CN103823990A - Method for calculating steering time of center of tracked vehicle - Google Patents

Abstract

The invention belongs to the technical field of tracked vehicles, aims at shortening the development cycle of a product and reducing the developing cost, and provides a method for calculating steering time of the center of the tracked vehicle. The method changes the unfavorable influence caused by the fact that the skidding turn of a track is not considered, and the technical difficult problem that the inaccuracy exists in the prediction on the steering time of the center is fundamentally improved. By using the method, the prediction precision for the steering time of the center of the tracked vehicle is greatly improved, and a technical basis is provided for the design of a steering mechanism and the total design of a comprehensive transmission device. By adopting the method, the design of the steering mechanism of the transmission device is more scientific, the prediction on the steering performance is more accurate, and the problem of larger deviation between the existing calculating method and a trail run experiment is solved.

Description

A kind of for endless-track vehicle zero turn radius Time Calculation method

Technical field

The invention belongs to endless-track vehicle technical field, be specifically related to a kind of for endless-track vehicle zero turn radius Time Calculation method.

Background technology

When certain endless-track vehicle propulsion system requirement demonstration and conceptual design, often propose the functional requirement of zero turn radius, and the minimum zero turn radius time is proposed to certain index request.The implication of endless-track vehicle zero turn radius is: turning center is positioned on the vehicle symmetrical plane in the middle of the crawler belt of both sides, both sides crawler belt winding speed opposite sign but equal magnitude, a side crawler belt travels forward, and opposite side crawler belt moves backward, and both sides driving wheel is dynamic output all.The realization of zero turn radius function is to be determined by the pattern of steering mechanism.Zero turn radius functional requirement is based on reason below:

1, relative steering (ratio of actual steering radius and crawler belt center square) equals 0 when zero turn radius, under the narrow surface conditions such as vehicle Neng street, end of the bridge or extreme terrain, turns to, and improves the maneuverability that turns to of endless-track vehicle.

2, the direction by vehicle is rotated, and realizes and on endless-track vehicle platform, fills turning of firepower, and this can realize direction and turn and aim at being rigidly fixed to cannon, missile launcher and tubular type air defence system etc. on endless-track vehicle car body.

The computing method (seeing the monograph such as Yan Qingdong, Zhang Liandi " tank construction and design " (volume two) P215-220) of current certain the endless-track vehicle zero turn radius generally adopting in the industry, these computing method think that crawler belt does not exist and trackslips, and the formula of the computing center's turnaround time adopting is as follows:

$t=\frac{30B}{R_{z}n}---\left(1\right)$

In formula (1), B represents track gage, R _zrepresent driving wheel radius (m), n represents driving wheel rotating speed (rpm).

For certain endless-track vehicle, zero turn radius computing method can improve product development quality accurately, meet the requirement of technical indicator, thereby shorten the research and development of products cycle, reduce product development cost.The current computing method about certain endless-track vehicle zero turn radius have been made more simplification and hypothesis, have ignored trackslipping or slippage of crawler belt and ground, and the instantaneous center of turn of both sides crawler belt is considered as overlapping with the geometric center of crawler belt.This kind simplified computing method and caused the result of real train test and the calculated results to have larger difference, practical center turnaround time, often than the large 1.5 times of left and right of theoretical value, need to be carried out the improvement design of many rounds and test the requirement that could meet design objective certain endless-track vehicle.Traditional zero turn radius computing method can not meet the requirement of certain endless-track vehicle lean research and development of a new generation.Dynamics and kinematics when modern R&D mode need to be to endless-track vehicle zero turn radius are furtherd investigate, and taking into account critical factor, proposes the new zero turn radius Time Calculation method that more meets current demand.

Summary of the invention

(1) technical matters that will solve

The technical problem to be solved in the present invention is to provide a kind of computing method that can improve endless-track vehicle zero turn radius time prediction precision, is conducive to shorten the research and development of products cycle, reduces development cost.

(2) technical scheme

For solving the problems of the technologies described above, the invention provides one for endless-track vehicle zero turn radius Time Calculation method, it is characterized in that: these computing method comprise the steps:

Step 1, based on following assumed condition research endless-track vehicle zero turn radius: level road at the uniform velocity turns to, and disregards centrifugal forces affect; The ground surface properties of crawler belt ground plane is identical, and ground contact pressure of track is uniformly distributed; Projection on surface level overlaps vehicle barycenter with geometric center, does not consider the dislocation of left and right side crawler belt, thinks that Vehicle Driving Cycle resistance coefficient does not change because turning to;

Step 2, dynamics and kinematics to endless-track vehicle zero turn radius are analyzed, i.e. utilization is set up polar method and crawler belt ground section is carried out to the derivation of equivalent force and equivalent moment, finally derives the zero turn radius Time Calculation formula of considering after track slip factor.

Wherein, described utilization is set up polar method and crawler belt ground section is carried out to equivalent force, equivalent moment and the derivation of zero turn radius time is specifically comprised the steps:

Step 1, calculates O ₁angular velocity around car body central rotation involve angular velocity; Tradition does not consider that the zero turn radius Time Calculation formula of track slip is as follows:

$t=\frac{30B}{R_{z}n}---\left(1\right)$

In formula (1), B represents track gage, R _zrepresent driving wheel radius (m), n represents driving wheel rotating speed (rpm).

