CN107844640A - A kind of computational methods of crawler travel device power attenuation - Google Patents
A kind of computational methods of crawler travel device power attenuation Download PDFInfo
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Abstract
The present invention relates to a kind of computational methods of crawler travel device power attenuation, it is related to endless-track vehicle technical field.The present invention by the analysis of the frictional force to the driving wheel gear teeth and crawler belt and friction displacement, the analysis to bogie wheel and rolling resistance of track and the relation of movement velocity, computational methods to crawler travel device power attenuation are proposed to power attenuation analysis of creeper tread kiss-coating pin torsional deflection etc., accuracy in computation is high, to provide data supporting to endless-track vehicle power match, dynamical system power selection.
Description
Technical field
The present invention relates to endless-track vehicle technical field, and in particular to a kind of calculating side of crawler travel device power attenuation
Method.
Background technology
Crawler travel device power attenuation computational problem is in technological gap state for a long time, and main cause is engineering skill
Excessive research is concentrated on New Products ＆ New Technology exploitation above by art personnel, ignores the calculating to properties of product.With vehicle
Power distribution becomes more meticulous, and the quantitative analysis to each system power demand and power attenuation is more and more urgent.
The content of the invention
(1) technical problems to be solved
The technical problem to be solved in the present invention is：How calculating to crawler belt behavioral system power attenuation is realized, to realize
To endless-track vehicle power match, dynamical system power selection.
(2) technical scheme
In order to solve the above-mentioned technical problem, the invention provides a kind of computational methods of crawler travel device power attenuation,
Comprise the following steps：
Step 1, the analysis based on the frictional force to the driving wheel gear teeth and crawler belt and the displacement that rubs, obtain the active gear teeth with carrying out
The meshing power loss of band plate；
Step 2, based on the analysis to bogie wheel and rolling resistance of track and the relation of movement velocity, obtain bogie wheel along carrying out
With ground section of rolling power attenuation；
Step 3, according in terms of following four crawler belt internal power consumption is calculated：To creeper tread kiss-coating pin torsional deflection
Power attenuation analysis, the calculating of power attenuation to causing kinetic energy change by changes of velocity, to making the change of pin ear rubber
The power attenuation of shape calculates, and power attenuation when stretching the creeper tread when leaving wheel to creeper tread calculates；
Step 4, the loss of the meshing power of the active gear teeth that steps 1 and 2,3 obtain and creeper tread, bogie wheel connect along crawler belt
The rolling power attenuation in location is added to obtain total power attenuation of crawler travel device with crawler belt internal power consumption three.
(3) beneficial effect
The present invention rolls by the analysis of the frictional force to the driving wheel gear teeth and crawler belt and the displacement that rubs, to bogie wheel and crawler belt
The analysis of the relation of dynamic resistance and movement velocity, power attenuation analysis of creeper tread kiss-coating pin torsional deflection etc. is proposed to carrying out
Computational methods with mobile devices power attenuation, accuracy in computation is high, for endless-track vehicle power match, the choosing of dynamical system power
Select and provide data supporting.
Brief description of the drawings
Fig. 1 is the active gear teeth of the present invention and the engaging friction resistance force analysis figure of creeper tread；
Fig. 2 is the residual deformation analysis chart of the elastic hinge of the present invention；
Fig. 3 is the motion principle figure for the creeper tread (1,2) that two connected on wheel；
Fig. 4 is the change curve of the kinetic energy when the creeper tread that is connected passes through wheel.
Embodiment
To make the purpose of the present invention, content and advantage clearer, with reference to the accompanying drawings and examples, to the present invention's
Embodiment is described in further detail.
The present invention is realized to the active gear teeth and the meshing power loss calculation of creeper tread：
The engaging friction resistance force analysis figure of the active gear teeth and creeper tread as shown in figure 1,
As shown in Figure 1, contact normal force is：
In formula：FNContact normal force；FTTo engage tangential force；αωFor track pin and the friction corner of the active gear teeth.
Contact friction force is：
FR=μ5FN (2)
In formula：FRFor contact friction force；μ5For coefficient of contact friction (for empirical value).
Contact friction force is in the component of lead：
FRE=FRsinαω (3)
In formula：FREFor contact friction force lead component.
It is comprehensive that three formulas, the engaging friction resistance for obtaining driving wheel and track pin are above：
FRE=μ5tanαωFT (4)
And when assuming that track pin moves in kerve, 1/4 only last engaging friction, therefore have：
In formula：--- between cog minute of angle；Z --- active tooth number.
