CN110206866A - Gear and its manufacturing method - Google Patents
Gear and its manufacturing method Download PDFInfo
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- CN110206866A CN110206866A CN201810923593.7A CN201810923593A CN110206866A CN 110206866 A CN110206866 A CN 110206866A CN 201810923593 A CN201810923593 A CN 201810923593A CN 110206866 A CN110206866 A CN 110206866A
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- gear
- tooth
- shape
- curve
- point
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Classifications
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- F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
- F16—ENGINEERING ELEMENTS AND UNITS; GENERAL MEASURES FOR PRODUCING AND MAINTAINING EFFECTIVE FUNCTIONING OF MACHINES OR INSTALLATIONS; THERMAL INSULATION IN GENERAL
- F16H—GEARING
- F16H55/00—Elements with teeth or friction surfaces for conveying motion; Worms, pulleys or sheaves for gearing mechanisms
- F16H55/02—Toothed members; Worms
- F16H55/08—Profiling
- F16H55/0806—Involute profile
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- B—PERFORMING OPERATIONS; TRANSPORTING
- B23—MACHINE TOOLS; METAL-WORKING NOT OTHERWISE PROVIDED FOR
- B23F—MAKING GEARS OR TOOTHED RACKS
- B23F5/00—Making straight gear teeth involving moving a tool relatively to a workpiece with a rolling-off or an enveloping motion with respect to the gear teeth to be made
- B23F5/20—Making straight gear teeth involving moving a tool relatively to a workpiece with a rolling-off or an enveloping motion with respect to the gear teeth to be made by milling
- B23F5/26—Making straight gear teeth involving moving a tool relatively to a workpiece with a rolling-off or an enveloping motion with respect to the gear teeth to be made by milling the tool having the same profile as a tooth or teeth of a rack, for making spur gears
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- Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
- Y10—TECHNICAL SUBJECTS COVERED BY FORMER USPC
- Y10T—TECHNICAL SUBJECTS COVERED BY FORMER US CLASSIFICATION
- Y10T409/00—Gear cutting, milling, or planing
- Y10T409/10—Gear cutting
- Y10T409/101431—Gear tooth shape generating
- Y10T409/105883—Using rotary cutter
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- Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
- Y10—TECHNICAL SUBJECTS COVERED BY FORMER USPC
- Y10T—TECHNICAL SUBJECTS COVERED BY FORMER US CLASSIFICATION
- Y10T74/00—Machine element or mechanism
- Y10T74/19—Gearing
- Y10T74/19949—Teeth
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- Engineering & Computer Science (AREA)
- General Engineering & Computer Science (AREA)
- Mechanical Engineering (AREA)
- Gears, Cams (AREA)
Abstract
The present invention is a kind of gear, rotary motion is transmitted with multiple teeth (3) and using being meshed with the tooth of other side's gear, the shape (b) of the tooth root side of each tooth (3) is formed comprising the 1st curve (c) and the 2nd curve (d), 1st curve (c) is the curved surface smoothly connecting with the flank of tooth (a) of involute curve, it is the curve that is protruded round about by the flank of tooth (a) relative to the involute curve to indicate, 2nd curve (d) is smoothly connect with the 1st curved surface (c), it is to be defined and relative to the 1st curved surface (c) to same direction hyperbolic function outstanding.Can be reduced when being meshed with the tooth of other side's gear as a result, tooth root side generate stress, it can be achieved that tooth high intensity.
Description
The application is the divisional application of following patent applications:
Application number: 201380049049.X
The applying date: on 09 17th, 2013
Denomination of invention: gear and its manufacturing method
Technical field
The present invention relates to a kind of to transmit in two between centers and rotate with multiple teeth and using being meshed with the tooth of other side's gear
The gear of movement, specifically, be related to it is a kind of when being meshed with the tooth of other side's gear reduce tooth root side generation stress, can be real
The gear and its manufacturing method of the castellated shape of the high intensity of existing tooth.
Background technique
In the past, it to the gear for power transfer mechanisms such as automobile or precision machineries, implements for improving tooth intensity
Various designs.
As this gear, in disk gear, that is, tooth with tooth and tooth socket and the other side's gear to be linked by the flank of tooth
(pinion gear) engages in the gear of form, and have such structure: the flank of tooth is after the last block chalaza of pinion gear from tooth top court
To bottom of the tooth and it is that the relative datum flank of tooth is drawn by pinion gear, close to the trochoid and the tooth socket for projecting to vertical cross-section from cross
Section, which is seen, forms the arch of point in the region of bottom of the tooth (for example, referring to patent document 1).
Patent document 1: Japanese Unexamined Patent Application Publication 2004-519644 bulletin
But in the gear documented by the patent document 1, the tooth socket between adjacent tooth and tooth in terms of cross section,
Since the region in bottom of the tooth forms the arch of point, the concave point of slightly pointed triangle is formed in bottom of the tooth.In this gear,
When being meshed with the tooth of other side's gear, be easy the concave point concentrated stress in bottom of the tooth, it is possible to produce stress increase and it is damaged.Cause
This, it is desirable that the high intensity comprising the tooth entirety including bottom of the tooth.
