CN109145526B - Method for calculating meshing efficiency of straight gear pair - Google Patents
Method for calculating meshing efficiency of straight gear pair Download PDFInfo
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Abstract
The invention discloses a method for calculating the meshing efficiency of a straight gear pair, which comprises the following steps: s1, acquiring related data of a straight gear pair; s2, calculating the length of the meshing line segment; s3, calculating the meshing efficiency of the instantaneous contact points; s4, calculating the meshing efficiency of the meshing line segment; and S5, calculating the meshing efficiency of the spur gear pair. The method can quickly and accurately calculate the meshing efficiency of the straight gear pair, is simple, and greatly improves the calculation accuracy.
Description
Technical Field
The invention relates to the technical field of gear transmission systems, in particular to a method for calculating the meshing efficiency of a straight gear pair.
Background
Gears are the most widely applied transmission mechanisms, the efficiency problem is more and more emphasized, and methods for calculating the meshing efficiency of gear pairs are numerous, but most of the methods are relatively complicated, and more importantly, the relationship between the gears and the design parameters of the gears is implicit rather than explicit, namely the relationship between the meshing efficiency of the gears and the design parameters of the gears cannot be intuitively reflected.
The relationship between the gear meshing efficiency and the gear design parameters can be directly established along the meshing line integral method, however, in the application of the method, the calculated meshing efficiency of a pair of gear teeth from meshing to meshing is not the meshing efficiency of a pair of gear transmissions, and the gear meshing efficiency calculated in this way does not accord with the actual situation of gear continuous transmission in the case of a pair of gear pair transmissions.
Disclosure of Invention
Aiming at the defects of the prior art, the invention provides a method for calculating the meshing efficiency of a spur gear pair, which can quickly and accurately calculate the meshing efficiency of the spur gear pair.
The technical scheme adopted for solving the technical problems is as follows:
the method for calculating the meshing efficiency of the spur gear pair provided by the embodiment of the invention is characterized in that the method comprises the following steps:
s1, acquiring related data of a straight gear pair;
s2, calculating the length of the meshing line segment;
s3, calculating the meshing efficiency of the instantaneous contact points;
s4, calculating the meshing efficiency of the meshing line segment;
and S5, calculating the meshing efficiency of the spur gear pair.
As a possible implementation manner of this embodiment, in step S1, the data related to the spur gear set includes: number of teeth of driving gear z 1 Modulus m, transmission ratio i 12 The tooth surface friction factor mu is calculated according to the tooth surface pressure coefficient alpha and the tooth crest height coefficient ha.
As a possible implementation manner of this embodiment, in step S2, the specific process of calculating the length of the meshing line segment is as follows:
calculating to obtain the base circle pitch P by a base circle pitch calculation formula b Calculating the length PB of the engagement point to the node through the length calculation formula of the engagement point to the node 1 Calculating to obtain the length PB of the node to the point of engagement through a length calculation formula of the node to the point of engagement 2 Calculating the length B of the meshing line by using a meshing line length calculation formula 1 B 2 Calculating the length PB from the starting point of the single-tooth meshing area to the node through a calculation formula of the length from the starting point of the single-tooth meshing area to the node 3 And calculating the length PB from the node to the end point of the single-tooth meshing zone through a length calculation formula from the node to the end point of the single-tooth meshing zone 4 。
As a possible implementation manner of this embodiment, the pitch calculation formula of the base circle is:
P b ＝πm cosα (1)
in the formula, P b A base circle tooth pitch, m is a modulus, and alpha is a reference circle pressure angle;
the length calculation formula from the engagement point to the node is as follows:
in the formula, PB 1 To mesh point-to-node length, i 12 M is the modulus, z is the transmission ratio 1 The number of teeth of the driving wheel, alpha is a reference circle pressure angle, and ha is a tooth crest coefficient;
the length calculation formula from the node to the meshing point is as follows:
in the formula, PB 2 Length of node to engagement point, m is modulus, z 1 The number of the driving gear teeth, alpha, a, ha and a tooth crest coefficient;
the length calculation formula of the meshing line is as follows:
B 1 B 2 ＝PB 1 +PB 2 (4)
in the formula, B 1 B 2 For length of meshing line, PB 1 For engagement of point-to-node length, PB 2 Is the length of the node to the engagement point;
the length calculation formula from the starting point of the single-tooth meshing area to the node is as follows:
PB 3 ＝P b -PB 2 (5)
in the formula, PB 3 Is the length from the starting point of the single-tooth meshing zone to the node point, P b To base pitch, PB 2 Is the length of the node to the engagement point;
the length calculation formula from the node to the end point of the single-tooth meshing area is as follows:
PB 4 ＝P b -PB 1 (6)
in the formula, PB 4 The length from the node point to the end point of the single-tooth meshing zone, P b Is base pitch, PB 1 Is the mesh point to node length.
