CN108897910A - The calculation method of Cycloidal Wheel equivalent torsional stiffness in a kind of RV retarder - Google Patents
The calculation method of Cycloidal Wheel equivalent torsional stiffness in a kind of RV retarder Download PDFInfo
- Publication number
- CN108897910A CN108897910A CN201810530491.9A CN201810530491A CN108897910A CN 108897910 A CN108897910 A CN 108897910A CN 201810530491 A CN201810530491 A CN 201810530491A CN 108897910 A CN108897910 A CN 108897910A
- Authority
- CN
- China
- Prior art keywords
- cycloidal wheel
- needle tooth
- tooth
- engagement
- needle
- Prior art date
- Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
- Pending
Links
- 238000004364 calculation method Methods 0.000 title claims abstract description 28
- 238000006073 displacement reaction Methods 0.000 claims abstract description 10
- 230000004048 modification Effects 0.000 claims description 6
- 238000012986 modification Methods 0.000 claims description 6
- 238000000034 method Methods 0.000 abstract description 11
- 238000004458 analytical method Methods 0.000 abstract description 7
- 238000007796 conventional method Methods 0.000 abstract 1
- 230000001186 cumulative effect Effects 0.000 abstract 1
- 238000011160 research Methods 0.000 description 6
- 239000000463 material Substances 0.000 description 5
- 230000008569 process Effects 0.000 description 5
- 230000005540 biological transmission Effects 0.000 description 4
- 230000008859 change Effects 0.000 description 4
- 238000001125 extrusion Methods 0.000 description 4
- 239000003638 chemical reducing agent Substances 0.000 description 3
- 238000013461 design Methods 0.000 description 3
- 238000010586 diagram Methods 0.000 description 3
- 239000011159 matrix material Substances 0.000 description 3
- 238000004088 simulation Methods 0.000 description 3
- 238000009434 installation Methods 0.000 description 2
- 230000009467 reduction Effects 0.000 description 2
- 230000009471 action Effects 0.000 description 1
- 238000013459 approach Methods 0.000 description 1
- 238000010835 comparative analysis Methods 0.000 description 1
- 239000002131 composite material Substances 0.000 description 1
- 238000011156 evaluation Methods 0.000 description 1
- 238000004519 manufacturing process Methods 0.000 description 1
- 238000005457 optimization Methods 0.000 description 1
- 230000000737 periodic effect Effects 0.000 description 1
- 230000008439 repair process Effects 0.000 description 1
- 210000001226 toe joint Anatomy 0.000 description 1
- 238000013519 translation Methods 0.000 description 1
- 230000007306 turnover Effects 0.000 description 1
Classifications
-
- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F30/00—Computer-aided design [CAD]
- G06F30/20—Design optimisation, verification or simulation
- G06F30/23—Design optimisation, verification or simulation using finite element methods [FEM] or finite difference methods [FDM]
-
- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F2119/00—Details relating to the type or aim of the analysis or the optimisation
- G06F2119/06—Power analysis or power optimisation
Abstract
The invention discloses a kind of calculation methods of Cycloidal Wheel equivalent torsional stiffness in RV retarder, solve the equivalent mesh stiffness of Cycloidal Wheel and needle tooth when concave-convex and two kinds of contact conditions of convexo-convex engage respectively using Hertz formula；The practical total number of teeth in engagement of Cycloidal Wheel calculates, and first passes through formula calculating solution and obtains the gap of each needle tooth and Cycloidal Wheel in path of contactDisplacement δ of each needle tooth in path of contact is obtained by equations againi, whenWhen, needle tooth at this participates in engagement, it is anti-regular to have neither part nor lot in engagement, and obtain the specific needle tooth tooth number for participating in engagement, calculate each mesh stiffness for participating in engagement needle tooth, it converts mesh stiffness to the torsion stiffness of Cycloidal Wheel, then these torsion stiffness is subjected to cumulative solution by formula, obtain the equivalent torsional stiffness of Cycloidal Wheel.The present invention has obtained more accurate Cycloidal Wheel equivalent torsional stiffness, carries out dynamic analysis to RV retarder and provides necessary condition.This method is compared with conventional method computational science, and accuracy is higher.