Summary of the invention
Problem to be solved by the invention
Therefore, this problem is coped with, problem to be solved by this invention is to provide the gear and its system of a kind of castellated shape
Make method, when being meshed with the tooth of other side's gear reduce tooth root side generate stress, it can be achieved that tooth high intensity.
Means for solving the problems
In order to realize the above problem, the gear of the 1st embodiment is a kind of with multiple teeth and utilization and other side's gear
Tooth is meshed and transmits the gear of rotary motion, and the shape of the tooth root side of each tooth is formed comprising the 1st curved surface and the 2nd curved surface
, the 1st curved surface is the curved surface smoothly connecting with the flank of tooth of involute curve, is by relative to the involute curve
The flank of tooth and the curve that protrudes round about and present, the 2nd curved surface is smoothly connect with the 1st curved surface, is to pass through
It is defined relative to the 1st curved surface to the hyperbolic function of same direction protrusion.
The shape of the tooth right-angle cross-section of 2nd curved surface, may be alternatively formed to have not with the other side's gear engaged
The curve shape of the radius of curvature of the motion profile interference of tooth.
The shape of the tooth right-angle cross-section of 1st curved surface, may be alternatively formed to along not with the tooth of the other side's gear engaged
Motion profile interference radius of curvature circular arc or the interference region along the motion profile spline curve shape.
It is a kind of to be passed with multiple teeth and using being meshed with the tooth of other side's gear in addition, the gear of the 2nd embodiment
The gear of rotary motion is passed, the shape of the tooth root side of each tooth, which has, carries out model into the shape phase after cutting with using rack cutter
Same shape, the rack cutter have the circular portion of the curve defined by hyperbolic function in point of a knife.
In addition, the manufacturing method of the gear of the 2nd embodiment is a kind of tooth with multiple teeth and utilization and other side's gear
It is meshed and is transmitted the manufacturing method of the gear of rotary motion, the tooth root side of each tooth is shaped as and is utilized rack cutter
Tool carries out model into the identical shape of shape after cutting, and the rack cutter has the curve defined by hyperbolic function in point of a knife
Circular portion.
The manufacturing method of the gear can also be, and the raw material of gear are metal, using rack cutter to the tooth of each tooth
The shape of root side carries out model into cutting, and the rack cutter has the rounded portions of the curve defined by hyperbolic function in point of a knife
Point.
The manufacturing method of the gear can also be, and the raw material of gear are resin, using gear die to each tooth
The shape of tooth root side carries out ejection formation, the gear die be based on using rack cutter progress model at the gear after cutting and
Manufactured, the rack cutter has the circular portion of the curve defined by hyperbolic function in point of a knife.
The effect of invention
According to the gear of the 1st embodiment, the shape of the tooth root side of each tooth is shape comprising the 1st curved surface and the 2nd curved surface
At, the 1st curved surface is the curved surface smoothly connecting with the flank of tooth of involute curve, is by bent relative to the involute
Come what is indicated, the 2nd curved surface is smoothly connect with the 1st curved surface, is logical for the flank of tooth of line and the curve protruded round about
The hyperbolic function protruded relative to the 1st curved surface to the same direction is crossed come what is defined, bottom of the tooth face not will form point as a result,
Triangle concave point, the curved surface defined by hyperbolic function can be formed.Therefore, tooth root side is difficult to generate stress concentration, with
When the tooth of other side's gear is meshed reduce tooth root side generate stress, it can be achieved that tooth high intensity.The length of tooth can be improved as a result,
Phase wear properties.
The three of point will not be formed in bottom of the tooth face for the shape of the tooth root side of each tooth according to the gear of the 2nd embodiment
Angular concave point can have and carry out model into the identical curved surface of shape after cutting with using rack cutter, and the rack cutter exists
Point of a knife has the circular portion of the curve defined by hyperbolic function.Therefore, tooth root side is difficult to generate stress concentration, with other side
When the tooth of gear is meshed reduce tooth root side generate stress, it can be achieved that tooth high intensity.The long-term resistance to of tooth can be improved as a result,
Long characteristic.
It will not be in bottom of the tooth face for the shape of the tooth root side of each tooth according to the manufacturing method of the gear of the 2nd embodiment
The concave point for forming the triangle of point, be formed as with using rack cutter progress model at the identical curved surface of shape after cutting, institute
State the circular portion that rack cutter has the curve defined by hyperbolic function in point of a knife.Therefore, tooth root side is difficult to generate stress
Concentrate, when being meshed with the tooth of other side's gear reduce tooth root side generate stress, it can be achieved that tooth high intensity.As a result, may be used
Improve the long-term wear properties of tooth.
Detailed description of the invention
Fig. 1 is the main view for indicating gear global shape of the invention.