Set O ₁, O, O ₂be respectively the instantaneous center of turn of instantaneous center of turn, car body geometric center and the right side crawler belt of left track, C ₁and C ₂be respectively the geometric center of left and right sides crawler belt, B, 2L and 2e represent respectively track gage, crawler belt ground connection length and crawler width, V _q, V _xand V _jrepresent that respectively crawler belt earth terminal is at O ₁the convected velocity of each particle, relative velocity and absolute velocity on O straight line; In traditional zero turn radius Time Calculation method, do not consider trackslipping of crawler belt, thereby by instantaneous center of turn O ₁be considered as and C ₁overlapping, is OC thereby obtain theoretical zero turn radius radius ₁, C ₁point is around the angular velocity omega of car body central rotation _c(rad/s) be:

${\mathrm{\ω}}_c=\frac{\mathrm{\π}{R}_{z}n}{15B}---\left(2\right)$

With instantaneous center of turn O ₁for research object, set O ₁convected velocity, relative velocity and the absolute velocity of point are respectively Vq _o1, Vx _o1, Vj _o1.

${\mathrm{Vx}}_{o1}=\frac{2\mathrm{\π}{R}_{z}n}{60}---\left(3\right)$

Vj _o1=0 （4）

By the relation between above-mentioned three speed

Vx _o1-Vq _o1＝Vj _o1 （5）

So obtain O ₁point relative velocity Vq _o1

${\mathrm{Vq}}_{o1}=\frac{2\mathrm{\π}{R}_{z}n}{60}---\left(6\right)$

Thereby obtain O ₁point is around the angular velocity omega q of car body central rotation _o1

${\mathrm{\ωq}}_{o1}=\frac{\mathrm{\π}}{30}\frac{R_{z}n}{{\mathrm{OO}}_1}---\left(7\right)$

Step 2, calculates OO ₁numerical value; Analyze as an example of the dynamics of left track and ground interaction example, the surface of contact on left track and ground can be approximated to be a rectangle, suppose that surface of contact is made up of numerous fine particle, because the direction of motion of zero turn radius left and right crawler belt is contrary, according to Newtonian mechanics, the equivalent force one of ground effects in one-sided crawler belt along car body longitudinal axis is positioned O point, guarantees thus dynamic balance and the equalising torque of whole car body;

First, ground being acted on to left track analyzes along the equivalent force F of car body longitudinal axis; Make O ₁c ₁=β L, OC ₁=α L, angle SO ₁c ₁=A;

Act on equivalent force that O orders by crawler belt ground plane area is carried out to integration acquisition, set up polar coordinate system, use the knowledge of Newtonian mechanics, can obtain

$\begin{array}{c}F=\∫\∫\mathrm{\μp}(r\·\mathrm{dr}\·\mathrm{d\θ})\cos \mathrm{\θ}\\ =\mathrm{\μp}{\∫}_{r_1}^{r_2}r\·\mathrm{dr}{\∫}_{-A}^A\cos \mathrm{\θd\θ}\end{array}---\left(8\right)$

In formula (8), μ represents ground drag coefficient, the pressure of p representation unit area; Formula is simplified for the integration of radius in (1), can obtain following formula

${\&Integral;}_{r_1}^{r_2}r\&CenterDot;\mathrm{dr}=\frac{r^2}{2}{|}_{r_1}^{r_2}=0.5({r_2}^2-{{\mathrm{<figure-callout\; id="1"\; label="r"\; filenames="HDA0000474619340000021.png"\; state="\{\{state\}\}">r</figure-callout>}}_1}^2)---\left(9\right)$

Make (β L+e)=B2; (β L-e)=B1 can obtain:

$r_2=(\mathrm{\&beta;L}+e)/\cos A=\frac{B2}{\cos A}---\left(10\right)$

$r_1=(\mathrm{\&beta;L}-e)/\cos A=\frac{B1}{\cos A}---\left(11\right)$

Formula is simplified for the integration of angle in (8), can obtain following formula:

${\&Integral;}_{-A}^A\cos \mathrm{\&theta;d\&theta;}=2{\&Integral;}_0^A\cos \mathrm{\&theta;d\&theta;}=\mathrm{<figure-callout\; id="1"\; label="ln"\; filenames="HDA0000474619340000021.png"\; state="\{\{state\}\}">ln</figure-callout>}\frac{1+\sin A}{1-\sin A}---\left(12\right)$

Geometric relationship analysis for A and L can obtain following formula:

$\sin A=\frac{L}{{(L^2+{\mathrm{\&beta;}}^2{L}^2)}^{0.5}}=\frac{1}{{(1+{\mathrm{\&beta;}}^2)}^{0.5}}---\left(13\right)$

Composite type (8), to formula (13), can obtain formula (14):

$F=0.5\mathrm{\&mu;p}({B2}^2-{\mathrm{<figure-callout\; id="1"\; label="B"\; filenames="HDA0000474619340000021.png"\; state="\{\{state\}\}">B</figure-callout>}1}^2)\ln \frac{{(1+{\mathrm{\&beta;}}^2)}^{0.5}+1}{{(1+{\mathrm{\&beta;}}^2)}^{0.5}-1}---\left(14\right)$

To the subitem in formula (14) simplify can obtain following various

B2 ²-B1 ²=4·β·L·e （15）

P=4·p·L·e （16）

In formula (16), P represents to act on the general pressure of one-sided crawler belt, and p represents to act on the pressure in one-sided crawler belt unit area;

For further simplified style (14), can introduce parameters C, be shown below:

$\ln C=0.5\ln \frac{{(1+{\mathrm{\&beta;}}^2)}^{0.5}+1}{{(1+{\mathrm{\&beta;}}^2)}^{0.5}-1}---\left(17\right)$

Comprehensively with above formula (8) to formula (17), can obtain formula (18):

F＝P·μ·β·lnC （18）

Secondly, ground is acted on to O ₁equivalent moment analyze; According to Newton mechanics law, can obtain following torque equilibrium equation, as the formula (19):

F(αL+βL)＝∫∫r·(r·dr·dθ)μp （19）

Formula is simplified for the integration of radius in (19), can obtain following formula:

${\&Integral;}_{r_1}^{r_2}{r}^2\&CenterDot;\mathrm{dr}=\frac{r^3}{3}{|}_{r_1}^{r_2}=\frac{1}{3}({r_2}^3-{{\mathrm{<figure-callout\; id="1"\; label="r"\; filenames="HDA0000474619340000021.png"\; state="\{\{state\}\}">r</figure-callout>}}_1}^3)---\left(20\right)$

By formula (20) substitution formula (19), can obtain formula (21):

$F(\mathrm{\&alpha;L}+\mathrm{\&beta;L})=\frac{2}{3}\mathrm{\&mu;p}({B2}^3-{\mathrm{<figure-callout\; id="1"\; label="B"\; filenames="HDA0000474619340000021.png"\; state="\{\{state\}\}">B</figure-callout>}1}^3){\&Integral;}_0^A\frac{\mathrm{d\&theta;}}{{\cos }^3\mathrm{\&theta;}}---\left(21\right)$

Formula is simplified for the integration of angle in (21), can obtain following formula:

${\&Integral;}_0^A\frac{\mathrm{d\&theta;}}{{\cos }^3\mathrm{\&theta;}}=\frac{1}{2}\frac{\sin A}{{\cos }^{2}A}+\frac{1}{4}\ln \left(\frac{1+\sin A}{1-\sin A}\right)---\left(22\right)$

Geometric relationship analysis for A and L can obtain following formula:

$\cos A=\frac{\mathrm{\&beta;L}}{{(L^2+{\mathrm{\&beta;}}^2{L}^2)}^{0.5}}=\frac{\mathrm{\&beta;}}{{(1+{\mathrm{\&beta;}}^2)}^{0.5}}---\left(23\right)$

Comprehensively with above formula (19) to formula (23), can obtain formula (24):

$F(\mathrm{\&alpha;L}+\mathrm{\&beta;L})=\frac{2e}{3}\mathrm{\&mu;p}({3\mathrm{\&beta;}}^2{L}^2+e^2)(\frac{{(1+{\mathrm{\&beta;}}^2)}^{0.5}}{{\mathrm{\&beta;}}^2}+\ln C)---\left(24\right)$

Formula (18) substitution formula (24) can be obtained to formula (25):

$\mathrm{\&alpha;}=\frac{1}{6\mathrm{\&beta;}\ln C}({3\mathrm{\&beta;}}^2+\frac{e^2}{L^2})(\frac{{(1+{\mathrm{\&beta;}}^2)}^{0.5}}{{\mathrm{\&beta;}}^2}+\ln C)-\mathrm{\&beta;}---\left(25\right)$

The further analysis of geometric relationship by B and L can obtain:

αL=0.5B （26）

O ₁O＝αL+βL=0.5B+βL （27）

Step 3, the time convolution (7) of endless-track vehicle zero turn radius obtains following formula:

$t=60\frac{0.5B+\mathrm{\&beta;L}}{R_{z}n}---\left(28\right)$

In formula (28): R _zrepresent endless-track vehicle driving wheel radius, unit (m); N represents endless-track vehicle driving wheel rotating speed, unit (rpm).

Wherein, the computing method of described parameter beta specifically comprise the steps:

Step 1, the numerical value of input whole-car parameters e, B and L, calculates α value by following formula (29);

$\mathrm{\&alpha;}=\frac{0.5B}{L}---\left(29\right)$

Step 2, sets β initial value, calculates α by formula (30) and (31) ₁; Compare α by criterion ₁with the gap of desired value α,

$C=\frac{1+\sqrt{1+{\mathrm{\&beta;}}^2}}{\mathrm{\&beta;}}---\left(30\right)$

${\mathrm{\&alpha;}}_1=\frac{1}{6\mathrm{\&beta;}\ln C}({3\mathrm{\&beta;}}^2+\frac{e^2}{L^2})(\frac{{(1+{\mathrm{\&beta;}}^2)}^{0.5}}{{\mathrm{\&beta;}}^2}+\ln C)-\mathrm{\&beta;}---\left(31\right)$

Step 3, relatively α ₁with the gap of desired value α, if meet criterion | α-α ₁| < 1e-8, export final β, if do not met, change β value, start the α of a new round ₁the calculating of value, until meet criterion, ends iterative computation, output final calculation result.

(3) beneficial effect

Compared with prior art, the present invention possesses following beneficial effect:

1, the computing method of endless-track vehicle zero turn radius time provided by the invention, change the adverse effect of in the past not considering track slip, fundamentally improve the inaccurate technical barrier of zero turn radius time prediction, utilize this method can significantly improve the precision of prediction of endless-track vehicle zero turn radius time, for technical foundation has been established in comprehensive actuator Design of Steering Mechanism and overall design;

2, employing the present invention makes the more science of design of gearing steering mechanism, more accurate for the prediction of steering behaviour, can effectively solve the problem that existing computing method and real train test deviation are larger.

