CN108644342A - The method for building up of not rounded bevel gear limited slip differential kinetic model - Google Patents
The method for building up of not rounded bevel gear limited slip differential kinetic model Download PDFInfo
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- CN108644342A CN108644342A CN201810433298.3A CN201810433298A CN108644342A CN 108644342 A CN108644342 A CN 108644342A CN 201810433298 A CN201810433298 A CN 201810433298A CN 108644342 A CN108644342 A CN 108644342A
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- bevel gear
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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
- F16H48/00—Differential gearings
- F16H48/06—Differential gearings with gears having orbital motion
- F16H48/08—Differential gearings with gears having orbital motion comprising bevel gears
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- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F30/00—Computer-aided design [CAD]
- G06F30/10—Geometric CAD
- G06F30/17—Mechanical parametric or variational design
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- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F30/00—Computer-aided design [CAD]
- G06F30/30—Circuit design
- G06F30/36—Circuit design at the analogue level
- G06F30/367—Design verification, e.g. using simulation, simulation program with integrated circuit emphasis [SPICE], direct methods or relaxation methods
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Abstract
The present invention relates to a kind of method for building up of not rounded bevel gear limited slip differential kinetic model, include the following steps：S1, the dynamics calculation physical model for establishing not rounded bevel gear limited slip differential；S2, selected planet carrier corner and planetary gear corner are generalized coordinates；S3, the inclined class speed for obtaining each component Relative Generalized coordinate；S4, the equivalent moment of inertia and generalized force that each component is calculated according to inclined class speed, obtain basic dynamic model；S5, according to not rounded Bevel Gear Transmission feature in not rounded bevel gear limited slip differential, obtain inner friction torque model, bring kinetic model into；S6, according to differential mechanism basic mechanical characteristic, bring locking coefficient into kinetics equation, obtain the kinetic model for embodying not rounded bevel gear limited slip differential feature.The present invention can be accurately obtained the equilbrium position of the planetary characteristics of motion and limited slip differential in the not rounded bevel gear limited slip differential course of work, have many advantages, such as that computational accuracy is high, computational efficiency is high.
Description
Technical field
The present invention relates to non-conical nonlinear dynamic behavior fields, more specifically to a kind of not rounded bevel gear anti-slip differential
The method for building up of device kinetic model.
Background technology
Not rounded bevel gear may be implemented variable ratio power and movement between two concurrent aceses or alternating axis and transmit, and be passed using becoming
It is dynamic not only to have many advantages, such as compact-sized, stable drive, efficient, long lifespan than the not rounded bevel differential that space is driven,
But also there is differential antiskid function, the cone gear differential mechanism traditional by performance ratio on the ground such as muddy, wet and slippery, ice and snow
It is improved largely.During not rounded bevel gear limited slip differential is on active service, dynamic performance has weight to vehicle driving performance
It influences.
Since not rounded bevel gear limited slip differential planetary gear is to do the movement of continuous rotary, while rotating around planet carrier,
Its corner of sensor measurement and angular speed can not be being fixed above.Therefore, at present to not rounded bevel gear limited slip differential dynamics
The research of performance mainly carries out qualitative research by Kinematics Simulation, and Kinematics Simulation needs cumbersome modeling, and computational efficiency is low,
And it is unable to get the equilbrium position of the accurate planetary gear characteristics of motion and not rounded bevel gear limited slip differential.
Invention content
The technical problem to be solved in the present invention is, provides the not rounded bevel gear that a kind of computational accuracy is high, computational efficiency is high
The method for building up of limited slip differential kinetic model.
The technical solution adopted by the present invention to solve the technical problems is：It is dynamic to construct a kind of not rounded bevel gear limited slip differential
The method for building up of mechanical model, includes the following steps：
S1, the dynamics calculation physical model for establishing not rounded bevel gear limited slip differential；
S2, selected planet carrier corner and planetary gear corner are generalized coordinates；
S3, according to the base of variable ratio function and not rounded bevel gear limited slip differential differential gear train between not rounded bevel gear
This length velocity relation obtains the inclined class speed of each component Relative Generalized coordinate；
S4, the equivalent moment of inertia and generalized force that each component is calculated according to inclined class speed, obtain basic dynamic model；
S5, according to not rounded Bevel Gear Transmission feature in not rounded bevel gear limited slip differential, obtain inner friction torque model, band
Enter kinetic model；
S6, according to differential mechanism basic mechanical characteristic, bring locking coefficient into kinetics equation, obtain embodying not rounded bevel gear
The kinetic model of limited slip differential feature.