Fig. 2 is the perspective view for indicating the tooth form of master gear.
Fig. 3 is the amplification explanatory diagram for indicating the tooth-formation of gear shape of the 1st embodiment.
Fig. 4 is the flank of tooth of the tooth top side for the other side's gear for indicating that the tooth of the gear of the 1st embodiment is contacted in engagement
The explanatory diagram of motion profile.
Fig. 5 is the explanatory diagram for indicating the detail shape in the portion A in Fig. 4.
Fig. 6 is to indicate to compare the curve graph that gear carries out the stress distribution of the result after simulated experiment parsing to the 1st.
Fig. 7 is the curve for indicating to carry out the gear of the 1st embodiment the stress distribution of the result after simulated experiment parsing
Figure.
Fig. 8 is the table being illustrated to the gear of the 1st embodiment and the 1st endurance test result for comparing gear.
Fig. 9 is the amplification explanatory diagram for indicating the deformation tooth-formation of gear shape of the 1st embodiment.
Figure 10 is the table being illustrated to the deformation gear of the 1st embodiment and the 1st endurance test result for comparing gear.
Figure 11 is the amplification explanatory diagram for indicating the tooth-formation of gear shape of the 2nd embodiment.
Figure 12 is to indicate that point of a knife has the explanatory diagram of the rack cutter of the circular portion of the curve defined by hyperbolic function.
Figure 13 is the explanatory diagram for indicating the detail shape in the portion B in Figure 12.
Figure 14 is to indicate to carry out model into the explanatory diagram of the motion profile of point of a knife when cutting using rack cutter shown in Figure 12.
Figure 15 is to indicate to compare the curve graph that gear carries out the stress distribution of the result after simulated experiment parsing to the 2nd.
Figure 16 is the curve for indicating to carry out the gear of the 2nd embodiment the stress distribution of the result after simulated experiment parsing
Figure.
Symbol description
1 ... gear
3 ... teeth
6 ... crest top lands
7 ... bottom of the tooth faces
10 ... rack cutters
The knife of 11 ... rack cutters
The point of a knife that 12 ... rack gears are found
A ... the flank of tooth
The flank of tooth of b ... tooth root side
The 1st curved surface of c ...
The 2nd curved surface of d ...
The circular arc of g ... previous example
The curve that h ... is defined by hyperbolic function
P ... pitch circle
T ... trochoid curves
U ... curve
Specific embodiment
In the following, illustrating embodiments of the present invention according to Figure of description.
Fig. 1 is the main view for indicating gear global shape of the invention.The gear has multiple teeth and utilizes and other side's tooth
The tooth of wheel be meshed and two between centers transmit rotary motion, for example, be widely used in automobile, precision machinery, industrial machinery and they
The power transfer mechanism of part etc..
In Fig. 1, gear 1 is that the peripheral side of substantially disk-shaped web 2 is formed with multiple teeth 3,3 ..., in web 2
Central part be formed with boss 5, which is equipped with the axis hole 4 that rotary shaft is fixed, transmits rotary motion in two between centers.Separately
Outside, symbol P indicates the pitch circle of the gear 1.
Generally as shown in Fig. 2, the tooth 3 of the gear 1 is formed to have the flank of tooth of involute curve and symmetrical mark
Quasi- tooth-formation of gear.That is, the facewidth W of the crest top land 6 of each tooth 31(refer in the tooth socket between adjacent tooth 3,3 most with bottom of the tooth face 7
Low bottom surface) facewidth W2It is formed identical size, whole depth H is formed constant in facewidth direction.
Fig. 3 is the amplification explanatory diagram for indicating the shape of the tooth 3 of gear 1 of the 1st embodiment.In Fig. 3, by the side of tooth 3
Face is known as flank of tooth a, and the shape of the tooth root side of flank of tooth a is known as flank of tooth b.Also, the tooth 3 of the gear 1 of the 1st embodiment is to tooth
The flank of tooth b shape of root side has made the tooth after design, and as shown in figure 3, the flank of tooth b shape of the tooth root side of each tooth 3 includes the 1st bent
Face c and the 2nd curved surface d and formed.
That is, the 1st curved surface c is the curved surface smoothly connecting with the flank of tooth a of involute curve, and be formed as by relative to institute
State the flank of tooth a of involute curve and the curve that protrudes round about represented by shape.
In addition, the 2nd curved surface d is formed as smoothly connecting with the 1st curved surface c, and relative to the 1st curved surface c
Shape defined in the hyperbolic function protruded to the same direction.As the hyperbolic function, it is expressed as y=cosh (x), referred to as
Hyperbolic cosine function.Or be formed as a part of hyperbolic function, it is expressed as y=kXcosh (x/k) (here, k is coefficient),
Referred to as catenary curve.