Accompanying drawing explanation

Fig. 1 is provided by the invention for endless-track vehicle zero turn radius Time Calculation method crawler belt zero turn radius kinematics schematic diagram;

Fig. 2 is for learning schematic diagram for provided by the invention for endless-track vehicle zero turn radius Time Calculation method crawler belt steering power;

Fig. 3 for provided by the invention for the calculation flow chart of endless-track vehicle zero turn radius Time Calculation method key parameter numerical value β.

Embodiment

For making object of the present invention, content and advantage clearer, below in conjunction with drawings and Examples, the specific embodiment of the present invention is described in further detail.

Certain endless-track vehicle practical center steering procedure must be accompanied by trackslipping of both sides crawler belt.Obviously conventional steering theory can not accurately reflect the dynamic variation rule of steering procedure.The characteristic of the brass tacks research endless-track vehicle actual steering process of trackslipping based on the relative ground of crawler belt ground section, and make quantitative comparison with conventional steering theory, the A+E that can be endless-track vehicle steering behaviour and structural design provides foundation.For zero turn radius operating mode, consider that skidding of crawler belt ground section meets the actual state that endless-track vehicle turns to more.When endless-track vehicle zero turn radius, kinematics schematic diagram as shown in Figure 1, has represented the vertical view that vehicle clockwise rotates in figure.

Provided by the invention for endless-track vehicle zero turn radius Time Calculation method, comprise the steps:

Step 1, based on following assumed condition research endless-track vehicle zero turn radius: level road at the uniform velocity turns to, and disregards centrifugal forces affect; The ground surface properties of crawler belt ground plane is identical, and ground contact pressure of track is uniformly distributed; Projection on surface level overlaps vehicle barycenter with geometric center, does not consider the dislocation of left and right side crawler belt, thinks that Vehicle Driving Cycle resistance coefficient does not change because turning to;

Step 2, dynamics and kinematics to endless-track vehicle zero turn radius are analyzed, i.e. utilization is set up polar method and crawler belt ground section is carried out to the derivation of equivalent force and equivalent moment, finally derives the zero turn radius Time Calculation formula of considering after track slip factor.

Wherein, described utilization is set up polar method and crawler belt ground section is carried out to equivalent force, equivalent moment and the derivation of zero turn radius time is specifically comprised the steps:

Step 1, calculates O ₁angular velocity around car body central rotation involve angular velocity; Tradition does not consider that the zero turn radius Time Calculation formula of track slip is as follows:

$t=\frac{30B}{R_{z}n}---\left(1\right)$

In formula (1), B represents track gage, R _zrepresent driving wheel radius (m), n represents driving wheel rotating speed (rpm).

As shown in Figure 1, O in figure ₁, O, O ₂be respectively the instantaneous center of turn of instantaneous center of turn, car body geometric center and the right side crawler belt of left track, C ₁and C ₂be respectively the geometric center of left and right sides crawler belt, B, 2L and 2e represent respectively track gage, crawler belt ground connection length and crawler width, V _q, V _xand V _jrepresent that respectively crawler belt earth terminal is at O ₁the convected velocity of each particle, relative velocity and absolute velocity on O straight line; In traditional zero turn radius Time Calculation method, do not consider trackslipping of crawler belt, thereby by instantaneous center of turn O ₁be considered as and C ₁overlapping, is OC thereby obtain theoretical zero turn radius radius ₁, C ₁point is around the angular velocity omega of car body central rotation _c(rad/s) be:

${\mathrm{\&omega;}}_c=\frac{\mathrm{\&pi;}{R}_{z}n}{15B}---\left(2\right)$

With instantaneous center of turn O ₁for research object, if obtain O ₁around the angular velocity of car body central rotation, involve angular velocity, just can be in the hope of the time of zero turn radius.Set O ₁convected velocity, relative velocity and the absolute velocity of point are respectively Vq _o1, Vx _o1, Vj _o1.

${\mathrm{<figure-callout\; id="1"\; label="Vx\; o"\; filenames="HDA0000474619340000021.png"\; state="\{\{state\}\}">Vx</figure-callout>}}_o=\frac{2\mathrm{\&pi;}{R}_{z}n}{60}---\left(3\right)$

Vj _o1=0 （4）

By the relation between above-mentioned three speed

Vx _o1-Vq _o1＝Vj _o1 （5）

So obtain O ₁point relative velocity Vq _o1

${\mathrm{<figure-callout\; id="1"\; label="Vq\; o"\; filenames="HDA0000474619340000021.png"\; state="\{\{state\}\}">Vq</figure-callout>}}_o=\frac{2\mathrm{\&pi;}{R}_{z}n}{60}---\left(6\right)$

Thereby obtain O ₁point is around the angular velocity omega q of car body central rotation _o1

${\mathrm{\&omega;<figure-callout\; id="1"\; label="q\; o"\; filenames="HDA0000474619340000021.png"\; state="\{\{state\}\}">q</figure-callout>}}_o=\frac{\mathrm{\&pi;}}{30}\frac{R_{z}n}{{\mathrm{OO}}_1}---\left(7\right)$

Step 2, calculates OO ₁numerical value; Analyze as an example of the dynamics of left track and ground interaction example.The surface of contact on left track and ground can be approximated to be a rectangle, supposes that surface of contact is made up of numerous fine particle, as shown in the profile line in Fig. 1.Because the direction of motion of zero turn radius left and right crawler belt is contrary, according to Newtonian mechanics rule, the equivalent force one of ground effects in one-sided crawler belt along car body longitudinal axis is positioned O point, the like this dynamic balance of the whole car body of guarantee and equalising torque.Respectively ground is acted on to left track along the equivalent force F of car body longitudinal axis and effect O below ₁equivalent moment analyze.

