Structural design method for 5-layer-winding ultra-deep mine hoist interlayer transition device

文档序号:1931158 发布日期:2021-12-07 浏览:16次 中文

阅读说明:本技术 一种超深矿井提升机层间过渡装置可缠5层的结构设计方法 (Structural design method for 5-layer-winding ultra-deep mine hoist interlayer transition device ) 是由 彭霞 冯迎洲 张立新 于 2021-10-12 设计创作,主要内容包括:本发明公开了一种超深矿井提升机层间过渡装置可缠5层的结构设计方法,所述方法首先将原来最多能缠绕3层的层间过渡装置改为能缠绕5层的凹状面层间过渡装置,进而增加缠绕层数增大提升深度。其次,与3~4层和4~5层层间过渡装置同处于一个圆周的其它区域新增平衡块,这样可以避免超深矿井提升机因质量分布不均匀在惯性的作用下使得整个提升系统产生振动,得到一套钢丝绳在层间过渡装置上各个阶段的横向、径向及纵向位移公式。本发明设计的层间过渡装置可以使缠绕式超深矿井提升机在高速、重载和超深的运行条件下,保证提升系统能顺利缠绕到5层,钢丝绳磨损小且过渡平稳。(The invention discloses a structural design method for winding 5 layers of an ultra-deep mine hoist interlayer transition device, which is characterized in that firstly, an original interlayer transition device capable of winding 3 layers at most is changed into a concave surface interlayer transition device capable of winding 5 layers, so that the number of winding layers is increased, and the lifting depth is increased. And secondly, newly adding balance blocks in other areas of the same circumference with the 3-4 layers and 4-5 layers of interlayer transition devices, so that the vibration of the whole lifting system caused by uneven mass distribution of the ultra-deep mine hoist under the action of inertia can be avoided, and a set of transverse, radial and longitudinal displacement formulas of the steel wire rope at each stage on the interlayer transition device can be obtained. The interlayer transition device designed by the invention can ensure that the winding type ultra-deep mine hoist can smoothly wind to 5 layers under the running conditions of high speed, heavy load and ultra-deep, and the steel wire rope has small abrasion and stable transition.)

1. The utility model provides a structure that transition device can twine 5 layers between ultra-deep mine winder includes transition piece between layer, go out the rope mouth, the balancing piece, the ring flange is constituteed, adopt the parallel broken line grooving of double transition, contain two broken line districts and two straight line districts, a ~ b, d ~ e, f ~ g, k ~ l are broken line district, b ~ d, e ~ a, g ~ k, l ~ f are the straight line district, it is located the ring flange left side to go out the rope mouth, 1 ~ 2 layers and 3 ~ 4 layers transition device are located the ring flange right side between layer by layer, 2 ~ 3 layers and 4 ~ 5 layers transition device are located the ring flange left side between layer by layer, wholly be down trapezoidal. The radial radius difference of the 1-2 layers and 3-4 layers of the transition devices is the same as the radial radius difference of the 3-4 layers and 4-5 layers of the transition devices, and the radial radius difference is the thickness of the two layers of steel wire rope loops. Wherein the sections a to b are interlayer transition sections of 1-2 interlayer transition devices, the sections b to d are support sections of 1-2 interlayer transition devices, the sections d to e are ring transition sections of 1-2 interlayer transition devices, the sections f to g are interlayer transition sections of 2-3 interlayer transition devices, the sections k to f are support sections of 2-3 interlayer transition devices, the sections g to k are ring transition sections of 2-3 interlayer transition devices, meanwhile, the sections a to b are also interlayer transition sections of 3-4 interlayer transition devices, the sections b to c are support sections of 3-4 interlayer transition devices, the sections c to e are ring transition sections of 3-4 interlayer transition devices, meanwhile, the sections f to g are also interlayer transition sections of 4-5 interlayer transition devices, the sections g to i are support sections of 4-5 interlayer transition devices, and the sections i to k are ring-to-ring transition sections of 4-5 interlayer transition devices.

2. The structural design method of the ultra-deep mine hoist interlayer transition device capable of winding 5 layers according to claim 1, characterized in that the 3-4 layer interlayer transition devices and the 4-5 layer interlayer transition devices are newly added interlayer transition devices and the contact between the steel wire rope and the transition block is surface contact.