This castellated shape is determining as follows.Firstly, the 2nd curved surface d is in Fig. 4, the tooth right-angle cross-section of tooth 3
Shape has not with the radius of curvature of the motion profile interference of the tooth of the other side's gear engaged, and is formed as and the full-height tooth
The curve shape that the bottom of the tooth face 7 (referring to Fig. 2) of wheel connects.That is, the other side's gear (diagram contacted when the tooth 3 of gear engages
Omit) tooth top side the flank of tooth motion profile, such trochoid T can obtain as shown in Figure 4.Trochoid curves T limitation
In such region: not reaching bottom of the tooth face 7 in the tooth socket between the tooth 3,3 of master gear.In this state, as long as having not
With the motion profile of the tooth of other side's gear, that is, trochoid curves T-phase interference radius of curvature, and determine at by as with the mark
The shape that the hyperbolic function for the curve that the bottom of the tooth face 7 of quasi- gear connects defines.In this case, due to the 2nd curved surface d at
For the shape that the inside of the side of the tooth root side of master gear shown in the dotted line f to Fig. 4 is stretched out, therefore, tooth compared with the past
The transverse tooth thickness of root side becomes larger.In addition, not forming the recessed of the triangle of point described in above patent document 1 in the bottom of the tooth face 7 of gear
Point.In addition, the 2nd curved form of hyperbolic function becomes the curve shape to connect with the bottom of the tooth face 7 of master gear in Fig. 4, but
The present invention is not limited thereto, as long as the position that do not interference with the motion profile of the tooth of other side's gear, can be set to arbitrary
Position.For example, the high-strength of tooth can be further realized if being set to the position more against the top than the bottom of the tooth face 7 of the master gear
Degreeization.
Then, the 1st curved surface c is in Fig. 4, the tooth right-angle cross-section of tooth 3 be shaped as along not with other side's tooth for engaging
The spline curve shape of the circular arc of the radius of curvature of the motion profile interference of the tooth of wheel or the interference region along the motion profile
Shape.Here, Fig. 5 indicates the detail shape in the portion A in Fig. 4.In Fig. 5, in the point that flank of tooth a intersects with curved surface d, it is bent to form involute
Curved shape (the curved shape phase with flank of tooth a of the curved shape of the flank of tooth a of line and the 2nd curved surface d defined by hyperbolic function
Anti- direction) the edge e that crosses.In this way, being easy concentrated stress here when the flank of tooth is there are when edge.Therefore, in order to eliminate this
Edge e, as long as the shape of the 1st curved surface c is determined that at as described above, edge be not time pendulum with the motion profile of the tooth of other side's gear
The circular arc of the radius of curvature of line curve T-phase interference or the spline curve shape of the interference region along trochoid curves T.?
In this case, the 1st curved surface c becomes the smooth flank of tooth there is no edge e, becomes and smoothly connect with the flank of tooth a of involute curve
The curved surface connect, the song for becoming the curve that protrudes round about and the flank of tooth a relative to the involute curve to indicate
Face.Therefore, it can be achieved that the castellated shape of the concentration of stress brought by edge will not be generated.
For the gear 1 of the 1st embodiment of identified castellated shape as above, illustrate by computer assisted
The generation stress of tooth root side and the result after (CAE) is parsed when simulated experiment finds out engagement.In this case, as progress
The gear compared, in the tooth form of master gear, be formed as having using point of a knife the rack gear of the circular portion defined by circular arc into
Row model is at the gear (hereinafter referred to as " the 1st compares gear ") after cutting.
Firstly, illustrating the computation model and analysis condition when the root stress of simulated experiment calculates.Used in the parsing
The gear of 1st embodiment and the 1st to compare gear be spur gear, modulus (m) is 1, and the number of teeth is 30.Material be Young's modulus=
The resin (POM) of 2800MPa, Poisson's ratio ≈ 0.38.Other side's gear shape of engagement becomes each specification and the 1st embodiment
Gear and the 1st to compare gear identical.Loading condition is the load for applying 10N to normal for tooth surface direction in worst point of load application position.
As analytic modell analytical model, parsed using the reticulated shell model for only pulling out a tooth.As the software for calculation that root stress calculates, make
With " SolidWorks ".
Firstly, Fig. 6 indicates the stress distribution for comparing the root stress of result after gear parses to the 1st.In Fig. 6,
Horizontal axis indicates the X-coordinate (mm) in whole depth direction, and the right side of coordinate indicates that tooth top side, left side indicate bottom of the tooth side.The origin of horizontal axis
It is gear centre (center of axis hole 4).The longitudinal axis indicates the size of generated principal stress (MPa).Compare in gear the 1st,
As shown in fig. 6, principal stress is gradually increased from tooth top side to bottom of the tooth side, and principal stress steeply rises from X-coordinate=14.3mm, most
Big principal stress σ max reaches 5.39MPa.
Then, Fig. 7 indicates the stress distribution of the root stress of result after parsing to the gear of the 1st embodiment.?