Therefore the engaging friction resistance of driving wheel and track pin can be written as again：
Therefore the engaging friction resistance of driving wheel and track pin is calculated, can be attributed to again and calculate FT。FTIt can be considered crawler belt slack list
The sum of tensile force and tractive force, i.e.,：
FT=F0+FK
In formula：F0For crawler belt slack list tensile force；
FKFor driving wheel tractive force.
It can obtain：
The engaging friction power consumption of the active gear teeth and creeper tread：
Monodentate engagement frictional work once is：
W51=FREs (7)
In formula：W51For frictional work；S is frictional distance (unit m).
Frictional distance can be calculated according to following recommended formula in above formula.
In formula：VTIt is track pin with respect to active gear teeth fricting movement speed, VT≈rkω；T is run duration；ω is actively
Wheel speed；rkFor driving wheel pitch radius；
Driving wheel turns around, and engages z times altogether, z is the driving wheel number of teeth.Then total work is zW51.If driving wheel turns around institute's used time
Between be T, and becauseVT=rKω, then the active gear teeth are represented by with the power consumption that engages of creeper tread：
Rolling power attenuation of the bogie wheel along track length on ground calculates：
Rolling resistance calculation formula is as follows between bogie wheel and crawler belt：
P=ffQ1 (9)
In formula：ff--- the coefficient of rolling resistance of bogie wheel.The coefficient is determined by test method, and scope is in 0.004-0.02
Between.Q1--- bogie wheel and crawler belt normal pressure, unit N.
Then rolling power attenuation of the bogie wheel along track length on ground can be calculated with equation below：
W6=ffQ1VF (10)
In formula：W6The rolling power attenuation for being bogie wheel along track length on ground；VFLinear velocity is rolled for bogie wheel opposing tracks
(m/s)。
Rolling loss of the bogie wheel along track length on ground and contact of the coefficient of rolling resistance, bogie wheel of bogie wheel with crawler belt
Power and the point-to-point speed of scroll wheel are directly proportional.
In step 3, crawler belt internal power consumption calculates：
The power attenuation analysis of creeper tread kiss-coating pin torsional deflection：
When two neighboring creeper tread relatively rotates, gum sleeve is by twisting action repeatedly, due to rubber hinge
Hysteresis, has energy loss in the Delay Process of rubber sleeve.Assuming that have two adjacent track plate A, B by hinge O link (see
Fig. 2), hinge is gum sleeve.Creeper tread A is fixed, adds a moment of torsion M on B, creeper tread B rotation alphas angle, and gone to by position 1
Position 2.If rubber tube is definitely elasticity, after moment of torsion M disappears, creeper tread B should be returned to position 1.Actually due to rubber
There is residual deformation in hysteresis, B can only be returned to position 3, i.e. recovery angle α ' is less than corner α, B from position 1 to position 2, then
Position 3 is returned to by position 2 and is referred to as a circulation.The energy of a part, this portion of energy will be lost by often repeating a circulation
Loss will make gum sleeve generate heat, and when cycle frequency is very high, or even rubber is lost its physical property.
In order to calculate the hysteresis loss of gum sleeve, it is necessary to determine its rigidity first.Gum sleeve rigidity calculation formula：
In formula：
The rigidity of k --- rubber hinge, it is called angle rigidity (10Nm)；
r1--- gum sleeve innermost layer radius (cm)；
r2--- gum sleeve outermost layer radius (cm)；
lx--- gum sleeve length (cm)；
G1--- gum sleeve shearing resistance coefficient (bar).
Assuming that the pre-add torsion angle of rubber hinge is α0, typically take half of single hinge torsion angle or so.Rubber hinge
Relative torsion occur entering and exiting at the point of contact of segmental arc, if the torque absolute value of torsion hinge and torsion angle are into just
Than being α into the maximum twist angle of segmental arcmax, due to pretwist corner α be present0, actual torsion angle is (αmax-α0), hinge gathers
The potential energy of collection is：
Due to hysteresis be present when rubber hinge reverses, with μzThe energy-loss factor of hysteresis is represented, is empirical value, damage
The energy lost in segmental arc is：
Above formula is removed from the time Δ t for being torqued into recovery with creeper tread B, produces and is lost in segmental arc creeper tread twist process
Average loss power：
If deformation coefficient：
In formula：NiIt is the crawler belt twist process average power consumption on the i-th wheel；
tr--- creeper tread pitch (m)；
ri--- each wheel (driving wheel, bogie wheel and inducer) segmental arc radius (m).
