IEEE AFRICON 2009
23 - 25 September 2009, Nairobi, Kenya
A New Energy Calculation Model of Belt Conveyor Shirong Zhang and Xiaohua Xia Centre of New Energy Systems Department of Electrical, Electronic and Computer Engineering University of Pretoria, Pretoria 0002, South Africa Email:
[email protected],
[email protected]
Abstract —The
model for ener energy gy calc calculati ulation on of the belt conveyor vey or is muc much h nee needed ded for the opt optimi imisat sation ion of its ope operat rating ing efficiency effici ency.. Ther Theree are two cate categorie goriess of model modelss in the lite literatur rature, e, one relying on resistance force calculation, and the other one on energy conversion through a compensation length. In the paper, we propose a new model. Our proposed model is evolved by the interlinkage of the two categories. This modified model is characterized by two compensation length variables. It is evidenced by com compar parati ative ve stu studie diess in ter terms ms of the bet better ter accuracy accuracy and applicability.. Further applicability Further,, the elaborative procedur proceduree for calibrating this model by field experiment is also proposed.
I. I NTRODUCTION Belt conveyor is believed to be the most effective among all means for handling the bulk material over short to medium conve con veyin ying g dis distan tances ces.. Ene Energ rgy y cos costt for forms ms a lar large ge par partt of the operating cost of belt conveyor system which is estimated up to 40%. The improvements of the efficiency of equipment or that of the operating mode lower the energy cost definitely. The majority of the literatures on energy savings on the belt conveyors focus on the improvement of the equipment’s efficiency [1],[2],[3],[9],[10]. That was done either by introducing highly efficient equipment or improving the efficiency of the existing equipment. The energy saving on belt conveyor can also be achieved by optimizing the operating parameters, for example, the transfer rate and belt speed [11]. In the cur curren rentt sce scenar narios ios,, the ex exist isting ing bel beltt con conve veyor yorss are focusing on feasibility and reliability and their operating points always deviate from the optimal ones. In order to save energy of the belt conveyor by optimizing the operating parameters the prac practica ticable ble ener energy gy calc calculat ulation ion model modelss are need needed. ed. There are several energy calculation models to design the drive system for belt conveyors. These models derive from well-known standa sta ndards rds or spe specifi cificat cation ions, s, suc such h as ISO 504 5048, 8, DIN 221 22101, 01, JIS B 880 8805, 5, CEM CEMA A (Co (Conv nvey eyor or Equ Equipm ipment ent Man Manufa ufactu cturer rerss Association) and FDA (Fenner Dunlop Australia) [4],[5],[7]. They incorporate design parameters and operation parameters togeth tog ether er to cal calcul culate ate the po power wer whi which ch is nee needed ded to dri drive ve the belt conveyor conveyor unde underr cert certain ain oper operating ating conditions. conditions. Since operating parameters are involved, these models can also be used to estimate the operating power of existing belt conveyor. Amon Am ong g th thes esee mo mode dels ls,, IS ISO O 50 5048 48,, DI DIN N 22 2210 101 1 an and d CE CEMA MA require requi re man many y para paramete meters, rs, whic which h make their appl applicat ications ions inconvenient. However, JIS B 8805 and FDA require relatively lesss par les parame ameter terss by lum lumpin ping g oth other er par parame ameter terss tog togeth ether er and compensating it with a length parameter, hence they are easy to use. But the compensation length constants in JIS B 8805
and FDA are inaccurately determined, which inevitably results in energy calculation errors [7], [8]. The main purpose of this paper is to propose a practicable new energy calculation model for belt conveyor. We begin with the analysis of the existing energy calculation models which are divided into two categories. The first category is based on resistance calculation methodology, and the other one is based on energy conversion methodology. Then a modified energy calculation model is proposed by interlinking the previously menti me ntione oned d cat categ egori ories. es. Thi Thiss mod model el is cha charac racter terize ized d by two compensa comp ensation tion leng length th var variabl iables. es. A belt con convey veyor or,, con convey veying ing coal in a harbour, is used for a comparative