3. The method as claimed in claim 2, wherein the balance weight is additionally provided in other regions of a circumference of the ultra-deep mine hoist inter-floor transition device which is located at the same position as the 3-4 and 4-5 inter-floor transition devices.

4. The method of claim 3, wherein the method comprises the steps of:

for ease of understanding, the list of parametric symbols used in the calculations herein is now shown in table 1.

TABLE 1 symbols of formulae herein

Design of one, 3 ~ 4 layer interlayer transition device

(1) Divide into transition piece, supporting shoe and circle transition piece between 3 ~ 4 layers transition device between layer, wherein: the interlayer transition blocks correspond to the positions a to b, the supporting blocks correspond to the positions b to c, and the inter-ring transition blocks correspond to the positions c to e.

(2) The last circle of steel wire rope on the 3 rd layer rises along the interlayer transition block at the sections a to b to complete interlayer transition, the central angle of the reel rotated in the rising process is gamma, and the angle range of the reel rotated is as follows:

0≤θ≤γ;

the corresponding angle Δ θ that the spool rotates during the layer transition is:

Δθ=γ;

the last circle of wire rope in layer 3 accomplishes the interlayer transition, and it has taken place the displacement at the reel axial, and then lateral displacement is:

wherein, d is the diameter of the steel wire rope on the transition block

On the transition piece between the layer 3 last round wire rope not only takes place the displacement in the reel axial but also takes place the displacement in the reel is radial, so wire rope also has radial displacement, owing to what design here is 3 ~ 4 layers of transition between layers, therefore the total radial displacement of wire rope is:

Sr=3h1

from the geometric relationship:namely, it is

There is also a longitudinal shift S in the layer transitionf(θ), the equivalent winding radius of the roll is:

wherein R is the diameter of the drum

The length delta S of the last circle of steel wire rope wound on the transition block at the 3 rd layer of the transition section between the a layer and the b layer1(θ) is:

the total length S (theta) of the last winding circle of the steel wire rope on the 3 rd layer in the transition process of the 3-4 layers is as follows:

(3) when the last circle of steel wire rope on the 3 rd layer enters the supporting sections b-c to complete the linear transition after finishing the ascending stage of the interlayer transition at the sections a-b, the steel wire rope on the winding drum does not displace in the axial direction, the radial direction and the axial direction of the winding drum in the process, therefore, the transverse displacement, the radial displacement and the longitudinal displacement of the steel wire rope on the transition block of the linear transition area are all 0, and the angle stroke interval of the winding drum of the linear transition area is as follows:

the angle Δ θ through which the spool turns during this process is:

wilting ═ θ -? (ii) a

The winding length delta S of the last circle of the 3 rd layer steel wire rope on the transition block of the linear transition area2Comprises the following steps:

the total travel S (θ) of the last turn of the steel wire rope on the layer 3 on the transition block is:

(4) when the last circle of steel wire rope on the 3 rd layer finishes the linear transition at the b-c section and then enters the ring transition section c-e to finish the ring transition, the last circle of steel wire rope on the 3 rd layer on the transition block of the ring transition section gradually rises to the top of the 2 nd last circle of steel wire rope on the 3 rd layer from the original linear transition area with the same height as the 4 th layer, and the rising height is h2And the angle stroke interval of the winding drum at the transition section between the rings is as follows:

the angle Δ θ that the spool turns during the turn-to-turn transition is:

because the last circle of steel wire rope on the 3 rd layer of the transition block reversely moves along the axial direction of the winding drum in the process of ring-to-ring transitionThus, the lateral displacement of the wire rope during this process is:

but the last circle of steel wire rope on the 3 rd layer of the transition block does not generate transverse displacement when the transition process is carried out among the 3-4 layers.

In the process that the last circle of steel wire rope on the 3 rd layer moves from the position c to the position e, as the reel is radially displaced, the radial displacement S of the steel wire rope on the transition blockr(θ) is:

wherein, the geometrical relationship is as follows:

in the process, the last circle of steel wire rope on the 3 rd layer on the transition block is also displaced along the axial direction of the steel wire rope, and the longitudinal displacement S of the steel wire ropef(θ) is:

in the process of ring-to-ring transition, the winding length delta S of the last circle of the steel wire rope on the 3 rd layer of the transition block3(θ) is:

therefore, the total length S (theta) of the winding of the last circle of the steel wire rope on the 3 rd layer on the whole transition block in the transition process of 3-4 layers is as follows:

design of two, 4 ~ 5 layers of interlayer transition device

(1) Divide 4 ~ 5 transition devices between layer into transition piece between layer, supporting shoe and circle transition piece, wherein: the interlayer transition blocks correspond to f-g positions, the supporting blocks correspond to g-i positions, and the inter-ring transition blocks correspond to i-k positions.

