CN207830468U - The oblique line gear mechanism of active line tooth is constructed with plane spiral of Archimedes - Google Patents
The oblique line gear mechanism of active line tooth is constructed with plane spiral of Archimedes Download PDFInfo
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- CN207830468U CN207830468U CN201721103836.XU CN201721103836U CN207830468U CN 207830468 U CN207830468 U CN 207830468U CN 201721103836 U CN201721103836 U CN 201721103836U CN 207830468 U CN207830468 U CN 207830468U
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Abstract
The utility model discloses a kind of oblique line gear mechanisms constructing active line tooth with plane spiral of Archimedes, including driving wheel and driven wheels at transmission, active exposure line construction is carried out using plane spiral of Archimedes, meet line gear space curve mesh theory, i.e. the active exposure line of spatial conjugation and driven contact line realize engaged transmission in the form of point contact, the active exposure line and driven contact line rely on active line tooth and respectively from moving-wire teeth, the active line tooth and from the wheel body that moving-wire tooth is distributed in driving wheel and driven wheel.The axis of the driving wheel and driven wheel is intersected with any angle, and any angle refers to unspecified angle in 0 ° 180 °.The circular helix that the utility model is commonly used for active exposure line from original line gear pair becomes plane spiral of Archimedes, reduce the Spatial Dimension of active exposure line, convenient for plane machining in minute manufacturing based on technique combined, be more advantageous to application of the line gear in small transmission field.
Description
Technical field
The utility model is related to the new gear transmission fields of small-power, small size, more particularly to one kind is with plane A Ji
Mead helix constructs the oblique axis line gear mechanism of active line tooth.
Background technology
Gear drive is a kind of most widely used transmission and transmission technology.It is different from the conjugation of traditional Involute Gear Pair
Curved surface mesh theory, new gear mechanism --- line gear transmission, application space grips curve mesh theory altogether, it can be achieved that axis
With any angle intersection or transmission staggeredly and large transmission ratio transmission.Line gear is also known as space curve engagement wheel, transmission process
In be that a pair of space curve of gripping altogether participates in engagement, this is to space curve respectively as active exposure line in line gear pair and driven
Contact line.No matter its principal and subordinate wheel axis is parallel, hangs down and intersect or interlock for existing line gear mechanism, and design requirement is constant speed
Transmission or gear all unanimously construct active exposure line, such as Chinese patent (number of patent application using circular helix
CN201010105902) disclosed " a kind of angular bevel gear mechanism "；Chinese patent (number of patent application CN201210449290) is public
" a kind of spatial intersecting shaft gear mechanism " opened；" a kind of change disclosed in Chinese patent (number of patent application CN201520611186)
Ratio line gear mechanism ".In view of the difficulty of processing of stock size transmission, circular helix is relative to other space curves
It more easily realizes digital control processing and ensures degree of precision.However the line gear key problem to be solved is short space transmission, line
The premise that gear is driven in microsize correct engagement is that line gear configuration is adapted to micro-nano technology technique.Micro-nano processing method adds
Work plane configuration is easier to and precision is high.In current crossed-axis gear pair, the biography of driving wheel is not built with flat shape still
Dynamic form.
Utility model content
The utility model is directed to current small transmission field problem of the existing technology, it is proposed that with plane Archimedes
Helix constructs the oblique line gear mechanism of active exposure line.The construction of active exposure line becomes flat from original circular helix
Face spiral of Archimedes, reduces the Spatial Dimension of contact line, reduces and processes small difficulty of processing, convenient for in minute manufacturing
Technique based on plane machining combines, and is more advantageous to application of the line gear in small transmission field.This kind of new line gear pair is abided by
Follow the space curve theory of engagement, by driving wheel and driven wheel active line tooth and between moving-wire tooth continuous engagement realize
Stable drive.