As a possible implementation manner of this embodiment, in step S3, the specific process of calculating the engagement efficiency of the instantaneous contact point is as follows:
calculating the instantaneous contact point meshing efficiency eta of the engagement point to the node section by using an instantaneous contact point meshing efficiency calculation formula of the engagement point to the node section 1 Calculating the instantaneous contact point meshing efficiency eta of the node to the nibbling section through an instantaneous contact point meshing efficiency calculation formula of the node to the nibbling section 2 。
As a possible implementation manner of this embodiment, the calculation formula of the instantaneous contact point engagement efficiency of the engagement point to the node segment is as follows:
in the formula eta 1 For the instantaneous contact point engagement efficiency from the engagement point to the node section, μ is the flank friction factor, i 12 M is the modulus, z is the transmission ratio 1 A reference pressure angle is a reference pressure angle, and x is a distance from an engagement point to an instantaneous contact point of the node segment;
the calculation formula of the instantaneous contact point meshing efficiency from the node to the meshing section is as follows:
in the formula eta 2 For the instantaneous contact point engagement efficiency from node to engaged section, μ is the flank friction factor, i 12 M is the modulus, z 1 The number of teeth of the driving gear, a reference circle pressure angle, and x are distances from the node to the instantaneous contact point of the meshing section.
As a possible implementation manner of this embodiment, in step S4, the specific process of calculating the engagement efficiency of the engagement line segment is as follows:
calculating the engagement efficiency from the engagement point to the starting point of the single-tooth engagement area by using the engagement efficiency calculation formula from the engagement point to the starting point of the single-tooth engagement area
The engagement efficiency from the starting point of the single-tooth engagement area to the node is calculated by the engagement efficiency calculation formula from the starting point of the single-tooth engagement area to the node>
The engagement efficiency from the node to the end point of the single-tooth engagement area is calculated by an engagement efficiency calculation formula from the node to the end point of the single-tooth engagement area>
The engagement efficiency (or the engagement efficiency) between the end point of the single-tooth engagement area and the meshing point is calculated through an engagement efficiency calculation formula from the end point of the single-tooth engagement area to the meshing point>
As a possible implementation manner of this embodiment, the engagement efficiency calculation formula from the engagement point to the starting point of the single-tooth engagement area is as follows:
in the formula (I), the compound is shown in the specification,
for the meshing efficiency from the point of engagement to the start of the single-tooth meshing zone, PB 1 For engagement of point-to-node length, PB 3 For the length from the start of the single-tooth meshing zone to the node point, eta 1 Instantaneous contact point meshing efficiency from a meshing point to a node section;
the calculation formula of the meshing efficiency from the starting point of the single-tooth meshing area to the node is as follows:
in the formula (I), the compound is shown in the specification,
for the efficiency of engagement from the start of the single-tooth engagement zone to the node, PB 3 For the length from the start of the single-tooth meshing zone to the node point, eta 1 Instantaneous contact point meshing efficiency from a meshing point to a node section;
the calculation formula of the meshing efficiency from the node to the end point of the single-tooth meshing area is as follows:
in the formula (I), the compound is shown in the specification,
for the meshing efficiency from node to end of the single-tooth meshing zone, PB 4 Length of node to end of single-tooth engagement zone, eta 2 The instantaneous contact point meshing efficiency from the node to the meshing section is obtained;
the calculation formula of the meshing efficiency from the end point of the single-tooth meshing area to the meshing point is as follows:
in the formula (I), the compound is shown in the specification,
for the efficiency of engagement from the end point of the single-tooth engagement zone to the point of engagement, PB 2 Length of node to point of engagement, PB 4 Length of node to end of single-tooth engagement zone, eta 2 The instantaneous contact point engagement efficiency of the node to the engaged section.
