Codeofchina.com is in charge of this English translation. In case of any doubt about the English translation, the Chinese original shall be considered authoritative.
This standard is developed in accordance with the rules given in GB/T 1.1-2009.
This standard was proposed by China Machinery Industry Federation.
This standard is under the jurisdiction of National Technical Committee 331 on Continuous Handling Equipment of Standardization Administration of China (SAC/TC 331).
Basis for calculation of belt conveyors
1 Scope
This standard specifies the basis for design calculation of belt conveyors, which is used to determine the basic parameters and layout design of their main components (such as driving unit, braking unit, take-up unit, pulley, idler and conveyor belt).
This standard is applicable to belt conveyors used for conveying bulk materials.
This standard is not applicable to the basis for design calculation of special belt conveyors such as cable, pipe and air cushion belt conveyors.
2 Normative references
The following referenced documents are indispensable for the application of this document. For dated references, only the edition cited applies. For undated references, the latest edition of the referenced document (including any amendments) applies.
GB/T 7984 Conveyor belts of textile construction for general use
GB/T 9770 Steel cord conveyor belts for general use
GB/T 10595 Belt conveyors
GB/T 14521 Terms of continuous handling equipment
GB/T 28267.1-2012 Steel cord conveyor belts - Part 1: Design, dimensions and mechanical requirements for conveyor belts for general use
GB/T 28267.2 Steel cord conveyor belts - Part 2: Preferred belt types
GB/T 28267.3 Steel cord conveyor belts - Part 3: Special safety requirements for belts for use in underground installations
GB/T 28267.4 Steel cord conveyor belts - Part 4: Vulcanized belt joints
GB/T 31256 Conveyor belts - Specification for rubber- or plastics-covered conveyor belts of textile construction for underground mining
GB 50431 Code for design of belt conveyor engineering
3 Terms and definitions
For the purposes of this document, the terms and definitions given in GB/T 14521 and the following apply.
3.1
starting for inherent characteristics
mode where the belt conveyor is started according to the inherent mechanical characteristics (relationship between rotational speed and torque) of driving unit
3.2
starting for motion control
starting mode where the belt conveyor is controlled according to the set starting acceleration or speed curve
3.3
nominal capacity
conveying capacity used for belt conveyor design according to the requirements of engineering design
4 Symbols, definitions and units
Symbols, definitions and units are given in Table 1.
Table 1 Symbols, definitions and units
Symbol Definition Unit
A Cross-sectional area of carried materials m2
A1 Cross-sectional area of the upper part of carried materials m2 (mm2)a
A2 Cross-sectional area of carried materials when θ = 0° (cross-sectional area of lower part of carried materials) (3-roller idler set)
Cross-sectional area of inverted trapezoidal part on outer roller (5-roller idler set) m2 (mm2)a
A3 Cross-sectional area of inverted trapezoidal part on inner roller (5-roller idler set) m2 (mm2)a
AN Cross-sectional area of carried materials under nominal capacity m2
AGr Effective contact area between the working face cleaner and the conveyor belt mm2
AGr1 Effective contact area between the non-working face cleaner and the conveyor belt mm2
B Belt width mm
C Additional resistance coefficient —
D Diameter of pulley mm
D1 Datum diameter of pulley determined according to the service life conditions of the conveyor belt mm
ELB Longitudinal elastic modulus of the conveyor belt N/mm
F Tension or resistance of the conveyor belt N
Fa Inertial force caused by acceleration/deceleration under unsteady operating condition N
FbA Inertial resistance of conveyed materials and/or frictional resistance between conveyed materials and the conveyor belt in feeding section N
Fc1 Conveyor belt tension at the start point of convex or concave curved section N
Fc2 Conveyor belt tension at the end point of convex or concave curved section N
FD Average tension of conveyor belt on the pulley N
FE Indentation rolling resistance per unit length obtained based on the test results N/m
Ff Frictional resistance between the conveyed materials and the side plates of the skirt board in feeding section N
FH Major resistance N
Fgl Frictional resistance between the conveyed materials and the side plates of the skirt board outside the feeding section N
FHs Locking force N
FI Bending resistance of conveyor belt when winding the pulley N
Fr Frictional resistance of the working surface cleaner N
Frl Frictional resistance of non-working face cleaner N
FN Additional resistance N
Fp Frictional resistance of the tripper N
FR Rotating resistance of idler per unit length obtained based on the test results N/m
FS Special resistance N
Fsbn Frictional resistance of buffer bed (sliding bed) N
FSk Frictional resistance of apron seal of skirt board in feeding section N
FSk1 Frictional resistance of apron seal of skirt board outside the feeding section N
FSp Take-up tension of take-up pulley N
FSt Lifting resistance of conveyed materials (which includes the lifting resistance of conveyor belt in section resistance calculation) N
Fl Pulley bearing resistance N
FT Tension of conveyor belt at characteristic point N
FT1 Tension at the point of contact between the conveyor belt and the pulley N
FT2 Tension at the separation point between the conveyor belt and the pulley N
FTm Average tension of the conveyor belt N
FTr Peripheral driving force of the pulley N
FU Traveling resistance (equal to the peripheral driving force of the pulley) N
FV Vector sum (numerical value) of the conveyor belt tension acting on the pulley and the weight of pulley rotor N
Fw Additional bending resistance of convex or concave curved section N
Ft Forward tilt resistance N
ΔFTm The difference between the average conveyor belt tension, FTm, and the minimum conveyor belt tension, FTmin N
Im,N Nominal capacity by mass kg/s
Im,th Theoretical capacity by mass kg/s
IV,N Nominal capacity by volume m3/s
IV,th Theoretical capacity by volume m3/s
J Moment of inertia of pulley kg·m2
JD Moment of inertia of driving unit rotor on the high-speed shaft of the reducer kg·m2
Jf Moment of inertia of flywheels kg·m2
L Conveyor length m
Ka Scraper coefficient N/m
PA Total power of driving pulley required to overcome traveling resistance under steady operating condition kW
PM Total power of driving motor kW
PM,N Rated power of driving motor kW
Q Nominal capacity t/h
Ra Curvature radius of vertical concave curved section m (mm)a
Re Curvature radius of vertical convex curved section m (mm)a
S Safety coefficient relative to nominal tensile strength of conveyor belt —
S0 Safety coefficient of conveyor belt determined with joint process conditions considered —
S1 Safety coefficient determined with expected life and working stress of conveyor belt considered —
Smin Minimum safety coefficient relative to the minimum nominal tensile strength of conveyor belt —
a Acceleration or deceleration m/s2
b Effective width of conveyor belt (theoretical width of conveyor belt carrying materials) m (mm)a
b1 Width of materials stacked on conveyor belt mm
b2 Width of materials on 3-roller idler set mm
bS Width of conveyor belt on side rollers (only for 2-roller and 3-roller idler sets) mm
bSch Clear width between skirt boards m
c0 Calculation coefficient used to determine the minimum diameter of pulley —
cK Coefficient of minimum joint fatigue strength determined based on edge tension of conveyor belt —