The specific technical solution of the utility model is as follows：
A kind of oblique line gear mechanism constructing active line tooth with plane spiral of Archimedes, including driving wheel and driven
The transmission of composition is taken turns, the driving wheel and driven wheel meet line gear space curve mesh theory, the i.e. active of spatial conjugation
Contact line and driven contact line realize engaged transmission in the form of point contact, and the active exposure line and driven contact line are relied on respectively
In active line tooth and from moving-wire tooth, the active line tooth and the wheel body for being distributed in driving wheel and driven wheel respectively from moving-wire tooth
On, the axis of the driving wheel and driven wheel can be intersected with any angle according to the design needs, form principal and subordinate wheel rotary shaft
Angle theta realizes that the transmission between any angle intersecting axle of space, any angle refer to unspecified angle in 0 °~180 °；It is described
Active exposure line is plane spiral of Archimedes, driven contact line according to the different designs of axis angle require using plane Ah
Base Mead helix, circular helix or conical spiral.
Further, the active exposure line and driven contact line parametric equation are：
In formula, t1For parameter, m is spiral of Archimedes parameter, and n is spiral of Archimedes intercept, and a, b are principal and subordinate
Horizontal distance and vertical distance between the origin of two referentials attached in dynamic contact line, θ press from both sides for principal and subordinate wheel rotary shaft
Angle, i21For transmission ratio.K is polar angle coefficient.
Further, described driven when θ is 0 ° or 180 ° according to the design requirement of the axis angle of cut θ of the transmission
Contact line is plane spiral of Archimedes；When θ is 90 °, the driven contact line is circular helix；When θ is other angles
When spending, the driven contact line is conical spiral.
Further, the active line tooth entity and from moving-wire tooth entity to scan building process as follows：
Active center line and driven center line are built first：
When external toothing, active line tooth center line be active contact line along its normal to center of curvature direction translate one away from
From r1It obtains, is that driven contact line reversely translates one along active exposure collimation method line to center of curvature direction from moving-wire tooth center line
Distance r2It obtains, when internal messing, translation direction is opposite；
Wherein, the active line tooth center line parametric equation is：
It is described to be from moving-wire tooth center line parametric equation：
Wherein, r1, r2Indicate the curvature of active line tooth and driven contact line at contact line in contact line plane half
Diameter, sign depend on external toothing or internal messing, and the direction that center line is translated is different；
Then it is scanned to obtain line tooth entity：
Make section circle from active center line starting point to active exposure line vertical direction respectively, driven center line starting point is to driven
Contact line vertical direction makees section circle, then is justified by section and scan to obtain line tooth entity along center line.Line tooth radius of curvature according to
Design requirement is chosen.The principal and subordinate moves contact line and principal and subordinate moves center line and ensure that principal and subordinate's moving-wire tooth near contact line
Shape and radius of curvature, driving wheel, active, can be designed from the shape of moving-wire tooth the wheel body of driven wheel according to physical condition.
In the above-mentioned angular bevel gear mechanism for constructing active exposure line with plane spiral of Archimedes, it is being driven certain moment
It realizes to active line tooth and from moving-wire tooth and engages, when not being disengaged, lower a pair of principal and subordinate moves contact line and enters engagement, ensure that
The engaged transmission of transmission continuous-stable.
Compared to previous unanimously using circular helix as active exposure line, the utility model uses plane Archimedes's spiral shell
Spin line reduces the Spatial Dimension of active exposure line as active exposure line, convenient for plane machining in minute manufacturing based on
Technique combines, and is more advantageous to application of the line gear in small transmission field, because in miniature scale processing, is limited by small ruler
Spend difficulty, residual stress and the surface of material property, structural strength and rigidity, geomery (dimensional effect), clamping and release
Integrality etc., processing three-dimensional curved surface need the control or movement of more dimensions, difficulty of high cost greatly；Process 2D or 2.5D
Processing technology it is more mature, the congenital adaptation plane of silicon micromachining technology on the one hand to grow up from integrated circuit processing technology
Processing, such as anisotropic silicon etching, photoetching, reactive ion etching, on the other hand non-silicon processing technique process planar graph
It is easier to, such as plane electric spark milling, electrolysis milling, ion beam processing etc..
Description of the drawings
Fig. 1 is the oblique line gear mechanism signal using plane spiral of Archimedes as active contact line in embodiment
Figure.