study of all of the above abo ve ment mentioned ioned energy calc calculat ulation ion mode models. ls. The influ influences ences on thes thesee mode models ls from conveyi conveying ng dist distance ance,, tran transfer sfer rate and beltt spe bel speed ed are ill illust ustrat rated. ed. Fo Forr the sak sakee of min minimi imizin zing g the errors err ors bet betwee ween n the ne newly wly pro propos posed ed mod model el and the act actual ual energy consumption, a practicable method and its procedure for calibration this model are also proposed. The layout layout of the paper paper is as fol follo lows: ws: In Sec Secti tion on II II,, two categorie cate goriess of exis existing ting energy models for belt con convey veyor or are revie re viewed wed.. In Sec Sectio tion n III III,, a ne new w ene energ rgy y mod model el is pro propos posed. ed. Section IV presents the comparative study results. Section V proposes prop oses the appli applicati cations ons and the calibration calibration method of the new model. The last section is conclusion. I I . T WO C ATEGORIES OF E NERGY C ALCULATION M ODEL The aforementioned energy calculation models are divided into two categories. ISO 5048, DIN 22101 and CEMA belong to the first category which is based on resistance calculation methodology. While JIS B 8805, FDA and Goodyear’s model [8] belong belong to ano anothe therr cat categ egory ory whi which ch is bas based ed on ene energ rgy y conver con version sion meth methodol odology ogy.. Ther Theree are stil stilll some other meth meth-ods to calc calculat ulatee the energy consumption consumption of belt conveyor conveyors. s. For inst instance ance,, refe referenc rencee [14] summ summariz arizes es a singl singlee resi resistan stance ce method. Since they also use resistances to calculate the power of belt conveyor, they are similar to ISO 5048, DIN 22101 and CEMA. Therefore, detailed comparison with them will not be carried out. A. Ener Energy gy Mode Modell Base Based d on Resi Resistanc stancee Calc Calculat ulation ion
A typical belt conveyor is shown in Fig.1. Under stationary operating conditions, the energy consumption of belt conveyor is mainly determined by the motion resistance in the loaded section of the belt and the return belt. The accessories, such as bel beltt cle cleane aners, rs, plo plows ws and ski skirt rt boa boards rds out outsid sidee the fee feeder der
978-1-4244-3919-5/09/$25.00 ©2009 IEEE
1
IEEE AFRICON 2009
23 - 25 September 2009, Nairobi, Kenya Carrying Idler
Drive pulley
or
Return Idler L h
In the view of energy conversion, the power of belt conveyor under stat under stationar ionary y cond conditio ition n can be main mainly ly div divided ided into thre threee components as follows [8]:
Typic ypical al belt belt convey conveyor or
station also contribute station contribute to the tota totall ener energy gy consu consumpti mption. on. ISO 5048 and DIN 22101 are quite similar, but they are different at dealing with the friction resistances of belt cleaners. Both of the them m di divid videe mot motion ion res resist istanc ances es int into o pri primar mary y res resist istanc ancee F H H , secondary resistance F N N , slop resistance F st st and special resistance F S . Primar Pri mary y res resist istanc ancee is the sum of all fri fricti ctionon-rel relate ated d resistances sist ances along the belt con convey veyor or with exception exception of speci special al resistances, and is calculated by
F H H = f Lg [QR0 + QRU + (2QB + QG )cos δ ],
(10 ≤ L < 1840) (1840 ≤ L)
Special resistance includes the resistance caused by forward tilted tilt ed idle idlers rs F f r , fri fricti ction on res resist istanc ancee fro from m the ski skirt rt boa boards rds outside the feeder station F sb , the resistance from belt cleaners sb F c and the resistance from material plows F p . Slop resistance result res ultss fro from m the ele eleva vatio tion n of the mat materi erial. al. It is acc accura uratel tely y = calculated using F st , where is the net change Q H g H st G in elevation (m). The total resistance is expressed as
F U U = F H H + F N N + F f r + F sb sb + F c + F p +F st st ,
1) the power power to run the empt empty y conveyor conveyor P ec ec ; 2) the power power to mo move ve the material material hor horizo izonta ntally lly ov over er a certain distance P h ; 3) the power power to lift the material material a certain height height P l . The accessaries also contribute to the total power of the belt conveyor, which is obtained through the special resistances.