In Fig. 7, horizontal axis, the longitudinal axis are identical as Fig. 6, indicate whole depth direction X-coordinate (mm) and generated principal stress (MPa) it is big
It is small.In the gear of the 1st embodiment, as shown in fig. 7, principal stress is also gradually increased from tooth top to bottom of the tooth, maximum principal stress σ
Max is 4.7MPa, and gear is compared to reduction about 13% or so compared with the 1st.In addition, even if in the stress variation from tooth top to bottom of the tooth
In, the 1st stress variation that compares as gear sharply is also small.
From the parsing result of above-mentioned simulated experiment it is found that according to the tooth-formation of gear shape of the 1st embodiment, compared to
1st compares gear, and the generation stress of tooth root side can be reduced when being meshed with the tooth of other side's gear, realizes the high intensity of tooth.
Therefore, the long-term wear properties of tooth are improved.
In addition, being shaped as the song defined by hyperbolic function due to tooth root side according to the gear of the 1st embodiment
Face, therefore, compared with bottom of the tooth forms the previous gear of the concave point of the triangle of point, tooth root side is difficult to generate stress concentration.
In the following, the gear to the 1st embodiment implement it is after endurance test as a result, compared with gear endurance test
As a result it makes a comparison description.
Fig. 8 is the table for illustrating gear endurance test result of gear compared with the 1st of the 1st embodiment.The endurance test
In, for the gear of the 1st embodiment shown in Fig. 3, use such gear: what is be referred to as defined to the 2nd curved surface d
A part of hyperbolic function, that is, catenary curve, in y=kXcosh (x/k), coefficient k=0.343.In addition, the 1st compare gear with
Gear when carrying out simulated experiment parsing (CAE) by above-mentioned area of computer aided is identical, is utilized in the tooth form of master gear
There is point of a knife the rack gear of the circular portion defined by circular arc to carry out model into the gear after cutting.The 1st embodiment as sample
Gear and the 1st compare gear each specification, be all spur gear, modulus (m) is 1, and pressure angle is 20 °, and the number of teeth is 30, the facewidth
For 5mm.Material is Young's modulus=2800MPa, the resin (POM) of Poisson's ratio ≈ 0.38, for example, being more plastic material companies
The resin for being known as " polyformaldehyde M90-44 " (Japanese: ジ ュ ラ U Application M90-44) of (Japanese: Port リ プ ラ ス チ ッ Network ス society) system.
The condition of endurance test is revolving speed: 1000rpm, lubricant: common grease company (Japanese: common grease society) system
Lubricating grease " grade quench TA NO.2 " (Japanese: マ Le テ Application プ TA No.2), environment temperature: 60 °, load torque:
2.00Nm.Test method is that gear together, makes to engage and make between identical gear compared with the gear and the 1st of the 1st embodiment
It is rotated to the same direction, some compared in meshed gears passes through time (hr) and engagement number (secondary) to what is destroyed.
As shown in figure 8, the 1st compares gear and begin to pass through 8.9 hours from rotation, engagement number reaches endurance test result
Destruction is produced after 534000 times.On the other hand, the gear of the 1st embodiment is begun to pass through 13.3 hours from rotation, engagement
Number produces destruction after reaching 798000 times.It is compared it follows that gear is compared in gear/1st of the 1st embodiment
Service life ratio afterwards is 149%, and by the high intensity of the gear of the 1st embodiment, wear properties are improved.
Fig. 9 is the amplification explanatory diagram for indicating the deformation tooth-formation of gear shape of the 1st embodiment.Flank of tooth a, flank of tooth b in Fig. 9
And the 1st curved surface c, the meaning of the 2nd curved surface d are identical as in Fig. 3.Here, it is such gear in Fig. 9: is being referred to as to the
The i.e. catenary curve of a part of hyperbolic function that 2 curved surface d are defined, in y=kXcosh (x/k), coefficient k=0.428.It should
The shape of the flank of tooth b of the lateral root side of the deformation gear of 1st embodiment compared to the 1st embodiment gear and be formed as close
Semicircular arc-shaped shape.To the deformation gear 1 of the 1st embodiment of so determining castellated shape, to illustrate endurance test
As a result.
Figure 10 be illustrate the 1st embodiment deformation gear and the 1st compare gear endurance test result table.This is durable
Test is to compare the endurance test after gear compares to the deformation gear and the above-mentioned 1st of the 1st embodiment shown in Fig. 9.
In this case, compare each specification of gear, material, endurance test as the deformation gear of the 1st embodiment of sample and the 1st
Condition and test method etc., it is all identical as endurance test shown in Fig. 8.
Endurance test result it is as shown in Figure 10, the 1st compares gear begins to pass through 8.9 hours from rotation, engagement number reach
Destruction is produced after to 534000 times.On the other hand, the deformation gear of the 1st embodiment is begun to pass through 23.1 hours from rotation,
Engagement number produces destruction after reaching 1386000 times.It follows that tooth is compared in deformation gear/1st of the 1st embodiment
Service life ratio after wheel is compared is 260%, and by the high intensity of the deformation gear of the 1st embodiment, wear properties are obtained
To improvement.
