CN110826161B - Full-face tunneling machine cutter arrangement design method based on stratum conditions - Google Patents

Full-face tunneling machine cutter arrangement design method based on stratum conditions Download PDF

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CN110826161B
CN110826161B CN201911189666.5A CN201911189666A CN110826161B CN 110826161 B CN110826161 B CN 110826161B CN 201911189666 A CN201911189666 A CN 201911189666A CN 110826161 B CN110826161 B CN 110826161B
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hob
lambda
diameter
cutter
radius
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CN110826161A (en
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李彤
韩爱民
施烨辉
程荷兰
韩如碧
张世豪
苏明
陈冬
翟维骏
张心远
李璇
王金铭
李闯
黄凌莉
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Nanjing Kentop Civil Engineering Technology Co ltd
Nanjing Tech University
China Design Group Co Ltd
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Nanjing Kentop Civil Engineering Technology Co ltd
Nanjing Tech University
China Design Group Co Ltd
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    • E—FIXED CONSTRUCTIONS
    • E21—EARTH OR ROCK DRILLING; MINING
    • E21D—SHAFTS; TUNNELS; GALLERIES; LARGE UNDERGROUND CHAMBERS
    • E21D9/00—Tunnels or galleries, with or without linings; Methods or apparatus for making thereof; Layout of tunnels or galleries
    • E21D9/10—Making by using boring or cutting machines
    • E21D9/11—Making by using boring or cutting machines with a rotary drilling-head cutting simultaneously the whole cross-section, i.e. full-face machines

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Abstract

The invention provides a full-face tunnel boring machine cutter arrangement design method based on actual stratum conditions, and relates to the technical field of full-face tunnel boring machine cutter head design. The method comprises the following steps: calculating the overlapping diameter of adjacent spokes of the cutter head according to the installation width of the cutter; determining the optimal amplitude of the cutter wire rod according to the passage of the muck particles; determining the number of cutters according to the formation parameters; calculating Archimedes spiral parameters of cutter arrangement in a classified manner; checking and adjusting the tool layout contradiction. The method can ensure the efficient rock breaking and continuous dumping of the hob and effectively improve the integral moment balance degree of the cutter head. The invention relates to a cutter head design method considering the actual stratum condition, which has clear calculation principle and simple calculation process.

Description

Full-face tunneling machine cutter arrangement design method based on stratum conditions
Technical Field
The invention relates to the technical field of cutter head design of a full-face tunnel boring machine, in particular to a full-face tunnel boring machine cutter arrangement design method based on stratum conditions.
Technical Field
The full-face tunneling machine crushes and cuts surrounding rocks through interaction between the cutter and the face, the cutter head is a bearing body of the cutter, the surrounding rocks form muck particles after being crushed and cut, the muck particles enter the rear area of the cutter head through an opening area on the cutter head and are conveyed out of the ground, and continuous tunneling is achieved. The arrangement mode of the cutters on the cutter head is the main content of cutter head design, and good cutter arrangement design can effectively improve the tunneling efficiency.
The existing cutter head design method comprises the following steps:
1 (cutter head design method for shield machine, application number: CN201810951874.3) aims at reducing the wear rate of the hob and prolonging the service life of the hob, proposes a design method according to the material of the cutter head, the structure of the cutter head and the diameter of the cutter head by taking the maximum stress which the actual cutter head needs to bear as a standard, and blurs the design process of cutter arrangement.
2 (a cutter head design method for full-section profiling excavation of a rounded rectangular tunnel, application number: CN201811633620.3) establishing a profiling cutter head theoretical profile model according to a profiling principle that a cutter head profile is tangent to a square section, and designing a cutter head structure through cutter head profile discretization and cutter head profile abrasion loss. The method does not take into account the effect of formation conditions on tool placement.
3 (Song Tian, Zhou Shunhua. Shield cutter head design research [ J ]. underground space and engineering report, 2007(03): 479-.
4 (Huo military, Stayan army, Teng hong Fei, Chailongfeng, Zhangli. full-section rock tunnel boring machine cutter layout design method [ J ] Chinese mechanical engineering, 2008(15):1832 and 1836.) provides an iterative calculation method of cutter layout mode, and the polar angle calculation method of the cutter on the cutter has multiple solutions and is not enough in the certainty of the solution result.
5 (Zhu palace, Sun bin, TBM positive hob multi-objective optimization layout [ J ] based on balanced rock breaking amount, mechanical design, 2017,34(11):1-6.) the cutter arrangement method is proposed from the perspective of balanced rock breaking, but the influence of the cutter arrangement mode on the rock breaking efficiency is not considered.
6 (Zhu palace, Song Li Rev, Guo Wei, research on the theory of the hob layout design of the cutter of the full-face rock tunnel boring machine based on the immune algorithm [ J ] mechanical design, 2018,35(11):31-38.) on the basis of artificially given number of the radiuses of the cutter, the cutter design method based on the cutter spacing optimization is provided, and a calculation method of the polar angle of the cutter on the cutter is not provided. Aiming at the defects of the prior art, the invention provides a cutter arrangement design method according to local conditions.
Disclosure of Invention
The technical problem solved by the invention is as follows: the method for designing the cutter arrangement of the full-face tunneling machine based on the stratum condition is provided, the tunneling efficiency can be effectively improved, and the design method is based on the stratum condition.
In order to solve the technical problems, the technical scheme provided by the invention is as follows: a full-face tunneling machine cutter arrangement design method based on stratum conditions comprises the following steps:
step one, calculating the overlapping radius r of the adjacent radii and the scrolls
The number of the radial strips of the cutter head is equal to the diameter strips of the cutter headNumber of strips NRTwice of each other, and the axes of the spokes of any radius are all collinear with the axes of the spokes of the other radius;
the cutter mounting width is w, the radius of the cutter head is R, the cutter mounting width is consistent with the width of the radial scroll where the hob on the cutter head is located, and the overlapping diameter R of adjacent radial scrollsThe intersection point of two radial boundary lines of a single opening area is connected with the center of a cutter head, the included angle between the axes of two adjacent radial spokes on the cutter head is theta, all the radial spokes divide the central angle 2 pi with the center of the cutter head as the center of a circle averagely, the relation between theta and the number c of the radial spokes of the cutter head is as shown in the formula (1), and c is not less than 4 and not more than [ pi/arcsin (w/(2 × R))]Even number of (d) [ pi/arcsin (w/(2 × R))]Is the largest positive integer not exceeding pi/arcsin (w/(2 × R));
when the width w of the radius scroll is taken as a chord with the length w of the circumference of the cutter head, the central angle corresponding to the width w of the radius scroll is 2arcsin (w/(2 × R)), if a cutter with the width w is arranged at one end, away from the center, of each radius scroll in the circumference of the cutter head, because the cutter and the cutter cannot be overlapped, c is an even number which is not less than 4 and does not exceed [ pi/arcsin (w/(2 × R)) ], and [ pi/arcsin (w/(2 × R)) ] is the maximum positive integer which does not exceed [ pi/arcsin (w/(2 × R));
if [ pi/arcsin (w/(2 × R)) ] < 4, then w and R should be reselected, and when [ pi/arcsin (w/(2 × R)) ] > 4, the calculation is carried out according to the step one.
θ＝2π/c (1)
Figure BDA0002293244430000021
Step two, calculating the optimal cutter head radius strip number according to the slag soil particle trafficability
Defining the maximum circumscribed circle diameter d of the slag particles generated when a certain stratum is tunneleds，dsObtained from a survey report, will be reported as dsThe critical condition that the diameter circle is tangent to the radial boundary of the opening area and the circumferential boundary of the opening area is taken as the critical condition that the muck particles pass through the opening area of the cutter head, and the critical condition satisfies the formula (3), wherein l is the height of the opening area of the cutter head, and the particle passing lower limit l of lminIs composed of
Figure BDA0002293244430000022
Figure BDA0002293244430000023
Arranging a cutter non-opening area with the width of B outside the circumferential boundary of the cutter opening area, wherein B is not less than the thickness of the shield body, the thickness of the shield body is between 0.02m and 0.5m according to engineering experience, the radius R of the cutter is a given value given according to a tunnel construction planning file, and the composition of R is required to satisfy the formula (4);
Figure BDA0002293244430000031
therefore, r is represented by the formulae (4) and (3)sThe formula (5) should be satisfied.