Description
Technical field
The invention belongs to reducer power field, it is related to Cycloidal Wheel torsion stiffness calculation method in a kind of RV retarder, tool
Body is related to a kind of calculation method of Cycloidal Wheel equivalent torsional stiffness in RV retarder.
Background technique
RV retarder is a kind of novel joint of robot precision speed reduction device, and compared with traditional retarder, it has
It small in size, the advantages that transmission ratio is high, driving torque is big, high-efficient, stability is high, is widely used in foreign countries.It is domestic right
It starts late in the research of RV retarder, wherein the dynamic analysis of RV retarder is always domestic hot research content, right
The dynamics research of RV retarder can obtain the intrinsic frequency of complete machine, and retarder inner body is avoided to generate resonance, and reduction subtracts
The noise of fast device and loss.To RV retarder carry out dynamic analysis when, stiffness matrix be to solve for complete machine intrinsic frequency and
It is significant to the dynamics research of RV retarder to obtain accurate rigidity for the necessary condition of vibration characteristics.
Summary of the invention
Background technique there are aiming at the problem that, the present invention provides a kind of more accurate for solving cycloid in RV retarder
Take turns the calculation method of equivalent torsional stiffness.
Technical scheme is as follows：
The calculation method of Cycloidal Wheel equivalent torsional stiffness in a kind of RV retarder, which is characterized in that include the following steps：
Step 1: rigidity when solving Cycloidal Wheel and needle tooth engagement respectively using Hertz formula, Cycloidal Wheel and needle tooth are nibbled
It closes and there are concave-convex and two kinds of contact conditions of convexo-convex, pass through the Cycloidal Wheel and needle under two kinds of contact conditions of Hertz equations respectively
The equivalent mesh stiffness of tooth；
Step 2: the practical total number of teeth in engagement of Cycloidal Wheel calculates, it is contemplated that Cycloidal Wheel is in order to reserve oil film space and what is carried out repair
Shape first passes through following formula calculating and solves so the practical total number of teeth in engagement of Cycloidal Wheel and needle tooth is no longer the half of the needle number of teeth
To the gap of each needle tooth and Cycloidal Wheel in path of contact：
In above formula,It is i-th of needle tooth for pivoted armCorner,Circle center O is distributed for needle toothPWith Cycloidal Wheel
Center OcLine, Δ rrpFor Cycloidal Wheel modification of equidistance amount, K1Curtate ratio, Δ rpIt is Cycloidal Wheel modification of moved distance amount；
Pass through againSolution obtains displacement δ of each needle tooth in path of contacti, whenWhen, the needle tooth at this participates in engagement, and it is anti-regular to have neither part nor lot in engagement, and obtain the specific needle tooth tooth number for participating in engagement,
Middle δmaxFor the deflection at Cycloidal Wheel and needle tooth stress maximum point；
Step 3: after obtaining actual participation engaging tooth number, since the position of engagement of each needle tooth and Cycloidal Wheel is different from,
By the angle where each needle toothCorresponding mesh stiffness is obtained by equations in step 1, the engagement for obtaining needle tooth is rigid
After degree, it converts mesh stiffness to the torsion stiffness of Cycloidal Wheel, then the torsion stiffness of actual participation engagement needle tooth is passed through into formulaCumulative solution is carried out, the equivalent torsional stiffness of Cycloidal Wheel is obtained, wherein m is first needle tooth number of engagement, and n is nibbled
The last one the needle tooth number closed, kiFor the torsion stiffness of i-th of needle tooth, liFor the arm of force of respective needle tooth.
Preferably, in step 1, when being calculated using Hertz formula, contact resilient shape when Cycloidal Wheel and needle tooth engagement
Become the surface area of an actually very little, therefore when being calculated using Hertz formula, needle tooth is seen with engaging for Cycloidal Wheel
Doing radius of curvature is ρ1、ρ2Two cylinder contacts；But due to the radius of curvature ρ of Cycloidal Wheel2Be variation andWherein rpFor centre circle of gear pins radius, K1Curtate ratio, zpFor the needle number of teeth,It is cycloid
Any point on tooth profile curve with respect to pivoted arm corner, as Cycloidal Wheel radius of curvature ρ2When > 0, Cycloidal Wheel and needle mark of mouth are convex
Contact, as Cycloidal Wheel radius of curvature ρ2It is contacted when < 0 for convexo-convex；The Cycloidal Wheel and needle tooth under two kinds of contact conditions are solved respectively
Equivalent mesh stiffness.