Figure 11 is the amplification explanatory diagram for indicating 3 shape of tooth of the gear 1 of the 2nd embodiment.In Figure 11, by the side of tooth 3
Face is known as flank of tooth a, and the shape of the tooth root side of flank of tooth a is known as flank of tooth b.Also, the tooth 3 of the gear 1 of the 2nd embodiment is to tooth
The shape of the tooth root side of face a has made the tooth after design, and as shown in figure 11, the flank of tooth b shape of the tooth root side of each tooth 3 has
Model is carried out into the identical shape of shape after cutting with using rack cutter, and rack cutter has in point of a knife to be determined by hyperbolic function
The circular portion of the curve of justice.In particular, being concave curved surface with the part that the bottom of the tooth face 7 is connect (referring to Fig. 2).
Also, the concave curved surface (b) is the curved surface smoothly connecting with the flank of tooth a of involute curve, that is, is formed as passing through
Relative to the involute curve flank of tooth a and the curve that protrudes round about the shape that indicates.In addition, as having this
The gear 1 of the shape of kind of tooth root side, but machining both carried out and manufactured metal gear to raw material metal, can also be by
Resin gives ejection formation and manufactured plastic gear.
Here, the gear 1 of castellated shape shown in Figure 11 is manufactured, as long as then by the shape shape of the tooth root side of each tooth 3
Model is carried out into the identical shape of shape after cutting as with using rack cutter, which has in point of a knife by double
The circular portion for the curve that curvilinear function defines.Used rack cutter 10 is as shown in figure 12 in this case, the knife of knife 11
Point 12 has the circular portion of the curve defined by hyperbolic function.As the hyperbolic function, it is expressed as y=cosh (x), is claimed
For hyperbolic cosine function.Alternatively, being formed as a part of hyperbolic function, being expressed as y=kXcosh (x/h), (here, k is to be
Number), referred to as catenary curve.
Figure 13 indicates the detail shape in the portion B in Figure 12.In Figure 13, the knife 11 of rack cutter 10 is usually, common
When manufacturing the high gear of dedendum strength in design of gears in such a way that model is at cutting, the part of point of a knife 12 is formed as arc-shaped
Shape.That is, the point C of point of a knife 121、D、C2Part be formed to have the circular arc g (previous example) of predetermined radius.In contrast, manufacture
The knife 11 of rack cutter 10 used in the gear 1 of 2nd embodiment, by the point C of point of a knife 12 shown in Figure 131、D、C2Part shape
As the circular portion after being replaced using the curve h defined by hyperbolic function.In this case, it is defined by hyperbolic function
Curve h compared to previous example circular arc g and be located inside, point of a knife 12 is slightly thin.Utilize the rack cutter with this point of a knife 12
10 carry out model into the gear 1 after cutting, the rack gear of previous example of the transverse tooth thickness of tooth root side than being formed as circular arc g using point of a knife 12
It is big at the gear after cutting that cutter carries out model.In addition, utilizing the curve h displacement point of a knife defined by hyperbolic function in Figure 13
12 point C1、D、C2Part, for left and right curve starting point (or tie point) C1、C2Position, can also not with engage
Arbitrary position is set in the range of the motion profile interference of the tooth of other side's gear.
Figure 14 is to indicate to carry out saying for point of a knife 12 motion profile of the model at cutting when using rack cutter 10 shown in Figure 12
Bright figure.In this case, the raw material of gear 1 are metal, indicate there is the curve defined by hyperbolic function using point of a knife 12
Circular portion rack cutter 10 and model is carried out to the shape of the tooth root side of each tooth 3 and manufactures the state of gear 1 at cutting.
The knife 11 of rack cutter 10 and the starting material of gear 1 and the motion profile for carrying out point of a knife 12 of the model at cutting when, can be by scheming
Curve U shown in 14 is obtained.Curve U becomes what its vertex connected in the tooth socket between the tooth 3,3 of master gear with bottom of the tooth face 7
State.In this case, concave curved surface (b) shown in Figure 11, the tooth root as becoming master gear shown in the dotted line i into Figure 14
The shape that the inside of the flank of tooth of side is stretched out, therefore, the transverse tooth thickness of tooth root side is bigger than previous example.In addition, in the bottom of the tooth face of gear
7, do not form the concave point of the triangle of point described in the patent document 1.In addition, in Figure 14, concave curved surface (b) be formed as with
The curve shape that the bottom of the tooth face 7 of master gear connects, but the 2nd embodiment is not limited to this, as long as not with other side's gear
The position of the motion profile interference of tooth, can also be set in arbitrary position.For example, if being set in the tooth than the master gear
The position against the top of bottom surface 7, then may further realize the high intensity of tooth.