cR Calculation coefficient for converting the rotating mass of idler to the equivalent mass on the periphery of the idler —
cRank Coefficient of active lateral pressure —
cS Speed correction coefficient of simulated friction coefficient —
CSchb Coefficient of additional resistance caused by material disturbance in the feeding section —
cT Temperature correction coefficient of simulated friction coefficient —
cTd Coefficient used to determine the datum value of the minimum length of the troughing transition section —
cε Calculation coefficient of forward tilt resistance —
d0 Inner diameter of pulley bearing mm
dB Thickness of tensile element (core) of conveyor belt (excluding the upper and lower coatings of conveyor belt) mm
dR Diameter of idler m
e The napierian base (e=2.718 28…) —
eK Height difference from neutral datum line to the edge of conveyor belt mm
eM Height difference from the neutral datum line to the center of the conveyor belt mm
fbase Datum value of simulated friction coefficient —
Δfs Correction of simulated friction coefficient related to belt speed —
ΔfT Correction of simulated friction coefficient related to temperature —
f Simulated friction coefficient —
fi Simulated friction coefficient for each section of the upper and lower branches —
fr Rotating frequency of rollers in an idler set at a certain belt speed Hz
fp Approximate inherent vibration frequency of cross-sectional of conveyor belt Hz
fRMBT Pulley load factor (determined by the maximum tension and nominal tensile strength of conveyor belt) —
g Gravitational acceleration (g=9.81 m/s2) m/s2
h Height difference (h > 0 in upward case; h<0 in downward case) m
hk0 Distance from the plane formed by the edges of both sides of the conveyor belt to the lowest plane of the trough m
hk1 Distance between the plane formed by the edges of both sides of the conveyor belt and the upper generatrix plane of the pulley m
hTr Distance between the upper generatrix plane of the pulley in the troughing transition section and the lowest plane of the trough (the height of pulley elevation) m
i Drive ratio —
k Conveyor belt tension relative to conveyor belt width (average conveyor belt tension over belt width) N/mm
kK Tension per unit width at the edge of conveyor belt N/mm
kM Tension per unit width in the central area of the conveyor belt N/mm
kN Nominal tensile strength of conveyor belt N/mm
kN,min Minimum nominal tensile strength of conveyor belt N/mm
hrel Sag of conveyor belt (ratio of the maximum sagging amount of conveyor belt between idler sets to the spacing between idler sets) —
kt Datum fatigue strength of conveyor belt joint (tensile strength of conveyor belt with strength reduction of conveyor belt joint considered) N/mm
kt,rel Relative datum fatigue strength of conveyor belt joint —
Δk Difference in tension per unit belt width between the edge and the central area of the conveyor belt N/mm
l Length of section m
l2 Length of 2 middle rollers (5-roller idler set) mm
lb Length of the skirt board in the feeding section m
lgl Length of the skirt board outside the feeding section m
lK Edge length of conveyor belt in troughing transition section m
lM Length of the middle idler of 3-roller idler set mm (m)a
lR Spacing between idler sets m
ls1 Contact length between outer idlers and materials m
lTd Length of troughing transition section m
lTd,eff Effective length of troughing transition section of steel cord conveyor belt m
ΔlTd Additional length of transition section, namely, lTd,eff-lTd of steel cord conveyor belt m
lw Length of turnover section of the conveyor belt m
mf Equivalent mass of flywheel converted to the periphery of the pulley kg
mD Equivalent mass of the pulley, flywheel (if set), driving and braking units converted to the periphery of the pulley kg
mL Equivalent mass of conveyor belt, material and idler on belt conveyor line kg
∑m Sum of equivalent mass of conveyor belt, material and idler on belt conveyor line and equivalent mass of pulley, driving and braking units on belt conveyor line converted to the periphery of the pulley kg
n Number of sections of belt conveyor divided —
nR Maximum allowable rotating speed of roller under steady operating condition of belt conveyor r/min
pA Starting coefficient related to driving pulley —
pA,0 Starting coefficient related to driving —
pB Braking coefficient related to braking pulley —
pB,0 Braking coefficient related to braking —
pD Power distribution coefficient —
pGr Pressure exerted by the working face cleaner on the conveyor belt N/mm2
pGr1 pressure exerted by the non-working face cleaner on the conveyor belt N/mm2
pSk Effective positive pressure per unit length between conveyor belt and seal N/m
pBp Allowable specific pressure of the conveyor belt N/mm2
pBs Allowable specific pressure under the steel wire rope of steel cord conveyor belt N/mm2
q Coefficient of estimation of major resistance —
qB Mass per unit length of conveyor belt kg/m
qR Mass per unit length of idler rotor kg/m
qG,i Mass per unit length of material on a section kg/m
s1 Thickness of conveyor belt mm
sSp Working distance of take-up pulley m
v Belt speed m/s
v0 Speed of the material fed to the conveyor belt in the conveying direction m/s
sB Braking distance m
t1 Spacing between steel wire ropes of conveyor belt mm
tB Braking time s
zD Number of driving or braking pulley Pcs.
zM Number of motors (driving units) Pcs.
zR Number of idler sets on a section (in upper or lower branch) Set
zTr Number of pulleys Pcs.
zε Number of forward tilting idler sets on a section (in upper or lower branch) Set
α Wrap angle ° or rad
αc Central angle corresponding to the convex or concave curved section rad
β Equivalent angle of move of materials used to calculate the cross-sectional area of materials °
θ Angle of move (angle of repose) of conveyed materials °
δ Conveying angle of inclination (δ>0 in upward case and δ<0 in downward case) °
ε Angle of inclination of side roller (top rake) °
φ Effective filling coefficient —
φSt Cross-sectional reduction coefficient of theoretical total carrying cross-sectional area during inclined conveying —
φSt1 Cross-sectional reduction coefficient of theoretical cross-sectional area of the upper part of carried materials during inclined conveying —
λ Trough angle of idler set and outer roller (4-roller and 5-roller idler sets) °
λ1 Trough angle of 2 middle rollers (4-roller and 5-roller idler sets) °
μ Friction coefficient between conveyor belt and pulley —
μ1 Friction coefficient between conveyor belt and conveyed material —
μ2 Friction coefficient between the conveyed materials and the side plates of the skirt board —
μ3 Friction coefficient between conveyor belt and idlers —
μ4 Friction coefficient between conveyor belt and cleaner —
μ5 Sliding friction coefficient between conveyor belt and sealing rubber —
μ6 Friction coefficient between buffer bed and conveyor belt —
ρ Bulk density of conveyed materials kg/m3
ΔεK Additional elongation (positive or negative) at the edge of conveyor belt relative to natural axial concave or convex curved section of conveyor belt —
ΔεK∞ The limit value of ΔεK at the edge of conveyor belt with long curved section —
ΔεM Additional elongation (positive or negative) at the central area of conveyor belt relative to natural axial concave or convex curved section of conveyor belt —
ΔεM∞ The limit value of ΔεM at the central area of conveyor belt with long curved section —
Δε∞ Difference in elongation between the central area and the edge of the conveyor belt with long curved section —
η1 Total efficiency of all driving links between motor shaft and pulley shaft in motor mode —
η2 Total efficiency of all driving links between motor shaft and pulley shaft in generator mode
a Units in brackets are used in some formulae.