As a possible implementation manner of this embodiment, the specific process of step S5 is:
the meshing efficiency eta of the spur gear pair is calculated by a calculation formula of the meshing efficiency of the spur gear pair shown in the formula (13),
wherein eta is the meshing efficiency of the spur gear pair,
for the engagement efficiency of the engagement point to the start of the single-tooth engagement zone>
For the engagement efficiency from the starting point of the single-tooth engagement zone to the node>
For the engagement efficiency from the node to the end of the single-tooth engagement zone>
For the efficiency of the engagement from the end point of the single-tooth engagement zone to the point of engagement, B 1 B 2 For the length of the meshing line, P b Is the pitch of the base circle.
The technical scheme of the embodiment of the invention has the following beneficial effects:
according to the method for calculating the meshing efficiency of the straight gear pair, disclosed by the technical scheme of the embodiment of the invention, the length of the meshing line segment is calculated by acquiring the related data of the straight gear pair, the meshing efficiency of the instantaneous contact point is calculated, the meshing efficiency of the meshing line segment is calculated, and the meshing efficiency of the straight gear pair is calculated. The method can quickly and accurately calculate the meshing efficiency of the straight gear pair, is simple, and greatly improves the calculation accuracy.
Drawings
Fig. 1 is a flowchart illustrating a method of calculating a meshing efficiency of a spur gear pair according to an exemplary embodiment;
FIG. 2 is a schematic illustration of meshing lines of segments during a gear continuum according to an exemplary embodiment;
the symbols in fig. 2 represent: b is 1 A point of engagement, B 3 A starting point of a single-tooth meshing area, P, a node, B 4 End point of single tooth engagement zone, B 2 A point of engagement, PB 1 Mesh point to node length, PB 2 Length of node to point of engagement, P b Base circle pitch.
Detailed Description
In order to clearly explain the technical features of the present invention, the following detailed description of the present invention is provided with reference to the accompanying drawings. To simplify the disclosure of the present invention, the components and arrangements of specific examples are described below. Furthermore, the present invention may repeat reference numerals and/or letters in the various examples. This repetition is for the purpose of simplicity and clarity and does not in itself dictate a relationship between the various embodiments and/or configurations discussed. It should be noted that the components illustrated in the figures are not necessarily drawn to scale. Descriptions of well-known components and processing techniques and procedures are omitted so as to not unnecessarily limit the invention.
The invention provides a method for calculating the meshing efficiency of a straight gear pair, which comprises the following steps as shown in figure 1: s1, acquiring related data of a straight gear pair; s2, calculating the length of the meshing line segment; s3, calculating the meshing efficiency of the instantaneous contact points; s4, calculating the meshing efficiency of the meshing line segment; and S5, calculating the meshing efficiency of the spur gear pair.
The embodiment of the invention provides a method for calculating the meshing efficiency of a straight gear pair, which comprises the following concrete implementation processes:
step 1, acquiring related data of a spur gear pair: number of teeth of driving gear z 1 M, i transmission ratio 12 The reference circle pressure angle α, the tooth crest coefficient ha, and the tooth surface friction factor μ are shown in table 1.
TABLE 1
And 2, step: calculating to obtain a base circle tooth pitch P through a base circle tooth pitch calculation formula shown in formula (14) by using the modulus m and the reference circle pressure angle alpha in the step 1 b Using the modulus m and the number of teeth z of the driving wheel in step 1 1 Reference circle pressure angle a, tooth top height coefficient ha, and transmission ratio i 12 Calculating the length PB of the engagement point to the node by using the calculation formula of the length PB of the engagement point to the node shown in the formula (15) 1 Using the modulus m and the number of teeth z of the driving wheel in step 1 1 And calculating the length PB from the node to the meshing point by using a calculation formula of the length from the node to the meshing point shown in formula (16) 2 Using the calculated length of engagement point to node PB in step 2 1 Length PB from node to point of engagement 2 The length B of the meshing line is calculated by the formula for calculating the length of the meshing line shown in the formula (17) 1 B 2 Step of useBase pitch P calculated in step 2 b Length PB from node to point of engagement 2 The length PB from the starting point of the single-tooth meshing area to the node is calculated by a calculation formula of the length from the starting point of the single-tooth meshing area to the node shown in the formula (18) 3 Using the pitch P of the base circle calculated in step 2 b Length PB of engagement point to node 1 And calculating the length PB from the node to the end point of the single-tooth meshing area by using a length calculation formula from the node to the end point of the single-tooth meshing area shown in formula (19) 4 The schematic diagram of each section meshing line in the gear continuous transmission process is shown in FIG. 2, and symbols in FIG. 2 indicate that: b is 1 A point of engagement, B 3 A starting point of a single-tooth meshing area, P, a node, B 4 End point of single tooth engagement zone, B 2 A point of engagement, PB 1 Mesh point to node length, PB 2 Length of node to point of engagement, P b And base circle pitch.