Preferably, torsion stiffness carries out cycle calculations by the way that parameter is substituted into MATLAB programming in the step 3.
Present invention has the advantages that：
The calculation method of Cycloidal Wheel equivalent torsional stiffness is fallen into a trap with the prior art in a kind of RV retarder proposed by the present invention
Calculation method is compared：
(1) in traditional Cycloidal Wheel Rigidity Calculation formula, engagement directly is participated in by half tooth of Cycloidal Wheel and is calculated, then
Multiplied by an approximate proportionality coefficient, while not considering that Cycloidal Wheel radius of curvature positive and negative values must change, so in calculating process yet
In, it is possible that the case where rigidity of certain several tooth is negative value, obtained value error is larger, engages in view of actual participation
The number of teeth and the positive and negative variation of Cycloidal Wheel radius of curvature after, obtained new Rigidity Calculation formula is more accurate.
(2) the advantages of this method is to obtain more accurate Cycloidal Wheel equivalent torsional stiffness, is moved to RV retarder
When mechanical analysis, accurate stiffness matrix is obtained, is to solve for the necessary condition of intrinsic frequency and vibration characteristics.
Detailed description of the invention
Fig. 1 is the deformation of Hertz formula cylinder contacts；
Fig. 2 is Cycloidal Wheel and needle tooth contact schematic diagram；
Wherein Fig. 2 a is that Cycloidal Wheel and needle tooth convexo-convex contact, and Fig. 2 b is Cycloidal Wheel and the convex contact of needle mark of mouth；
Fig. 3 is Cycloidal Wheel primary clearance figure；
Fig. 4 is MATLAB calculation process block diagram；
Fig. 5 is equivalent torsional stiffness change curve；
Fig. 6 is that SolidWorks engages illustraton of model；
In figure, number 3 to 11 indicates that No. 3 is arrived o.11 needle tooth, and 12 indicate pin wheel housing, and 13 indicate Cycloidal Wheel；
Fig. 7 is Workbench simulation result diagram.
Specific embodiment
Below in conjunction with the accompanying drawings and embodiment the invention will be further described.
The present invention relates to a kind of calculation methods of Cycloidal Wheel equivalent torsional stiffness in RV retarder, it is intended to obtain more accurate
Cycloidal Wheel torsion stiffness, the dynamics research of RV retarder.Specific implementation process：
1, Cycloidal Wheel and needle tooth engagement Rigidity Calculation
Cycloidal Wheel is contacted with multiple needle teeth in RV retarder, and actual conditions bottom line wheel is in the process with needle tooth engagement
In deformation has occurred, then when it is considered that Cycloidal Wheel is with needle tooth contact is approximately that two cylindrical surfaces are contacted, then can be sharp
It is calculated with hertz formula (Hertz formula).
As shown in Figure 1, being by the half-breadth that contact surface can be obtained in hertz formula when the contact of two cylindrical bodies：
Wherein F is contact force, and L is the half-breadth of contact surface, μ1, μ2The respectively Poisson's ratio of needle tooth and Cycloidal Wheel, E1, E2Point
Not Wei needle tooth and Cycloidal Wheel material elasticity modulus, ρ1, ρ2The respectively radius of curvature of needle tooth and Cycloidal Wheel, due to Cycloidal Wheel with
The material of needle tooth is identical, then can be simplified as formula (1)(ρ, ρ when calculating2Always
For positive value), since needle tooth is cylindrical body, radius of curvature ρ1For definite value, equal to the cylindrical radius r of itselfrp, ρ is needle
Tooth and Cycloidal Wheel composite curve radius, the radius of curvature of Cycloidal Wheel by《Mechanical design handbook》Known to (Xu Hao) inquiry：
Work as ρ2When for positive value, curve concaves, and needle tooth is contacted with Cycloidal Wheel bumps, and curvature summation is negative sign, works as ρ2For negative value
When, curve convex, needle tooth is contacted with Cycloidal Wheel convexo-convex, and curvature summation is positive sign, r in formula (2)pIt is the half of centre circle of gear pins
Diameter, zpFor the needle number of teeth, K1For curtate ratio and K1=azp/rp, a is Cycloidal Wheel eccentricity.