Figure BDA0002293244430000032
According to the formulae (2) and (5), θ should satisfy the formula (6)
Figure BDA0002293244430000033
The optimum cutterhead radius amplitude c is that the cutterhead design with the radius amplitude as much as possible is selected to improve the tunneling efficiencymaxShould be not more than
Figure BDA0002293244430000034
A maximum positive even number of c, andmaxnot less than 4. Step three, determining the number of cutters according to the stratum parameters
The path of each cutter on the face is circular motion, the circle center is the center of the cutter head, and the circular radius is the cutter installation radius, namely the closest distance between the contact position of the cutter and the face and the normal of the cutter head plane passing through the center of the cutter head. The installation radiuses of different cutters are different, and the difference of the track radiuses of two cutters with adjacent motion tracks is the cutter spacing s, and the unit is millimeter;
according to engineering experience, the space s' between cutters is determined at the beginning when a cohesive soil layer, a silt layer and a sand layer are tunneled, the unit is millimeter, and the value can be obtained according to the formula (7), wherein wr is the moisture content of the stratum; tunnelling soft rock, i.e. rock saturated uniaxial compressive strength RcWhen the pressure is not more than 30MPa, s' can be taken as the value of the formula (8), RcThe unit is MPa; tunnelling hard rock, i.e. rock saturated uniaxial compressive strength RcWhen s 'is greater than 30MPa, s' can be selected according to formula (9), RcThe unit is MPa;
s'＝100+20wr(7)
Figure BDA0002293244430000035
Figure BDA0002293244430000036
if the radius of the cutter head of the full-face tunneling machine is R, the number of the cutters is initially determined to be Ns1Calculated according to equation (10) < rho >1The installation radius of the first tool is rho is more than or equal to 0.5s according to engineering experience1≤300mm，
Figure BDA0002293244430000037
Is not more than
Figure BDA0002293244430000038
The largest non-negative integer of (d);
number of cutters NsDetermined according to equation (11), the actual blade spacing s is determined according to equation (12), NsMust be an even number;
Figure BDA0002293244430000041
Figure BDA0002293244430000042
Figure BDA0002293244430000043
step four, calculating Archimedes spiral parameters of cutter arrangement in classification mode
According to the surrounding rock types of the tunnel face in the construction area range provided in the geological survey report, ds、wr、RcAccording to dsDetermining c by step twomaxAccording to the type of face surrounding rock, wr and RcDetermination of N by step threesDetermining Archimedes spiral parameters of cutter arrangement;
the number of the radial strips of the cutterhead is equal to the number of the radial strips N of the cutterheadRTwice as much;
defining lambda as the corresponding serial number of a certain cutter on the cutter head in the ascending order of the installation radiuses of the cutters in all cutter categories on the cutter head, wherein the difference value between the installation radiuses of the adjacent numbered cutters is a cutter spacing s, and the s of any two cutters with adjacent tracks on the cutter head are the same according to the surrounding rock type, wr and R of the tunnel facecDetermining s through the third step;
(I) when c is going tomax＝NsWhen the temperature of the water is higher than the set temperature,
Figure BDA0002293244430000044
establishing a polar coordinate system, wherein the pole is O, the polar axis is Ox, and the counterclockwise direction is the positive direction of a corner; recording the radius scroll where the hob with the minimum radius is arranged as a first scroll, wherein the included angle between the first scroll and the Ox is theta1，θ1Less than 2 pi, the diameter of the first web is the first diameter, if the lambda-th hob and the lambda + 1-th hob are both ξ th(λ&λ+1)On diameter, turn counterclockwise from the first diameter
Figure BDA0002293244430000045
To obtain the ξ th(λ&λ+1)Diameter, ξ(λ&λ+1)＝1,2,...,NR；
If and only if the lambda-th hob and the lambda + 1-th hob are on the same diameter and are respectively positioned on two radial scroll webs on two sides of the middle point of the diameter, the diameter is numbered ξ(λ&λ+1)，ξ(λ&λ+1)Directly calculating according to the formula (13);
when the lambda tool hob and the lambda +1 tool hob are not on the same diameter, it is not necessary to directly makeThe number of diameters of the lambda tool hob should be calculated using equation (13), and lambda should be assigned as lambda-1, substituting the reassigned lambda into equation (13) to obtain the diameter number ξ of the tool with the tool number of lambda not reassigned(λ&λ+1)；
θλThe polar axis Ox rotates anticlockwise to the radian passed by the lambda-th hob, and theta is only when the lambda-th hob and the lambda +1 hob are on the same diameter and are respectively positioned on two radial scroll strips at two sides of the middle point of the diameterλξ in equation (14) when the λ tool hob and the λ +1 tool hob are not on the same diameter(λ&λ+1)The term is calculated by not calculating the diameter number of the lambda tool hob, but assigning lambda to lambda-1 using equation (13) directly, and substituting the reassigned lambda into equation (13) to obtain the diameter number ξ of the tool with the tool number of the tool being the non-reassigned lambda(λ&λ+1)；
ρλCalculating the installation radius of the lambda-th hob, namely the distance between the lambda-th hob and the pole O according to the formula (15);
Figure BDA0002293244430000051
Figure BDA0002293244430000052
ρλ＝ρ1+s(λ-1),λ＞1 (15)
(II) when cmax＞NsWhen the temperature of the water is higher than the set temperature,
Figure BDA0002293244430000053
establishing a polar coordinate system, wherein the pole is O, the polar axis is Ox, and the counterclockwise direction is the positive direction of a corner; recording the radius scroll where the hob with the minimum radius is arranged as a first scroll, wherein the included angle between the first scroll and the Ox is theta1，θ1Less than 2 pi, the diameter of the first web is the first diameter, if the lambda-th hob and the lambda + 1-th hob are both ξ th(λ&λ+1)On diameter, turn counterclockwise from the first diameter
Figure BDA0002293244430000054
To obtain the ξ th(λ&λ+1)Diameter, ξ(λ&λ+1)＝1,2,...,NR；
If and only if the lambda-th hob and the lambda + 1-th hob are on the same diameter and are respectively positioned on two radial scroll webs on two sides of the middle point of the diameter, the diameter is numbered ξ(λ&λ+1)，ξ(λ&λ+1)Directly calculating according to the formula (13);
when the lambda tool hob and the lambda +1 tool hob are not on the same diameter, the number of the diameter of the lambda tool hob should not be calculated directly using equation (13), and the lambda should be assigned to lambda-1, and the newly assigned lambda is substituted into equation (13) to obtain the diameter number ξ of the tool with the tool number of the unreassigned lambda(λ&λ+1)；
θλThe polar axis Ox rotates anticlockwise to the radian passed by the lambda-th hob, and theta is only when the lambda-th hob and the lambda +1 hob are on the same diameter and are respectively positioned on two radial scroll strips at two sides of the middle point of the diameterλξ in equation (14) when the λ tool hob and the λ +1 tool hob are not on the same diameter(λ&λ+1)The term is calculated by not calculating the diameter number of the lambda tool hob, but assigning lambda to lambda-1 using equation (13) directly, and substituting the reassigned lambda into equation (13) to obtain the diameter number ξ of the tool with the tool number of the tool being the non-reassigned lambda(λ&λ+1)；
ρλCalculating the installation radius of the lambda-th hob, namely the distance between the lambda-th hob and the pole O according to the formula (15);
(III) when cmax＜NsWhen the temperature of the water is higher than the set temperature,
Figure BDA0002293244430000061
there are cases where the number of cutters on the same diameter is more than 2; defining the cutter number sc under the condition of multilayer arrangementλ,χ,λ is the corresponding serial number of a certain cutter on the cutter head in the ascending order of the installation radius of the cutters in all cutter categories on the cutter head, and χ is the position of the cutterLayer number, which is the number of the corresponding sequence in the ascending arrangement of the cutter installation diameter of the cutters in the same layer, and c is more than or equal to 1max(ii) a The layer number χ is calculated according to equation (16),
Figure BDA0002293244430000062
is not more than
Figure BDA0002293244430000063
The largest non-negative integer of (d);
establishing a polar coordinate system, wherein the pole is O, the polar axis is Ox, and the counterclockwise direction is the positive direction of a corner; recording the radius scroll where the hob with the minimum radius is arranged as a first scroll, wherein the included angle between the first scroll and the Ox is theta1，θ1Less than 2 pi, the diameter of the first web is the first diameter, if scλ,χ,With hob and scλ+1,χ,+1With roller cutters commonly known as ξ(&+1)On diameter, turn counterclockwise from the first diameter
Figure BDA0002293244430000064
To obtain the ξ th(&+1)Diameter, ξ(&+1)＝1,2,...,NR；
The in-layer number of the cutter is calculated according to the formula (17)
Figure BDA0002293244430000065
＝λ-(χ-1)cmax(17)