5 Capacity by volume and by mass
5.1 Theoretical cross-sectional area of materials
The theoretical capacity by volume and by mass of belt conveyor are determined by the theoretical cross-sectional area and traveling speed of materials stacking on the conveyor belt. The cross-sectional area of materials depends on the angle of move of the conveyed materials, the specific structural type of the idler set and the feeding mode.
In calculating the theoretical capacity by volume and by mass, this standard assumes that the cross section of the conveyed materials has upper surface with parabolic contour line. Figure 1 shows a cross section of materials on the supporting conveyor belt of a common troughing 3-roller idler set.
Figure 1 Theoretical cross section of
horizontally-carried materials conveyed by 3-roller idler set
The theoretical cross-sectional area of carried materials is determined by the length, lM, of middle roller, the trough angle, λ, the effective width, b, of the conveyor belt, and the angle of move, θ. The effective width, b, is the width of the conveyor belt with a certain margin reserved to avoid spillage; it can be calculated using Formulae (1) and (2):
b=0.9B-50 (if B≤2,000) (1)
b=B-250 (if B>2,000) (2)
where,
B——the belt width, mm;
b——the effective width of conveyor belt (theoretical width of conveyor belt carrying materials), mm.
As for the belt conveyor with horizontal curves, the effective width of the conveyor belt may be reduced due to the inclined arrangement of rollers.
As for the materials carried by supporting conveyor belt of 3-roller idler set on a horizontally-arranged belt conveyor, the theoretical cross-sectional area, Ath, calculated based on the angle of move θ may be determined based on the sum of cross-sectional areas, A1,th and A2,th, (see Figure 1); Formulae (3), (4) and (5) shall be used for calculation:
(3)
(4)
Ath=A1,th+A2,th (5)
where,
Ath——the theoretical cross-sectional area of carried materials, m2;
A1,th——the theoretical cross-sectional area of the upper part of carried materials, m2;
A2,th——the theoretical cross-sectional area of carried materials when θ = 0° (cross-sectional area of lower part of carried materials), m2;
lM——the length of the middle idler of 3-roller idler set, m;
θ——the angle of move of materials, °;
λ——the trough angle of idler set, °;
b——the effective width of conveyor belt (theoretical width of conveyor belt carrying materials), m.
When used to calculate the cross-sectional area A1,th, the equivalent angle of move β shall be calculated using Formula (6):
(6)
where, β=θ/1.5.
The angle of move of materials depends on the characteristics of conveyed materials and factors of belt conveyors, such as length and belt speed. If empirical value of angle of move is not available, the following may be chosen:
——for materials with normal fluidity, take 0≤θ≤20°;
——for materials with high fluidity, take 20°≤θ≤30°.
Theoretical cross-sectional area of materials carried by 2-roller idler set shall be calculated by substituting lM=0 into Formulae (3) and (4);
Theoretical cross-sectional area of materials carried by 1-roller idler set shall be calculated by substituting lM=0 and λ=0 into Formulae (3) and (4).
See Annex A for the calculation of the theoretical cross-sectional area, Ath, of materials carried by 1-roller, 2-roller, 4-roller and 5-roller idler sets respectively.
Theoretical capacity by volume shall be calculated using Formula (7) based on the theoretical cross-sectional area of carried materials:
IV,th=Ath·v (7)
Theoretical capacity by mass shall be calculated using Formula (8):
Im,th=ρAth·v (8)
where,
IV,th——the theoretical capacity by volume, m3/s;
Im,th——the theoretical capacity by mass, kg/s;
v——the belt speed, m/s;
ρ——the bulk density of conveyed materials, kg/m3.
5.2 Cross-sectional reduction coefficient during inclined conveying
When a belt conveyor feeds uniformly and travels horizontally and straightly, its theoretical cross section of materials can be fully utilized.
Under the influence of material weight, internal friction angle and other factors, the area of the upper part, A1,th, shown in Figure 1 will be reduced. When the belt conveyor is well centered, uniformly feeds and conveys materials with small particle size and the maximum angle of inclination, δmax on the belt conveyor line ≤θ, the reduction coefficient of the upper part shall be calculated using Formula (9):
(9)
where,
φSt1——the cross-sectional reduction coefficient of theoretical cross-sectional area, A1,th, of the upper part of carried materials during inclined conveying, dimensionless;
δmax——the maximum angle of inclination on the belt conveyor line, °;
θ——the same as that in Formula (3).
The reduction coefficient, φSt, of theoretical cross-sectional area of carried materials during inclined conveying shall be calculated using Formula (10):
(10)
where,
φSt——the cross-sectional reduction coefficient of theoretical cross-sectional area, Ath, of the carried materials during inclined conveying, dimensionless.
If Formulae (9) and (10) are used, attention shall be paid to that the maximum angle of inclination during inclined conveying can only be equal to the angle of move, θ. In this case, only cross-sectional areas A2,th is used for material conveying.
5.3 Nominal capacity and effective filling coefficient
When nominal capacity by mass, Im,N, is given, nominal capacity by volume, IV,N, shall be calculated using Formula (11):
(11)
where:
Im,N——the nominal capacity by mass, kg/s;
IV,N——the nominal capacity by volume, m3/s.
The cross-sectional area required shall be calculated using Formula (12):
(12)
where:
AN——the cross-sectional area of carried materials required under nominal capacity, m2.
The effective filling coefficient of belt conveyor shall be calculated using Formula (13):
(13)
where:
φ——the effective filling coefficient of belt conveyor, dimensionless.
The effective filling coefficient φ depends on:
——characteristics of conveyed materials;
——particle size and composition;
——angle of move θ;
——operating conditions of belt conveyor;
——uniformity of feeding;
——line layout of conveyor;
——conveying angle of inclination;
——reserve of conveying capacity.
The effective filling coefficient, φ, is used to evaluate whether the theoretical sectional area, Ath, of materials matches with the sectional area required under nominal capacity. In this standard, some calculation parameters are selected on premise that the effective filling coefficient φ satisfies 0.7<φ<1.1; otherwise, the calculation parameters selected shall be corrected; in some cases, the effective filling coefficient will be out of the above range, in which the specific values will be determined based on the test data and the experience of the engineer.
The mass per unit length of materials under nominal capacity shall be calculated using Formula (14):
or qG=φρAth (14)
where,
qG——the mass per unit length of materials under nominal capacity, kg/m.
Nominal capacity shall be calculated using Formula (15):
(15)
where,
Q——the nominal capacity, t/h.
6 Traveling resistance and power consumption under steady operating condition
6.1 Calculation principle
As a general rule, before calculating the traveling resistance, it needs to estimate the datum values of the parameters used (such as mass per unit length and simulated friction coefficient of conveyor belt and idler). These values shall be confirmed or corrected according to actual selection during calculation. In general, repeated calculations shall be carried out to achieve calculation results that are completely applicable to specific applications.