According to hertz formula, the extrusion deformation degree of needle tooth and Cycloidal Wheel is：
According to document《RV braking maneuver mechanical modeling and Analysis of Parameters》(magnify and defend) is described, withFor variable,
It is unfolded using Taylor's formula,Place's expansion substitutes into formula (3) after ignoring higher-order shear deformation, can obtain the extrusion deformation of needle tooth
Measure cr：
Since needle tooth and Cycloidal Wheel are made of identical material, the Poisson's ratio and elasticity modulus of the two material are homogeneous
Deng using common elastic modulus E instead of E in subsequent calculating1And E2, μ is replaced using common Poisson's ratio μ1And μ2；
The mesh stiffness that single needle tooth can then be calculated is：
Substituting into formula (4) can obtain, as 2 > 0 of ρ：
Evaluation is taken as 2 < 0 of ρ | ρ2| it calculates：
In formula (7) It is i-th of needle tooth for turning
ArmCorner, OPFor the center of circle (needle tooth is distributed circle center) of centre circle of gear pins, OcCycloidal Wheel center, pivoted armTake needle tooth
It is distributed circle center OPWith Cycloidal Wheel center OcLine, state as shown in Figure 3.
The rigidity of single Cycloidal Wheel can be similarly acquired by following formula：
Cycloidal gear teeth extrusion deformation degree ccIt is calculated by following formula
WithFor variable, using Taylor's formula,Place's expansion, ignores higher-order shear deformation, then substitute into formula
(8), cycloidal gear teeth extrusion deformation degree is obtained：
The mesh stiffness that single cycloidal gear teeth can then be acquired is：
Then work as ρ2When > 0
Work as ρ2When < 0,
Individually the mesh stiffness of cycloidal gear teeth and needle tooth is：Substitute into kc, krAbbreviation can obtain, and work as ρ2> 0
When：
Work as ρ2When < 0：
kiFor the mesh stiffness of i-th needle tooth and cycloidal gear teeth；From the above equation, we can see that when needle tooth is contacted with Cycloidal Wheel convexo-convex
When, mesh stiffness is definite value.
2, the practical total number of teeth in engagement of Cycloidal Wheel calculates
In actual manufacturing process, Cycloidal Wheel can pass through mending teeth of gear, either modification of equidistance or modification of moved distance, all can
Cause initial engagement gap, so that the number of teeth of the effective force engaged simultaneously is reduced, the needle number of teeth is not achieved in practical total number of teeth in engagement
All there is corresponding gap between remaining each tooth pair when first tooth in Cycloidal Wheel enters engagement in half.
As shown in figure 3, the i-th pair gear teeth are along the primary clearance with meshing point normal directionIt can be calculated as follows：
In formula (15)It is i-th of needle tooth for pivoted armCorner；K1For curtate ratio, K1=azp/rp；
It enablesIt can be solved by formula (15)The solution is the angle that primary clearance is zero, when unloaded,
Only closestA pair of of tooth engagement at place.
Cycloidal Wheel is in torque TcUnder the action of, since Cycloidal Wheel is contacted with the juxtaposition metamorphose W of pinwheel and needle tooth with pin wheel housing
F is deformed, Cycloidal Wheel turns over a corner β, ignores the lesser deflection of pin wheel housing and crank axle, then knows that Cycloidal Wheel is respectively nibbled
Chalaza should be in the total deformation W+f of common normal direction quotient and in the displacement of to be engaged normal directionβ is the corner (rad) of the Cycloidal Wheel due to caused by juxtaposition metamorphose after load in formula；liFor
The normal of the common normal of i-th needle tooth engagement point or point to be engaged is to Cycloidal Wheel center OcDistance (mm)；
R in formula (16)cFor the pitch radius (mm) of Cycloidal Wheel；rc=a*Zc, a be eccentricity, ZcIt is cycloidal gear teeth
Number, ZcThan needle tooth number ZpIt is one few.
Cycloidal Wheel and the maximum point of needle tooth stress existPlace, if deflection herein is δmax, due to lmax≈rc, then i-th
Displacement of the Cycloidal Wheel in meshing point common normal be at a needle tooth：
WhenWhen Cycloidal Wheel and needle tooth contact.