In said program, the variable ratio function in the step S3 between not rounded bevel gear isWithRoot
According to the base speed relationship of differential gear train, have：
Above-mentioned two formula is integrated, can be obtained：
Each component in not rounded bevel gear limited slip differential system is acquired relative to two generalized coordinates according to above-mentioned formula
Inclined class speed uki 1、uki 2(i=1,2,3, H；)：
In formula, ωHFor the speed of planet carrier, ω1For planetary absolute angular velocities, ω2、ω3Respectively left and right semiaxis
The angular speed of gear,For the rotational angle of planet carrier,For planetary rotational angle,Respectively left and right half
The rotational angle of shaft gear.
In said program, the equivalent moment of inertia J of component11、J22、J12For：
JHIt is planet carrier to the rotary inertia of its shaft, J1For planetary rotary inertia, J2、J3Respectively left and right half
The rotary inertia of shaft gear.
In said program, not rounded bevel gear limited slip differential system generalized force Q1、Q2Expression formula be：
Wherein, TrCalculation expression be：In formula
Δ ω is that the minimum speed of moment variations changes；
THFor the torque that engine transmission comes, T2、T3The torque that respectively left and right axle shaft gear is born, TrIt is that gear turns
The dynamic moment of friction generated in the process.
In said program, kinetic energy is possessed by entire not rounded bevel gear limited slip differential system：
T2And T3Calculation expression be：
In said program, the kinetics equation of entire not rounded bevel gear limited slip differential system is：
In formula：
Implement the method for building up of the not rounded bevel gear limited slip differential kinetic model of the present invention, has below beneficial to effect
Fruit：
The method of the present invention is solved based on Lagrange's equation according to the operation principle of not rounded bevel gear limited slip differential
Generalized coordinates is selected, inclined class speed, equivalent moment of inertia, generalized force, inner friction torque and limited slip differential locking coefficient meter
The Dynamic Modelings critical issues such as calculation, and then establish accurate not rounded bevel gear limited slip differential system dynamics model.It should
Method can be accurately obtained planet tooth in the not rounded bevel gear limited slip differential course of work by the solution to built kinetics equation
The characteristics of motion of wheel and the equilbrium position of limited slip differential have computational accuracy height, computational efficiency high compared with Kinematics Simulation
The advantages that.
Description of the drawings
Present invention will be further explained below with reference to the attached drawings and examples, in attached drawing：
Fig. 1 is the flow chart of the method for building up of the not rounded bevel gear limited slip differential kinetic model of the present invention
Fig. 2 is not rounded bevel gear limited slip differential dynamics calculation physical model；
Fig. 3 is that planetary gear rotation angle change of the not rounded bevel gear limited slip differential under different start-up phase parallactic angles is bent
Line；
Fig. 4 is rotational angle change curve of the not rounded bevel gear limited slip differential in different coefficients of friction lower planetary gear.
Specific implementation mode
For a clearer understanding of the technical characteristics, objects and effects of the present invention, now control attached drawing is described in detail
The specific implementation mode of the present invention.
As shown in Figure 1, the method for building up of the not rounded bevel gear limited slip differential kinetic model of the present invention includes following step
Suddenly it is：
S1, the dynamics calculation physical model for establishing not rounded bevel gear limited slip differential；
S2, selected planet carrier corner and planetary gear corner are generalized coordinates；
S3, according to the base of variable ratio function and not rounded bevel gear limited slip differential differential gear train between not rounded bevel gear
This length velocity relation obtains the inclined class speed of each component Relative Generalized coordinate；
S4, the equivalent moment of inertia and generalized force that each component is calculated according to inclined class speed, obtain basic dynamic model；
S5, according to not rounded Bevel Gear Transmission feature in not rounded bevel gear limited slip differential, obtain inner friction torque model, band
Enter kinetic model；
S6, according to differential mechanism basic mechanical characteristic, bring locking coefficient into kinetics equation, obtain embodying not rounded bevel gear
The kinetic model of limited slip differential feature.