ViFor relatively each wheel (driving wheel, bogie wheel and inducer) tangential velocity of crawler belt；
In view of all segmental arcs, hysteresis loss (the power damage of creeper tread kiss-coating pin torsional deflection of whole crawler belt can be obtained
Consumption) be：
The calculating of power attenuation when creeper tread winds train：
For creeper tread during train is wound, total power attenuation is by the change of velocity when creeper tread enters wheel
Cause the power attenuation of kinetic energy change, plus the power attenuation for making pin ear rubber deformation, make shoe when leaving wheel plus creeper tread
Power attenuation when band plate stretches.
Crawler belt changes in winding in inducer, the first bogie wheel, last bogie wheel and driving wheel joint chain link curvature
During change, because the change of creeper tread velocity causes kinetic energy change, crawler belt internal power consumption can be caused.Creeper tread winding wheel
It is that power attenuation (does not consider supporting section and outside equal to the summation that creeper tread is added together by the power attenuation of all flex portions
The interaction of medium).
When creeper tread, which enters, to be wound with wheel, generally, only one initial around creeper tread up and crawler belt
Position tilts.Two adjacent single-pin track plates, the motion of motion and toggle when entering wheel is similar,
See Fig. 3.
The position of creeper tread be defined on generalized coordinates α andOn, at this moment have in cartesian coordinate：
z1=R-r1sinα；
X in formula1, z1For coordinate value of any point on creeper tread 1 under x, z coordinate system；x2, z2For any point on creeper tread 2
Coordinate value under x, z coordinate system；r1And r2It is above-mentioned arbitrfary point to crawler belt end points length；R is wheel radius and creeper tread raceway
Sum of the face to bearing pin centre distance；trIt is creeper tread pitch.
For α, β, φ implication as shown in figure 3, α is creeper tread 1 and horizontal line angle, β is the movable end of creeper tread 1 and the origin of coordinates
Angle between line, with the normal of creeper tread 2, φ are the movable end of creeper tread 1 and origin of coordinates line and horizontal line angle；
Generalized coordinates system passes through angleRepresented with following relationship：
A=R/ (t in formularCos β), B=R/tr, κ=pi/2-β.WhereinIt is creeper tread 2 and horizontal line angle, κ is crawler belt
Angle between the movable end of plate 1 and origin of coordinates line and creeper tread 2.
Time-derivative in first calculating formula (13), their square is sought, substitute into formula and calculate kinetic energy
In formula：M is creeper tread weight；ρ=m/trFor crawler belt unit weight；
When wheel by when calculate power attenuation, draw
In formula：I0, ICMoment of inertia for creeper tread to the moments of inertia of hinge axes and creeper tread to creeper tread center of gravity；S
Statical moment for creeper tread to hinge axes；
RiFor each wheel (driving wheel, bogie wheel and inducer) segmental arc radius (m).
From formula (16) as can be seen that kinetic energy depends on the quality and pitch and wheel rim size of crawler belt.It is moved through in creeper tread
Cheng Zhong, kinetic energy change are shown in schematic diagram 4.When drawing curve map, it is believed that creeper tread exit wheel and enter wheel when be as,
Only order is opposite.
WhenThe kinetic energy of forward travel creeper tread is：
V in formulaCFor crawler travel device travel speed.
WhenForward travel is transformed into rotary motion, the kinetic energy K for the creeper tread that is connectediIIWith
Formula (15) calculates；
WhenWhen, the kinetic energy that creeper tread is rotated together with wheel is：
Power attenuation NDFor instantaneous value, this value should be made in t=tr/vTIn the range of it is average.In selected averaging method,
It is believed that kinetic equation loss is determined by the positive time-derivative of kinetic energy.
At this moment the average value of power attenuation is：
It is fashionable entering,
The average value of power attenuation when entering certain wheel (wheel i) for creeper tread；
For,The kinetic energy of forward travel creeper tread：
When exiting,
The average value of power attenuation during to exit；
Drawn according to formula (16)
In formula：ForForward travel is transformed into rotary motion, the kinetic energy for the creeper tread that is connected；
Kinetic equation loss on single-pin track is obtained as follows：
It is fashionable entering,
When exiting,
In formula：Single-pin track enters fashionable kinetic equation loss；Creeper tread kinetic energy loss when exiting；Qr- carry out
Tape unit length weight；G- acceleration of gravity；
Crawler belt ring Point of Inflection is typically four, i.e. n=4.Generally assume that the quality of creeper tread along pitch length direction
It is evenly distributed.
Should be in schematic diagram 3 and equation (13)~(15) in view of the pitch of creeper tread and connector for double-pin creeper tread
Respectively t1And t2, quality is respectively m1And m2.Now the formula of calculating power attenuation is
It is fashionable entering,
In formula：Double-pin crawler belt enters fashionable kinetic equation loss；
When exiting,
In formula：Kinetic equation loss when double-pin crawler belt exits.