First, ground being acted on to left track analyzes along the equivalent force F of car body longitudinal axis; Make O ₁c ₁=β L, OC ₁=α L, angle SO ₁c ₁=A;

Act on equivalent force that O orders by crawler belt ground plane area is carried out to integration acquisition, by setting up polar coordinate system, use Newtonian mechanics rule, can obtain

$\begin{array}{c}F=\&Integral;\&Integral;\mathrm{\&mu;p}(r\&CenterDot;\mathrm{dr}\&CenterDot;\mathrm{d\&theta;})\cos \mathrm{\&theta;}\\ =\mathrm{\&mu;p}{\&Integral;}_{r_1}^{r_2}r\&CenterDot;\mathrm{dr}{\&Integral;}_{-A}^A\cos \mathrm{\&theta;d\&theta;}\end{array}---\left(8\right)$

In formula (8), μ represents ground drag coefficient, the pressure of p representation unit area; Formula is simplified for the integration of radius in (1), can obtain following formula

${\&Integral;}_{r_1}^{r_2}r\&CenterDot;\mathrm{dr}=\frac{r^2}{2}{|}_{r_1}^{r_2}=0.5({r_2}^2-{{\mathrm{<figure-callout\; id="1"\; label="r"\; filenames="HDA0000474619340000021.png"\; state="\{\{state\}\}">r</figure-callout>}}_1}^2)---\left(9\right)$

Make (β L+e)=B2; (β L-e)=B1 can obtain:

$r_2=(\mathrm{\&beta;L}+e)/\cos A=\frac{B2}{\cos A}---\left(10\right)$

${\mathrm{<figure-callout\; id="1"\; label="r"\; filenames="HDA0000474619340000021.png"\; state="\{\{state\}\}">r</figure-callout>}}_1=(\mathrm{\&beta;L}-e)/\cos A=\frac{\mathrm{<figure-callout\; id="1"\; label="B"\; filenames="HDA0000474619340000021.png"\; state="\{\{state\}\}">B</figure-callout>}1}{\cos A}---\left(11\right)$

Formula is simplified for the integration of angle in (8), can obtain formula (12):

${\&Integral;}_{-A}^A\cos \mathrm{\&theta;d\&theta;}=2{\&Integral;}_0^A\cos \mathrm{\&theta;d\&theta;}=\mathrm{<figure-callout\; id="1"\; label="ln"\; filenames="HDA0000474619340000021.png"\; state="\{\{state\}\}">ln</figure-callout>}\frac{1+\sin A}{1-\sin A}---\left(12\right)$

Can obtain formula (13) for the geometric relationship analysis of A and L:

$\sin A=\frac{L}{{(L^2+{\mathrm{\&beta;}}^2{L}^2)}^{0.5}}=\frac{1}{{(1+{\mathrm{\&beta;}}^2)}^{0.5}}---\left(13\right)$

Composite type (8), to formula (13), can obtain formula (14):

$F=0.5\mathrm{\&mu;p}({B2}^2-{\mathrm{<figure-callout\; id="1"\; label="B"\; filenames="HDA0000474619340000021.png"\; state="\{\{state\}\}">B</figure-callout>}1}^2)\ln \frac{{(1+{\mathrm{\&beta;}}^2)}^{0.5}+1}{{(1+{\mathrm{\&beta;}}^2)}^{0.5}-1}---\left(14\right)$

Subitem in formula (14) is simplified and can be obtained formula (15) and (16)

B2 ²-B1 ²=4·β·L·e （15）

P=4·p·L·e （16）

In formula (16), P represents to act on the general pressure of one-sided crawler belt, and p represents to act on the pressure in one-sided crawler belt unit area;

For further simplified style (14), can introduce parameters C, see formula (30), draw formula (17):

$\ln C=0.5\ln \frac{{(1+{\mathrm{\&beta;}}^2)}^{0.5}+1}{{(1+{\mathrm{\&beta;}}^2)}^{0.5}-1}---\left(17\right)$

Comprehensively with above formula (8) to formula (17), can obtain formula (18):

F＝P·μ·β·lnC （18）

Secondly, ground is acted on to O ₁equivalent moment analyze; According to Newton mechanics law, can obtain following torque equilibrium equation, as the formula (19):

F(αL+βL)＝∫∫r·(r·dr·dθ)μp （19）

Formula is simplified for the integration of radius in (19), can obtain following formula:

${\&Integral;}_{r_1}^{r_2}{r}^2\&CenterDot;\mathrm{dr}=\frac{r^3}{3}{|}_{r_1}^{r_2}=\frac{1}{3}({r_2}^3-{{\mathrm{<figure-callout\; id="1"\; label="r"\; filenames="HDA0000474619340000021.png"\; state="\{\{state\}\}">r</figure-callout>}}_1}^3)---\left(20\right)$

By formula (20) substitution formula (19), can obtain formula (21):