The traveling resistance, FU, generated under steady operating condition is the total resistance generated by friction, gravity and other resistances together. The power, PA, required by the driving pulley of the belt conveyor is obtained by multiplying the sum of traveling resistances generated by the upper and lower branches by the traveling speed, v, as shown in Formula (16):
(16)
where,
PA——total power on periphery of driving pulley required to overcome traveling resistance under steady operating condition, kW;
FU——the sum of traveling resistances generated by the upper and lower branches, N.
For the purpose of calculation, the traveling resistances of belt conveyor are classified into:
——major resistance FH (see 6.2);
——additional resistance FN (see 6.3);
——lifting resistance FSt (see 6.4);
——special resistance FS (see 6.5).
The sum, FU, of traveling resistances is equal to the peripheral driving force, FTr, of pulley transmitted from the driving pulley to the conveyor belt, as shown in Formula (17):
(17)
where,
FTr——the sum of peripheral driving force of pulley, N;
FU,o,i, FU,u,i——the traveling resistance on sections i of the upper and lower branches respectively, N;
no, nu——the number of sections divided in upper and lower branches respectively.
Resistance shall be determined by section. The sectioning principle is to have the same calculation parameters in each section, such as the angle of inclination δi, the simulated friction coefficient, fi, the mass per unit length of materials, qG,i, and the mass per unit length of the idler rotor, qR,i, on each section in the upper and lower branches of the belt conveyor. To facilitate computer programming calculation, during the resistance calculation, the sections shall be numbered from the tail section to the head section of the belt conveyor, with subscripted i as the serial number of the section, the subscripted o as the upper branch and the subscripted u as the lower branch (see Figure 2), and pulley numbered as separate section. In the text below, for the sake of uniform expression, the pulley number is indicated by subscripted j, and the point of contact by subscripted T1 and the separation point by subscripted T2. (See Figures 5 and 6).
6.2 Major resistance
6.2.1 Calculation of major resistance
The major resistance is generated over the entire length of the conveying lines of all belt conveyors. It includes rotating resistance of idler, indentation rolling resistance of conveyor belt, bending resistance of conveyor belt and internal friction resistance of materials. The major resistance shall be calculated separately for each section.
In order to simplify the calculation of section resistance, the major resistance FH,i in each section of upper and lower branches shall be calculated based on the linear relationship between resistance and motion load, as shown in Formula (18):
FH,i=lifig[qR,i+(qB+qG,i)cosδi] (18)
where,
FH,i——the major resistance on section i, N;
li——the length on section i, N;
fi——the simulated friction coefficient on section i, dimensionless;
qR,i——the mass per unit length of the idler rotor on section i, kg/m;
qB——the mass per unit length of conveyor belt, kg/m;
qG,i——the mass per unit length of materials on section i, kg/m;
δi——the conveying angle of inclination of section i, °;
g——the gravitational acceleration, m/s2.
To determine the conveyor belt tension, the major resistances, FH,o,i and FH,u,i, in sections of upper and lower branches respectively must be determined firstly (see 8.3).
The major resistance of a belt conveyor is the sum of the major resistances, FH,o and FH,u, of upper and lower branches, as shown in Formula (19):
(19)
where:
FH——the total major resistance of upper and lower branches, N;
FH,o,i, FH,u,i——the major resistance on sections i of the upper and lower branches respectively, N;
FH,o, FH,u——the sum of the major resistances of upper and lower branches respectively, N.
Key:
0, 1, 2——characteristic points of conveyor line;
lo,1, lo,2, lu,1, lu2——the lengths of sections 1 and 2 of upper branch and lower branch, respectively;
FU,o,1, FU,o,2, FU,u,1, FU, u,2——the traveling resistance of sections 1 and 2 of upper and lower branches, respectively.
Figure 2 Section division and traveling resistance of
each section under steady operating condition
In calculating the major resistance of each section, the effective filling coefficient, φ, of materials shall satisfy 0.7<φ<1.1. Otherwise, the datum values of calculation parameters given in this standard shall be corrected.
The major resistance shall be calculated under extreme load conditions (nonuniform feeding, partial load and no load) if upward and downward sections are included on the line of belt conveyor, because the sum of resistances in this case may greatly exceed the resistance under steady operating condition.
6.2.2 Determination of simulated friction coefficient
Choosing the simulated friction coefficient fi is more important than calculating the major resistance, because fi determines the major resistance, especially for belt conveyors with small lifting resistance. The simulated friction coefficient fi given in Table 2 may be used to calculate the major resistance of upper and lower branches.
If measured or empirical value is unavailable, or only rough equipment parameters are available, the datum value of the simulated friction coefficient f may be selected according to the operating condition and structural characteristics given in Table 2. These datum values are obtained by summary based on a large number of measurements on the upper and lower branches and with the following restrictions considered:
Foreword i
1 Scope
2 Normative references
3 Terms and definitions
4 Symbols, definitions and units
5 Capacity by volume and by mass
5.1 Theoretical cross-sectional area of materials
5.2 Cross-sectional reduction coefficient during inclined conveying
5.3 Nominal capacity and effective filling coefficient
6 Traveling resistance and power consumption under steady operating condition
6.1 Calculation principle
6.2 Major resistance
6.3 Additional resistance
6.4 Lifting resistance
6.5 Special resistance
6.6 Calculation method of total traveling resistance of belt conveyor
7 Design calculation of driving system
7.1 Contents of design calculation
7.2 Position of driving unit, specification and number of driving motor
7.3 Starting, braking and stopping
8 Calculation of tension and take-up tension of conveyor belt
8.1 Factors affecting conveyor belt tension
8.2 Conveyor belt tension
8.3 Traveling resistance and tension at characteristic point of upper and lower branch sections
8.4 Take-up tension and working distance of take up unit
8.5 Tension of conveyor belt at characteristic point of upper and lower branches
9 Tension distribution across the width of conveyor belt
9.1 Calculation principle
9.2 Troughing transition section
9.3 Curve section
10 Determination of tensile strength and coating thickness of conveyor belt
10.1 Selection principles
10.2 Calculation of break strength of conveyor belt
10.3 Determination of coating thickness of conveyor belt
11 Method for determination of minimum diameter of pulley
11.1 Principle
11.2 Determination based on the service life of conveyor belt
11.3 Determination based on allowable specific pressure of conveyor belt
12 Selection of idler and design of idler spacing
12.1 Calculation principle
12.2 Determination of roller diameter
12.3 Spacing between idler sets
12.4 Design to avoid resonance
13 Design of curvature radius of troughing transition section and vertical curved section
13.1 Calculation principle
13.2 Determination of minimum length of troughing transition section
13.3 Determination of minimum radius of vertical curved section
14 Design of turnover of the conveyor belt
Annex A (Informative) Calculation of cross-sectional area of materials carried by 5-roller idler sets
Annex B (Informative) Determination of total additional resistance based on additional resistance coefficient
Annex C (Informative) Calculation of maximum conveyor belt tension for simply arranged belt conveyors
Bibliography
Codeofchina.com is in charge of this English translation. In case of any doubt about the English translation, the Chinese original shall be considered authoritative.