Creeper tread makes the power attenuation of pin ear rubber deformation into winding：
Assuming that the quality of creeper tread is evenly distributed along pitch length direction.Power attenuation in rubber pin ear is by hinge
Internal work when torsion angle carries out generalized displacement determines.So for single-pin track be exactly enter it is fashionable：
In formula：Single-pin track enters fashionable rubber pin ear work rate loss.
C- sells ear angular rigidity.
And double-pin crawler belt is entered fashionable
In formula：Double-pin crawler belt enters fashionable rubber pin ear work rate loss.
The energy (hysteresis loss is not in it) stored in track link pin ear is when exiting wheel for making what is be connected
Creeper tread stretches, and in other words translates into the kinetic energy of creeper tread.Certainly, creeper tread may be stretched enough by selling the energy stored in ear
Directly, it is also possible to not enough, the energy required for being stretched depending on creeper tread, but it will always be discharged completely anyway.This
When for the pin ear of two kinds of form crawler belts, power attenuation
In formula：The power attenuation of ear rubber is sold when being exited for two kinds of creeper treads (single pin and double-pin)；
Enter fashionable power attenuation for rubber belt track (selects single pin or double-pin to be counted according to caterpillar band type
Calculate)；
η=0.15~0.30 is hysteresis loss coefficient；
Crawler belt winds total power attenuation equation：
In formula
To be calculated aboveOrUnified representation, select one to enter according to caterpillar band type during calculating
Row calculates.
To be calculated aboveOrUnified representation, one is selected according to caterpillar band type during calculating
Calculated.
That is, when
When
Formula (23) represents that for creeper tread during train is wound, total power attenuation is by speed when creeper tread enters wheel
The change of degree vector causes the power attenuation of kinetic energy change, plus the power attenuation for making pin ear rubber deformation, plus creeper tread from
Power attenuation when stretching the creeper tread when opening wheel.
The power attenuation that crawler belt internal power consumption is equal to creeper tread kiss-coating pin torsional deflection winds total work(plus crawler belt
Rate is lost.
Total power attenuation of last crawler travel device is by the loss of the meshing power of the active gear teeth and creeper tread, bogie wheel
It is added to obtain with crawler belt internal power consumption three along the rolling power attenuation of track length on ground.
Described above is only the preferred embodiment of the present invention, it is noted that for the ordinary skill people of the art
For member, without departing from the technical principles of the invention, some improvement and deformation can also be made, these are improved and deformation
Also it should be regarded as protection scope of the present invention.
Claims (5)
1. a kind of computational methods of crawler travel device power attenuation, it is characterised in that comprise the following steps：
Step 1, the analysis based on the frictional force to the driving wheel gear teeth and crawler belt and the displacement that rubs, obtain the active gear teeth and creeper tread
Meshing power loss；
Step 2, based on the analysis to bogie wheel and rolling resistance of track and the relation of movement velocity, obtain bogie wheel and connect along crawler belt
The rolling power attenuation in location；
Step 3, according in terms of following four crawler belt internal power consumption is calculated：To the work(of creeper tread kiss-coating pin torsional deflection
Rate loss analysis, the calculating of power attenuation to causing kinetic energy change by the change of velocity, to making pin ear rubber deformation
Power attenuation calculates, and power attenuation when stretching the creeper tread when leaving wheel to creeper tread calculates；
The meshing power loss of step 4, the active gear teeth that steps 1 and 2,3 are obtained and creeper tread, bogie wheel are along track length on ground
Rolling power attenuation be added to obtain total power attenuation of crawler travel device with crawler belt internal power consumption three.