(2) The last circle of steel wire rope on the 4 th layer rises along the interlayer transition block at the f-g section to complete interlayer transition, the central angle of the reel rotated in the rising process is gamma, and the angle range of the reel rotated is as follows:

0≤θ≤γ;

the corresponding angle Δ θ that the spool rotates during the layer transition is:

Δθ=θ;

the last circle of wire rope in layer 4 accomplishes the interlayer transition, and it has taken place the displacement at the reel axial, and then lateral displacement is:

on the transition piece transition between layers, 4 th layer last round wire rope not only takes place the displacement in the reel axial but also takes place the displacement in the reel radial, so wire rope also has radial displacement, because what design here is 4 ~ 5 layers of transition between layers, therefore the total radial displacement of wire rope is:

Sr=4h1

from the geometric relationship:namely, it is

There is also a longitudinal shift S in the transition between the layersf(theta) the equivalent winding radius of the roll is

The length delta S of the last circle of steel wire rope wound on the transition block at the 4 th layer of the transition section between the f layer and the g layer1(θ) is:

the total length S (theta) of the last winding circle of the 4 th layer of steel wire rope in the transition process of 4-5 layers is as follows:

(3) when the last circle of steel wire rope on the 4 th layer enters the supporting sections g-i to complete the linear transition after finishing the ascending stage of the interlayer transition at the sections f-g, the steel wire rope on the winding drum does not displace in the axial direction, the radial direction and the axial direction of the winding drum in the process, therefore, the transverse displacement, the radial displacement and the longitudinal displacement of the steel wire rope on the transition block of the linear transition area are all 0, and the angle stroke interval of the winding drum of the linear transition area is as follows:

the angle Δ θ through which the spool turns during this process is:

Δθ=θ-γ;

the winding length delta S of the last steel wire rope circle of the 4 th layer on the transition block of the linear transition area2Comprises the following steps:

the total travel S (θ) of the last turn of the steel wire rope on the 4 th layer on the transition block is:

(4) when the last circle of steel wire rope on the 4 th layer finishes the linear transition at the g-i section and enters the inter-circle transition sections i-k to finish the inter-circle transition, the last circle of steel wire rope on the 4 th layer on the inter-circle transition section transition block gradually rises to the top of the 4 th layer 2 last circle of steel wire rope from the original linear transition zone with the same height as the 5 th layer, and the rising height is h2And the angle stroke interval of the winding drum at the transition section between the rings is as follows:

the angle Δ θ that the spool turns during the turn-to-turn transition is:

because the last circle of steel wire rope on the 4 th layer on the transition block reversely moves along the axial direction of the winding drum in the process of ring-to-ring transitionThus, the lateral displacement of the wire rope during this process is:

but the last circle of steel wire rope on the 4 th layer on the transition block does not generate transverse displacement when the transition process is carried out between 4-5 layers.

The last circle of steel wire rope on the 4 th layer is displaced in the radial direction of the winding drum in the process of moving from the position i to the position k, and the radial displacement S of the steel wire rope on the transition blockr(θ) is:

wherein, the geometrical relationship is as follows:

in the process, the last circle of the steel wire rope on the 4 th layer on the transition block is also displaced along the axial direction of the steel wire rope, and the longitudinal displacement S of the steel wire ropef(θ) is:

the winding length delta S of the last circle of the steel wire rope on the 4 th layer of the transition block in the process of ring-to-ring transition3(θ) is:

therefore, the total length S (theta) of the winding of the last circle of the steel wire rope on the 4 th layer on the whole transition block in the transition process of 4-5 layers is as follows:

Technical Field

The invention relates to a structural design method for a super-deep mine hoist interlayer transition device capable of winding 5 layers

Background

A mine with the depth of more than 1500m in the mine industry belongs to an ultra-deep mine. The rotation of reel drives wire rope winding and realizes promoting mostly in the super deep mine promotion, and multilayer winding hoisting wire rope need realize wire rope's climbing and switching-over with the help of transition device between the layer when the winding is close to the rope baffle on reel both sides. If the interlayer transition device with reasonable structure is not arranged at the position, close to the flange, of the two sides of the winding drum for guiding and transition, the steel wire rope can be subjected to abrasion and rope clamping caused by serious impact and vibration caused by high speed and heavy load when in transition, the stability of the steel wire rope arrangement can be influenced in the process, and the service life of the whole lifting system can be influenced.