When it is at scλ,χ,With hob and scλ+1,χ,+1With roller cutters commonly known as ξ(&+1)On diameter, turn counterclockwise from the first diameter
Figure BDA0002293244430000071
To obtain the ξ th(&+1)Diameter, ξ(&+1)＝1,2,...,NR；
Even for the cutters which are not in the same layer, the cutters are distributed on the same diameter as long as the serial numbers in the layers are consistent;
if and only if the scλ,χ,With a hob andsc thλ+1,χ,+1When two radial scroll bars with the hob cutters on the same diameter and respectively positioned at two sides of the middle point of the diameter are provided, the diameter is numbered ξ(&+1)Directly calculating according to the formula (18);
when it is at scλ,χ,With hob and scλ+1,χ,+1When the hob is not on the same diameter, the number of the diameter of the cutter with the number of the layer is not directly calculated by using the formula (18), and after the value is assigned to-1, the reassigned formula (18) is replaced to obtain the number ξ of the diameter of the cutter with the number of the cutter layer being not reassigned(&+1)；
Figure BDA0002293244430000072
Figure BDA0002293244430000073
Rotate the polar axis Ox counterclockwise to the scλ,χ,With the radian traversed by the hob
Figure BDA0002293244430000074
Is sc-thλ,χ,The mounting radius of the hob, i.e. the distance between the lambda-th hob and the pole O is taken as scλ,χ,With hob and scλ+1,χ,+1When the hob is on the same diameter,
Figure BDA0002293244430000075
directly calculating according to the formula (19);
when it is at scλ,χ,With hob and scλ+1,χ,+1ξ in formula (19) when the hob is not on the same diameter(&+1)The calculation method of the term is as follows: when it is at scλ,χ,With hob and scλ+1,χ,+1The hob is not on the same diameter, the number of the diameter of the cutter with the number of the layer is calculated by using the formula (18), the number of the cutter with the number of the layer is-1, the reassigned formula (18) is replaced, and the diameter number ξ of the cutter with the number of the cutter layer not reassigned is obtained(&+1)；
Figure BDA0002293244430000076
According to the formula (20)
Figure BDA0002293244430000077
Figure BDA0002293244430000078
Sc thλ+1,χ+1,1With roller cutters and
Figure BDA0002293244430000079
the hob tracks are adjacent but not on the same diameter, and the cutter distribution has interlayer transition.
Preferably, cmaxShould be not more than
Figure BDA0002293244430000081
If c in step two is the maximum positive even numbermaxIf < 4, the tunnel construction planning department should be informed to reselect R, and the above operations are carried out under the condition of the reselected R until cmaxC is obtained at a time of not less than 4max；
The radius breadth number of the cutter head is assigned as cmaxAnd in combination with formula (1) and formula (2) to givemaxCorresponding rsIf and cmaxCorresponding rsAnd l obtained according to formula (3)minSatisfy lmin≤R-B-rsThen c should be directly appliedmaxAnd carrying out the operation of the step four. If it can not satisfy lmin≤R-B-rsInforming the tunnel construction planning department to reselect R, and carrying out the operation of the step two under the condition of the reselected R until lmin≤R-B-rsWill satisfy lmin≤R-B-rsC ofmaxOperation in input step four
Preferably, the method further comprises the following steps:
checking and adjusting tool layout contradiction
ct is the maximum thickness of the hob, the installation width of the cutter is w,ρλthe lambda is the mounting radius of the hob, and pλ+2＝ρλ+2s, s is the tool pitch, if the lambda tool hob and the lambda +2 tool hob do not satisfy the formula (21), the position of the lambda tool hob calculated according to the steps one to four and the position installation space of the lambda +2 tool hob calculated according to the steps one to four have an overlapping conflict, and at this time, the lambda tool hob should be positioned at rhoλAnd under the condition of no change, setting the final design position of the roller cutter on the scroll with the radius of the lambda +2 tool roller cutter to eliminate the overlapping contradiction, wherein the final design position of the lambda +2 tool roller cutter is still the position obtained by calculation according to the step one to the step four. For other cutters without position installation space overlapping contradiction obtained by calculation according to the steps from the first step to the fourth step, the final design position is the position obtained by calculation according to the steps from the first step to the fourth step;
Figure BDA0002293244430000082
preferably, when the number of cutters on the same diameter of the cutter head is not less than 2, the tunneling efficiency is negatively related to the number of cutters on the same diameter of the cutter head, and the cutter head design with the largest number of radius strips is selected to improve the tunneling efficiency.
Preferably, the trajectories of two cutters in the same layer on the same diameter are adjacent to each other and are located on two radii of the same diameter respectively.
Preferably, the relative relationship of the installation radius between the two cutters in the same layer on each diameter is rotationally symmetric about the pole O, and the relative relationship of the installation radius between the two cutters in the same layer on each diameter, which belong to two adjacent layers, is opposite, that is, the combined torque directions of the cutters in the same layer on the two adjacent layers, which belong to the two adjacent layers, are opposite, so that the combined torque about the pole O of the cutters in the same layer on each diameter, which belong to two adjacent layers, is mutually offset, and rock breaking is performed in sequence, that is, theta is satisfiedscλ,χ,The unbalanced moment borne by the whole cutter head is further reduced under the condition that the rotating direction is not changed all the time when the lambda is increased, the moment balance degree of the whole cutter head is improved, and the rule of interlayer reversion exists in comparison of the installation radius of paired cutters.
Has the advantages that:
the method firstly provides a tool arrangement Archimedes spiral parameter design calculation method (step four) with paired tool installation radius comparison and interlayer reversion effect, is the only explicit calculation method in the existing tool arrangement Archimedes spiral parameter design method, strictly accords with the condition of minimizing the total moment of a cutter head, has great application value, and is important theoretical innovation and method innovation in the tool arrangement design method. The method also provides a tool number design method (step three) based on the tool spacing empirical formula for the first time, and the tool spacing empirical formula is the latest research result provided for the first time.
The method simultaneously puts forward a calculation basis for determining the upper limit of the cutter head radius swath by taking the slag soil particle passability geometry principle as a calculation basis, takes the geometric correlation among the overlapping diameter of adjacent radius swaths, the axis included angle of the adjacent radius swaths, the maximum circumscribed circle diameter of the slag soil particles and the width of the radius swaths as a derivation logic, puts forward an explicit simplified calculation method for determining the unique solution of the radius swath number according to the stratum conditions by using an extreme value method for the first time, and a cutter number design method (step three) and a cutter spiral design method (step four) jointly form the cutter arrangement design method.
Drawings
The invention will be further explained with reference to the drawings.
FIG. 1 is a schematic view of overlapping radii of adjacent radii swaths
FIG. 2 is a schematic diagram of a single cutterhead with two cutters for tunneling
FIG. 3 is a schematic diagram of a single cutterhead with multiple cutters for tunneling
FIG. 4 is a schematic diagram of critical conditions for passage of slag particles through the opening area of the cutter head
FIG. 5 is a schematic view of the radius of the cutter head
FIG. 6 is a schematic diagram of the principle of continuous spiral positioning of adjacent cutters between adjacent diameters
FIG. 7 is a schematic diagram of the arrangement method of the cutter distribution with interlayer transition
FIG. 8 is a schematic view of the interlaminar reversal of paired tool mounting radius comparison
FIG. 9 schematic diagram of tool layout checking conditions
FIG. 10 schematic view of the arrangement of the cutters in embodiment 1
FIG. 11 schematic view of the arrangement of the cutters in embodiment 2
FIG. 12 schematic view of the arrangement of the cutters in embodiment 3
FIG. 13 is a schematic diagram of the tool position calculated in the first to fourth steps in embodiment 4
FIG. 14 is a schematic diagram of the tool position adjusted according to step five in embodiment 4
Detailed description of the invention
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are some, not all, embodiments of the present invention. All other embodiments, which can be obtained by a person skilled in the art without inventive effort based on the embodiments of the present invention, are within the scope of the present invention.
Step one, calculating overlapping diameters of adjacent radii and banners
The number of the radial strips of the cutterhead is equal to the number of the radial strips N of the cutterheadRTwo times, and the axes of each radius swathe are all and only the axis of the other radius swathe is collinear therewith.