2. the method as described in claim 1, it is characterised in that step 1 is specially：
Contact normal force of the active gear teeth with creeper tread be：
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In formula：FNContact normal force；FTTo engage tangential force；
αωFor track pin and the friction corner of the active gear teeth；
Contact friction force is：
FR=μ5FN (2)
In formula：FRFor contact friction force；
μ5For coefficient of contact friction；
Contact friction force is in the component of lead：
FRE=FRsinαω (3)
In formula：FREFor contact friction force lead component；
It is comprehensive that three formulas, the engaging friction resistance for obtaining driving wheel and track pin are above：
FRE=μ5tanαωFT (4)
And when assuming that track pin moves in kerve, 1/4 only last engaging friction, therefore have：
In formula：For between cog minute of angle；Z is the driving wheel number of teeth；
Therefore the engaging friction resistance of driving wheel and track pin is：
FT=F0+FK
In formula：F0For crawler belt slack list tensile force；
FKFor driving wheel tractive force；
Obtain：
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The engaging friction power consumption of the active gear teeth and creeper tread：
Monodentate engagement frictional work once is：
W51=FREs (7)
In formula：W51For frictional work；S is frictional distance；
Frictional distance is calculated according to formula below in above formula；
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In formula：VTIt is track pin with respect to active gear teeth fricting movement speed, VT≈rkω；T is run duration；ω turns for driving wheel
Speed；rkFor driving wheel pitch radius；Z is the driving wheel number of teeth；
Driving wheel turns around, and engages z times altogether, z is the driving wheel number of teeth, then total work is zW51If driving wheel turns around, the time used is
T,VT=rKω, the active gear teeth are expressed as with the power consumption that engages of creeper tread：
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3. the method as described in claim 1, it is characterised in that step 2 is specially：
Rolling resistance calculation formula is as follows between bogie wheel and crawler belt：
P=ffQ1 (9)
In formula：ffFor the coefficient of rolling resistance of bogie wheel；Q1For bogie wheel and crawler belt normal pressure；
Then rolling power attenuation of the bogie wheel along track length on ground is calculated with equation below：
W6=ffQ1VF (10)
In formula：W6The rolling power attenuation for being bogie wheel along track length on ground；VFLinear velocity is rolled for bogie wheel opposing tracks.
4. the method as described in claim 1, it is characterised in that step 3 is specially：
Assuming that there is two adjacent track plate A, B to be linked by hinge O, hinge is gum sleeve；Creeper tread A is fixed, adds a moment of torsion M
In on B, creeper tread B rotation alphas angle, and position 2 is gone to by position 1, and if rubber tube is definitely elasticity, after moment of torsion M disappears, crawler belt
Plate B should be returned to position 1, and actually because the hysteresis of rubber has residual deformation, B can only be returned to position 3, that is, reply
Angle α ' is less than corner α, B from position 1 to position 2, then is returned to position 3 by position 2 and is referred to as a circulation, an often repeatedly circulation
The energy of a part will be lost；
Gum sleeve rigidity calculation formula：
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In formula：The rigidity of k --- rubber hinge, it is called angle rigidity；r1--- gum sleeve innermost layer radius；r2--- rubber sleeve
Pipe outermost layer radius；lx--- gum sleeve length；G1--- gum sleeve shearing resistance coefficient；
Assuming that the pre-add torsion angle of rubber hinge is α0, the relative torsion of rubber hinge occurs entering and exiting cutting for segmental arc
It is α into the maximum twist angle of segmental arc if the torque absolute value of torsion hinge is directly proportional to torsion angle at pointmax, due to depositing