P b ＝πm cosα (14)
In the formula, P b The reference circle tooth pitch, m is a modulus, and alpha is a reference circle pressure angle;
in the formula, PB 1 For mesh point to node length, i 12 M is the modulus, z is the transmission ratio 1 The number of the driving gear teeth, alpha, a, ha and a tooth crest coefficient;
in the formula, PB 2 Length of node to engagement point, m is modulus, z 1 The number of the driving gear teeth, alpha, a, ha and a tooth crest coefficient;
B 1 B 2 ＝PB 1 +PB 2 (17)
in the formula, B 1 B 2 For lines of engagementLength, PB 1 For engagement of point-to-node length, PB 2 Is the length of the node to the engagement point;
PB 3 ＝P b -PB 2 (18)
in the formula, PB 3 Is the length from the starting point of the single-tooth meshing area to the node point, P b Is base pitch, PB 2 Is the length of the node to the engagement point;
PB 4 ＝P b -PB 1 (19)
in the formula, PB 4 The length from the node point to the end point of the single-tooth meshing zone, P b To base pitch, PB 1 Is the mesh point to node length.
And step 3: using the tooth flank friction factor μ, gear ratio i in step 1 12 Modulus m, number of teeth of driving wheel z 1 And a reference circle pressure angle alpha, and calculating the instantaneous contact point meshing efficiency eta from the meshing point to the node section by using a meshing point-to-node section instantaneous contact point meshing efficiency calculation formula shown in formula (20) 1 Using the tooth flank friction factor mu, gear ratio i in step 1 12 Modulus m, number of teeth of driving wheel z 1 And the reference circle pressure angle alpha is calculated by an instantaneous contact point meshing efficiency calculation formula of the node to the meshing section shown in the formula (21) to obtain the instantaneous contact point meshing efficiency eta of the node to the meshing section 2 。
In the formula eta 1 For the instantaneous contact point engagement efficiency from the engagement point to the node section, μ is the flank friction factor, i 12 M is the modulus, z is the transmission ratio 1 Is the number of active gear teeth, a is the reference circle pressure angle, and x is the distance from the mesh point to the node segment's instantaneous contact point;
in the formula eta 2 For the instantaneous contact point engagement efficiency of the node to the meshing section, μ is the flank friction factor, i 12 M is the modulus, z is the transmission ratio 1 The number of teeth of the driving gear, a reference circle pressure angle, and x are distances from the node to the instantaneous contact point of the meshing section.