By document《Mechanical design handbook》Known to:
The maximum tooth institute stress F of stress in all teeth of available power transmission simultaneouslymax, maximum deformation quantity δ heremax=
Wmax+fmax, wherein WmaxAnd fmaxSize again and FmaxCorrelation, so first providing a F when calculatingmax0Initial value carry out
It solves, acquires corresponding starting tooth number, final tooth number and δmax0, then the δ that will be obtainedmax0It substitutes into formula (18), acquires Fmax1,
Compare Fmax0And Fmax1If Fmax0With Fmax1Absolute value of the difference is greater than 0.1%Fmax1, just by Fmax1It is iterated again, until
Obtained FmaxkMeet | Fmaxk-Fmax(k-1)| < 0.1%Fmax, then takeFor actual FmaxValue.
3, example calculation
By taking RV-40E type speed reducer as an example, its Cycloidal Wheel equivalent torsional stiffness is calculated, then with traditional Cycloidal Wheel
Calculation method compares, and retarder major parameter is as follows：
1 retarder parameter list of table
When Cycloidal Wheel and needle tooth engagement, the equivalent torsional stiffness that any one tooth generates is：
In traditional Cycloidal Wheel mesh stiffness calculation formula, k0iCalculation formula be：
After the mesh stiffness for calculating each tooth, added up by the torsion stiffness that formula (19) is converted to Cycloidal Wheel,
Multiplied by the proportionality coefficient λ between a value about 0.6~0.7, calculated result is as follows：
Using approach described herein, through document《The original gap and force analysis of cycloid pinwheel planetary gear transmission system》(Lee
Vertical row) what is calculated is 9 to the number of teeth for actually simultaneously participating in engagement, it is the 3rd~11 tooth, obtained range of numbers of teeth is updated to
It is solved in MATLAB program, the program chart of MATLAB is as shown in Figure 4.
The equivalent torsional stiffness of thus obtained Cycloidal Wheel is：
When due to cycloidal-pin wheel rotation, meshing point is also in variation simultaneously, and answering this equivalent torsional stiffness is also variation,
Cycloidal Wheel has a translation counterclockwise around centre circle of gear pins, while also having rotating clockwise around central axis, then can ask
Obtaining its frequency is：Wherein ωHFor the revolving speed of crank axle.
During installation due to RV retarder, it can choose and exported with shell output either Cycloidal Wheel, so stiffness variation
For frequency also with the frequency dependence of installation, crankshaft-rotation is bigger, and the frequency of stiffness variation is bigger.
It is studied with RV-40E type speed reducer, it is as shown in Figure 5 to obtain its torsion stiffness changing rule：
By comparative analysis it is found that the equivalent torsional stiffness of Cycloidal Wheel and needle tooth contact is worth around one into periodic wave
Dynamic, period of change is identical as the crankshaft rotation period, and the variation fluctuation amplitude of equivalent torsional stiffness is less than 1.5%, so
The approximate equivalent torsional stiffness that can consider Cycloidal Wheel is exactly the center of amplitude.
4, finite element simulation
Cycloidal Wheel, needle tooth and pin wheel housing are modeled in SolidWorks (due to mainly consider Cycloidal Wheel with
The power that the contact of needle tooth generates, so simplifying when modeling to pin wheel housing), in above-mentioned calculating, solve to obtain in text
Described under conditions of, actual participation engagement the number of teeth be the 3rd~No. 11 tooth, so modeling when equally also only retain the 3rd~
No. 11 needle teeth, by document《Anti- bow tooth exterior feature research and its optimization design in cycloid pinwheel planetary gear transmission system》(Guan Tianmin) is it is found that cycloid
When taking turns in the unloaded state with first needle tooth contact, first have to turn over certain angle, the relative rotation at this is：
So turning timing in Cycloidal Wheel and needle tooth, need to give Cycloidal Wheel phase
For a corner β of centre circle of gear pins0.Obtained figure is illustrated in fig. 6 shown below：
Established model is imported into Workbench and is emulated, the material of Cycloidal Wheel, needle tooth and pin wheel housing is defined
Expect attribute, due to mainly considering contact of the needle tooth with Cycloidal Wheel, and contact of the needle tooth with pin wheel housing is considered as rigid body and contacts, so building
Mould hour hands tooth and pin wheel housing regard an entirety as, when grid dividing, since hexahedral mesh precision is higher and convergence rate is very fast,
So being divided when to Cycloidal Wheel grid dividing using hexahedral mesh, while the side length for defining each grid cell is
1mm。
Because last solve will obtain rotation radian value of the Cycloidal Wheel around own axes, one is defined in Cycloidal Wheel
The heart is the cylindrical-coordinate system of coordinate origin, and wherein x-axis, z-axis are identical as original coordinate system direction, what y-axis was transformed to rotate around z-axis
Displacement.