In pretwist corner α0, actual torsion angle is (αmax-α0), the potential energy of hinge aggregation is：
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There is hysteresis in rubber hinge, when reversing with μzThe energy-loss factor of hysteresis is represented, is lost in the energy of segmental arc
For：
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<mi>&alpha;</mi>
<mi>max</mi>
</msub>
<mo>-</mo>
<msub>
<mi>&alpha;</mi>
<mn>0</mn>
</msub>
<mo>)</mo>
</mrow>
<mn>2</mn>
</msup>
</mrow>
<mn>2</mn>
</mfrac>
</mrow>
Above formula is removed from the time Δ t for being torqued into recovery with creeper tread B, must be lost in the average damage of segmental arc creeper tread twist process
Wasted work rate：
<mrow>
<mfrac>
<mrow>
<mi>&Delta;</mi>
<mi>E</mi>
</mrow>
<mrow>
<mi>&Delta;</mi>
<mi>t</mi>
</mrow>
</mfrac>
<mo>=</mo>
<mfrac>
<mrow>
<msub>
<mi>&mu;</mi>
<mi>z</mi>
</msub>
<mi>k</mi>
<msup>
<mrow>
<mo>(</mo>
<msub>
<mi>&alpha;</mi>
<mi>max</mi>
</msub>
<mo>-</mo>
<msub>
<mi>&alpha;</mi>
<mn>0</mn>
</msub>
<mo>)</mo>
</mrow>
<mn>2</mn>
</msup>
</mrow>
<mrow>
<mn>2</mn>
<mi>&Delta;</mi>
<mi>t</mi>
</mrow>
</mfrac>
</mrow>
If deformation coefficient：
<mrow>
<msub>
<mi>N</mi>
<mi>i</mi>
</msub>
<mo>=</mo>
<mfrac>
<mrow>
<msub>
<mi>&mu;</mi>
<mi>z</mi>
</msub>
<mi>k</mi>
<msup>
<mrow>
<mo>(</mo>
<mn>1</mn>
<mo>-</mo>
<mi>&alpha;</mi>
<mo>)</mo>
</mrow>
<mn>2</mn>
</msup>
</mrow>
<mn>2</mn>
</mfrac>
<mfrac>
<msub>
<mi>t</mi>
<mi>r</mi>
</msub>
<msubsup>
<mi>r</mi>
<mi>i</mi>
<mn>2</mn>
</msubsup>
</mfrac>
<msub>
<mi>V</mi>
<mi>i</mi>
</msub>
</mrow>
In formula：NiIt is the crawler belt twist process average power consumption on the i-th wheel；tr--- creeper tread pitch；ri--- including driving wheel,
The segmental arc radius of one of many wheels including bogie wheel and inducer；ViFor the tangential velocity of relatively each wheel of crawler belt；
The hysteresis loss of whole crawler belt, the i.e. power attenuation of creeper tread kiss-coating pin torsional deflection are：
<mrow>
<mi>N</mi>
<mo>=</mo>
<mfrac>
<mrow>
<msub>
<mi>&mu;</mi>
<mi>z</mi>
</msub>
<mi>k</mi>
<msup>
<mrow>
<mo>(</mo>
<mn>1</mn>
<mo>-</mo>
<mi>&alpha;</mi>
<mo>)</mo>
</mrow>
<mn>2</mn>
</msup>
<msub>
<mi>t</mi>
<mi>r</mi>
</msub>
</mrow>
<mn>2</mn>
</mfrac>
<msub>
<mi>V</mi>
<mi>i</mi>
</msub>
<mo>&Sigma;</mo>
<mfrac>
<mn>1</mn>
<msubsup>
<mi>r</mi>
<mi>i</mi>
<mn>2</mn>
</msubsup>
</mfrac>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>12</mn>
<mo>)</mo>
</mrow>
</mrow>
The calculating of power attenuation when creeper tread winds train：
Two adjacent single-pin track plates 1,2, the motion when entering wheel is suitable with the motion of toggle, creeper tread
Position be defined on generalized coordinates α andOn, at this moment have in cartesian coordinate：
In formula, x1, z1For coordinate value of any point on creeper tread 1 under x, z coordinate system；x2, z2For any point on creeper tread 2 x,
Coordinate value under z coordinate system；r1And r2It is above-mentioned arbitrfary point to crawler belt end points length；R is that wheel radius arrives with creeper tread roller surface
The sum of bearing pin centre distance；trIt is creeper tread pitch；
α is creeper tread 1 and horizontal line angle, and β is between the movable end of creeper tread 1 and origin of coordinates line, with the normal of creeper tread 2
Angle, φ are the movable end of creeper tread 1 and origin of coordinates line and horizontal line angle；
Generalized coordinates system passes through angleRepresented with following relationship：
A=R/ (t in formularCos β), B=R/tr, κ=pi/2-β, whereinIt is creeper tread 2 and horizontal line angle, κ is that creeper tread 1 is lived
Angle between moved end and origin of coordinates line and creeper tread 2；
Time-derivative in first calculating formula (13), their square is sought, substitute into formula and calculate kinetic energy
<mrow>
<msub>
<mi>K</mi>
<mi>i</mi>
</msub>
<mo>=</mo>
<mfrac>
<mi>&rho;</mi>
<mn>2</mn>
</mfrac>
<munderover>