It is described in detail with reference to Fig. 2-4 pairs of embodiments：
Non-circular gear limited slip differential is the differential gear train of two degrees of freedom, according to the work of not rounded bevel gear limited slip differential
Principle establishes the physical model of not rounded bevel gear limited slip differential dynamics calculation, as shown in Figure 2.
In Fig. 2, ωHFor the speed (i.e. the speed of differential mechanism input terminal gear wheel) of planet carrier, THCome for engine transmission
Torque, JHIt is planet carrier (including planetary gear) to the rotary inertia of its shaft.ω1For planetary absolute angular velocities, J1For row
The rotary inertia of star gear, ω2、ω3The respectively angular speed of left and right axle shaft gear, T2、T3Respectively left and right axle shaft gear is held
The torque (acting on the torque on wheel) received, J2、J3The respectively rotary inertia of left and right axle shaft gear (including wheel).Tr
It is the moment of friction generated in gear rotation process.
Since engine has very hard engineering properties, speed can remain unchanged within the scope of certain torque, and semiaxis
The speed of gear 2 and 3 is all with planetary gear 1 for reference quantity, therefore during establishing kinetic model, choose planetary gear
Rotational angleWith the rotational angle of planet carrierFor generalized coordinates.
In not rounded bevel gear limited slip differential, the transmission ratio function of not rounded bevel gear 1 and 2 is：
Transmission ratio function between not rounded bevel gear 1,3 is：Engine is even
Speed operating, then differential casing uniform motion, takes engine speed for 36deg/s, then the rotational angle of differential casingWith
Angular speedMeet relational expression：
Not rounded bevel gear limited slip differential system is the differential gear train of two degrees of freedom, is closed according to the base speed of differential gear train
System, has：
Above-mentioned two formula is integrated, can be obtained：
According to above-mentioned formula (1), obtains each component in not rounded bevel gear limited slip differential system and sat relative to two broad sense
The inclined class speed u of targetki 1、uki 2(i=1,2,3, H；) be：
According to the inclined class speed of each component Relative Generalized coordinate in above-mentioned formula (2), the equivalent moment of inertia of component is obtained
J11、J22、J12For：
In formula, J1、J2、J3、JHRespectively it is the rotary inertia of planetary gear, left and right axle shaft gear and planet carrier, J2=J3,
Value is carried out according to the parameter of not rounded bevel gear in kinetic model solution procedure, takes J1=3 × 10-3kg.m2, J2=J3=6
×10-3kg.m2, JH=1.5 × 10-2kg.m2。
System generalized force Q1、Q2Expression formula be：
Wherein, TrCalculation expression be：
In solution procedure, T is takenH=200Nm, Δ ω=0.01.
Kinetic energy is possessed by entire not rounded bevel gear limited slip differential system：
The torque come from engine transmission is fully allocated to left and right half gear, therefore has：TH=T2+T3
Locking coefficient k is used for weighing the partition characteristic of the non-skid property and torque of limited slip differential, is equal to vehicle speed two
The torque ratio of side drive wheel, therefore：
T2By the torque distributed on the larger side semiaxis of ground attaching coefficient, T3For the smaller side semiaxis of attachment coefficient
On the torque distributed.
It can obtain：
Bring the expression formula in formula (2), formula (3), formula (4), formula (5), formula (6) into Lagrange's equation
In, the kinetic model that entire not rounded bevel gear limited slip differential system can be obtained is：
In formula：
The not rounded bevel gear limited slip differential kinetic model established contains start-up phase parallactic angleIt locking coefficient k and rubs
Torque tri- parameters of μ are wiped,K and μ is the major parameter of non-conical gear limited slip differential dynamic analysis, can be as needed
It takes different constant values to bring kinetic model into and carries out solution calculating.Runge- is used in MATLAB to gained kinetic model
Kutta methods are programmed solution, obtain planetary gear rotation angle change curve, you can anti-to not rounded bevel gear under different operating modes
The dynamic performance of slip differential carries out theory analysis.
Friction coefficient μ takes 0, locking coefficient k to take 1, start-up phase parallactic angleIt is asked by kinetics equation when taking -45 ° and -60 °
The planetary gear rotation angle change curve that solution obtains is as shown in Figure 3.