$F(\mathrm{\&alpha;L}+\mathrm{\&beta;L})=\frac{2}{3}\mathrm{\&mu;p}({B2}^3-{\mathrm{<figure-callout\; id="1"\; label="B"\; filenames="HDA0000474619340000021.png"\; state="\{\{state\}\}">B</figure-callout>}1}^3){\&Integral;}_0^A\frac{\mathrm{d\&theta;}}{{\cos }^3\mathrm{\&theta;}}---\left(21\right)$

Formula is simplified for the integration of angle in (21), can obtain following formula:

${\&Integral;}_0^A\frac{\mathrm{d\&theta;}}{{\cos }^3\mathrm{\&theta;}}=\frac{1}{2}\frac{\sin A}{{\cos }^{2}A}+\frac{1}{4}\ln \left(\frac{1+\sin A}{1-\sin A}\right)---\left(22\right)$

Geometric relationship analysis for A and L can obtain following formula:

$\cos A=\frac{\mathrm{\&beta;L}}{{(L^2+{\mathrm{\&beta;}}^2{L}^2)}^{0.5}}=\frac{\mathrm{\&beta;}}{{(1+{\mathrm{\&beta;}}^2)}^{0.5}}---\left(23\right)$

Comprehensively with above formula (19) to formula (23), can obtain formula (24):

$F(\mathrm{\&alpha;L}+\mathrm{\&beta;L})=\frac{2e}{3}\mathrm{\&mu;p}({3\mathrm{\&beta;}}^2{L}^2+e^2)(\frac{{(1+{\mathrm{\&beta;}}^2)}^{0.5}}{{\mathrm{\&beta;}}^2}+\ln C)---\left(24\right)$

Formula (18) substitution formula (24) can be obtained to formula (25):

$\mathrm{\&alpha;}=\frac{1}{6\mathrm{\&beta;}\ln C}({3\mathrm{\&beta;}}^2+\frac{e^2}{L^2})(\frac{{(1+{\mathrm{\&beta;}}^2)}^{0.5}}{{\mathrm{\&beta;}}^2}+\ln C)-\mathrm{\&beta;}---\left(25\right)$

The further analysis of geometric relationship by B and L can obtain:

αL=0.5B （26）

O ₁O＝αL+βL=0.5B+βL （27）

Step 3, the time convolution (7) of endless-track vehicle zero turn radius obtains following formula:

$t=60\frac{0.5B+\mathrm{\&beta;L}}{R_{z}n}---\left(28\right)$

In formula (28): R _zrepresent endless-track vehicle driving wheel radius, unit (m); N represents endless-track vehicle driving wheel rotating speed, unit (rpm).

Wherein, the computing method of described parameter beta specifically comprise the steps:

Step 1, the numerical value of input whole-car parameters e, B and L, calculates α value by following formula (29);

$\mathrm{\&alpha;}=\frac{0.5B}{L}---\left(29\right)$

Step 2, sets β initial value, calculates α by formula (30) and (31) ₁; Compare α by criterion ₁with the gap of desired value α,

$C=\frac{1+\sqrt{1+{\mathrm{\&beta;}}^2}}{\mathrm{\&beta;}}---\left(30\right)$

${\mathrm{\&alpha;}}_1=\frac{1}{6\mathrm{\&beta;}\ln C}({3\mathrm{\&beta;}}^2+\frac{e^2}{L^2})(\frac{{(1+{\mathrm{\&beta;}}^2)}^{0.5}}{{\mathrm{\&beta;}}^2}+\ln C)-\mathrm{\&beta;}---\left(31\right)$

Step 3, relatively α ₁with the gap of desired value α, if meet criterion | α-α ₁| < 1e-8, export final β, if do not met, change β value, start the α of a new round ₁the calculating of value, until meet criterion, ends iterative computation, output final calculation result.

By the minimum zero turn radius time real train test result to two models, classic method and this method result of calculation are compared, as shown in table 1.

Table 1 calculated value and trial value

Model	ChxxxB	ChxxxxA
			Classic method	7.8	9.2
The inventive method	12.5	14.8
			Trial value	13	16.5
Classic method and test difference	40%	44%
			The inventive method and test difference	4%	10%

From table 1, can obviously find out, compared with adopting classic method, adopt numerical value and the trial value of the inventive method gained very approaching, also very little with the difference of test.Zero turn radius Time Calculation method provided by the invention can solve traditional computing method and the larger problem of real train test deviation effectively.

Endless-track vehicle zero turn radius Time Calculation method has determined the accuracy of zero turn radius time prediction, has affected the optimal design of gearing steering mechanism and complete machine.Effect of the present invention is: the present invention has changed the drawback of in the past not considering the factors such as track slip, only need to obtain needed complete vehicle structure parameter in formula (28), utilize this formula to try to achieve fast and accurately the zero turn radius time, make the more science of design of gearing steering mechanism, more accurate for the prediction of steering behaviour.Zero turn radius Time Calculation method of the present invention can solve existing computing method and the larger problem of real train test deviation effectively.

The above is only the preferred embodiment of the present invention; it should be pointed out that for those skilled in the art, do not departing under the prerequisite of the technology of the present invention principle; can also make some improvement and distortion, these improvement and distortion also should be considered as protection scope of the present invention.

Claims (3)

1. for an endless-track vehicle zero turn radius Time Calculation method, it is characterized in that: these computing method comprise the steps:

Step 1, based on following assumed condition research endless-track vehicle zero turn radius: level road at the uniform velocity turns to, and disregards centrifugal forces affect; The ground surface properties of crawler belt ground plane is identical, and ground contact pressure of track is uniformly distributed; Projection on surface level overlaps vehicle barycenter with geometric center, does not consider the dislocation of left and right side crawler belt, thinks that Vehicle Driving Cycle resistance coefficient does not change because turning to;

Step 2, dynamics and kinematics to endless-track vehicle zero turn radius are analyzed, i.e. utilization is set up polar method and crawler belt ground section is carried out to the derivation of equivalent force and equivalent moment, finally derives the zero turn radius Time Calculation formula of considering after track slip factor.