P T T = P ec ec + P h + P l + P Acs Acs .
(2)
(5)
According to [8], P ec According calcul culate ated d usi using ng the ec , P h and P l is cal following empirical formulae
(1)
where f is the friction factor, L is the centre-to-centre distance (m), QR0 is the unit mass of the rotating parts of carrying idler rollers (kg/m), QRU is the unit mass of rotating parts of return idler rollers (kg/m), QB is the unit mass of the belt (kg/m), δ is the inclination angle ( o ) and QG is the unit mass of the load (kg/m) which is determined determined by QG = 3.T . T is the 6V transfer tran sfer rate (t/h (t/h)) and V is the bel beltt spe speed ed (m/ (m/s). s). Equ Equati ation on (1) is a sim simpli plified fied cal calcul culati ation on of pri primar mary y res resist istanc ancee whi which ch is suit suitable able for engin engineeri eering ng appli applicati cations, ons, while [6] propo proposed sed the complicated and non-linear calculation models for primary resistance. Secondary resistance includes the friction or inertia resistances which occur only at certain parts of the belt conveyor. They are the inertia resistance and friction resistance between material and belt at the feeder station F bA bA , the friction resistance between skirt boards and material within the accelerating zone F f f , the wrap resistance between belt and pulley F w and the bearing resistance F t . ISO 5048 and DIN 22101 allow a coefficient C be used to estimate F N N , which is named as a C coefficient method. That is F N N = ( C − 1)F H H . The relation between C and L from ISO 5048 [4] can be fitted using
C = 0 .85 + 13.31L−0.576 , C = 1 .025.
(3)
B. Ener Energy gy Mode Modell Base Based d on Energy Conversi Conversion on
Take-up
Under stationary condition, the total power P T T is thus obtained by (4) P T T = F U U V.
H
Fig. 1. 1.
F U U = CF H H + F fr fr + F sb sb + F c + F p +F st st .
L
P ec ec = gf (Lh + L0 )QV,
(6)
T , 3.6
(7)
P h = gf (Lh + L0 )
T (8) , 3.6 where Lh is the horizontal centre-to-centre distance (m), L0 is comp compensat ensation ion leng length th const constant ant (m) and Q is the ma mass ss of movin mo ving g par parts ts of the equ equipm ipment entss in kil kilogr ogram am per meter of centre cen tre-to -to-ce -centr ntree dis distan tance ce (kg (kg/m /m). ). It is ex expre presse ssed d as Q = QR0 + QRU + 2QB . In (6) and (7), L0 is used to compensate some components of the frictional force which are independent of the belt length and therefore are treated as constant. JIS B 8805, FDA and Goodyear’s model are all based on this ener energy gy con convers version ion meth methodol odology ogy [7],[ [7],[8], 8], but the dete deterrministic specifications for L0 are quite different. JIS B 8805 and Goodyear’s Goodyear’s mode modell use just one value for comp compensa ensation tion constant L0 . It is independent of L and relates to the friction facto fa ctorr and wor workin king g con condit dition ions. s. Ho Howe weve ver, r, FD FDA A use usess thr three ee piecewise values for compensation length constant L0 , which are determined according to L and working conditions. Since the ener energy gy calc calculat ulation ion mode models ls base based d on this energy converconversion meth methodolo odology gy are requi requiring ring rela relativ tively ely less para paramete meters, rs, it is much simpler simpler than resistance resistance based models. Mark and Calmeyer [12],[13] have used this kind of energy calculation model for energy auditing and load shifting. P l = gH