In terms of defining constraint, fixed constraint is added to pin wheel housing periphery, the center circle of Cycloidal Wheel is added without friction
Support constraint replaces the output torque of Cycloidal Wheel to Cycloidal Wheel addition one around the torque that centre circle of gear pins rotates counterclockwise.
The displacement for obtaining Cycloidal Wheel with needle toe joint contacting surface in the direction y is solved to be in when due to participating in engagementThe needle tooth at place
Enter engagement at first, is calculatedPlace is No. 5 needle tooth, chooses the engagement that the displacement at this is Cycloidal Wheel entirety and is displaced,
As shown in Figure 7
The average value for the displacement being calculated is about between 0.00026995~0.00063915mm, and approximation takes among it
Value 0.000454mm, the rotational angle θ of Cycloidal Wheel are the ratio of Cycloidal Wheel rotation displacement and its radius, and result is substituted into and is put
The torsion stiffness of line wheel is：
The result and calculated result acquired has certain deviation, in Workbench only to Cycloidal Wheel be added to one around
Itself axial torque, and the movement of actual conditions bottom line wheel should be rotation of the Cycloidal Wheel around centre circle of gear pins and itself
Rotation, so practical can be variant with the contact situation emulated in Workbench with the engagement situation of needle tooth, so as to cause mistake
The generation of difference.
Has following advantages by above-mentioned verifying calculation method of the present invention：
(1) in traditional Cycloidal Wheel Rigidity Calculation formula, engagement directly is participated in by half tooth of Cycloidal Wheel and is calculated, then
Multiplied by an approximate proportionality coefficient, while not considering that Cycloidal Wheel radius of curvature positive and negative values must change, so in calculating process yet
In, it is possible that the case where rigidity of certain several tooth is negative value, obtained value error is larger, engages in view of actual participation
The number of teeth and the positive and negative variation of Cycloidal Wheel radius of curvature after, obtained new Rigidity Calculation formula is more accurate.
(2) the advantages of this method is to obtain more accurate Cycloidal Wheel equivalent torsional stiffness, is moved to RV retarder
When mechanical analysis, accurate stiffness matrix is obtained, is to solve for the necessary condition of intrinsic frequency and vibration characteristics.In illustrative example
After being calculated, be that simulation result compares checking computations, it was demonstrated that the more traditional calculation method of this method moreover, accuracy more
It is high.
Claims (3)
1. the calculation method of Cycloidal Wheel equivalent torsional stiffness in a kind of RV retarder, which is characterized in that include the following steps：
Step 1: rigidity when solving Cycloidal Wheel and needle tooth engagement respectively using Hertz formula, Cycloidal Wheel and needle tooth engagement are deposited
In concave-convex and two kinds of contact conditions of convexo-convex, pass through the Cycloidal Wheel and needle tooth under two kinds of contact conditions of Hertz equations respectively
Equivalent mesh stiffness；
Step 2: the practical total number of teeth in engagement of Cycloidal Wheel calculates, it is contemplated that the correction of the flank shape that Cycloidal Wheel carries out to reserve oil film space, institute
Practical total number of teeth in engagement with Cycloidal Wheel and needle tooth is no longer the half of the needle number of teeth, first pass through following formula calculate solve obtain it is each
The gap of needle tooth and Cycloidal Wheel in path of contact：
In above formula,It is i-th of needle tooth for pivoted armCorner,Circle center O is distributed for needle toothPWith Cycloidal Wheel center
OcLine, Δ rrpFor Cycloidal Wheel modification of equidistance amount, K1Curtate ratio, Δ rpIt is Cycloidal Wheel modification of moved distance amount；
Pass through againSolution obtains displacement δ of each needle tooth in path of contacti, when
When, the needle tooth participation engagement at this is anti-regular to have neither part nor lot in engagement, and obtains the specific needle tooth tooth number for participating in engagement, wherein δmaxFor
Deflection at Cycloidal Wheel and needle tooth stress maximum point；
Step 3: after obtaining actual participation engaging tooth number, it, will be each since the position of engagement of each needle tooth and Cycloidal Wheel is different from
Angle where needle toothCorresponding mesh stiffness is obtained by equations in step 1, obtains the mesh stiffness of needle tooth
Afterwards, mesh stiffness is converted to the torsion stiffness of Cycloidal Wheel, then the torsion stiffness of actual participation engagement needle tooth is passed through into formulaCumulative solution is carried out, the equivalent torsional stiffness of Cycloidal Wheel is obtained, wherein m is first needle tooth number of engagement, and n is nibbled
The last one the needle tooth number closed, kiFor the torsion stiffness of i-th of needle tooth, liFor the arm of force of respective needle tooth.