Fig. 2 is the driving wheel vertical view of the oblique line gear mechanism using plane spiral of Archimedes as active contact line.
Fig. 3 is the driven wheel vertical view of the oblique line gear mechanism using plane spiral of Archimedes as active contact line.
Fig. 4 is the driven wheel side view of the oblique line gear mechanism using plane spiral of Archimedes as active contact line.
Fig. 5 is Fig. 2, and 3 driving wheels are reached the standard grade tooth cross-sectional view.
Fig. 6 is respective coordinates system schematic diagram in Fig. 1.
Specific implementation mode
The specific implementation of the utility model is described further below in conjunction with the accompanying drawings, the implementation of the utility model is not limited to
This.
As shown in Figure 1, a kind of oblique line gear mechanism constructing active line tooth with plane spiral of Archimedes, including master
Driving wheel and driven wheels at transmission, the driving wheel and driven wheel meet line gear space curve mesh theory, i.e. space
The active exposure line of conjugation and driven contact line realize engaged transmission in the form of point contact, the active exposure line and driven connect
Tactile line relies on active line tooth and respectively from moving-wire tooth, the active line tooth and from moving-wire tooth be distributed in respectively driving wheel and from
On the wheel body of driving wheel, the axis of the driving wheel and driven wheel can be intersected with any angle according to the design needs, form principal and subordinate
Driven wheel rotation axis angle theta realizes the transmission between any angle intersecting axle of space, and any angle refers to any in 0 °~180 °
Angle；The active exposure line is plane spiral of Archimedes, and driven contact line is required according to the different designs of axis angle
Using plane spiral of Archimedes, circular helix or conical spiral.Wherein, driving wheel 3 is connected firmly with drive shaft 2, driven
Wheel 4 is connected firmly with driven shaft 5, and drive shaft 2 is connected firmly with motor 1, as shown in Fig. 2, active line tooth 6 is evenly arranged in driving wheel 3
On wheel body, as shown in figure 4, from the wheel body that moving-wire tooth 7 is evenly arranged in driven wheel 4.
Its transmission principle is：The rotation of motor 1 makes drive shaft 2 and driving wheel 3 rotate, and driving wheel 3 engages biography with driven wheel 4
It is dynamic, and then driven shaft 5 is made to rotate, realize the transmission process of intersecting axle.Any time is real to active line tooth and from moving-wire tooth
It now engages, when not being disengaged, lower a pair of principal and subordinate moves contact line and enters engagement, ensure that the engagement of transmission continuous-stable passes
It is dynamic.
Active line tooth and the construction process from moving-wire tooth in the utility model are further illustrated below in conjunction with the accompanying drawings.
The coordinate system of spatial conjugation curve as shown in Figure 5 is corresponding with gear mechanism transmission position shown in FIG. 1, indicates
Motion reference coordinate when the reference coordinate of a pair of of spatial conjugation curve in space and transmission engagement.Specially：O-xyz and o-
xpypzpTwo spaces coordinate system indicates the fixed coordinate system of driving wheel and driven wheel position, o-x1y1z1And o-x2y2z2Two
A space coordinates are consolidated with driving wheel and driven wheel respectively, with rotating together for principal and subordinate wheel.Respectively with driving wheel, driven
The axis of rotation of wheel overlaps.xpAxis and the angle of x-axis are θ.opThe distance of point to z axis is a, and the distance to x-axis is b.It is originating
Moment, o-x1y1z1And o-x2y2z2Respectively with o-xyz and o-xpypzpIt overlaps, driving wheel and driven wheel are respectively with angular speedWithAround z1Axis and z2Axis rotates, from initial position by after a certain period of time, driving wheel and driven wheel turn over respectivelyWithAngle.
Then active exposure line and the space curve equation of driven contact line are represented by：
Wherein formulaIt is the kinematic conditions at meshing point, the equation is known as
Mesh equation, physical significance are that principal and subordinate moves relative velocity of the contact line at meshing point hanging down in plane where active exposure line
Straight durection component is zero, i.e., driven contact line is kept in contact always with active exposure line and without departing from flat where active exposure line
Face.