As shown in fig. 1, the cutter mounting width is w, the radius of the cutter head is R, and the cutter mounting width is consistent with the width of the radius scroll where the hob on the cutter head is located. Overlapping radius r of adjacent radius scrollsThe intersection point of two radial boundary lines of a single opening area is connected with the center of a cutter head, the included angle between the axes of two adjacent radial spokes on the cutter head is theta, all the radial spokes divide the central angle 2 pi with the center of the cutter head as the center of a circle averagely, theta is related to the number c of the radial spokes of the cutter head, and the formula (1) c is not less than 4 and not more than [ pi/arcsin (w/(2 × R))]Even number of (d) [ pi/arcsin (w/(2 × R))]Is the largest positive integer not exceeding pi/arcsin (w/(2 × R))。
When the width w of the radius scroll is taken as a chord with the length w of the circumference of the cutter head, the central angle corresponding to the width w of the radius scroll is 2arcsin (w/(2 × R)), if a cutter with the width w is arranged at one end, away from the center, of each radius scroll in the circumference of the cutter head, because the cutter and the cutter cannot be overlapped, c is an even number which is not less than 4 and not more than [ pi/arcsin (w/(2 × R)) ], and [ pi/arcsin (w/(2 × R)) ] is the maximum positive integer which is not more than pi/arcsin (w/(2 × R)).
If [ pi/arcsin (w/(2 × R)) ] < 4, then w and R should be reselected, and when [ pi/arcsin (w/(2 × R)) ] > 4, the calculation is carried out according to the step one.
θ＝2π/c (1)
Figure BDA0002293244430000101
From the formulas (1) and (2), when c is in the range of {4,6, 8.., 30}, rsThe approximate values of (a) are shown in table 1.
TABLE 1 approximate values for the overlap of radii swaths when c ranges from {4,6, 8.., 30}
c θ(rad) θ/2(rad) rs(m)
4 π/2 π/4 0.71w
6 π/3 π/6 1.00w
8 π/4 π/8 1.31w
10 π/5 π/10 1.62w
12 π/6 π/12 1.93w
14 π/7 π/14 2.25w
16 π/8 π/16 2.56w
18 π/9 π/18 2.88w
20 π/10 π/20 3.20w
22 π/11 π/22 3.51w
24 π/12 π/24 3.83w
26 π/13 π/26 4.15w
28 π/14 π/28 4.47w
30 π/15 π/30 4.78w
Step two, calculating the optimal cutter head radius strip number according to the slag soil particle trafficability
As shown in figure 2, when two cutters are arranged on one cutterhead, because two points determine a straight line, the two cutters are not in contact with the tunnel face and are not separated, the cutter is stressed by F in the tunneling process of the full-face tunneling machine1≈F2Distance u between cutter and driving axis1≈u2，F1u1≈F2u2The tool is moment balanced with respect to the axis. As shown in FIG. 3, when the total number of cutters of the cutterhead is a fixed value, when the number of cutters on the same diameter is increased, the total number of cutters on the cutterhead is a fixed value, becauseThe probability that cutters are empty and do not participate in tunneling is increased due to the fact that the number of the cutters distributed on the diameter is larger than two cutters, if the adjacent cutters participate in tunneling, the distance between the cutters and the contact point of rock is reduced, stress restraint of the rock in a compression area is enhanced, the shear strength of surrounding rock is improved, torque and thrust required by rock breaking are increased, the area of a stratum clamped by the radius without the cutter effect on the face at any moment is increased, and finally the tunneling efficiency is reduced. Therefore, when the number of cutters on the same diameter of the cutter head is not less than 2, the number of cutters is increased, and the tunneling efficiency is reduced.
Therefore, when the number of cutters on the same diameter of the cutter head is not less than 2, the tunneling efficiency is negatively related to the number of cutters on the same diameter of the cutter head, and the cutter head design with the largest number of radius strips is selected to improve the tunneling efficiency.
However, when the area of the cutterhead is constant, with the increase of the number c of the radius swaths of the cutterhead, the opening area of the cutterhead clamped between the radius swaths of the adjacent cutterheads is reduced, and the opening area of the cutterhead meets the condition that the largest particles of the dregs on the tunnel face can pass through.
Defining the maximum circumscribed circle diameter d of the slag particles generated when a certain stratum is tunneleds，dsObtained from a survey report. As in fig. 4, will be given dsThe diameter circle is tangent to the radial boundary of the opening area and the circumferential boundary of the opening area to serve as the critical condition for the slag particles to pass through the opening area of the cutter head, and at the moment, the formula (3) is satisfied, wherein l is the height of the opening area of the cutter head. Particle passage lower limit l according to formula (3)minIs composed of
Figure BDA0002293244430000121
When c has a value in the range of {4,6, 8.., 30}, lminThe approximate values are shown in table 2.
Figure BDA0002293244430000122
TABLE 2 values of l when c ranges from {4,6, 8.., 30}minApproximate value
Figure BDA0002293244430000123
Figure BDA0002293244430000131
And arranging a cutter head non-opening area with the width of B outside the circumferential boundary of the cutter head opening area, wherein the width of B is not less than the thickness of the shield body, and the thickness of the shield body is between 0.02m and 0.5m according to engineering experience. The radius R of the cutter head is a given value given according to a tunnel construction planning file, and the composition of R satisfies the following formula (4) and fig. 5.
Figure BDA0002293244430000132
Therefore, r is represented by the formulae (4) and (3)sThe formula (5) should be satisfied.
Figure BDA0002293244430000133
According to the formulae (2) and (5), θ should satisfy the formula (6).
Figure BDA0002293244430000134
The optimum cutterhead radius amplitude c is that the cutterhead design with the radius amplitude as much as possible is selected to improve the tunneling efficiencymaxShould be not more than
Figure BDA0002293244430000135
A maximum positive even number of c, andmaxnot less than 4. If c ismaxIf < 4, the tunnel construction planning department should be informed to reselect R, and the operation of the second step is carried out under the condition of the reselected R until cmaxC is obtained at a time of not less than 4max。
The radius breadth number of the cutter head is assigned as cmaxAnd in combination with formula (1) and formula (2) to givemaxCorresponding rsIf and cmaxCorresponding rsAnd l obtained according to formula (3) and Table 2minSatisfy lmin≤R-B-rsThen c should be directly appliedmaxAnd carrying out the operation of the step four. If it can not satisfy lmin≤R-B-rsInforming the tunnel construction planning department to reselect R, and carrying out the operation of the step two under the condition of the reselected R until lmin≤R-B-rsWill satisfy lmin≤R-B-rsC ofmaxAnd the input step four is operated.
Step three, determining the number of cutters according to the stratum parameters
The path of each cutter on the face is circular motion, the circle center is the center of the cutter head, and the circular radius is the cutter installation radius, namely the closest distance between the contact position of the cutter and the face and the normal of the cutter head plane passing through the center of the cutter head. The installation radiuses of different cutters are different, and the difference of the track radiuses of two cutters with adjacent motion tracks is the cutter spacing s, and the unit is millimeter.
According to engineering experience, the initial cutter spacing s' (unit is millimeter) can be taken as a value according to a formula (7) when a cohesive soil layer, a silt layer and a sand layer are tunneled, wherein wr is the water content of the stratum; tunneling soft rock (rock saturated uniaxial compressive strength R)cNot more than 30MPa) s' can be taken as in formula (8), RcThe unit is MPa; tunneling hard rock (rock saturated uniaxial compressive strength R)cGreater than 30MPa) s' can be taken as in formula (9), RcThe units are in MPa.
s'＝100+20wr(7)
Figure BDA0002293244430000141
Figure BDA0002293244430000142
If the radius of the cutter head of the full-face tunneling machine is R, the number of the cutters is initially determined to be Ns1Calculated according to equation (10) < rho >1The installation radius of the first tool is rho is more than or equal to 0.5s according to engineering experience1≤300mm，
Figure BDA0002293244430000143
Is not more than
Figure BDA0002293244430000144
Is the largest non-negative integer.
Number of cutters NsThe actual blade pitch s is determined by equation (12) and equation (11). N is a radical ofsMust be an even number.