2. according to claim 1 for endless-track vehicle zero turn radius Time Calculation method, it is characterized in that: described utilization is set up polar method and crawler belt ground section is carried out to equivalent force, equivalent moment and the derivation of zero turn radius time specifically comprised the steps:

Step 1, calculates O ₁angular velocity around car body central rotation involve angular velocity; Tradition does not consider that the zero turn radius Time Calculation formula of track slip is as follows:

$t=\frac{30B}{R_{z}n}---\left(1\right)$

In formula (1), B represents track gage, R _zrepresent driving wheel radius (m), n represents driving wheel rotating speed (rpm).

Set O ₁, O, O ₂be respectively the instantaneous center of turn of instantaneous center of turn, car body geometric center and the right side crawler belt of left track, C ₁and C ₂be respectively the geometric center of left and right sides crawler belt, B, 2L and 2e represent respectively track gage, crawler belt ground connection length and crawler width, V _q, V _xand V _jrepresent that respectively crawler belt earth terminal is at O ₁the convected velocity of each particle, relative velocity and absolute velocity on O straight line; In traditional zero turn radius Time Calculation method, do not consider trackslipping of crawler belt, thereby by instantaneous center of turn O ₁be considered as and C ₁overlapping, is OC thereby obtain theoretical zero turn radius radius ₁, C ₁point is around the angular velocity omega of car body central rotation _c(rad/s) be:

${\mathrm{\&omega;}}_c=\frac{\mathrm{\&pi;}{R}_{z}n}{15B}---\left(2\right)$

With instantaneous center of turn O ₁for research object, set O ₁convected velocity, relative velocity and the absolute velocity of point are respectively Vq _o1, Vx _o1, Vj _o1.

${\mathrm{Vx}}_{o1}=\frac{2\mathrm{\&pi;}{R}_{z}n}{60}---\left(3\right)$

Vj _o1=0 （4）

By the relation between above-mentioned three speed

Vx _o1-Vq _o1＝Vj _o1 （5）

So obtain O ₁point relative velocity Vq _o1

${\mathrm{Vq}}_{o1}=\frac{2\mathrm{\&pi;}{R}_{z}n}{60}---\left(6\right)$ Thereby obtain O ₁point is around the angular velocity omega q of car body central rotation _o1

${\mathrm{\&omega;q}}_{o1}=\frac{\mathrm{\&pi;}}{30}\frac{R_{z}n}{{\mathrm{OO}}_1}---\left(7\right)$

Step 2, calculates OO ₁numerical value; Analyze as an example of the dynamics of left track and ground interaction example, the surface of contact on left track and ground can be approximated to be a rectangle, suppose that surface of contact is made up of numerous fine particle, because the direction of motion of zero turn radius left and right crawler belt is contrary, according to Newtonian mechanics rule, the equivalent force one of ground effects in one-sided crawler belt along car body longitudinal axis is positioned O point, guarantees thus dynamic balance and the equalising torque of whole car body;

First, ground being acted on to left track analyzes along the equivalent force F of car body longitudinal axis; Make O ₁c ₁=β L, OC ₁=α L, angle SO ₁c ₁=A;

Act on equivalent force that O orders by crawler belt ground plane area is carried out to integration acquisition, set up polar coordinate system, use the knowledge of Newtonian mechanics, can obtain

$\begin{array}{c}F=\&Integral;\&Integral;\mathrm{\&mu;p}(r\&CenterDot;\mathrm{dr}\&CenterDot;\mathrm{d\&theta;})\cos \mathrm{\&theta;}\\ =\mathrm{\&mu;p}{\&Integral;}_{r_1}^{r_2}r\&CenterDot;\mathrm{dr}{\&Integral;}_{-A}^A\cos \mathrm{\&theta;d\&theta;}\end{array}---\left(8\right)$

In formula (8), μ represents ground drag coefficient, the pressure of p representation unit area; Formula is simplified for the integration of radius in (1), can obtain following formula

${\&Integral;}_{r_1}^{r_2}r\&CenterDot;\mathrm{dr}=\frac{r^2}{2}{|}_{r_1}^{r_2}=0.5({r_2}^2-{r_1}^2)---\left(9\right)$

Make (β L+e)=B2; (β L-e)=B1 can obtain:

$r_2=(\mathrm{\&beta;L}+e)/\cos A=\frac{B2}{\cos A}---\left(10\right)$

$r_1=(\mathrm{\&beta;L}-e)/\cos A=\frac{B1}{\cos A}---\left(11\right)$

Formula is simplified for the integration of angle in (8), can obtain following formula:

${\&Integral;}_{-A}^A\cos \mathrm{\&theta;d\&theta;}=2{\&Integral;}_0^A\cos \mathrm{\&theta;d\&theta;}=\ln \frac{1+\sin A}{1-\sin A}---\left(12\right)$

Geometric relationship analysis for A and L can obtain following formula:

$\sin A=\frac{L}{{(L^2+{\mathrm{\&beta;}}^2{L}^2)}^{0.5}}=\frac{1}{{(1+{\mathrm{\&beta;}}^2)}^{0.5}}---\left(13\right)$