Friction coefficient μ takes 0.05,0.06 and 0.08, locking coefficient k to take 2, start-up phase parallactic angleBy dynamics side when taking 0
The planetary gear rotation angle change curve that journey solves is as shown in Figure 4.
The embodiment of the present invention is described with above attached drawing, but the invention is not limited in above-mentioned specific
Embodiment, the above mentioned embodiment is only schematical, rather than restrictive, those skilled in the art
Under the inspiration of the present invention, without breaking away from the scope protected by the purposes and claims of the present invention, it can also make very much
Form, all of these belong to the protection of the present invention.
Claims (6)
1. a kind of method for building up of not rounded bevel gear limited slip differential kinetic model, which is characterized in that include the following steps：
S1, the dynamics calculation physical model for establishing not rounded bevel gear limited slip differential；
S2, selected planet carrier corner and planetary gear corner are generalized coordinates；
S3, according between not rounded bevel gear variable ratio function and not rounded bevel gear limited slip differential differential gear train it is substantially fast
Degree relationship obtains the inclined class speed of each component Relative Generalized coordinate；
S4, the equivalent moment of inertia and generalized force that each component is calculated according to inclined class speed, obtain basic dynamic model；
S5, according to not rounded Bevel Gear Transmission feature in not rounded bevel gear limited slip differential, obtain inner friction torque model, bring into dynamic
Mechanical model；
S6, according to differential mechanism basic mechanical characteristic, bring locking coefficient into kinetics equation, obtain embodying not rounded bevel gear anti-skidding
The kinetic model of differential mechanism feature.
2. the method for building up of not rounded bevel gear limited slip differential kinetic model according to claim 1, which is characterized in that
Variable ratio function in the step S3 between not rounded bevel gear isWithAccording to the base speed of differential gear train
Relationship has：
Above-mentioned two formula is integrated, can be obtained：
Inclined class of each component relative to two generalized coordinates in not rounded bevel gear limited slip differential system is acquired according to above-mentioned formula
Speed
In formula, ωHFor the speed of planet carrier, ω1For planetary absolute angular velocities, ω2、ω3Respectively left and right axle shaft gear
Angular speed,For the rotational angle of planet carrier,For planetary rotational angle,Respectively left and right half axle gear
The rotational angle of wheel.
3. the method for building up of not rounded bevel gear limited slip differential kinetic model according to claim 2, which is characterized in that
The equivalent moment of inertia J of component11、J22、J12For：
JHIt is planet carrier to the rotary inertia of its shaft, J1For planetary rotary inertia, J2、J3Respectively left and right axle shaft gear
Rotary inertia.
4. the method for building up of not rounded bevel gear limited slip differential kinetic model according to claim 3, which is characterized in that
Not rounded bevel gear limited slip differential system generalized force Q1、Q2Expression formula be：
Wherein, TrCalculation expression be：Δ ω in formula
Change for the minimum speed of moment variations；
THFor the torque that engine transmission comes, T2、T3The torque that respectively left and right axle shaft gear is born, TrIt is gear rotation process
The moment of friction of middle generation.
5. the method for building up of not rounded bevel gear limited slip differential kinetic model according to claim 4, which is characterized in that
Kinetic energy is possessed by entire not rounded bevel gear limited slip differential system：
T2And T3Calculation expression be：
6. the method for building up of not rounded bevel gear limited slip differential kinetic model according to claim 5, which is characterized in that
Entirely the kinetics equation of not rounded bevel gear limited slip differential system is：
In formula：
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Cited By (1)
| Publication number | Priority date | Publication date | Assignee | Title |
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| CN110083939A (en) * | 2019-04-28 | 2019-08-02 | 南京理工大学 | Pure electric vehicle differential gear correction of the flank shape optimization method |
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| US20100234163A1 (en) * | 2009-03-12 | 2010-09-16 | Eaton Corporation | Fluctuating gear ratio limited slip differential |
| CN101839307A (en) * | 2009-03-12 | 2010-09-22 | 伊顿公司 | Fluctuating gear ratio limited slip differential |
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| CN104214304A (en) * | 2014-09-18 | 2014-12-17 | 武汉理工大学 | Arc-tooth non-conical gear antiskid differential mechanism |
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