And 4, step 4: using the calculated engagement point to node length PB in step 2 1 Length PB from the start of the single tooth engagement zone to the node 3 Instantaneous contact point engagement efficiency eta from the engagement point to the node section calculated in step 3 1 The meshing efficiency from the meshing point to the starting point of the single-tooth meshing area is calculated by the formula (22) for calculating the meshing efficiency from the meshing point to the starting point of the single-tooth meshing area
Using the length PB from the start of the single tooth engagement zone to the node calculated in step 2 3 Instantaneous contact point engagement efficiency eta from the engagement point to the node section calculated in step 3 1 The engagement efficiency from the starting point of the single-tooth engagement area to the node is calculated and obtained through the calculation formula of the engagement efficiency from the starting point of the single-tooth engagement area to the node shown in the formula (23)>
Using the node-to-single tooth meshing zone end length PB calculated in step 2 4 Instantaneous contact point engagement efficiency eta from the node to the mesh-out section calculated in step 3 2 The engagement efficiency between the node and the end point of the single-tooth engagement zone is calculated and obtained through an engagement efficiency calculation formula from the node to the end point of the single-tooth engagement zone shown in the formula (24)>
Using the node-to-nibble length PB calculated in step 2 2 Length PB from node to end of single tooth engagement zone 4 And the instantaneous contact point engagement efficiency eta from the node to the nibbled section calculated in the step 3 2 And calculating the engagement efficiency from the end point of the single-tooth engagement area to the mesh-out point by using an engagement efficiency calculation formula shown in the formula (25)>
In the formula (I), the compound is shown in the specification,
for the meshing efficiency from the point of engagement to the start of the single-tooth meshing zone, PB 1 For engagement of point-to-node length, PB 3 For the length from the start of the single-tooth meshing zone to the node point, eta 1 Instantaneous contact point meshing efficiency from a meshing point to a node section;
in the formula (I), the compound is shown in the specification,
for the efficiency of engagement from the start of the single-tooth engagement zone to the node, PB 3 For the length from the start of the single-tooth meshing zone to the node point, eta 1 Instantaneous contact point meshing efficiency from a meshing point to a node section;
in the formula (I), the compound is shown in the specification,
for the meshing efficiency from node to end of the single-tooth meshing zone, PB 4 Length of node to end of single-tooth engagement zone, eta 2 The instantaneous contact point meshing efficiency from the node to the meshing section is obtained;
in the formula (I), the compound is shown in the specification,
for the efficiency of engagement from the end point of the single-tooth engagement zone to the point of engagement, PB 2 Length of node to point of engagement, PB 4 Length of node to end of single-tooth engagement zone, eta 2 The instantaneous contact point engagement efficiency of the node to the engaged section.
And 5: using the meshing efficiency from the meshing point calculated in step 4 to the start of the single-tooth meshing zone
The engagement efficiency from the start of the single-tooth engagement zone to the node is->
Engagement efficiency in conjunction with a node at the end of a single-tooth engagement zone>
Engagement efficiency from the end of the single-tooth engagement zone to the point of engagement>
Length B of the meshing line calculated in step 2 1 B 2 Base circle pitch P b The meshing efficiency η of the spur gear pair is calculated by the meshing efficiency calculation formula of the spur gear pair shown in the formula (26).
Wherein eta is the meshing efficiency of the straight gear pair,
for the engagement efficiency of the engagement point to the start of the single-tooth engagement zone>
For the efficiency of the engagement of the start of the single-tooth engagement zone into a node>
For the engagement efficiency from the node to the end of the single-tooth engagement zone>
For the meshing efficiency from the end point of the single-tooth meshing zone to the point of engagement, B 1 B 2 For the length of the meshing line, P b Is the pitch of the base circle.
Base circle pitch P b Mesh point to node length PB 1 Length PB from node to point of engagement 2 Length of mesh line B 1 B 2 Length PB from the start of the single tooth engagement zone to the node 3 Node to end point of single tooth engagement zone length PB 4 The calculation results of (a) are shown in table 2; efficiency of engagement from engagement point to starting point of single-tooth engagement zone
Meshing efficiency from starting point of single-tooth meshing area to node
Engagement efficiency from node to end of single-tooth engagement zone>
Engagement efficiency from the end of the single-tooth engagement zone to the point of engagement>
The results of calculation of the meshing efficiency η of the spur gear pair are shown in table 3.
TABLE 2
TABLE 3
According to the invention, the length of the meshing line segment is calculated by acquiring the related data of the straight gear pair, the meshing efficiency of the instantaneous contact point is calculated, the meshing efficiency of the meshing line segment is calculated, and the meshing efficiency of the straight gear pair is calculated. The method can quickly and accurately calculate the meshing efficiency of the straight gear pair, has simple calculation method, greatly improves the calculation accuracy, and has obvious beneficial effects of implementation.
The foregoing is only a preferred embodiment of the present invention, and it will be apparent to those skilled in the art that various modifications and improvements can be made without departing from the principle of the invention, and such modifications and improvements are also considered to be within the scope of the invention.