2. calculation method as described in claim 1, it is characterised in that：In step 1, when being calculated using Hertz formula, pendulum
Contact resilient deformation is actually the surface area of a very little when line wheel and needle tooth engagement, therefore is utilizing Hertz formula meter
When calculation, needle tooth is regarded as radius of curvature with engaging for Cycloidal Wheel for ρ1、ρ2Two cylinder contacts；But due to the curvature of Cycloidal Wheel
Radius ρ2Be variation andWherein rpFor centre circle of gear pins radius, K1Curtate ratio, zpFor
The needle number of teeth,It is any point on Cycloid tooth profile curve with respect to pivoted armCorner, as Cycloidal Wheel radius of curvature ρ2> 0
When, Cycloidal Wheel with needle mark of mouth is convex contacts, as Cycloidal Wheel radius of curvature ρ2It is contacted when < 0 for convexo-convex；Two kinds of contact shapes are solved respectively
The equivalent mesh stiffness of Cycloidal Wheel and needle tooth under state.
3. calculation method as claimed in claim 2, it is characterised in that：In the step 3, torsion stiffness is by by parameter generation
Enter MATLAB programming and carries out cycle calculations.
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201810530491.9A CN108897910A (en) | 2018-05-29 | 2018-05-29 | The calculation method of Cycloidal Wheel equivalent torsional stiffness in a kind of RV retarder |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201810530491.9A CN108897910A (en) | 2018-05-29 | 2018-05-29 | The calculation method of Cycloidal Wheel equivalent torsional stiffness in a kind of RV retarder |
Publications (1)
| Publication Number | Publication Date |
|---|---|
| CN108897910A true CN108897910A (en) | 2018-11-27 |
Family
ID=64343319
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CN201810530491.9A Pending CN108897910A (en) | 2018-05-29 | 2018-05-29 | The calculation method of Cycloidal Wheel equivalent torsional stiffness in a kind of RV retarder |
Country Status (1)
| Country | Link |
|---|---|
| CN (1) | CN108897910A (en) |
Cited By (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN110399662A (en) * | 2019-07-12 | 2019-11-01 | 东华大学 | A kind of Cycloid tooth profile correction method |
| CN111125898A (en) * | 2019-12-17 | 2020-05-08 | 之江实验室 | Rapid optimization method for profile modification coefficient of cycloidal gear tooth profile |
| CN111639293A (en) * | 2020-05-25 | 2020-09-08 | 济南大学 | Method for calculating tooth profile curvature radius of cycloidal gear at needle tooth meshing position of cycloidal gear |
Citations (1)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN107256282A (en) * | 2017-05-08 | 2017-10-17 | 华南理工大学 | A kind of RV Key Part of Cycloid Cam Planetary Speed Reducer profile modification methods compensated based on deformation quantity |
-
2018
- 2018-05-29 CN CN201810530491.9A patent/CN108897910A/en active Pending
Patent Citations (1)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN107256282A (en) * | 2017-05-08 | 2017-10-17 | 华南理工大学 | A kind of RV Key Part of Cycloid Cam Planetary Speed Reducer profile modification methods compensated based on deformation quantity |
Non-Patent Citations (2)
| Title |
|---|
| 张迎辉等: "机器人用RV减速器针摆传动啮合刚度计算", 《大连交通大学学报》 * |
| 祝鹏: "RV减速器的传动精度分析", 《中国优秀硕士学位论文全文数据库.工程科技II辑》 * |
Cited By (5)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN110399662A (en) * | 2019-07-12 | 2019-11-01 | 东华大学 | A kind of Cycloid tooth profile correction method |
| CN111125898A (en) * | 2019-12-17 | 2020-05-08 | 之江实验室 | Rapid optimization method for profile modification coefficient of cycloidal gear tooth profile |