<mo>&Integral;</mo>
<mn>0</mn>
<msub>
<mi>t</mi>
<mi>r</mi>
</msub>
</munderover>
<mrow>
<mo>(</mo>
<msup>
<msub>
<mi>x</mi>
<mn>1</mn>
</msub>
<mn>2</mn>
</msup>
<msup>
<msub>
<mi>x</mi>
<mn>2</mn>
</msub>
<mn>2</mn>
</msup>
<msup>
<msub>
<mi>z</mi>
<mn>1</mn>
</msub>
<mn>2</mn>
</msup>
<msup>
<msub>
<mi>z</mi>
<mn>2</mn>
</msub>
<mn>2</mn>
</msup>
<mo>)</mo>
</mrow>
<mi>d</mi>
<mi>r</mi>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>15</mn>
<mo>)</mo>
</mrow>
</mrow>
In formula：M is creeper tread weight；ρ=m/trFor crawler belt unit weight；
When wheel by when calculate power attenuation, draw
In formula：I0, ICMoment of inertia for creeper tread to the moments of inertia of hinge axes and creeper tread to creeper tread center of gravity；S is shoe
Statical moment of the band plate to hinge axes；
RiFor each wheel segmental arc radius；
WhenThe kinetic energy of forward travel creeper tread is：
<mrow>
<msub>
<mi>K</mi>
<mrow>
<mi>i</mi>
<mi>I</mi>
</mrow>
</msub>
<mo>=</mo>
<msubsup>
<mi>mV</mi>
<mi>C</mi>
<mn>2</mn>
</msubsup>
</mrow>
V in formulaCFor crawler travel device travel speed；
WhenForward travel is transformed into rotary motion, the kinetic energy K for the creeper tread that is connectediIIUse formula
(15) calculate；
WhenWhen, the kinetic energy that creeper tread is rotated together with wheel is：
<mrow>
<msub>
<mi>K</mi>
<mrow>
<mi>i</mi>
<mi>I</mi>
<mi>I</mi>
<mi>I</mi>
</mrow>
</msub>
<mo>=</mo>
<mrow>
<mo>(</mo>
<mi>m</mi>
<mo>+</mo>
<mfrac>
<msub>
<mi>I</mi>
<mi>c</mi>
</msub>
<msub>
<mi>R</mi>
<mi>i</mi>
</msub>
</mfrac>
<mo>)</mo>
</mrow>
<msub>
<mi>V</mi>
<mi>C</mi>
</msub>
</mrow>
Power attenuation NDFor instantaneous value, make this value in t=tr/vTIn the range of it is average；
At this moment the average value of power attenuation is：
It is fashionable entering,
The average value of power attenuation when entering wheel i for creeper tread；
For,The kinetic energy of forward travel creeper tread：
When exiting,
The average value of power attenuation during to exit；
Drawn according to formula (16)
In formula：ForForward travel is transformed into rotary motion, the kinetic energy for the creeper tread that is connected；
Kinetic equation loss on single-pin track is obtained as follows：
It is fashionable entering,
When exiting,
In formula：Single-pin track enters fashionable kinetic equation loss；Creeper tread kinetic energy loss when exiting；QrFor crawler belt list
Bit length weight；G is acceleration of gravity；
Crawler belt ring Point of Inflection is four, n=4, it is assumed that the quality of creeper tread is evenly distributed along pitch length direction；
It is respectively t for pitch of the double-pin creeper tread in view of creeper tread and connector in equation (13)~(15)1And t2, matter
Amount is respectively m1And m2, now calculate power attenuation formula be
It is fashionable entering,
In formula：Double-pin crawler belt enters fashionable kinetic equation loss；
When exiting,
In formula：Kinetic equation loss when double-pin crawler belt exits；
Creeper tread makes the power attenuation of pin ear rubber deformation into winding：
Assuming that the quality of creeper tread is evenly distributed along pitch length direction, the power attenuation in rubber pin ear is reversed by hinge
Internal work when angle carries out generalized displacement determines, then for single-pin track be exactly enter it is fashionable：
In formula：Single-pin track enters fashionable rubber pin ear work rate loss, C- pin ear angular rigidities；
And double-pin crawler belt is entered fashionable
In formula：It is that double-pin crawler belt enters fashionable rubber pin ear work rate loss；
For the pin ear of two kinds of form crawler belts, power attenuation
<mrow>
<msubsup>
<mi>N</mi>
<mrow>
<mi>r</mi>
<mi>u</mi>
<mi>b</mi>
<mi>b</mi>
<mi>e</mi>
<mi>r</mi>
</mrow>
<mrow>
<mi>o</mi>
<mi>u</mi>
<mi>t</mi>
</mrow>
</msubsup>
<mo>=</mo>
<mrow>
<mo>(</mo>
<mn>1</mn>
<mo>-</mo>
<mi>&eta;</mi>
<mo>)</mo>
</mrow>
<msubsup>
<mi>N</mi>
<mrow>
<mi>r</mi>
<mi>u</mi>
<mi>b</mi>