This standard is developed in accordance with the rules given in GB/T 1.1-2009.
This standard was proposed by China Machinery Industry Federation.
This standard is under the jurisdiction of National Technical Committee 331 on Continuous Handling Equipment of Standardization Administration of China (SAC/TC 331).
Basis for calculation of belt conveyors
1 Scope
This standard specifies the basis for design calculation of belt conveyors, which is used to determine the basic parameters and layout design of their main components (such as driving unit, braking unit, take-up unit, pulley, idler and conveyor belt).
This standard is applicable to belt conveyors used for conveying bulk materials.
This standard is not applicable to the basis for design calculation of special belt conveyors such as cable, pipe and air cushion belt conveyors.
2 Normative references
The following referenced documents are indispensable for the application of this document. For dated references, only the edition cited applies. For undated references, the latest edition of the referenced document (including any amendments) applies.
GB/T 7984 Conveyor belts of textile construction for general use
GB/T 9770 Steel cord conveyor belts for general use
GB/T 10595 Belt conveyors
GB/T 14521 Terms of continuous handling equipment
GB/T 28267.1-2012 Steel cord conveyor belts - Part 1: Design, dimensions and mechanical requirements for conveyor belts for general use
GB/T 28267.2 Steel cord conveyor belts - Part 2: Preferred belt types
GB/T 28267.3 Steel cord conveyor belts - Part 3: Special safety requirements for belts for use in underground installations
GB/T 28267.4 Steel cord conveyor belts - Part 4: Vulcanized belt joints
GB/T 31256 Conveyor belts - Specification for rubber- or plastics-covered conveyor belts of textile construction for underground mining
GB 50431 Code for design of belt conveyor engineering
3 Terms and definitions
For the purposes of this document, the terms and definitions given in GB/T 14521 and the following apply.
3.1
starting for inherent characteristics
mode where the belt conveyor is started according to the inherent mechanical characteristics (relationship between rotational speed and torque) of driving unit
3.2
starting for motion control
starting mode where the belt conveyor is controlled according to the set starting acceleration or speed curve
3.3
nominal capacity
conveying capacity used for belt conveyor design according to the requirements of engineering design
4 Symbols, definitions and units
Symbols, definitions and units are given in Table 1.
Table 1 Symbols, definitions and units
Symbol Definition Unit
A Cross-sectional area of carried materials m2
A1 Cross-sectional area of the upper part of carried materials m2 (mm2)a
A2 Cross-sectional area of carried materials when θ = 0° (cross-sectional area of lower part of carried materials) (3-roller idler set)
Cross-sectional area of inverted trapezoidal part on outer roller (5-roller idler set) m2 (mm2)a
A3 Cross-sectional area of inverted trapezoidal part on inner roller (5-roller idler set) m2 (mm2)a
AN Cross-sectional area of carried materials under nominal capacity m2
AGr Effective contact area between the working face cleaner and the conveyor belt mm2
AGr1 Effective contact area between the non-working face cleaner and the conveyor belt mm2
B Belt width mm
C Additional resistance coefficient —
D Diameter of pulley mm
D1 Datum diameter of pulley determined according to the service life conditions of the conveyor belt mm
ELB Longitudinal elastic modulus of the conveyor belt N/mm
F Tension or resistance of the conveyor belt N
Fa Inertial force caused by acceleration/deceleration under unsteady operating condition N
FbA Inertial resistance of conveyed materials and/or frictional resistance between conveyed materials and the conveyor belt in feeding section N
Fc1 Conveyor belt tension at the start point of convex or concave curved section N
Fc2 Conveyor belt tension at the end point of convex or concave curved section N
FD Average tension of conveyor belt on the pulley N
FE Indentation rolling resistance per unit length obtained based on the test results N/m
Ff Frictional resistance between the conveyed materials and the side plates of the skirt board in feeding section N
FH Major resistance N
Fgl Frictional resistance between the conveyed materials and the side plates of the skirt board outside the feeding section N
FHs Locking force N
FI Bending resistance of conveyor belt when winding the pulley N
Fr Frictional resistance of the working surface cleaner N
Frl Frictional resistance of non-working face cleaner N
FN Additional resistance N
Fp Frictional resistance of the tripper N
FR Rotating resistance of idler per unit length obtained based on the test results N/m
FS Special resistance N
Fsbn Frictional resistance of buffer bed (sliding bed) N
FSk Frictional resistance of apron seal of skirt board in feeding section N
FSk1 Frictional resistance of apron seal of skirt board outside the feeding section N
FSp Take-up tension of take-up pulley N
FSt Lifting resistance of conveyed materials (which includes the lifting resistance of conveyor belt in section resistance calculation) N
Fl Pulley bearing resistance N
FT Tension of conveyor belt at characteristic point N
FT1 Tension at the point of contact between the conveyor belt and the pulley N
FT2 Tension at the separation point between the conveyor belt and the pulley N
FTm Average tension of the conveyor belt N
FTr Peripheral driving force of the pulley N
FU Traveling resistance (equal to the peripheral driving force of the pulley) N
FV Vector sum (numerical value) of the conveyor belt tension acting on the pulley and the weight of pulley rotor N
Fw Additional bending resistance of convex or concave curved section N
Ft Forward tilt resistance N
ΔFTm The difference between the average conveyor belt tension, FTm, and the minimum conveyor belt tension, FTmin N
Im,N Nominal capacity by mass kg/s
Im,th Theoretical capacity by mass kg/s
IV,N Nominal capacity by volume m3/s
IV,th Theoretical capacity by volume m3/s
J Moment of inertia of pulley kg·m2
JD Moment of inertia of driving unit rotor on the high-speed shaft of the reducer kg·m2
Jf Moment of inertia of flywheels kg·m2
L Conveyor length m
Ka Scraper coefficient N/m
PA Total power of driving pulley required to overcome traveling resistance under steady operating condition kW
PM Total power of driving motor kW
PM,N Rated power of driving motor kW
Q Nominal capacity t/h
Ra Curvature radius of vertical concave curved section m (mm)a
Re Curvature radius of vertical convex curved section m (mm)a
S Safety coefficient relative to nominal tensile strength of conveyor belt —
S0 Safety coefficient of conveyor belt determined with joint process conditions considered —
S1 Safety coefficient determined with expected life and working stress of conveyor belt considered —
Smin Minimum safety coefficient relative to the minimum nominal tensile strength of conveyor belt —
a Acceleration or deceleration m/s2
b Effective width of conveyor belt (theoretical width of conveyor belt carrying materials) m (mm)a
b1 Width of materials stacked on conveyor belt mm
b2 Width of materials on 3-roller idler set mm
bS Width of conveyor belt on side rollers (only for 2-roller and 3-roller idler sets) mm
bSch Clear width between skirt boards m
c0 Calculation coefficient used to determine the minimum diameter of pulley —
cK Coefficient of minimum joint fatigue strength determined based on edge tension of conveyor belt —
cR Calculation coefficient for converting the rotating mass of idler to the equivalent mass on the periphery of the idler —