| CN111125898B (en) * | 2019-12-17 | 2021-06-01 | 之江实验室 | Rapid optimization method for profile modification coefficient of cycloidal gear tooth profile |
| CN111639293A (en) * | 2020-05-25 | 2020-09-08 | 济南大学 | Method for calculating tooth profile curvature radius of cycloidal gear at needle tooth meshing position of cycloidal gear |
| CN111639293B (en) * | 2020-05-25 | 2022-05-20 | 济南大学 | Method for calculating tooth profile curvature radius of cycloidal gear at pin tooth meshing position of cycloidal gear |
Similar Documents
| Publication | Publication Date | Title |
|---|---|---|
| CN108897910A (en) | The calculation method of Cycloidal Wheel equivalent torsional stiffness in a kind of RV retarder | |
| CN107944174A (en) | A kind of roller gear Longitudinal Load Distribution Factors acquisition methods | |
| Zou et al. | Deformation and stress analysis of short flexspline in the harmonic drive system with load | |
| CN109783840B (en) | Calculation method for time-varying meshing stiffness of straight-tooth cylindrical gear internal meshing gear pair | |
| Gurumani et al. | Modeling and contact analysis of crowned spur gear teeth | |
| CN110516345A (en) | Planetary roller screw error source coupling modeling method | |
| Song et al. | Parameter design of double-circular-arc tooth profile and its influence on meshing characteristics of harmonic drive | |
| CN110688614B (en) | Multi-tooth meshing composite stress solving method for cup-shaped flexible wheel of harmonic reducer | |
| CN107763173B (en) | Finite element analysis-based helical gear time-varying meshing stiffness calculation method | |
| Mao | An approach for powertrain gear transmission error prediction using the non-linear finite element method | |
| Ma et al. | Tooth surface reconstruction and tooth profile geometric analysis of circular arc tooth trace cylindrical gears | |
| Yang et al. | Study on mesh stiffness and sensitivity analysis of planetary gear system considering the deformation effect of carrier and bearing | |
| Tsai et al. | Dynamic analysis and reliability evaluation for an eccentric speed reducer based on fem | |
| Huang et al. | Mesh stiffness analysis of beveloid gears for the rotating vector transmission | |
| Bodzás | Analysis of the effect of the addendum modification coefficient for contact surfaces of spur gear | |
| Ma et al. | Analysis of the tooth surface contact area of a circular-arc-tooth-Trace cylindrical gear under load | |
| Li et al. | Meshing theory and simulation of noninvolute beveloid gears | |
| Ivanović et al. | Specific sliding of trochoidal gearing profile in the gerotor pumps | |
| Gründer et al. | Advanced calculation of the deflection of worm shafts with FEM | |
| Kikuchi et al. | Stress analysis of cup type strain wave gearing | |
| CN113010978A (en) | Aviation straight gear shaping method based on dynamic simulation | |
| Daffner et al. | Method of measuring the load distribution of spur gear stages | |
| Chen et al. | The investigation of elongation of the neutral line in harmonic drive | |
| CN113361031B (en) | Three-dimensional tooth shape design method for flexible gear of harmonic reducer | |
| Li et al. | STATICS ANALYSIS OF CYLINDRICAL GEAR DRIVE AT ANY MESHING POSITION BASED ON ANSYS. |
Legal Events
| Date | Code | Title | Description |
|---|---|---|---|
| PB01 | Publication | ||
| PB01 | Publication | ||
| SE01 | Entry into force of request for substantive examination | ||
| SE01 | Entry into force of request for substantive examination | ||
| RJ01 | Rejection of invention patent application after publication |
Application publication date: 20181127 |
|
| RJ01 | Rejection of invention patent application after publication |