Figure BDA0002293244430000145
Figure BDA0002293244430000146
Figure BDA0002293244430000147
Step four, calculating Archimedes spiral parameters of cutter arrangement in classification mode
According to the surrounding rock types of the tunnel face in the construction area range provided in the geological survey report, ds、wr、RcAccording to dsDetermining c by step twomaxAccording to the type of face surrounding rock, wr and RcDetermination of N by step threesAnd determining the Archimedes spiral parameters of the cutter arrangement.
According to the second step, when the number of the strips is as large as possible, the number of the cutters on the same diameter is as small as possible and is not less than 2, if u is1And u2A large difference results in F1u1And F2u2The difference is large, so that the unbalance of the overall moment of the cutter head is aggravated. Therefore, u should be adjusted1And u2With as little phase difference as possible and not on the same radius.
U between two tools with closely adjacent paths1And u2The difference is minimum (the difference is the distance between the cutters), so that a cutter is respectively arranged on two radiuses with the same diameter, and the tracks of the two cutters with the same diameter are adjacent to each other, thereby realizing u1And u2The difference is as small as possible, and the overall moment of the cutter head is approximately balanced.
Cutter radius scrollThe number of the spokes is equal to the number N of the spokes with the diameter of the cutter headRTwice as much.
Defining lambda as the corresponding serial number of a certain cutter on the cutter head in the ascending order of the installation radiuses of the cutters in all cutter categories on the cutter head, wherein the difference value between the installation radiuses of the adjacent numbered cutters is a cutter spacing s, and the s of any two cutters with adjacent tracks on the cutter head are the same according to the surrounding rock type, wr and R of the tunnel facecAnd determining s through the step three.
(I) When c is going tomax＝NsWhen the temperature of the water is higher than the set temperature,
Figure BDA0002293244430000151
a polar coordinate system is established as shown in FIG. 6, the pole is O, the polar axis is Ox, and the counterclockwise direction is the positive direction of the rotation angle. Recording the radius scroll where the hob with the minimum radius is arranged as a first scroll, wherein the included angle between the first scroll and the Ox is theta1，θ1Less than 2 pi, the diameter of the first web is the first diameter, if the lambda-th hob and the lambda + 1-th hob are both ξ th(λ&λ+1)On diameter, turn counterclockwise from the first diameter
Figure BDA0002293244430000152
To obtain the ξ th(λ&λ+1)Diameter, ξ(λ&λ+1)＝1,2,...,NR。
If and only if the lambda-th hob and the lambda + 1-th hob are on the same diameter and are respectively positioned on two radial scroll webs on two sides of the middle point of the diameter, the diameter is numbered ξ(λ&λ+1)，ξ(λ&λ+1)Directly according to equation (13).
When the lambda tool hob and the lambda +1 tool hob are not on the same diameter, the number of the diameter of the lambda tool hob should not be calculated directly using equation (13), and the lambda should be assigned to lambda-1, and the newly assigned lambda is substituted into equation (13) to obtain the diameter number ξ of the tool with the tool number of the unreassigned lambda(λ&λ+1)。
θλThe polar axis Ox rotates anticlockwise to the radian passed by the lambda-th hob, and if and only if the lambda-th hob and the lambda +1 hob are in the same straight lineTwo radial swaths on the diameter and respectively positioned at two sides of the diameter midpoint, thetaλξ in equation (14) when the λ tool hob and the λ +1 tool hob are not on the same diameter(λ&λ+1)The term is calculated by not calculating the diameter number of the lambda tool hob, but assigning lambda to lambda-1 using equation (13) directly, and substituting the reassigned lambda into equation (13) to obtain the diameter number ξ of the tool with the tool number of the tool being the non-reassigned lambda(λ&λ+1)。
ρλThe mounting radius of the λ -th hob, i.e. the distance between the λ -th hob and the pole O, is calculated according to equation (15).
Figure BDA0002293244430000161
Figure BDA0002293244430000162
ρλ＝ρ1+s(λ-1),λ＞1 (15)
(II) when cmax＞NsWhen the temperature of the water is higher than the set temperature,
Figure BDA0002293244430000163
establishing a polar coordinate system, wherein the pole is O, the polar axis is Ox, and the counterclockwise direction is the positive direction of a corner; recording the radius scroll where the hob with the minimum radius is arranged as a first scroll, wherein the included angle between the first scroll and the Ox is theta1，θ1Less than 2 pi, the diameter of the first web is the first diameter, if the lambda-th hob and the lambda + 1-th hob are both ξ th(λ&λ+1)On diameter, turn counterclockwise from the first diameter
Figure BDA0002293244430000164
To obtain the ξ th(λ&λ+1)Diameter, ξ(λ&λ+1)＝1,2,...,NR；
If and only if the lambda-th hob and the lambda + 1-th hob are on the same diameter and are respectively positioned on two radial scroll webs on two sides of the middle point of the diameter, the diameter is numbered ξ(λ&λ+1)，ξ(λ&λ+1)Directly according to equation (13).
When the lambda tool hob and the lambda +1 tool hob are not on the same diameter, the number of the diameter of the lambda tool hob should not be calculated directly using equation (13), and the lambda should be assigned to lambda-1, and the newly assigned lambda is substituted into equation (13) to obtain the diameter number ξ of the tool with the tool number of the unreassigned lambda(λ&λ+1)。
θλThe polar axis Ox rotates anticlockwise to the radian passed by the lambda-th hob, and theta is only when the lambda-th hob and the lambda +1 hob are on the same diameter and are respectively positioned on two radial scroll strips at two sides of the middle point of the diameterλξ in equation (14) when the λ tool hob and the λ +1 tool hob are not on the same diameter(λ&λ+1)The term is calculated by not calculating the diameter number of the lambda tool hob, but assigning lambda to lambda-1 using equation (13) directly, and substituting the reassigned lambda into equation (13) to obtain the diameter number ξ of the tool with the tool number of the tool being the non-reassigned lambda(λ&λ+1)。
ρλThe mounting radius of the λ -th hob, i.e. the distance between the λ -th hob and the pole O, is calculated according to equation (15).
(III) when cmax＜NsWhen the temperature of the water is higher than the set temperature,
Figure BDA0002293244430000165
there are cases where the number of cutters on the same diameter is more than 2. Defining the cutter number sc under the condition of multilayer arrangementλ,χ,λ is the corresponding serial number of a certain cutter on the cutter head in the ascending order of the installation radius of the cutters in all cutter categories on the cutter head, χ is the layer number of the cutter, and is the corresponding serial number of the cutters in the same layer in the ascending order of the installation diameter of the cutters, and c is more than or equal to 1max. The layer number χ is calculated according to equation (16),
Figure BDA0002293244430000171
is not more than
Figure BDA0002293244430000172
Is the largest non-negative integer.
Establishing a polar coordinate system, wherein the pole is O, the polar axis is Ox, and the counterclockwise direction is the positive direction of a corner; recording the radius scroll where the hob with the minimum radius is arranged as a first scroll, wherein the included angle between the first scroll and the Ox is theta1，θ1Less than 2 pi, the diameter of the first web is the first diameter, if scλ,χ,With hob and scλ+1,χ,+1With roller cutters commonly known as ξ(&+1)On diameter, turn counterclockwise from the first diameter
Figure BDA0002293244430000173
To obtain the ξ th(&+1)Diameter, ξ(&+1)＝1,2,...,NR；
The in-layer number of the tool is calculated by equation (17).
Figure BDA0002293244430000174
＝λ-(χ-1)cmax(17)
When it is at scλ,χ,With hob and scλ+1,χ,+1With roller cutters commonly known as ξ(&+1)On diameter, turn counterclockwise from the first diameter
Figure BDA0002293244430000175
To obtain the ξ th(&+1)Diameter, ξ(&+1)＝1,2,...,NR。
Even for the cutters which are not in the same layer, the cutters are distributed on the same diameter as long as the numbers in the layers are consistent.
If and only if the scλ,χ,With hob and scλ+1,χ,+1When two radial scroll bars with the hob cutters on the same diameter and respectively positioned at two sides of the middle point of the diameter are provided, the diameter is numbered ξ(&+1)Directly according to equation (18).
When it is at scλ,χ,With hob and scλ+1,χ,+1When the hob is not on the same diameter, the equation (18) should not be used directly to calculate the location of the cutter numbered in the layerThe diameter is numbered, and if the value is assigned to-1, the reassigned formula (18) is substituted to obtain the diameter in which the tool numbered in the tool layer as not reassigned ξ(&+1)。
Figure BDA0002293244430000176
Figure BDA0002293244430000181
Rotate the polar axis Ox counterclockwise to the scλ,χ,With the arc traversed by the hob.