The curve parametric equation of active exposure line is：
The parameter of curve of active exposure line is the space curve parametric equation of plane spiral of Archimedes.
Driven Contact line equations are：
In upper two formula：
Subscript (1) indicates that equation reference frame is o-x1y1z1, subscript M expression Contact line equations, in the present invention
Using plane spiral of Archimedes as active exposure line, a particular solution of mesh equation is：
K-polar angle coefficient.
M-spiral of Archimedes coefficient, the incrementss of polar diameter, m when indicating often to rotate 1 degree>0.
N-Archimedes's spiral shell intercept indicates distance of the initial position apart from dot.
t1- polar angle indicates the number of degrees that spiral of Archimedes turns over.
The supplementary angle of θ-driven wheel axis angle, ranging from 0 ° -180 °；
a,b—opThe distance of point to z-axis is a, and the distance to x-axis is b, a>0, b>0；
i21The transmission ratio namely active line number of teeth amount of-driving wheel and driven wheel and driven wheel line tooth ratio of number；
In upper two formula, as the parameter a, b, θ, i of transmission21Value when determining, the contact line for the slave moving-wire tooth gripped altogether therewith
Curve parametric equation determines therewith.
Pass through matrix conversion relationship M21=M2p·Mpo·Mo1O-x can be obtained1y1z1And o-x2y2z2Between transformation matrix：
Active exposure line equation becomes driven Contact line equations by above-mentioned transition matrix：
In formula：
- subscript (2) expression parameter equation reference frame is o-x2y2z2, subscript M expression contacts
Line；
The supplementary angle of θ-driven wheel axis angle, ranging from 0 ° -180 °；
a,b—opThe distance of point to z-axis is a, and the distance to x-axis is b, a>0, b>0；
Indicate that driving wheel and driven wheel are according to the transmission condition formula that given transmission ratio rotates：
In formula：
i21The transmission ratio of-driving wheel and driven wheel, i.e. active line number of teeth amount and driven wheel line tooth ratio of number；
The angular speed of-driving wheel and driven wheel rotation；
- pass through after a certain period of time, the angle that driving wheel and driven wheel turn over respectively；
As the parameter a, b, θ, i of transmission21Value when determining, the contact line parameter of curve side for the slave moving-wire tooth gripped altogether therewith
Journey determines therewith.
The active line tooth entity and from moving-wire tooth entity to scan building process as follows：
Active center line and driven center line are built first：When external toothing, active center line is active contact line along its method
Line translates a distance r to center of curvature direction1Obtain, driven center line be driven contact line along active exposure collimation method line to song
Rate center position reversely translates a distance r2It obtains, when internal messing, translation direction is opposite；
Wherein, active line tooth center line parametric equation is：
In formulaSubscript (1) expression parameter equation reference frame is o-x1y1z1, during subscript C is indicated
Heart line；r1Indicate radius of curvature of the active line tooth at contact line in contact line plane.
It is from moving-wire tooth center line parametric equation：
In formulaSubscript (2) expression parameter equation reference frame is o-x2y2z2, during subscript C is indicated
Heart line；r2Indicate that the radius of curvature from moving-wire tooth at contact line in contact line plane, sign depend on nibbling outside
It closes or internal messing, the direction that center line is translated is different；
When determining radius of curvature r of principal and subordinate's moving-wire tooth at contact line1, r2Afterwards, shape of the line tooth near contact line is also true
It is fixed.According to space curve mesh theory, as long as ensureing that the precision that a pair of of spatial conjugation curve, that is, principal and subordinate moves contact line is protected
Demonstrate,prove line gear pair transmission accuracy, driving wheel, the wheel body of driven wheel, active, can be according to practical item from the shape of moving-wire tooth
Part designs, such as processing technology, machining accuracy, Lubrication Design, stock utilization, stiffness and strength design.
Then it is scanned to obtain line tooth entity：Line tooth is formed from driving and driven contact line respectively to active exposure collimation method line
Positive and negative direction translates a distance r1And r2Two lines tooth center line is formed, makes section circle, then justified by section and swept along center line
It plunders to obtain line tooth entity.