<mi>b</mi>
<mi>e</mi>
<mi>r</mi>
</mrow>
<mrow>
<mi>i</mi>
<mi>n</mi>
</mrow>
</msubsup>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>22</mn>
<mo>)</mo>
</mrow>
</mrow>
In formula：The power attenuation of ear rubber is sold when being exited for single pin and two kinds of creeper treads of double-pin；
Enter fashionable power attenuation for rubber belt track, select single pin or double-pin to be calculated according to caterpillar band type；η is
Hysteresis loss coefficient；
Crawler belt winds total power attenuation equation：
<mrow>
<msub>
<mi>N</mi>
<mrow>
<mi>A</mi>
<mi>l</mi>
<mi>l</mi>
</mrow>
</msub>
<mo>=</mo>
<msubsup>
<mi>N</mi>
<mi>D</mi>
<mrow>
<mi>i</mi>
<mi>n</mi>
</mrow>
</msubsup>
<mo>+</mo>
<msubsup>
<mi>N</mi>
<mrow>
<mi>r</mi>
<mi>u</mi>
<mi>b</mi>
<mi>b</mi>
<mi>e</mi>
<mi>r</mi>
</mrow>
<mrow>
<mi>i</mi>
<mi>n</mi>
</mrow>
</msubsup>
<mo>+</mo>
<msup>
<mi>N</mi>
<mrow>
<mi>o</mi>
<mi>u</mi>
<mi>t</mi>
</mrow>
</msup>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>23</mn>
<mo>)</mo>
</mrow>
</mrow>
In formula
For orUnified representation, select one to be calculated according to caterpillar band type during calculating；
ForOrUnified representation, select one to be calculated according to caterpillar band type during calculating；
That is, when
<mrow>
<msub>
<mi>N</mi>
<mrow>
<mi>A</mi>
<mi>l</mi>
<mi>l</mi>
</mrow>
</msub>
<mo>=</mo>
<msubsup>
<mi>N</mi>
<mi>D</mi>
<mrow>
<mi>i</mi>
<mi>n</mi>
</mrow>
</msubsup>
<mo>+</mo>
<msubsup>
<mi>N</mi>
<mrow>
<mi>r</mi>
<mi>u</mi>
<mi>b</mi>
<mi>b</mi>
<mi>e</mi>
<mi>r</mi>
</mrow>
<mrow>
<mi>i</mi>
<mi>n</mi>
</mrow>
</msubsup>
<mo>+</mo>
<msubsup>
<mi>N</mi>
<mi>D</mi>
<mrow>
<mi>o</mi>
<mi>u</mi>
<mi>t</mi>
</mrow>
</msubsup>
<mo>-</mo>
<msubsup>
<mi>N</mi>
<mrow>
<mi>r</mi>
<mi>u</mi>
<mi>b</mi>
<mi>b</mi>
<mi>e</mi>
<mi>r</mi>
</mrow>
<mrow>
<mi>o</mi>
<mi>u</mi>
<mi>t</mi>
</mrow>
</msubsup>
<mo>=</mo>
<msubsup>
<mi>N</mi>
<mi>D</mi>
<mrow>
<mi>i</mi>
<mi>n</mi>
</mrow>
</msubsup>
<mo>+</mo>
<msubsup>
<mi>N</mi>
<mi>D</mi>
<mrow>
<mi>o</mi>
<mi>u</mi>
<mi>t</mi>
</mrow>
</msubsup>
<mo>+</mo>
<mi>&eta;</mi>
<mo>&CenterDot;</mo>
<msubsup>
<mi>N</mi>
<mrow>
<mi>r</mi>
<mi>u</mi>
<mi>b</mi>
<mi>b</mi>
<mi>e</mi>
<mi>r</mi>
</mrow>
<mrow>
<mi>i</mi>
<mi>n</mi>
</mrow>
</msubsup>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>24</mn>
<mo>)</mo>
</mrow>
</mrow>
When
<mrow>
<msub>
<mi>N</mi>
<mrow>
<mi>A</mi>
<mi>l</mi>
<mi>l</mi>
</mrow>
</msub>
<mo>=</mo>
<msubsup>
<mi>N</mi>
<mi>D</mi>
<mrow>
<mi>i</mi>
<mi>n</mi>
</mrow>
</msubsup>
<mo>+</mo>
<msubsup>
<mi>N</mi>
<mrow>
<mi>r</mi>
<mi>u</mi>
<mi>b</mi>
<mi>b</mi>
<mi>e</mi>
<mi>r</mi>
</mrow>
<mrow>
<mi>i</mi>
<mi>n</mi>
</mrow>
</msubsup>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>25</mn>
<mo>)</mo>
</mrow>
<mo>.</mo>
</mrow>
5. method as claimed in claim 4, it is characterised in that η=0.15~0.30.
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| Publication number | Priority date | Publication date | Assignee | Title |
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| CN111597639A (en) * | 2020-05-19 | 2020-08-28 | 北京理工大学 | Coupling analysis method for crawler belt and cross-country road surface |
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| JPS5893680A (en) * | 1981-11-30 | 1983-06-03 | Yokohama Rubber Co Ltd:The | Endless track shoe |
| CN101814099A (en) * | 2009-02-23 | 2010-08-25 | 朱爱斌 | Analysis and calculation method of internal resistance and power consumption of crawler attachment |
| CN102867092A (en) * | 2012-09-18 | 2013-01-09 | 西安交通大学 | Analysis and calculation method for internal resistance and power consumption of crawler travelling mechanism |
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| Publication number | Priority date | Publication date | Assignee | Title |
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| CN111597639A (en) * | 2020-05-19 | 2020-08-28 | 北京理工大学 | Coupling analysis method for crawler belt and cross-country road surface |
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