Figure BDA0002293244430000182
Is sc-thλ,χ,The mounting radius of the hob, i.e. the distance between the lambda-th hob and the pole O.
When it is at scλ,χ,With hob and scλ+1,χ,+1When the hob is on the same diameter,
Figure BDA0002293244430000183
directly according to equation (19).
When it is at scλ,χ,With hob and scλ+1,χ,+1ξ in formula (19) when the hob is not on the same diameter(&+1)The calculation method of the term is as follows: when it is at scλ,χ,With hob and scλ+1,χ,+1The hob is not on the same diameter, the number of the diameter of the cutter with the number of the layer is calculated by using the formula (18), the number of the cutter with the number of the layer is-1, the reassigned formula (18) is replaced, and the diameter number ξ of the cutter with the number of the cutter layer not reassigned is obtained(&+1)。
Figure BDA0002293244430000184
Calculated according to equation (20).
Figure BDA0002293244430000185
Figure BDA0002293244430000186
As shown in FIG. 7, scλ+1,χ+1,1With roller cutters and
Figure BDA0002293244430000187
the hob tracks are adjacent but not on the same diameter, and the cutter distribution has interlayer transition.
As shown in fig. 8, the reason why the tool positions are set according to the archimedes' spiral equations of equations (16) to (20) is that the relative relationship of the installation radius between two tools in the same layer on each diameter is rotationally symmetric about the pole O, and the relative relationship of the installation radius between two tools in the same layer on each diameter belonging to two adjacent layers is opposite, that is, the resultant torque directions of the tools in the same layer belonging to two adjacent layers are opposite to the pole O, so that the resultant torques of the tools in the same layer belonging to two adjacent layers about the pole O cancel each other out, and rock breaking is performed in sequence (the resultant torque about the pole O is satisfied) (rock breaking is performed in sequence)
Figure BDA0002293244430000188
The rotating direction is always unchanged when the lambda is increased), the unbalanced moment borne by the whole cutter head is further reduced, the moment balance degree of the whole cutter head is improved, and the rule of interlayer reversion exists in comparison of the installation radius of paired cutters.
Checking and adjusting tool layout contradiction
In FIG. 9, ct is the maximum thickness of the hob, and the mounting width of the hob is w, ρλThe lambda is the mounting radius of the hob, and pλ+2＝ρλ+2s, s is the blade pitch. If the lambda tool hob and the lambda +2 tool hob do not satisfy the formula (21), the position of the lambda tool hob calculated according to the steps one to four and the position installation space of the lambda +2 tool hob calculated according to the steps one to four are overlapped and contradictory, and at this time, the lambda tool hob should be arranged at rhoλUnder the condition of no change, the final design position is set on the scroll with the radius of the lambda +2 tool hob so as to eliminate the overlapping contradiction, and the lambda +2 tool hobThe final design position of the knife is still the position calculated according to the steps one to four. And for other cutters without position installation space overlapping contradiction obtained by calculation according to the steps from the first step to the fourth step, the final design position is the position obtained by calculation according to the steps from the first step to the fourth step.
Figure BDA0002293244430000191
Example 1
The face is sand layer soil, wr is 30%, ds0.03m, 0.5m for shield machine R, 0.02m for B, 0.08m for cutter w, 0.01m for ct, theta1＝0，ρ1＝70mm。
According to the formula (6), the corresponding c is calculated to be theta more than or equal to 13.586 DEGmaxIs 26.
To cmaxThe test was carried out 26: according to formula (1) and formula (2), cmaxWhen the value is 26 rs＝4.15×0.08＝0.332m，R-B-rs＝0.148m＞lmin4.65 × 0.03.03 ═ 0.1395m, so c in step fourmax＝26。
According to formula (7), s' is 106 mm.
According to the formula (10),
Figure BDA0002293244430000192
then N iss1＝6。
According to formula (11), Ns＝6。
According to the formula (12),
Figure BDA0002293244430000193
according to step four, when cmax＞NsWhen the temperature of the water is higher than the set temperature,
Figure BDA0002293244430000194
obtaining the table 3 according to the formula (13), the formula (14), the formula (15) and the step four.
Table 3 tool layout design results of example 1
Figure BDA0002293244430000195
Figure BDA0002293244430000201
According to the fifth step, each cutter satisfies the formula (21), so the cutter arrangement design is as shown in fig. 10.
Example 2
The tunnel face is a medium weathering tuff layer with coagulated limestone Rc＝24MPa，ds0.3m, 1m for shield machine R, 0.1m for B, 0.1m for cutter w, 0.02m for ct, theta1＝1，ρ1＝80mm。
According to the formula (6), theta is calculated to be more than or equal to 31 degrees, and the corresponding cmaxIs 10.
To cmaxThe test was performed as 10: according to formula (1) and formula (2), cmaxWhen the value is 10 rs＝1.62×0.1＝0.162m，R-B-rs＝0.738m＞lmin2.12 × 0.3.3 is 0.636m, so step four cmax＝10。
According to formula (8), s' is 92 mm.
According to the formula (10),
Figure BDA0002293244430000202
then N iss1＝11。
According to formula (11), Ns＝12。
According to the formula (12),
Figure BDA0002293244430000203
according to step four, when cmax＜NsWhen the temperature of the water is higher than the set temperature,
Figure BDA0002293244430000204
obtaining the table 4 according to the formula (16), the formula (17), the formula (18), the formula (19), the formula (20) and the step four.
Table 4 tool layout design results of example 2
Figure BDA0002293244430000205
Figure BDA0002293244430000211
According to the fifth step, each cutter satisfies the formula (21), so the cutter arrangement design is as shown in fig. 11.
Example 3
The face is a moderately weathered granite layer, Rc＝60MPa，ds0.12m, 0.3m for shield machine R, 0.05m for B, 0.12m for cutter w, 0.02m for ct, theta1＝0，ρ1＝60mm。
According to the formula (6), theta is calculated to be more than or equal to 78.34 degrees, and the corresponding cmaxIs 4.
To cmaxThe test was performed as 4: according to formula (1) and formula (2), cmaxWhen the value is 4 rs＝0.71×0.12＝0.0852m，R-B-rs＝0.1648m＞lmin1.21 × 0.12 0.1452m, so c in step fourmax＝4。
According to equation (9), s' is ≈ 84.5 mm.
According to the formula (10),
Figure BDA0002293244430000212
then N iss1＝4。
According to formula (11), Ns＝4。
According to the formula (12),
Figure BDA0002293244430000221
according to step four, when cmax＝NsWhen the temperature of the water is higher than the set temperature,
Figure BDA0002293244430000222
obtaining the table 5 according to the formula (13), the formula (14), the formula (15) and the step four.
Table 5 design results for tool layout of example three
Figure BDA0002293244430000223
According to the fifth step, each cutter satisfies the formula (21), so the cutter arrangement design is as shown in fig. 12.
Example 4
Cutter w of the shield machine is 166.04mm, ct is 22.72mm, rho1＝60mm、s＝30mm、N R4. As shown in fig. 13, according to the fifth step, when λ is 1, the 1 st hob and the 3 rd hob do not satisfy the formula (21), and there is an overlap conflict between the position of the 1 st hob calculated according to the first to fourth steps and the position installation space of the 3 rd hob calculated according to the first to fourth steps, and at this time, the 1 st hob should be set to ρ £1And under the condition of no change, setting the final design position of the third hob in the scroll with the radius where the third hob is located to eliminate the overlapping contradiction, wherein the final design position of the third hob is still the position obtained by calculation according to the first step to the fourth step. And for other cutters without position installation space overlapping contradiction obtained by calculation according to the steps from the first step to the fourth step, the final design position is the position obtained by calculation according to the steps from the first step to the fourth step. The adjusted tool position is shown in fig. 14.