In addition, in the above description, although the description of the state of manufacture metal gear, but the 2nd embodiment is not limited to
This, can also be the raw material of gear 1 being set as resin, to the shape of the tooth root side of each tooth 3, using based on utilizing rack cutter
10 progress models manufactured gear die (mold) at the gear after cutting, plastic gear is manufactured by injection molding method,
10 point of a knife 12 of rack cutter has the circular portion of the curve defined by hyperbolic function.Gear die under in this case
The production of tool can also be used as electrode at the metal gear after cutting for model is carried out using the rack cutter 10, utilize electric discharge
Processing is to manufacture gear die.Alternatively, using the previous known method other than electro-discharge machining, to manufacture gear die.
For the gear 1 of the 2nd embodiment of above-mentioned castellated shape determining like that, illustrate to utilize computer assisted mould
Draft experiment is come the generation stress of tooth root side when calculating engagement and is parsed the result after (CAE).In this case, as progress
The gear compared, in the tooth form of master gear, be formed as having using point of a knife the rack gear of the circular portion defined by circular arc into
Row model is at the gear (becoming " the 2nd compares gear " below) after cutting.
Firstly, illustrating the computation model and analysis condition when the root stress of simulated experiment calculates.Used in the parsing
The gear of 2nd embodiment and the 2nd to compare gear be spur gear, modulus (m) is 1, and the number of teeth is 30.Material be Young's modulus=
2800MPa, Poisson's ratio=0.38 resin (POM).Other side's gear shape of engagement becomes each specification and the 2nd embodiment
Gear and the 2nd to compare gear identical.Loading condition is the load for applying 10N to normal for tooth surface direction in worst point of load application position.
As analytic modell analytical model, parsed using the reticulated shell model for only pulling out a tooth.As root stress calculate software for calculation,
" SolidWorks " is used.
Firstly, Figure 15 indicates the stress distribution for comparing the root stress of result after gear parses to the 2nd.In Figure 15
In, horizontal axis indicates the X-coordinate (mm) in whole depth direction, and the right side of coordinate indicates that tooth top side, left side indicate bottom of the tooth side.The original of horizontal axis
Point is gear centre (center of axis hole 4).The longitudinal axis indicates the size of generated principal stress (MPa).Compare gear the 2nd
In, as shown in figure 15, principal stress is gradually increased from tooth top side to bottom of the tooth side, and principal stress from X-coordinate=14.3mm sharply on
It rises, maximum principal stress σ max reaches 5.39MPa.
Then, Figure 16 indicates the stress distribution of the root stress of result after parsing to the gear of the 2nd embodiment.?
In Figure 16, horizontal axis, the longitudinal axis are identical as Figure 15, indicate the X-coordinate (mm) and generated principal stress (MPa) in whole depth direction
Size.In the gear of the 2nd embodiment, as shown in figure 16, principal stress is also gradually increased from tooth top to bottom of the tooth, although principal stress
Increase from X-coordinate=14.3mm, but maximum principal stress σ max is 5.05MPa.In this case, the lifting position of principal stress at
For the roughly the same position of the gear compared with the 2nd.In addition, also to become the gear compared with the 2nd roughly the same for the state of the rising.But
It is that in the 2nd embodiment, it is low (reducing about 6%) that maximum principal stress σ max compares gear than the 2nd.Also, observe tooth root side
Stress distribution, the 2nd, which compares gear, becomes place on one point, and there is the convex of peak value (maximum) to be distributed, but in the 2nd embodiment
In gear, become the widely-dispersed form of stress (being flattened), is considered maximum stress decline as a result,.
From the parsing result of above-mentioned simulated experiment it is found that according to the tooth-formation of gear shape of the 2nd embodiment, compared to
2nd compares gear, and the generation stress of tooth root side can be reduced when being meshed with the tooth of other side's gear, realizes the high intensity of tooth.
Therefore, the long-term wear properties of tooth are improved.
In addition, for the shape of the tooth root side of each tooth, forming point with bottom of the tooth face according to the gear of the 2nd embodiment
The gear of the conventional art of the concave point of triangle is compared, and tooth root side is difficult to generate stress concentration.
In addition, in the above embodiment, although the description of the example for applying the present invention to master gear, but this hair
It is bright to be not limited to this, for example, can be naturally also applied to profile modified gear.
In addition, gear of the invention is not limited to spur gear, it also can be widely used to helical gear, herringbone bear, bevel gear, put down
The castellated shape of face gear, turbine and worm device and hypoid gear etc..In addition, gear of the invention is not limited to the tooth of resin
Wheel can also be applied to the gear of metal (such as mechanical realization steel alloy, carbon steel, stainless steel, brass and phosphor bronze etc.) system.
Claims (4)
1. a kind of gear is that have multiple teeth and utilize the gear for being meshed and transmitting rotary motion with the tooth of other side's gear, institute
Gear is stated to be characterized in that,
The shape of the tooth root side of each tooth have with using rack cutter progress model at the identical shape of shape after cutting, it is described
Rack cutter has the circular portion of the curve defined by hyperbolic function in point of a knife.