In the past, a great deal of exploration and research are carried out on ultra-deep mine interlayer transition devices at home and abroad, but so far, detailed information of ideal interlayer transition devices from theory to practice is not seen. Wieschel applied for patent "winding reel with ladder ring flange", and proposed the arrangement form of the transition device between the wire rope layers under the low-speed light load running state and even say that the wire rope can wind more than 6 layers or even more on the reel, but did not give concrete design calculation process. Chin ei boani a я describes the addition of transition blocks on both sides of a parallel polyline rope groove drum to assist in rope transition, but does not give specific dimensions and detailed calculation of the transition blocks. The Lebus rope groove is 1 type of rope groove suitable for multi-layer winding of steel wire ropes, and the company proposes that the parallel broken line rope groove can be wound to 50 layers, but does not see data information of the detailed rope groove and a transition device.

And the penxia is improved on the basis of a Lebus rope groove, a new interlayer transition device suitable for lifting the ultra-deep well is designed, the geometric relationship of the interlayer transition positions of the parallel section, the broken line section and different layers on two sides of the winding drum during interlayer guiding and climbing of the steel wire rope is analyzed, and a theoretical calculation formula is given. Gong constitution is used to research the section geometry of spiral rope groove, rope groove with three different single and double transition parallel broken line rope grooves and interlayer transition device, and obtain the calculation formula of section. The method comprises the steps that 1-2 interlayer transition devices based on a high-order Bezier curve are designed by the ox navy, and the effectiveness of the interlayer transition devices for ensuring stable interlayer transition of the steel wire rope is analyzed and calculated. The root of hushui, the profit song etc. have carried out comparatively detailed geometric derivation to 2 layers and 3 layers of transition devices, but the grooving degree of depth is not considered in its mathematics derivation process, still can creep in the clearance that keeps off rope board and 2 nd layer 1 ring wire rope at last after 2 ~ 3 layers climb moreover, very easily form the card rope. However, the motion curve of the steel wire rope in the transition between the rings is considered to be the same as that of the interlayer transition, and the motion state of the steel wire rope in the interlayer transition is not analyzed in detail.

In conclusion, although students at home and abroad make a lot of researches on the multi-layer winding interlayer transition device for the ultra-deep mine, the problems that the number of winding layers of the interlayer transition device is small, the structural design parameters of the interlayer transition device are insufficient and the like exist. On the basis, the ultra-deep mine hoisting interlayer transition device capable of winding 5 layers is designed, the motion process of each stage when a hoisting steel wire rope is wound on the interlayer transition device is analyzed, and a theoretical calculation formula for determining the motion process is given.

Disclosure of Invention

The invention relates to a structural design method for winding 5 layers of an ultra-deep mine hoist interlayer transition device, aiming at solving the defects of insufficient winding layer number of a steel wire rope, insufficient structural design parameters and the like in the ultra-deep mine hoisting process. The invention firstly designs a novel interlayer transition device which can wind 5 layers of concave surfaces, the contact with the steel wire rope is surface contact in the transition process, and the local pressure in the transition process is reduced, thereby reducing the abrasion of the steel wire rope and prolonging the service life of the steel wire rope. Secondly, in the interlayer transition device, a balance block is additionally arranged in the other areas of the other part of the circumference of the 3-4 layers and 4-5 layers of the interlayer transition device as shown in figure 1, so that the mass distribution of the whole interlayer transition device is uniform, and the whole interlayer transition device can not generate large vibration even if rotating under the conditions of high speed and heavy load. And the various stages of the interlayer transition process will be presented in detail in the form of a diagram. And finally, calculating the changes of the transverse displacement, the radial displacement and the longitudinal displacement of the steel wire rope in an interlayer transition section, a support section and an inter-ring transition section when the 3-4-layer and 4-5-layer interlayer transition devices rotate along with the winding drum by taking the change of the central angle theta corresponding to the rotation of the winding drum as a variable, so as to further describe the dynamic process of the steel wire rope on the interlayer transition block.