cRank Coefficient of active lateral pressure —
cS Speed correction coefficient of simulated friction coefficient —
CSchb Coefficient of additional resistance caused by material disturbance in the feeding section —
cT Temperature correction coefficient of simulated friction coefficient —
cTd Coefficient used to determine the datum value of the minimum length of the troughing transition section —
cε Calculation coefficient of forward tilt resistance —
d0 Inner diameter of pulley bearing mm
dB Thickness of tensile element (core) of conveyor belt (excluding the upper and lower coatings of conveyor belt) mm
dR Diameter of idler m
e The napierian base (e=2.718 28…) —
eK Height difference from neutral datum line to the edge of conveyor belt mm
eM Height difference from the neutral datum line to the center of the conveyor belt mm
fbase Datum value of simulated friction coefficient —
Δfs Correction of simulated friction coefficient related to belt speed —
ΔfT Correction of simulated friction coefficient related to temperature —
f Simulated friction coefficient —
fi Simulated friction coefficient for each section of the upper and lower branches —
fr Rotating frequency of rollers in an idler set at a certain belt speed Hz
fp Approximate inherent vibration frequency of cross-sectional of conveyor belt Hz
fRMBT Pulley load factor (determined by the maximum tension and nominal tensile strength of conveyor belt) —
g Gravitational acceleration (g=9.81 m/s2) m/s2
h Height difference (h > 0 in upward case; h<0 in downward case) m
hk0 Distance from the plane formed by the edges of both sides of the conveyor belt to the lowest plane of the trough m
hk1 Distance between the plane formed by the edges of both sides of the conveyor belt and the upper generatrix plane of the pulley m
hTr Distance between the upper generatrix plane of the pulley in the troughing transition section and the lowest plane of the trough (the height of pulley elevation) m
i Drive ratio —
k Conveyor belt tension relative to conveyor belt width (average conveyor belt tension over belt width) N/mm
kK Tension per unit width at the edge of conveyor belt N/mm
kM Tension per unit width in the central area of the conveyor belt N/mm
kN Nominal tensile strength of conveyor belt N/mm
kN,min Minimum nominal tensile strength of conveyor belt N/mm
hrel Sag of conveyor belt (ratio of the maximum sagging amount of conveyor belt between idler sets to the spacing between idler sets) —
kt Datum fatigue strength of conveyor belt joint (tensile strength of conveyor belt with strength reduction of conveyor belt joint considered) N/mm
kt,rel Relative datum fatigue strength of conveyor belt joint —
Δk Difference in tension per unit belt width between the edge and the central area of the conveyor belt N/mm
l Length of section m
l2 Length of 2 middle rollers (5-roller idler set) mm
lb Length of the skirt board in the feeding section m
lgl Length of the skirt board outside the feeding section m
lK Edge length of conveyor belt in troughing transition section m
lM Length of the middle idler of 3-roller idler set mm (m)a
lR Spacing between idler sets m
ls1 Contact length between outer idlers and materials m
lTd Length of troughing transition section m
lTd,eff Effective length of troughing transition section of steel cord conveyor belt m
ΔlTd Additional length of transition section, namely, lTd,eff-lTd of steel cord conveyor belt m
lw Length of turnover section of the conveyor belt m
mf Equivalent mass of flywheel converted to the periphery of the pulley kg
mD Equivalent mass of the pulley, flywheel (if set), driving and braking units converted to the periphery of the pulley kg
mL Equivalent mass of conveyor belt, material and idler on belt conveyor line kg
∑m Sum of equivalent mass of conveyor belt, material and idler on belt conveyor line and equivalent mass of pulley, driving and braking units on belt conveyor line converted to the periphery of the pulley kg
n Number of sections of belt conveyor divided —
nR Maximum allowable rotating speed of roller under steady operating condition of belt conveyor r/min
pA Starting coefficient related to driving pulley —
pA,0 Starting coefficient related to driving —
pB Braking coefficient related to braking pulley —
pB,0 Braking coefficient related to braking —
pD Power distribution coefficient —
pGr Pressure exerted by the working face cleaner on the conveyor belt N/mm2
pGr1 pressure exerted by the non-working face cleaner on the conveyor belt N/mm2
pSk Effective positive pressure per unit length between conveyor belt and seal N/m
pBp Allowable specific pressure of the conveyor belt N/mm2
pBs Allowable specific pressure under the steel wire rope of steel cord conveyor belt N/mm2
q Coefficient of estimation of major resistance —
qB Mass per unit length of conveyor belt kg/m
qR Mass per unit length of idler rotor kg/m
qG,i Mass per unit length of material on a section kg/m
s1 Thickness of conveyor belt mm
sSp Working distance of take-up pulley m
v Belt speed m/s
v0 Speed of the material fed to the conveyor belt in the conveying direction m/s
sB Braking distance m
t1 Spacing between steel wire ropes of conveyor belt mm
tB Braking time s
zD Number of driving or braking pulley Pcs.
zM Number of motors (driving units) Pcs.
zR Number of idler sets on a section (in upper or lower branch) Set
zTr Number of pulleys Pcs.
zε Number of forward tilting idler sets on a section (in upper or lower branch) Set
α Wrap angle ° or rad
αc Central angle corresponding to the convex or concave curved section rad
β Equivalent angle of move of materials used to calculate the cross-sectional area of materials °
θ Angle of move (angle of repose) of conveyed materials °
δ Conveying angle of inclination (δ>0 in upward case and δ<0 in downward case) °
ε Angle of inclination of side roller (top rake) °
φ Effective filling coefficient —
φSt Cross-sectional reduction coefficient of theoretical total carrying cross-sectional area during inclined conveying —
φSt1 Cross-sectional reduction coefficient of theoretical cross-sectional area of the upper part of carried materials during inclined conveying —
λ Trough angle of idler set and outer roller (4-roller and 5-roller idler sets) °
λ1 Trough angle of 2 middle rollers (4-roller and 5-roller idler sets) °
μ Friction coefficient between conveyor belt and pulley —
μ1 Friction coefficient between conveyor belt and conveyed material —
μ2 Friction coefficient between the conveyed materials and the side plates of the skirt board —
μ3 Friction coefficient between conveyor belt and idlers —
μ4 Friction coefficient between conveyor belt and cleaner —
μ5 Sliding friction coefficient between conveyor belt and sealing rubber —
μ6 Friction coefficient between buffer bed and conveyor belt —
ρ Bulk density of conveyed materials kg/m3
ΔεK Additional elongation (positive or negative) at the edge of conveyor belt relative to natural axial concave or convex curved section of conveyor belt —
ΔεK∞ The limit value of ΔεK at the edge of conveyor belt with long curved section —
ΔεM Additional elongation (positive or negative) at the central area of conveyor belt relative to natural axial concave or convex curved section of conveyor belt —
ΔεM∞ The limit value of ΔεM at the central area of conveyor belt with long curved section —
Δε∞ Difference in elongation between the central area and the edge of the conveyor belt with long curved section —
η1 Total efficiency of all driving links between motor shaft and pulley shaft in motor mode —
η2 Total efficiency of all driving links between motor shaft and pulley shaft in generator mode
a Units in brackets are used in some formulae.