2. a kind of manufacturing method of gear is that have multiple teeth and utilize to be meshed with the tooth of other side's gear and transmit rotary motion
Gear manufacturing method, the manufacturing method of the gear is characterized in that,
Being shaped as the tooth root side of each tooth is subjected to model into the identical shape of shape after cutting with using rack cutter,
The rack cutter has the circular portion of the curve defined by hyperbolic function in point of a knife.
3. the manufacturing method of gear as claimed in claim 2, which is characterized in that the raw material of gear are metal, utilize rack gear
Cutter carries out model into cutting to the shape of the tooth root side of each tooth, and the rack cutter has in point of a knife to be defined by hyperbolic function
Curve circular portion.
4. the manufacturing method of gear as claimed in claim 2, which is characterized in that the raw material of gear are resin, use gear
Mold and to the shape of the tooth root side of each tooth carry out ejection formation, the gear die be based on using rack cutter progress model
Manufactured at the gear after cutting, the rack cutter has the rounded portions of the curve defined by hyperbolic function in point of a knife
Point.
Applications Claiming Priority (8)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| JP2012207917 | 2012-09-21 | ||
| JP2012-207917 | 2012-09-21 | ||
| JP2012-222037 | 2012-10-04 | ||
| JP2012222037A JP6129507B2 (en) | 2012-10-04 | 2012-10-04 | Gear and manufacturing method thereof |
| JP2013-178160 | 2013-08-29 | ||
| JP2013178160A JP6267458B2 (en) | 2012-09-21 | 2013-08-29 | gear |
| CN201380049049.XA CN104662331B (en) | 2012-09-21 | 2013-09-17 | Gear |
| PCT/JP2013/075043 WO2014046090A1 (en) | 2012-09-21 | 2013-09-17 | Gear and method for producing same |
Related Parent Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CN201380049049.XA Division CN104662331B (en) | 2012-09-21 | 2013-09-17 | Gear |
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| CN110206866A true CN110206866A (en) | 2019-09-06 |
| CN110206866B CN110206866B (en) | 2022-07-22 |
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| Application Number | Title | Priority Date | Filing Date |
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| CN201810923593.7A Active CN110206866B (en) | 2012-09-21 | 2013-09-17 | Gear and method for manufacturing same |
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| CN (1) | CN110206866B (en) |
| WO (1) | WO2014046090A1 (en) |
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| US3937098A (en) * | 1974-11-18 | 1976-02-10 | Rouverol William S | High torque gearing |
| DE2644331A1 (en) * | 1976-10-01 | 1978-04-06 | Hurth Masch Zahnrad Carl | DEVICE FOR THE MANUFACTURING OR MACHINING OF SPUR WHEELS |
| CN1060343A (en) * | 1991-10-24 | 1992-04-15 | 太原工业大学 | Bidirectional circular-arc gear |
| CN101526129A (en) * | 2009-02-27 | 2009-09-09 | 南京航空航天大学 | Helical involute gear and processing method thereof |
| US20100111628A1 (en) * | 2007-04-26 | 2010-05-06 | Hpg Nederland B.V. | Method for Designing and Manufacturing a Gear |
| CN101749404A (en) * | 2008-11-28 | 2010-06-23 | 恩普乐股份有限公司 | Gear |
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|---|---|---|---|---|
| JPH1194052A (en) * | 1997-09-25 | 1999-04-09 | Shigeyoshi Osada | Gear |
| JP4148579B2 (en) * | 1998-11-30 | 2008-09-10 | 浜井産業株式会社 | Manufacturing method of resin gear mold using hobbing machine |
| DE10208408A1 (en) * | 2002-02-27 | 2003-09-11 | Schwaebische Huettenwerke Gmbh | gear teeth |
| JP4707523B2 (en) * | 2005-09-30 | 2011-06-22 | アスモ株式会社 | Gear manufacturing method and gear manufacturing apparatus |
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| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US3937098A (en) * | 1974-11-18 | 1976-02-10 | Rouverol William S | High torque gearing |
| DE2644331A1 (en) * | 1976-10-01 | 1978-04-06 | Hurth Masch Zahnrad Carl | DEVICE FOR THE MANUFACTURING OR MACHINING OF SPUR WHEELS |
| CN1060343A (en) * | 1991-10-24 | 1992-04-15 | 太原工业大学 | Bidirectional circular-arc gear |
| US20100111628A1 (en) * | 2007-04-26 | 2010-05-06 | Hpg Nederland B.V. | Method for Designing and Manufacturing a Gear |
| CN101749404A (en) * | 2008-11-28 | 2010-06-23 | 恩普乐股份有限公司 | Gear |
| CN101526129A (en) * | 2009-02-27 | 2009-09-09 | 南京航空航天大学 | Helical involute gear and processing method thereof |
| CN101982673A (en) * | 2010-11-04 | 2011-03-02 | 吉林大学 | Design method of hypoid gear pair |
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|---|---|
| CN110206866B (en) | 2022-07-22 |
| WO2014046090A1 (en) | 2014-03-27 |
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