Claims (8)

1. A full-face tunneling machine cutter arrangement design method based on stratum conditions is characterized by comprising the following steps: the method comprises the following steps:
step one, calculating the overlapping radius r of the adjacent radii and the scrolls
The number of the radial strips of the cutterhead is equal to the number of the radial strips N of the cutterheadRTwice of each other, and the axes of the spokes of any radius are all collinear with the axes of the spokes of the other radius;
the cutter mounting width is w, the radius of the cutter head is R, the cutter mounting width is consistent with the width of the radial scroll where the hob on the cutter head is located, and the overlapping diameter R of adjacent radial scrollsThe intersection point of two radial boundary lines of a single opening area is connected with the center of a cutter head, the included angle between the axes of two adjacent radius scroll strips on the cutter head is theta, all radius scroll strips divide the center angle 2 pi with the center of the cutter head as the center of a circle in an average way, and the relation between theta and the number c of the radius scroll strips of the cutter head is as shown in the formula (1);c should be not less than 4 and not more than [ pi/arcsin (w/(2 × R))]Even number of (d) [ pi/arcsin (w/(2 × R))]Is the largest positive integer not exceeding pi/arcsin (w/(2 × R));
θ＝2π/c (1)
Figure FDA0002468755310000011
step two, calculating the optimal cutter head radius strip number according to the slag soil particle trafficability
Defining the maximum circumscribed circle diameter d of the slag particles generated when a certain stratum is tunneleds，dsObtained from a survey report, will be reported as dsThe critical condition that the diameter circle is tangent to the radial boundary of the opening area and the circumferential boundary of the opening area is taken as the critical condition that the muck particles pass through the opening area of the cutter head, and the critical condition satisfies the formula (3), wherein l is the height of the opening area of the cutter head, and the particle passing lower limit l of lminIs composed of
Figure FDA0002468755310000012
Figure FDA0002468755310000013
Arranging a cutter non-opening area with the width of B outside the circumferential boundary of the cutter opening area, wherein B is not less than the thickness of the shield body, the thickness of the shield body is between 0.02m and 0.5m according to engineering experience, the radius R of the cutter is a given value given according to a tunnel construction planning file, and the composition of R is required to satisfy the formula (4);
Figure FDA0002468755310000021
therefore, r is represented by the formulae (4) and (3)sShould satisfy the formula (5)
Figure FDA0002468755310000022
According to the formulae (2) and (5), θ should satisfy the formula (6)
Figure FDA0002468755310000023
The optimum cutterhead radius amplitude c is realized because the cutterhead with large radius amplitude is designed to improve the tunneling efficiencymaxShould be not more than
Figure FDA0002468755310000024
A maximum positive even number of c, andmax≥4；
step three, determining the number of cutters according to the stratum parameters
The path of each cutter on the face is circular motion, the circle center is the center of a cutter disc, and the circular radius is the cutter installation radius, namely the closest distance between the contact position of the cutter and the face and the normal of the cutter disc plane passing through the center of the cutter disc;
the installation radiuses of different cutters are different, and the difference of the track radiuses of two cutters with adjacent motion tracks is the cutter spacing s, and the unit is millimeter;
according to engineering experience, the space s' between cutters is determined at the beginning when a cohesive soil layer, a silt layer and a sand layer are tunneled, the unit is millimeter, and the value can be obtained according to the formula (7), wherein wr is the moisture content of the stratum; tunnelling soft rock, i.e. rock saturated uniaxial compressive strength RcWhen the pressure is not more than 30MPa, s' can be taken as the value of the formula (8), RcThe unit is MPa; tunnelling hard rock, i.e. rock saturated uniaxial compressive strength RcWhen s 'is greater than 30MPa, s' can be selected according to formula (9), RcThe unit is MPa;
s'＝100+20wr (7)
Figure FDA0002468755310000025
Figure FDA0002468755310000026
if the radius of the cutter head of the full-face tunneling machine is R, the number of the cutters is initially determined to be Ns1Calculated according to equation (10) < rho >1The installation radius of the first tool is determined according to the engineeringTest 0.5s ≤ rho1≤300mm，
Figure FDA0002468755310000027
Is not more than
Figure FDA0002468755310000028
The largest non-negative integer of (d);
number of cutters NsDetermined according to equation (11), the actual blade spacing s is determined according to equation (12), NsMust be an even number;
Figure FDA0002468755310000031
Figure FDA0002468755310000032
Figure FDA0002468755310000033
step four, calculating Archimedes spiral parameters of cutter arrangement in classification mode
According to the surrounding rock types of the tunnel face in the construction area range provided in the geological survey report, ds、wr、RcAccording to dsDetermining c by step twomaxAccording to the type of face surrounding rock, wr and RcDetermination of N by step threesDetermining Archimedes spiral parameters of cutter arrangement;
the number of the radial strips of the cutterhead is equal to the number of the radial strips N of the cutterheadRTwice as much;
defining lambda as the corresponding serial number of a certain cutter on the cutter head in the ascending order of the installation radiuses of the cutters in all cutter categories on the cutter head, wherein the difference value between the installation radiuses of the adjacent numbered cutters is a cutter spacing s, and the s of any two cutters with adjacent tracks on the cutter head are the same according to the surrounding rock type, wr and R of the tunnel facecDetermining s through the third step;
(I) when c is going tomax＝NsWhen the temperature of the water is higher than the set temperature,
Figure FDA0002468755310000034
establishing a polar coordinate system, wherein the pole is O, the polar axis is Ox, and the counterclockwise direction is the positive direction of a corner; recording the radius scroll where the hob with the minimum radius is arranged as a first scroll, wherein the included angle between the first scroll and the Ox is theta1，θ1Less than 2 pi, the diameter of the first web is the first diameter, if the lambda-th hob and the lambda + 1-th hob are both ξ th(λ&λ+1)On diameter, turn counterclockwise from the first diameter
Figure FDA0002468755310000035
To obtain the ξ th(λ&λ+1)Diameter, ξ(λ&λ+1)＝1,2,...,NR；
If and only if the lambda-th hob and the lambda + 1-th hob are on the same diameter and are respectively positioned on two radial scroll webs on two sides of the middle point of the diameter, the diameter is numbered ξ(λ&λ+1)，ξ(λ&λ+1)Directly calculating according to the formula (13);
when the lambda tool hob and the lambda +1 tool hob are not on the same diameter, the number of the diameter of the lambda tool hob should not be calculated directly using equation (13), and the lambda should be assigned to lambda-1, and the newly assigned lambda is substituted into equation (13) to obtain the diameter number ξ of the tool with the tool number of the unreassigned lambda(λ&λ+1)；
θλThe polar axis Ox rotates anticlockwise to the radian passed by the lambda-th hob, and theta is only when the lambda-th hob and the lambda +1 hob are on the same diameter and are respectively positioned on two radial scroll strips at two sides of the middle point of the diameterλξ in formula (14) when the lambda tool hob and the lambda +1 tool hob are not on the same diameter(λ&λ+1)The term is calculated by not calculating the diameter number of the lambda tool hob, but assigning lambda to lambda-1 using equation (13) directly, and substituting the reassigned lambda into equation (13) to obtain the diameter number ξ of the tool with the tool number of the tool being the non-reassigned lambda(λ&λ+1)；
ρλCalculating the installation radius of the lambda-th hob, namely the distance between the lambda-th hob and the pole O according to the formula (15);
Figure FDA0002468755310000041
Figure FDA0002468755310000042
ρλ＝ρ1+s(λ-1),λ＞1 (15)
(II) when cmax＞NsWhen the temperature of the water is higher than the set temperature,
Figure FDA0002468755310000043
establishing a polar coordinate system, wherein the pole is O, the polar axis is Ox, and the counterclockwise direction is the positive direction of a corner; recording the radius scroll where the hob with the minimum radius is arranged as a first scroll, wherein the included angle between the first scroll and the Ox is theta1，θ1Less than 2 pi, the diameter of the first web is the first diameter, if the lambda-th hob and the lambda + 1-th hob are both ξ th(λ&λ+1)On diameter, turn counterclockwise from the first diameter
Figure FDA0002468755310000044
To obtain the ξ th(λ&λ+1)Diameter, ξ(λ&λ+1)＝1,2,...,NR；
If and only if the lambda-th hob and the lambda + 1-th hob are on the same diameter and are respectively positioned on two radial scroll webs on two sides of the middle point of the diameter, the diameter is numbered ξ(λ&λ+1)，ξ(λ&λ+1)Directly calculating according to the formula (13);
when the lambda tool hob and the lambda +1 tool hob are not on the same diameter, the number of the diameter of the lambda tool hob should not be calculated directly using equation (13), and the lambda should be assigned to lambda-1, and the newly assigned lambda is substituted into equation (13) to obtain the diameter number ξ of the tool with the tool number of the unreassigned lambda(λ&λ+1)；