As shown in figure 5, for the schematic cross-section of main moving-wire tooth, line tooth matrix relies on driving wheel 3, wherein 8 represent master
Any point in dynamic contact line, 9 be the corresponding points with point 8 on active center line, represents active exposure curvature of a curve center, curvature half
Diameter is r1, according to space curve mesh theory, as long as ensureing that the precision of a pair of of dynamic contact line of spatial conjugation curve, that is, principal and subordinate can
To ensure the transmission accuracy of line gear pair, driving wheel, the wheel body of driven wheel, active, can be according to reality from the shape of moving-wire tooth
Border condition design, such as processing technology, machining accuracy, Lubrication Design, stock utilization, stiffness and strength design.
Embodiment：Line tooth pair suitable for 3D printing
In the implementation case, to ensure the rigidity of line tooth, active line tooth section is designed as the structure of bearing diagonal, contact line
The left side of online tooth matrix, right side are support construction, and the processing method of this example is plastics 3D printing, in order to before keeping rigidity
Saving material is put, line tooth uses part circular section.As shown in Figure 5.
When in upper two formula:The parametric equation of active exposure line is
Given design parameter is θ=135 °, m=10, n=100, a=10, b=10, i21=0.25, Z1=10, Z2=
40,r1=2, r2=2.
According to the above method, acquires from moving-wire tooth contact line equation and be：
Active line tooth center line equation is：
It is from moving-wire tooth center line equation：
It is led after adding wheel body and D-shaped hole according to above four formula and the above-mentioned line tooth building method suitable for 3D printing
Driving wheel from moving-wire tooth as shown in Fig. 2, use identical line tooth cross-sectional configuration as shown in Figure 5, addition spoke type wheel body and D-shaped hole
Afterwards, it obtains such as Fig. 3, driven wheel shown in 4.Wherein Fig. 3 is the vertical view of driven wheel, and Fig. 4 is the side view of driven wheel.
As shown in Figure 1, the oblique line for constructing active line tooth with plane spiral of Archimedes that this example design is completed
The driving wheel and driven wheel of gear mechanism are mounted on according to design angle and wheelbase in drive shaft 2 and driven shaft 5, can be carried out
Transmission test, by measuring, the gear pair instantaneous transmission ratio and average ratios are stablized, and can realize that the engagement of continuous-stable passes
It is dynamic.This shows the oblique line gear mechanism driving that active line tooth is constructed with plane spiral of Archimedes of the utility model development
Method is feasible.
It is provided under the online gear space conjugate curves mesh theory frame of the utility model a kind of new with plane A Ji
Line tooth building method of the Mead helix as active exposure line is different from existing line gear mechanism and unanimously uses cylindrical screw
Line constructs active exposure line.The mechanism can be used in the method and mechanism of arbitrary intersecting axle continuous-stable engaged transmission.The mechanism
Have a series of advantages of line gear：Simplify the structure of gear mechanism and micromechanics transmission device, reduce geometric dimension, reduces matter
Amount improves the flexibility of operation, and makes simply, cheap.And since the construction of active exposure line is by original cylinder
Helix becomes plane spiral of Archimedes, reduces the Spatial Dimension of active exposure line, is convenient for and plane in minute manufacturing
Technique based on processing combines, and is more advantageous to processing and application of the line gear in small transmission field.
Above-described embodiment of the utility model is only intended to clearly illustrate the utility model example, and is not
Restriction to the embodiment of the utility model.For those of ordinary skill in the art, on the basis of above description
On can also make other variations or changes in different ways.There is no necessity and possibility to exhaust all the enbodiments.
All any modification, equivalent and improvement made within the spirit and principle of the present invention etc., should be included in this reality
Within novel scope of the claims.