The invention discloses ultra-deep mine hoisting equipment which is suitable for the field of ultra-deep mine hoisting with the well depth of more than 1500m, and can be known from figure 1, a novel multilayer winding interlayer transition device mainly comprises an interlayer transition block, a rope outlet, a balance block and a flange plate, a double-transition parallel broken line rope groove is adopted, and comprises two broken line areas and two straight line areas, as shown in figure 2, a-b, d-e, f-g and k-l are broken line areas, b-d, e-a, g-k and l-f are straight line areas, the rope outlet is positioned on the left side of the flange plate, 1-2 layers and 3-4 layers of interlayer transition devices are positioned on the right side of the flange plate, 2-3 layers and 4-5 layers of interlayer transition devices are positioned on the left side of the flange plate, and the whole body is in an inverted trapezoid shape. The radial radius difference of the 1-2 layers and 3-4 layers of the transition devices is the same as the radial radius difference of the 3-4 layers and 4-5 layers of the transition devices, and the radial radius difference is the thickness of the two layers of steel wire rope loops. Wherein the sections a to b are interlayer transition sections of 1-2 interlayer transition devices, the sections b to d are support sections of 1-2 interlayer transition devices, the sections d to e are ring transition sections of 1-2 interlayer transition devices, the sections f to g are interlayer transition sections of 2-3 interlayer transition devices, the sections k to f are support sections of 2-3 interlayer transition devices, the sections g to k are ring transition sections of 2-3 interlayer transition devices, meanwhile, the sections a to b are also interlayer transition sections of 3-4 interlayer transition devices, the sections b to c are support sections of 3-4 interlayer transition devices, the sections c to e are ring transition sections of 3-4 interlayer transition devices, meanwhile, the sections f to g are also interlayer transition sections of 4-5 interlayer transition devices, the sections g to i are support sections of 4-5 interlayer transition devices, and the sections i to k are ring-to-ring transition sections of 4-5 interlayer transition devices.

Description of transition process between 1-2 layers and 3-4 layers

In order to describe the dynamic process of the hoisting steel wire rope on the interlayer transition device more clearly, each section is represented by a numeral, as shown in fig. 3 below, when the steel wire rope moves to the position of section 1 in fig. 3 along with the drum, the last circle of the steel wire rope on the 1 st layer in the rope groove of the drum continues to move along the rope groove along with the rotation of the drum, and at this position, the last circle of the steel wire rope on the 3 rd layer does not start the layer-to-layer transition of 3-4 layers. When the steel wire rope moves to a section along with the winding drumWhen the surface 2 is in position, the last circle of steel wire rope on the 1 st layer rises to the top of the rope groove under the action of the guide device to prepare for the layer-to-layer transition of the 1 st to the 2 nd layers at the back, and the last circle of steel wire rope on the 3 rd layer at the position is in the same state as that of the position of the section 1. When the steel wire rope moves to the position of the section 3 along with the winding drum, the last circle of steel wire rope on the 1 st layer gradually rises along with the movement of the winding drum under the support of the 1-2 layers of interlayer transition blocks, and the width of the interlayer transition blocks is reduced toA rise height ofThe total height of the steel wire rope isCorresponding to a central angle of arc ofAt the position, the last circle of steel wire rope on the 3 rd layer also gradually rises along with the movement of the winding drum under the support of the 3-4 layers of interlayer transition blocks, and the width of the interlayer transition blocks is increasedA rise height ofThe total height of the steel wire rope isCorresponding to a central angle of arc ofWhen the steel wire rope moves to the position of the section 4 along with the winding drum, the last circle of steel wire rope on the 1 st layer continuously rises along with the movement of the winding drum under the support of the transition blocks between the 1 st layer and the 2 nd layer until the steel wire rope rises to the same height with the steel wire rope on the 2 nd layer, and the width of the transition blocks is reduced to beA rise height ofThe total height of the steel wire rope isCorresponding to a central angle of arc ofAt the position, the last circle of steel wire rope on the 3 rd layer also gradually rises along with the movement of the winding drum under the support of the 3-4 layers of interlayer transition blocks until the steel wire rope rises to the same height as the steel wire rope on the 4 th layer and the width of the interlayer transition block is increased to the same heightA rise height ofThe total height of the steel wire rope isCorresponding to a central angle of arc of

