establishing a cylindrical gear loading contact analysis model considering friction influence, setting the friction coefficient of a gear pair as mu, and calculating tooth surface deformation of the gear pair under the theoretical meshing condition;
and (B) step (B): calculating a gear engagement area after considering the out-of-line engagement effect according to the tooth surface deformation;
step C: calculating gear pair load distribution considering the influence of external engagement of the wire and transmission efficiency;
the friction coefficient mu of the gear pair is a constant friction coefficient or a time-varying friction coefficient;
in the step a, the loaded contact calculation analysis model taking the friction effect into consideration equally divides the meshing process of the gear pair into N calculation steps, and the calculation process for each calculation step includes:
step A1: calculating a theoretical meshing line and a corresponding theoretical meshing point of the gear according to the basic parameters of the gear;
step A2: calculating a tooth surface reduction stiffness matrix of the gear;
step A3: the deformation coordination equation is satisfied at each meshing point of each calculation step;
step A4: each meshing line of each calculation step satisfies a load balancing equation;
step A5: satisfying a contact pressure convergence equation at each engagement point of each calculation step;
step A6: carrying out iterative solution on the steps A3 to A5 by utilizing a Newton-Laporthelson method until three equations in the steps A3 to A5 are converged, and reading the tooth surface deformation delta of each calculation step;
the deformation coordination equation satisfied at each meshing point is:
δ b +δ s +δ c -(Z-d 0 )<ε 1
wherein Z is the rigid body rotation of the gear, d 0 Is the initial clearance of the gear, epsilon 1 Is a convergence tolerance;
δ b is tooth surface bending deformation:
δ b ＝([R 1 ]+[R 2 ])·({F N }+{F f })·n p
R 1 and R is 2 To calculate a compliance matrix from the reduced stiffness matrix, n p As normal vector at tooth-surface engagement point, F N F is the tooth surface normal contact force f Is tooth surface friction force delta c For tooth-surface contact deformation, delta s Is tooth surface shear deformation:
in E 1 And E is 2 Is the elastic modulus of the driving gear and the driven gear, v 1 And v 2 Poisson ratio, h, of the driving and driven gears 1 And h 2 Is the distance between the contact point of the driving gear and the driven gear and the center line of the gear, b f Is the hertz contact half width and l is the contact line length.
2. The method of calculating gear transmission efficiency according to claim 1, wherein the load balancing equation satisfied by each meshing line is:
where m is the number of contact lines per calculation step, n is the number of aliquoting contact points on each contact line, r is the position vector of the contact points, p is the axial vector of the drive gear, T load Is the load torque, epsilon, on the driven gear determined by the load condition 2 Is a convergence tolerance;
the contact pressure convergence equation satisfied at each meshing point is:
Ph k -Ph k-1 <ε 3
wherein Ph is k Is the maximum contact pressure of the tooth surface on the kth contact line, ph k-1 For maximum contact pressure on the (k-1) th contact line, ε 3 To converge tolerances.
3. The method of calculating gear transmission efficiency according to claim 1, wherein the step B includes the steps of:
step B1: reading tooth surface deformations at theoretical engagement start and end points, i.e. deformation of engagement section line external engagement end point and engagement section line external engagement start point, from the calculation result of step A, which are respectively denoted as delta 1 And delta 2 ；
Step B2: calculating the actual engagement start point and engagement end point after considering the line external engagement phenomenon, and dividing the line external engagement area of the engagement section into N 1 The outside line engagement area of the engagement section is divided into N 2 And (3) step (c).
4. The method of calculating gear transmission efficiency according to claim 1, wherein the calculation process for each calculation step includes:
step C1: calculating the meshing point of the two-section line external meshing area;
step C2: the deformation coordination equation after the out-of-line engagement factors are considered is satisfied at each engagement point of each calculation step;
step C3: the meshing line of each calculation step meets a load balance equation;
step C4: satisfying a contact pressure convergence equation at each meshing line of each calculation step;
step C5: and (3) carrying out iterative solution on the steps C2 to C4 by utilizing a Newton-Laporthelson method until three equations in the steps C2 to C4 are converged, and obtaining the load distribution and the transmission efficiency of the complete meshing process.
5. The method of calculating gear transmission efficiency according to claim 4, wherein the deformation coordination equation after taking into account the out-of-line engagement factor is satisfied at each engagement point:
δ b +δ s +δ c +δ sd -(Z-d 0 )<ε 1
wherein, in the engaged section:
in the engaged section:
the load balancing equation satisfied at each line of engagement is:
the contact pressure convergence equation satisfied at each meshing line is:
Ph k -Ph k-1 <ε 3
wherein Z is the rigid body rotation of the gear, d 0 Is the initial gear play, delta b Is the bending deformation of tooth surface delta s Is the tooth surface shear deformation, delta c For tooth-surface contact deformation, delta sd Is the tooth surface deformation of the engaging and the engaging section epsilon 1 In order to converge the tolerance of the light,m is the number of contact lines of each calculation step, n is the number of equal contact points on each contact line, r is the position vector of the contact points, p is the axial vector of the driving gear, T load For load torque, ε, on driven gear determined by load conditions 2 To converge tolerance, ph k For maximum contact pressure of tooth surface on kth contact line, ph k-1 For maximum contact pressure on the (k-1) th contact line, ε 3 To converge tolerances.
6. A computer apparatus comprising a memory and a processor; the memory is used for storing a computer program; the processor for implementing the method of calculating gear transmission efficiency according to any one of claims 1 to 5 when executing the computer program.
7. A computer storage medium, wherein a computer program is stored on the storage medium, which, when executed by a processor, implements the method of calculating gear transmission efficiency according to any one of claims 1 to 5.
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