Claims (4)
1. a kind of oblique line gear mechanism constructing active line tooth with plane spiral of Archimedes, including driving wheel and driven wheel
The transmission of composition, it is characterised in that：The driving wheel and driven wheel meet line gear space curve mesh theory, i.e. space is total
The active exposure line of yoke and driven contact line realize engaged transmission, the active exposure line and driven contact line in the form of point contact
Active line tooth is relied on respectively and from moving-wire tooth, the active line tooth and be distributed in driving wheel and driven wheel respectively from moving-wire tooth
Wheel body on, the axis of the driving wheel and driven wheel can be intersected with any angle according to the design needs, formed principal and subordinate wheel
Rotary shaft angle theta realizes that the transmission between any angle intersecting axle of space, any angle refer to any angle in 0 °~180 °
Degree；The active exposure line is plane spiral of Archimedes, and driven contact line requires to adopt according to the different designs of axis angle
With plane spiral of Archimedes, circular helix or conical spiral.
2. the oblique line gear mechanism according to claim 1 that active line tooth is constructed with plane spiral of Archimedes,
It is characterized in that：The active exposure line and driven contact line parametric equation are：
In formula, t1For parameter, m is spiral of Archimedes parameter, and n is spiral of Archimedes intercept, driven based on a, b to connect
The horizontal distance and vertical distance between the origin of two referentials attached in line are touched, θ is principal and subordinate wheel rotary shaft angle, i21
For transmission ratio, k is polar angle coefficient.
3. the oblique line gear mechanism according to claim 2 that active line tooth is constructed with plane spiral of Archimedes,
It is characterized in that：According to the design requirement of the axis angle of cut θ of the transmission, when θ is 0 ° or 180 °, the driven contact line
For plane spiral of Archimedes；When θ is 90 °, the driven contact line is circular helix；When θ is other angles, institute
It is conical spiral to state driven contact line.
4. the oblique line gear mechanism according to claim 3 that active line tooth is constructed with plane spiral of Archimedes,
It is characterized in that：The active line tooth entity and from moving-wire tooth entity to scan building process as follows：
Active center line and driven center line are built first：
When external toothing, active line tooth center line is that active contact line translates a distance r along its normal to center of curvature direction1
It obtains, is that driven contact line reversely translates a distance along active exposure collimation method line to center of curvature direction from moving-wire tooth center line
r2It obtains, when internal messing, translation direction is opposite；
Wherein, the active line tooth center line parametric equation is：
It is described to be from moving-wire tooth center line parametric equation：
Wherein, r1, r2Indicate the radius of curvature of active line tooth and driven contact line at contact line in contact line plane,
Sign depends on external toothing or internal messing, and the direction that center line is translated is different；
Then it is scanned to obtain line tooth entity：
Make section circle from active center line starting point to active exposure line vertical direction respectively, driven center line starting point is to driven contact
Line vertical direction makees section circle, then is justified by section and scan to obtain line tooth entity along center line.
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201721103836.XU CN207830468U (en) | 2017-08-31 | 2017-08-31 | The oblique line gear mechanism of active line tooth is constructed with plane spiral of Archimedes |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201721103836.XU CN207830468U (en) | 2017-08-31 | 2017-08-31 | The oblique line gear mechanism of active line tooth is constructed with plane spiral of Archimedes |
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| CN207830468U true CN207830468U (en) | 2018-09-07 |
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| CN201721103836.XU Withdrawn - After Issue CN207830468U (en) | 2017-08-31 | 2017-08-31 | The oblique line gear mechanism of active line tooth is constructed with plane spiral of Archimedes |
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Cited By (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN107448552A (en) * | 2017-08-31 | 2017-12-08 | 华南理工大学 | With the oblique line gear mechanism of plane spiral of Archimedes construction active line tooth |
| CN109253228A (en) * | 2018-11-20 | 2019-01-22 | 李民涛 | Indent class truncated cone-shaped gear |
-
2017
- 2017-08-31 CN CN201721103836.XU patent/CN207830468U/en not_active Withdrawn - After Issue
Cited By (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN107448552A (en) * | 2017-08-31 | 2017-12-08 | 华南理工大学 | With the oblique line gear mechanism of plane spiral of Archimedes construction active line tooth |
| CN109253228A (en) * | 2018-11-20 | 2019-01-22 | 李民涛 | Indent class truncated cone-shaped gear |
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