5 Capacity by volume and by mass
5.1 Theoretical cross-sectional area of materials
The theoretical capacity by volume and by mass of belt conveyor are determined by the theoretical cross-sectional area and traveling speed of materials stacking on the conveyor belt. The cross-sectional area of materials depends on the angle of move of the conveyed materials, the specific structural type of the idler set and the feeding mode.
In calculating the theoretical capacity by volume and by mass, this standard assumes that the cross section of the conveyed materials has upper surface with parabolic contour line. Figure 1 shows a cross section of materials on the supporting conveyor belt of a common troughing 3-roller idler set.
Figure 1 Theoretical cross section of
horizontally-carried materials conveyed by 3-roller idler set
The theoretical cross-sectional area of carried materials is determined by the length, lM, of middle roller, the trough angle, λ, the effective width, b, of the conveyor belt, and the angle of move, θ. The effective width, b, is the width of the conveyor belt with a certain margin reserved to avoid spillage; it can be calculated using Formulae (1) and (2):
b=0.9B-50 (if B≤2,000) (1)
b=B-250 (if B>2,000) (2)
where,
B——the belt width, mm;
b——the effective width of conveyor belt (theoretical width of conveyor belt carrying materials), mm.
As for the belt conveyor with horizontal curves, the effective width of the conveyor belt may be reduced due to the inclined arrangement of rollers.
As for the materials carried by supporting conveyor belt of 3-roller idler set on a horizontally-arranged belt conveyor, the theoretical cross-sectional area, Ath, calculated based on the angle of move θ may be determined based on the sum of cross-sectional areas, A1,th and A2,th, (see Figure 1); Formulae (3), (4) and (5) shall be used for calculation:
(3)
(4)
Ath=A1,th+A2,th (5)
where,
Ath——the theoretical cross-sectional area of carried materials, m2;
A1,th——the theoretical cross-sectional area of the upper part of carried materials, m2;
A2,th——the theoretical cross-sectional area of carried materials when θ = 0° (cross-sectional area of lower part of carried materials), m2;
lM——the length of the middle idler of 3-roller idler set, m;
θ——the angle of move of materials, °;
λ——the trough angle of idler set, °;
b——the effective width of conveyor belt (theoretical width of conveyor belt carrying materials), m.
When used to calculate the cross-sectional area A1,th, the equivalent angle of move β shall be calculated using Formula (6):
(6)
where, β=θ/1.5.
The angle of move of materials depends on the characteristics of conveyed materials and factors of belt conveyors, such as length and belt speed. If empirical value of angle of move is not available, the following may be chosen:
——for materials with normal fluidity, take 0≤θ≤20°;
——for materials with high fluidity, take 20°≤θ≤30°.
Theoretical cross-sectional area of materials carried by 2-roller idler set shall be calculated by substituting lM=0 into Formulae (3) and (4);
Theoretical cross-sectional area of materials carried by 1-roller idler set shall be calculated by substituting lM=0 and λ=0 into Formulae (3) and (4).
See Annex A for the calculation of the theoretical cross-sectional area, Ath, of materials carried by 1-roller, 2-roller, 4-roller and 5-roller idler sets respectively.
Theoretical capacity by volume shall be calculated using Formula (7) based on the theoretical cross-sectional area of carried materials:
IV,th=Ath·v (7)
Theoretical capacity by mass shall be calculated using Formula (8):
Im,th=ρAth·v (8)
where,
IV,th——the theoretical capacity by volume, m3/s;
Im,th——the theoretical capacity by mass, kg/s;
v——the belt speed, m/s;
ρ——the bulk density of conveyed materials, kg/m3.
5.2 Cross-sectional reduction coefficient during inclined conveying
When a belt conveyor feeds uniformly and travels horizontally and straightly, its theoretical cross section of materials can be fully utilized.
Under the influence of material weight, internal friction angle and other factors, the area of the upper part, A1,th, shown in Figure 1 will be reduced. When the belt conveyor is well centered, uniformly feeds and conveys materials with small particle size and the maximum angle of inclination, δmax on the belt conveyor line ≤θ, the reduction coefficient of the upper part shall be calculated using Formula (9):
(9)
where,
φSt1——the cross-sectional reduction coefficient of theoretical cross-sectional area, A1,th, of the upper part of carried materials during inclined conveying, dimensionless;
δmax——the maximum angle of inclination on the belt conveyor line, °;
θ——the same as that in Formula (3).
The reduction coefficient, φSt, of theoretical cross-sectional area of carried materials during inclined conveying shall be calculated using Formula (10):
(10)
where,
φSt——the cross-sectional reduction coefficient of theoretical cross-sectional area, Ath, of the carried materials during inclined conveying, dimensionless.
If Formulae (9) and (10) are used, attention shall be paid to that the maximum angle of inclination during inclined conveying can only be equal to the angle of move, θ. In this case, only cross-sectional areas A2,th is used for material conveying.
5.3 Nominal capacity and effective filling coefficient
When nominal capacity by mass, Im,N, is given, nominal capacity by volume, IV,N, shall be calculated using Formula (11):
(11)
where:
Im,N——the nominal capacity by mass, kg/s;
IV,N——the nominal capacity by volume, m3/s.
The cross-sectional area required shall be calculated using Formula (12):
(12)
where:
AN——the cross-sectional area of carried materials required under nominal capacity, m2.
The effective filling coefficient of belt conveyor shall be calculated using Formula (13):
(13)
where:
φ——the effective filling coefficient of belt conveyor, dimensionless.
The effective filling coefficient φ depends on:
——characteristics of conveyed materials;
——particle size and composition;
——angle of move θ;
——operating conditions of belt conveyor;
——uniformity of feeding;
——line layout of conveyor;
——conveying angle of inclination;
——reserve of conveying capacity.
The effective filling coefficient, φ, is used to evaluate whether the theoretical sectional area, Ath, of materials matches with the sectional area required under nominal capacity. In this standard, some calculation parameters are selected on premise that the effective filling coefficient φ satisfies 0.7<φ<1.1; otherwise, the calculation parameters selected shall be corrected; in some cases, the effective filling coefficient will be out of the above range, in which the specific values will be determined based on the test data and the experience of the engineer.
The mass per unit length of materials under nominal capacity shall be calculated using Formula (14):
or qG=φρAth (14)
where,
qG——the mass per unit length of materials under nominal capacity, kg/m.
Nominal capacity shall be calculated using Formula (15):
(15)
where,
Q——the nominal capacity, t/h.
6 Traveling resistance and power consumption under steady operating condition
6.1 Calculation principle
As a general rule, before calculating the traveling resistance, it needs to estimate the datum values of the parameters used (such as mass per unit length and simulated friction coefficient of conveyor belt and idler). These values shall be confirmed or corrected according to actual selection during calculation. In general, repeated calculations shall be carried out to achieve calculation results that are completely applicable to specific applications.