Description of transition process between 2-3 layers and 4-5 layers

When the steel wire rope moves to the position 1' of the cross section along with the winding drum, the last circle of steel wire rope on the 2 nd layer reaches the supporting block with the same height as the steel wire rope on the 2 nd layer, and 4-5 layer-to-layer transition is not started yet on the last circle of steel wire rope on the 4 th layer at the position. When the steel wire rope moves to the positions of the sections 2 ', 3 ' and 4 ' along with the winding drum, the height of the last circle of the steel wire rope on the 2 nd layer is always kept unchanged, but the width of the supporting block is changed from 0 to 4The last circle of the steel wire rope on the 4 th layer at the 3 positions is the same as that at the position 1', and 4-5 layer-to-layer transition is not started.When the steel wire rope moves to the position 5' of the cross section along with the winding drum, the last circle of steel wire rope on the 2 nd layer gradually rises along with the rotation of the winding drum under the support of the transition blocks between the 2-3 layers, and the rising height isThe total height of the steel wire rope isCorresponding to a central angle of arc ofAt the position, the last circle of steel wire rope on the 4 th layer is supported by the transition blocks between 4 to 5 layers, the steel wire rope also gradually rises along with the movement of the winding drum, and the steel wire rope deflects towards the direction of the transition device between 2 to 3 layersA rise height ofThe total height of the steel wire rope isCorresponding to a central angle of arc ofWhen the steel wire rope moves to the position of 6' of the cross section along with the winding drum, the last circle of steel wire rope on the 2 nd layer continuously rises to the same height as the steel wire rope on the 3 rd layer under the support of the transition blocks between the 2-3 layers, and the rising height isThe total height of the steel wire rope isCorresponding to a central angle of arc ofIn this position the last layer 4 steel wire rope turn is at 4EGradually rising to the same height as the 5 th layer of steel wire rope under the support of the 5-layer interlayer transition blocks, and deflecting the steel wire rope towards the 2-3-layer interlayer transition deviceA rise height ofThe total height of the steel wire rope isCorresponding to a central angle of arc ofWhen the steel wire rope moves to the position of the section 7' along with the winding drum, the last circle of steel wire rope on the 2 nd layer slowly rises under the support of the transition blocks between the 2-3 layers, and the rising height isThe total height of the steel wire rope isCorresponding to a central angle of arc ofAt the position, the last layer of steel wire rope at the 4 th layer enters a linear area along with the rotation of the winding drum, the height of the steel wire rope in the linear area is the same as that of the steel wire rope at the 5 th layer, and the height of the steel wire rope is equal to that of the steel wire rope at the 4 th layerCorresponding to a central angle of arc ofWhen the steel wire rope moves to the position of the section 8' along with the winding drum, the last circle of steel wire rope on the 2 nd layer starts to slowly rise under the support of the transition block between the 2-3 layers of circles, and the rising height isThe total height of the steel wire rope isCorresponding to a central angle of arc ofAt the position, the last circle of steel wire rope at the 4 th layer starts to slowly rise under the support of the transition block between the 4-5 layers of circles, and the rising height isThe total height of the steel wire rope isCorresponding to a central angle of arc ofWhen the steel wire rope moves to the position of the section 9' along with the winding drum, the last circle of steel wire rope on the 2 nd layer slowly climbs to the top of the 2 nd to last circle of steel wire rope on the 2 nd layer under the support of the transition block between the 2 to 3 layers of circles, and the ascending height isThe total height of the steel wire rope isCorresponding to a central angle of arc ofAt the position, the last circle of the steel wire rope on the 4 th layer slowly rises to the top of the 4 th layer of the 2 nd last circle of the steel wire rope under the support of the transition block between 4-5 circles, and the rising height isThe total height of the steel wire rope isCorresponding to a central angle of arc ofWhen the steel wire rope moves to the position 1' of the cross section again along with the winding drum, the 2 nd to 3 rd layers and the 4 th to 5 th layers are all transited, and the steel wire rope is wound to one side of the 1 st to 2 th and 3 th to 4 th layers of the transition device according to a certain motion rule.

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