Composite type (8), to formula (13), can obtain formula (14):

$F=0.5\mathrm{\&mu;p}({B2}^2-{B1}^2)\ln \frac{{(1+{\mathrm{\&beta;}}^2)}^{0.5}+1}{{(1+{\mathrm{\&beta;}}^2)}^{0.5}-1}---\left(14\right)$

To the subitem in formula (14) simplify can obtain following various

B2 ²-B1 ²=4·β·L·e （15）

P=4·p·L·e （16）

In formula (16), P represents to act on the general pressure of one-sided crawler belt, and p represents to act on the pressure in one-sided crawler belt unit area;

For further simplified style (14), can introduce parameters C, be shown below:

$\ln C=0.5\ln \frac{{(1+{\mathrm{\&beta;}}^2)}^{0.5}+1}{{(1+{\mathrm{\&beta;}}^2)}^{0.5}-1}---\left(17\right)$

Comprehensively with above formula (8) to formula (17), can obtain formula (18):

F＝P·μ·β·lnC （18）

Secondly, ground is acted on to O ₁equivalent moment analyze; According to Newton mechanics law, can obtain following torque equilibrium equation, as the formula (19):

F(αL+βL)＝∫∫r·(r·dr·dθ)μp （19）

Formula is simplified for the integration of radius in (19), can obtain following formula:

${\&Integral;}_{r_1}^{r_2}{r}^2\&CenterDot;\mathrm{dr}=\frac{r^3}{3}{|}_{r_1}^{r_2}=\frac{1}{3}({r_2}^3-{r_1}^3)---\left(20\right)$

By formula (20) substitution formula (19), can obtain formula (21):

$F(\mathrm{\&alpha;L}+\mathrm{\&beta;L})=\frac{2}{3}\mathrm{\&mu;p}({B2}^3-{B1}^3){\&Integral;}_0^A\frac{\mathrm{d\&theta;}}{{\cos }^3\mathrm{\&theta;}}---\left(21\right)$

Formula is simplified for the integration of angle in (21), can obtain following formula:

${\&Integral;}_0^A\frac{\mathrm{d\&theta;}}{{\cos }^3\mathrm{\&theta;}}=\frac{1}{2}\frac{\sin A}{{\cos }^{2}A}+\frac{1}{4}\ln \left(\frac{1+\sin A}{1-\sin A}\right)---\left(22\right)$

Geometric relationship analysis for A and L can obtain following formula:

$\cos A=\frac{\mathrm{\&beta;L}}{{(L^2+{\mathrm{\&beta;}}^2{L}^2)}^{0.5}}=\frac{\mathrm{\&beta;}}{{(1+{\mathrm{\&beta;}}^2)}^{0.5}}---\left(23\right)$

Comprehensively with above formula (19) to formula (23), can obtain formula (24):

$F(\mathrm{\&alpha;L}+\mathrm{\&beta;L})=\frac{2e}{3}\mathrm{\&mu;p}({3\mathrm{\&beta;}}^2{L}^2+e^2)(\frac{{(1+{\mathrm{\&beta;}}^2)}^{0.5}}{{\mathrm{\&beta;}}^2}+\ln C)---\left(24\right)$

Formula (18) substitution formula (24) can be obtained to formula (25):

$\mathrm{\&alpha;}=\frac{1}{6\mathrm{\&beta;}\ln C}({3\mathrm{\&beta;}}^2+\frac{e^2}{L^2})(\frac{{(1+{\mathrm{\&beta;}}^2)}^{0.5}}{{\mathrm{\&beta;}}^2}+\ln C)-\mathrm{\&beta;}---\left(25\right)$

The further analysis of geometric relationship by B and L can obtain:

αL=0.5B （26）

O ₁O＝αL+βL=0.5B+βL （27）

Step 3, the time convolution (7) of endless-track vehicle zero turn radius obtains following formula:

$t=60\frac{0.5B+\mathrm{\&beta;L}}{R_{z}n}---\left(28\right)$

In formula (28): R _zrepresent endless-track vehicle driving wheel radius, unit (m); N represents endless-track vehicle driving wheel rotating speed, unit (rpm).

3. according to claim 2 for endless-track vehicle zero turn radius Time Calculation method, it is characterized in that: the computing method of described parameter beta specifically comprise the steps:

Step 1, the numerical value of input whole-car parameters e, B and L, calculates α value by following formula (29);

$\mathrm{\&alpha;}=\frac{0.5B}{L}---\left(29\right)$

Step 2, sets β initial value, calculates α by formula (30) and (31) ₁; Compare α by criterion ₁with the gap of desired value α,

$C=\frac{1+\sqrt{1+{\mathrm{\&beta;}}^2}}{\mathrm{\&beta;}}---\left(30\right)$

${\mathrm{\&alpha;}}_1=\frac{1}{6\mathrm{\&beta;}\ln C}({3\mathrm{\&beta;}}^2+\frac{e^2}{L^2})(\frac{{(1+{\mathrm{\&beta;}}^2)}^{0.5}}{{\mathrm{\&beta;}}^2}+\ln C)-\mathrm{\&beta;}---\left(31\right)$

Step 3, relatively α ₁with the gap of desired value α, if meet criterion | α-α ₁| < 1e-8, export final β, if do not met, change β value, start the α of a new round ₁the calculating of value, until meet criterion, ends iterative computation, output final calculation result.

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