Claims (1)
1. A method for calculating the meshing efficiency of a spur gear pair, wherein the contact ratio 1< epsilon <2 of the spur gear pair, is characterized by comprising the following steps:
s1, acquiring related data of a straight gear pair;
in step S1, the data relating to the spur gear set includes: number of teeth of driving gear z 1 Modulus m, transmission ratio i 12 The reference circle pressure angle alpha, the tooth crest height coefficient ha and the tooth surface friction factor mu;
s2, calculating the length of the meshing line segment;
in step S2, the specific process of calculating the length of the meshing line segment is:
calculating to obtain the base circle pitch P by a base circle pitch calculation formula b Calculating the length PB of the engagement point to the node through the length calculation formula of the engagement point to the node 1 Calculating to obtain the length PB of the node to the point of engagement through a length calculation formula of the node to the point of engagement 2 Calculating the length B of the meshing line by using a meshing line length calculation formula 1 B 2 Calculating to obtain the length from the starting point of the single-tooth meshing area to the node through a calculation formula of the length from the starting point of the single-tooth meshing area to the nodeLength PB 3 And calculating the length PB from the node to the end point of the single-tooth meshing zone through a length calculation formula from the node to the end point of the single-tooth meshing zone 4 ；
The pitch calculation formula of the base circle is as follows:
P b ＝πm cosα (1)；
in the formula, P b The reference circle tooth pitch, m is a modulus, and alpha is a reference circle pressure angle;
the length calculation formula from the engagement point to the node is as follows:
in the formula, PB 1 To mesh point-to-node length, i 12 M is the modulus, z is the transmission ratio 1 The number of teeth of the driving wheel, alpha is a reference circle pressure angle, and ha is a tooth crest coefficient;
the length calculation formula from the node to the meshing point is as follows:
in the formula, PB 2 Length of node to engagement point, m is modulus, z 1 The number of teeth of the driving wheel, alpha is a reference circle pressure angle, and ha is a tooth crest coefficient;
the length calculation formula of the meshing line is as follows:
B 1 B 2 ＝PB 1 +PB 2 (4)；
in the formula, B 1 B 2 For length of meshing line, PB 1 For engagement of point-to-node length, PB 2 Is the length of the node to the engagement point;
the length calculation formula from the starting point of the single-tooth meshing area to the node is as follows:
PB 3 ＝P b -PB 2 (5)；
in the formula, PB 3 Is the length from the starting point of the single-tooth meshing area to the node point, P b To base pitch, PB 2 The length from the node to the engagement point;
the length calculation formula from the node to the end point of the single-tooth meshing area is as follows:
PB 4 ＝P b -PB 1 (6)；
in the formula, PB 4 The length from the node point to the end point of the single-tooth meshing zone, P b Is base pitch, PB 1 The length from the engagement point to the node;
s3, calculating the meshing efficiency of the instantaneous contact points;
in step S3, the specific process of calculating the engagement efficiency of the instantaneous contact point is:
calculating the instantaneous contact point meshing efficiency eta of the engagement point to the node section by using an instantaneous contact point meshing efficiency calculation formula of the engagement point to the node section 1 Calculating the instantaneous contact point meshing efficiency eta from the node to the nibbling section by using an instantaneous contact point meshing efficiency calculation formula from the node to the nibbling section 2 ；
The calculation formula of the instantaneous contact point meshing efficiency from the meshing point to the node section is as follows:
in the formula eta 1 For the instantaneous contact point engagement efficiency from the engagement point to the node section, μ is the flank friction factor, i 12 M is the modulus, z 1 A reference pressure angle is a reference pressure angle, and x is a distance from an engagement point to an instantaneous contact point of the node segment;
the calculation formula of the instantaneous contact point meshing efficiency from the node to the meshing section is as follows:
in the formula eta 2 For the instantaneous contact point engagement efficiency from node to engaged section, μ is the flank friction factor, i 12 Is a transmission ratio, m isModulus, z 1 The number of the driving gear teeth, alpha, a reference circle pressure angle and x are distances from a node to an instantaneous contact point of a meshing section to the node;
s4, calculating the meshing efficiency of the meshing line segment;
in step S4, the specific process of calculating the engagement efficiency of the engagement line segment is as follows:
calculating the engagement efficiency from the engagement point to the starting point of the single-tooth engagement area through an engagement efficiency calculation formula from the engagement point to the starting point of the single-tooth engagement area
The engagement efficiency from the starting point of the single-tooth engagement area to the node is calculated through an engagement efficiency calculation formula from the starting point of the single-tooth engagement area to the node>
The engagement efficiency between the node and the terminal point of the single-tooth engagement area is calculated through an engagement efficiency calculation formula from the node to the terminal point of the single-tooth engagement area>
The engagement efficiency (or the engagement efficiency) between the end point of the single-tooth engagement area and the meshing point is calculated through an engagement efficiency calculation formula from the end point of the single-tooth engagement area to the meshing point>
The engagement efficiency calculation formula from the engagement point to the starting point of the single-tooth engagement area is as follows:
in the formula (I), the compound is shown in the specification,
for the meshing efficiency from the point of engagement to the start of the single-tooth meshing zone, PB 1 For engagement of point-to-node length, PB 3 For the length from the start of the single-tooth meshing zone to the node point, eta 1 Instantaneous contact point meshing efficiency from a meshing point to a node section;
the calculation formula of the meshing efficiency from the starting point of the single-tooth meshing area to the node is as follows:
in the formula, S PB3 For the efficiency of engagement from the start of the single-tooth engagement zone to the node, PB 3 For the length from the start of the single-tooth meshing zone to the node point, eta 1 Instantaneous contact point meshing efficiency from a meshing point to a node section; the calculation formula of the meshing efficiency from the node to the end point of the single-tooth meshing area is as follows:
in the formula (I), the compound is shown in the specification,
for meshing efficiency from node to end of single-tooth meshing zone, PB 4 Length of node to end of single-tooth engagement zone, eta 2 The instantaneous contact point meshing efficiency from the node to the meshing section is obtained; the calculation formula of the meshing efficiency from the end point of the single-tooth meshing area to the meshing point is as follows:
in the formula (I), the compound is shown in the specification,
for the efficiency of engagement from the end point of the single-tooth engagement zone to the point of engagement, PB 2 Length of node to point of engagement, PB 4 Length of node to end of single-tooth engagement zone, eta 2 The instantaneous contact point meshing efficiency from the node to the meshing section is obtained;
s5, calculating the meshing efficiency of the straight gear pair;
the specific process of the step S5 is as follows:
the meshing efficiency eta of the spur gear pair is calculated by a calculation formula of the meshing efficiency of the spur gear pair shown in the formula (13),
wherein eta is the meshing efficiency of the spur gear pair,
for the engagement efficiency of the engagement point to the start of the single-tooth engagement zone>
For the engagement efficiency from the starting point of the single-tooth engagement zone to the node>
For the engagement efficiency from the node to the end of the single-tooth engagement zone>
For the meshing efficiency from the end point of the single-tooth meshing zone to the point of engagement, B 1 B 2 For the length of the meshing line, P b Is the pitch of the base circle. />
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Citations (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| JP2006090467A (en) * | 2004-09-24 | 2006-04-06 | Fuji Heavy Ind Ltd | Conical shape involute gear pair |
| CN107066678A (en) * | 2017-01-22 | 2017-08-18 | 北京工业大学 | Mesh impact model with base pitch error |
| CN108561526A (en) * | 2018-05-02 | 2018-09-21 | 济南大学 | A kind of computational methods of 2K-H types Closed Epicyclic Gear Train transmission efficiency |
-
2018
- 2018-11-09 CN CN201811328670.0A patent/CN109145526B/en active Active
Patent Citations (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| JP2006090467A (en) * | 2004-09-24 | 2006-04-06 | Fuji Heavy Ind Ltd | Conical shape involute gear pair |
| CN107066678A (en) * | 2017-01-22 | 2017-08-18 | 北京工业大学 | Mesh impact model with base pitch error |
| CN108561526A (en) * | 2018-05-02 | 2018-09-21 | 济南大学 | A kind of computational methods of 2K-H types Closed Epicyclic Gear Train transmission efficiency |
Non-Patent Citations (2)
| Title |
|---|
| 渐开线圆柱齿轮副滑动率、重合度计算浅析;莫江涛等;《机械》;20170325(第03期);全文 * |
| 齿轮基本参数对内啮合效率影响的研究;赵宁等;《现代制造工程》;20090818(第08期);全文 * |
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