θλThe polar axis Ox rotates anticlockwise to the radian passed by the lambda-th hob, and theta is only when the lambda-th hob and the lambda +1 hob are on the same diameter and are respectively positioned on two radial scroll strips at two sides of the middle point of the diameterλξ in formula (14) when the lambda tool hob and the lambda +1 tool hob are not on the same diameter(λ&λ+1)The term is calculated by not calculating the diameter number of the lambda tool hob, but assigning lambda to lambda-1 using equation (13) directly, and substituting the reassigned lambda into equation (13) to obtain the diameter number ξ of the tool with the tool number of the tool being the non-reassigned lambda(λ&λ+1)；
ρλCalculating the installation radius of the lambda-th hob, namely the distance between the lambda-th hob and the pole O according to the formula (15);
(III) when cmax＜NsWhen the temperature of the water is higher than the set temperature,
Figure FDA0002468755310000051
there are cases where the number of cutters on the same diameter is more than 2; defining the cutter number sc under the condition of multilayer arrangementλ,χ,λ is the corresponding serial number of a certain cutter on the cutter head in the ascending order of the installation radius of the cutters in all cutter categories on the cutter head, χ is the layer number of the cutter, and is the corresponding serial number of the cutters in the same layer in the ascending order of the installation diameter of the cutters, and c is more than or equal to 1max(ii) a The layer number χ is calculated according to equation (16),
Figure FDA0002468755310000052
is not more than
Figure FDA0002468755310000053
The largest non-negative integer of (d);
establishing a polar coordinate system, wherein the pole is O, the polar axis is Ox, and the counterclockwise direction is the positive direction of a corner; recording the radius scroll where the hob with the minimum radius is arranged as a first scroll, wherein the included angle between the first scroll and the Ox is theta1，θ1Less than 2 pi, the diameter of the first web is the first diameter, if scλ,χ,With hob and scλ+1,χ,+1With roller cutters commonly known as ξ(&+1)On diameter, turn counterclockwise from the first diameter
Figure FDA0002468755310000054
To obtain the ξ th(&+1)Diameter, ξ(&+1)＝1,2,...,NR；
The in-layer number of the cutter is calculated according to the formula (17)
Figure FDA0002468755310000055
＝λ-(χ-1)cmax(17)
When it is at scλ,χ,With hob and scλ+1,χ,+1With roller cutters commonly known as ξ(&+1)On diameter, turn counterclockwise from the first diameter
Figure FDA0002468755310000061
To obtain the ξ th(&+1)Diameter, ξ(&+1)＝1,2,...,NR；
Even for the cutters which are not in the same layer, the cutters are distributed on the same diameter as long as the serial numbers in the layers are consistent;
if and only if the scλ,χ,With hob and scλ+1,χ,+1When two radial scroll bars with the hob cutters on the same diameter and respectively positioned at two sides of the middle point of the diameter are provided, the diameter is numbered ξ(&+1)Directly calculating according to the formula (18);
when it is at scλ,χ,With hob and scλ+1,χ,+1When the hob is not on the same diameter, the number of the diameter of the cutter with the number of the layer is not directly calculated by using the formula (18), and after the value is assigned to-1, the reassigned formula (18) is replaced to obtain the number ξ of the diameter of the cutter with the number of the cutter layer being not reassigned(&+1)；
Figure FDA0002468755310000062
Figure FDA0002468755310000063
Rotate the polar axis Ox counterclockwise to the scλ,χ,With the radian traversed by the hob
Figure FDA0002468755310000064
Is sc-thλ,χ,With the mounting radius of the hob, i.e. the distance between the lambda-th hob and the pole O
When it is at scλ,χ,With hob and scλ+1,χ,+1When the hob is on the same diameter,
Figure FDA0002468755310000065
directly calculating according to the formula (19);
when it is at scλ,χ,With hob and scλ+1,χ,+1ξ in formula (19) when the hob is not on the same diameter(&+1)The calculation method of the term is as follows: when it is at scλ,χ,With hob and scλ+1,χ,+1The hob is not on the same diameter, the number of the diameter of the cutter with the number of the layer is calculated by using the formula (18), the number of the cutter with the number of the layer is-1, the reassigned formula (18) is replaced, and the diameter number ξ of the cutter with the number of the cutter layer not reassigned is obtained(&+1)；
Figure FDA0002468755310000066
According to the formula (20)
Figure FDA0002468755310000067
Figure FDA0002468755310000068
Sc thλ+1,χ+1,1With roller cutters and
Figure FDA0002468755310000069
the hob tracks are adjacent but not on the same diameter, and the cutter distribution has interlayer transition.
2. The method of claim 1, wherein the method comprises the steps of: c. CmaxShould be not more than
Figure FDA0002468755310000071
If c in step two is the maximum positive even numbermaxIf < 4, the tunnel construction planning department should be informed to reselect R, and the above operations are carried out under the condition of the reselected R until cmaxC is obtained at a time of not less than 4max；
The radius breadth number of the cutter head is assigned as cmaxAnd in combination with formula (1) and formula (2) to givemaxCorresponding rsIf and cmaxCorresponding rsAnd l obtained according to formula (3)minSatisfy lmin≤R-B-rsThen c should be directly appliedmaxCarrying out the operation of the step four; if it can not satisfy lmin≤R-B-rsInforming the tunnel construction planning department to reselect R, and carrying out the operation of the step two under the condition of the reselected R until lmin≤R-B-rsWill satisfy lmin≤R-B-rsC ofmaxAnd the input step four is operated.
3. The method of claim 1, wherein the method comprises the steps of: further comprising the steps of:
checking and adjusting tool layout contradiction
ct is the maximum thickness of the hob, and the installation width of the hob is w, rhoλThe lambda is the mounting radius of the hob, and pλ+2＝ρλ+2s, s is the blade spacing; if the lambda tool hob and the lambda +2 tool hob do not satisfy the formula (21), calculating the position of the lambda tool hob calculated according to the steps one to four and the position of the lambda +2 tool hob according to the steps one to fourThe calculated position installation space has overlapping contradiction, and the lambda tool hob should be positioned at rhoλUnder the condition of no change, the final design position of the roller cutter is arranged on the scroll with the radius of the lambda +2 tool roller cutter to eliminate the overlapping contradiction, and the final design position of the lambda +2 tool roller cutter is still the position obtained by calculation according to the first step to the fourth step; for other cutters without position installation space overlapping contradiction obtained by calculation according to the steps from the first step to the fourth step, the final design position is the position obtained by calculation according to the steps from the first step to the fourth step;
Figure FDA0002468755310000072
4. the method of claim 1, wherein the method comprises the steps of: when the number of cutters on the same diameter of the cutter head is not less than 2, the tunneling efficiency is negatively related to the number of cutters on the same diameter of the cutter head, and the cutter head with more radius strips is designed to improve the tunneling efficiency.
5. The method of claim 1, wherein the method comprises the steps of: the tracks of two cutters in the same layer on the same diameter are adjacent to each other and are respectively positioned on two radiuses with the same diameter.
6. The method of claim 1, wherein the method comprises the steps of: the relative relation of the installation radius between the two cutters in the same layer on each diameter is rotationally symmetrical about the pole O, and the relative relation of the installation radius between the two cutters in the same layer on each diameter, which belong to two adjacent layers, is opposite, namely the combined torque directions of the cutters in the same layer on the two adjacent layers are opposite, so that the combined torque of the cutters in the same layer on the two adjacent layers about the pole O are mutually offset, and rock breaking is realized in sequence, namely
Figure FDA0002468755310000081
The unbalanced moment borne by the whole cutter head is further reduced under the condition that the rotating direction is not changed all the time when the lambda is increased, the moment balance degree of the whole cutter head is improved, and the rule of interlayer reversion exists in comparison of the installation radius of paired cutters.
7. The method according to claim 1, wherein in the first step, when the width w of the radius swath is taken as a chord of the length w of the cutter head circumference, the central angle of the radius swath width w is 2arcsin (w/(2 × R)), and if a cutter with the width w is arranged at the end of each radius swath away from the central angle in the cutter head circumference, c is not less than 4 and not more than 4 because there is no overlap between the cutters
Figure FDA0002468755310000082
Even number of (d) [ pi/arcsin (w/(2 × R))]Is the largest positive integer not exceeding pi/arcsin (w/(2 × R)).
8. The method of claim 1, wherein the method comprises the steps of: in the first step, if
Figure FDA0002468755310000083
Then w and R should be reselected when
Figure FDA0002468755310000084
And calculating according to the step one.
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