The traveling resistance, FU, generated under steady operating condition is the total resistance generated by friction, gravity and other resistances together. The power, PA, required by the driving pulley of the belt conveyor is obtained by multiplying the sum of traveling resistances generated by the upper and lower branches by the traveling speed, v, as shown in Formula (16):
(16)
where,
PA——total power on periphery of driving pulley required to overcome traveling resistance under steady operating condition, kW;
FU——the sum of traveling resistances generated by the upper and lower branches, N.
For the purpose of calculation, the traveling resistances of belt conveyor are classified into:
——major resistance FH (see 6.2);
——additional resistance FN (see 6.3);
——lifting resistance FSt (see 6.4);
——special resistance FS (see 6.5).
The sum, FU, of traveling resistances is equal to the peripheral driving force, FTr, of pulley transmitted from the driving pulley to the conveyor belt, as shown in Formula (17):
(17)
where,
FTr——the sum of peripheral driving force of pulley, N;
FU,o,i, FU,u,i——the traveling resistance on sections i of the upper and lower branches respectively, N;
no, nu——the number of sections divided in upper and lower branches respectively.
Resistance shall be determined by section. The sectioning principle is to have the same calculation parameters in each section, such as the angle of inclination δi, the simulated friction coefficient, fi, the mass per unit length of materials, qG,i, and the mass per unit length of the idler rotor, qR,i, on each section in the upper and lower branches of the belt conveyor. To facilitate computer programming calculation, during the resistance calculation, the sections shall be numbered from the tail section to the head section of the belt conveyor, with subscripted i as the serial number of the section, the subscripted o as the upper branch and the subscripted u as the lower branch (see Figure 2), and pulley numbered as separate section. In the text below, for the sake of uniform expression, the pulley number is indicated by subscripted j, and the point of contact by subscripted T1 and the separation point by subscripted T2. (See Figures 5 and 6).
6.2 Major resistance
6.2.1 Calculation of major resistance
The major resistance is generated over the entire length of the conveying lines of all belt conveyors. It includes rotating resistance of idler, indentation rolling resistance of conveyor belt, bending resistance of conveyor belt and internal friction resistance of materials. The major resistance shall be calculated separately for each section.
In order to simplify the calculation of section resistance, the major resistance FH,i in each section of upper and lower branches shall be calculated based on the linear relationship between resistance and motion load, as shown in Formula (18):
FH,i=lifig[qR,i+(qB+qG,i)cosδi] (18)
where,
FH,i——the major resistance on section i, N;
li——the length on section i, N;
fi——the simulated friction coefficient on section i, dimensionless;
qR,i——the mass per unit length of the idler rotor on section i, kg/m;
qB——the mass per unit length of conveyor belt, kg/m;
qG,i——the mass per unit length of materials on section i, kg/m;
δi——the conveying angle of inclination of section i, °;
g——the gravitational acceleration, m/s2.
To determine the conveyor belt tension, the major resistances, FH,o,i and FH,u,i, in sections of upper and lower branches respectively must be determined firstly (see 8.3).
The major resistance of a belt conveyor is the sum of the major resistances, FH,o and FH,u, of upper and lower branches, as shown in Formula (19):
(19)
where:
FH——the total major resistance of upper and lower branches, N;
FH,o,i, FH,u,i——the major resistance on sections i of the upper and lower branches respectively, N;
FH,o, FH,u——the sum of the major resistances of upper and lower branches respectively, N.
Key:
0, 1, 2——characteristic points of conveyor line;
lo,1, lo,2, lu,1, lu2——the lengths of sections 1 and 2 of upper branch and lower branch, respectively;
FU,o,1, FU,o,2, FU,u,1, FU, u,2——the traveling resistance of sections 1 and 2 of upper and lower branches, respectively.
Figure 2 Section division and traveling resistance of
each section under steady operating condition
In calculating the major resistance of each section, the effective filling coefficient, φ, of materials shall satisfy 0.7<φ<1.1. Otherwise, the datum values of calculation parameters given in this standard shall be corrected.
The major resistance shall be calculated under extreme load conditions (nonuniform feeding, partial load and no load) if upward and downward sections are included on the line of belt conveyor, because the sum of resistances in this case may greatly exceed the resistance under steady operating condition.
6.2.2 Determination of simulated friction coefficient
Choosing the simulated friction coefficient fi is more important than calculating the major resistance, because fi determines the major resistance, especially for belt conveyors with small lifting resistance. The simulated friction coefficient fi given in Table 2 may be used to calculate the major resistance of upper and lower branches.
If measured or empirical value is unavailable, or only rough equipment parameters are available, the datum value of the simulated friction coefficient f may be selected according to the operating condition and structural characteristics given in Table 2. These datum values are obtained by summary based on a large number of measurements on the upper and lower branches and with the following restrictions considered:
Contents of GB/T 36698-2018
Foreword i
1 Scope
2 Normative references
3 Terms and definitions
4 Symbols, definitions and units
5 Capacity by volume and by mass
5.1 Theoretical cross-sectional area of materials
5.2 Cross-sectional reduction coefficient during inclined conveying
5.3 Nominal capacity and effective filling coefficient
6 Traveling resistance and power consumption under steady operating condition
6.1 Calculation principle
6.2 Major resistance
6.3 Additional resistance
6.4 Lifting resistance
6.5 Special resistance
6.6 Calculation method of total traveling resistance of belt conveyor
7 Design calculation of driving system
7.1 Contents of design calculation
7.2 Position of driving unit, specification and number of driving motor
7.3 Starting, braking and stopping
8 Calculation of tension and take-up tension of conveyor belt
8.1 Factors affecting conveyor belt tension
8.2 Conveyor belt tension
8.3 Traveling resistance and tension at characteristic point of upper and lower branch sections
8.4 Take-up tension and working distance of take up unit
8.5 Tension of conveyor belt at characteristic point of upper and lower branches
9 Tension distribution across the width of conveyor belt
9.1 Calculation principle
9.2 Troughing transition section
9.3 Curve section
10 Determination of tensile strength and coating thickness of conveyor belt
10.1 Selection principles
10.2 Calculation of break strength of conveyor belt
10.3 Determination of coating thickness of conveyor belt
11 Method for determination of minimum diameter of pulley
11.1 Principle
11.2 Determination based on the service life of conveyor belt
11.3 Determination based on allowable specific pressure of conveyor belt
12 Selection of idler and design of idler spacing
12.1 Calculation principle
12.2 Determination of roller diameter
12.3 Spacing between idler sets
12.4 Design to avoid resonance
13 Design of curvature radius of troughing transition section and vertical curved section
13.1 Calculation principle
13.2 Determination of minimum length of troughing transition section
13.3 Determination of minimum radius of vertical curved section
14 Design of turnover of the conveyor belt
Annex A (Informative) Calculation of cross-sectional area of materials carried by 5-roller idler sets
Annex B (Informative) Determination of total additional resistance based on additional resistance coefficient
Annex C (Informative) Calculation of maximum conveyor belt tension for simply arranged belt conveyors
Bibliography