III. T HE M ODIFIED E NERGY C ALCULATION M ODEL Energy Ener gy calc calculat ulation ion mode models ls based on the meth methodolo odology gy of resistance calculation consider almost all the issues contributing to the total energy consumption, so they are believed to be mor moree acc accura urate te tha than n tho those se bas based ed on the methodol methodology ogy of energ ene rgy y con conve versi rsion on . But ma many ny ex exact act des design ign and ope operat rating ing paramete para meters rs are requ required ired by thes thesee resi resistan stance ce base based d mode models. ls. Whilee the models base Whil based d on ener energy gy con conver version sion simplify simplify the
978-1-4244-3919-5/09/$25.00 ©2009 IEEE
2
IEEE AFRICON 2009
23 - 25 September 2009, Nairobi, Kenya TABLE I T HE
PARAMETERS OF THE BELT CONVEYOR FOR COMPARATIVE STUDY
Parameter description
Symbol
Value
Unit
Parameter description
Symbol
Value Va
Unit
Transfer rate
T ρ
2000
t/h kg/m3
Centre-to-centre distance of the belt The net change in elevation
L H
313.25
Density of the material
9.98
m m
Inclination angle
δ
1.825
◦
Width of the belt
B
1400
mm
900
Belt speed
V
3.15
m/s
Average spacing of the carrying idlers
a0
1.2
m
Troughing angle
λ
35
◦
Average spacing of the return idlers
au
3
m
Forwards tiling angle of idlers
ε
2
◦
Length of skirt boards outside feeder station
lsb
4.5
m
Diameter of carrying idlers
Φ
133
Φ
133
La0
530
mm mm
Diameter of return idlers
Length of carrying idlers
Mass of the moving parts of each carrying idler
qr0
6.3
mm kg
Length of return idlers
Lau
800
mm
Mass of the moving parts of each return idler
qru
11.64
kg
Unit mass of the belt
QB
18.73
kg/m
Unit mass of rota rotating ting parts of carry carrying ing idlers
QR0
15.75
kg/m
Unit mass of the load
QG
176.37
kg/m
Unit mass of rotating parts of return idlers
QRU
7.76
kg/m
Surcharge angle
β
30
◦
Friction factor between belt and idlers
μ0
0.3
0.3−0.4
Length for forwards tiling idlers
313.25
m m
Fiction factor between material and belt
0.5−0.7
Fiction factor between material and skirt board
μ1 μ2
0.6
Diameter of the pulley
lr D
0.6
0.5−0.7
Inclination coefficient
k
1.0
Fiction factor between belt and its cleane rs rs
μ3
0.6
Interval of the skirt boards
b1
0.85
m
Maximum sectional area
A
0.253
m2
Thickness Thick ness of the belt
d
0.01
m
Pressure Press ure exerted on belt by belt cleaner
P
100000
N/m2
Friction factor
f
0.024
Coefficient of the troughing shape
C e
0.45
Coefficient of the scraping board
K s
1500
0.8
N/m
energy calculation by introducing the empirical compensation length constants L0 ’s int into o the models, models, so the they y are easy to use. However However,, sinc sincee the they y use just one or few compensati compensation on length constants to satisfy all cases, there must be some energy calculation errors. This paper proposes a modified energy calculation model for belt con convey veyor or by inte interlin rlinking king afor aforemen emention tioned ed two cate cate-gories. It follows the basic structure of the models based on the methodology of energy conversion, and characterized by two compensation length variables, L01 and L02 . L01 is the compensation length variable for P ec ec and L02 is for P l . When the belt is empty (T=0), F N and F N st equal zero. Under this st condition, the total resistance becomes F U U |T =0 = F H H + F S and (5) becomes P T T |T =0 = P ec ec + P Acs Acs . F U U |T =0 and P T T |T =0 are obtained under the same condition, so
F U U |T =0 =
P T T |T =0 . V
(9)
Combining (1), (6) and (9), L01 is obtained by
L01 = L(1 − cos δ )(1 −
2QB Q
).
(10)
L02
L02 =
3.6C F t V T (V + + ), 2 1.8b1 ρ gf T
(12)
where b1 is the interval of the skirt boards. Then the modified energy calculation model is expressed as follows.
T T + gH + P Acs Acs . 3.6 3.6 (13) It is ob obvio vious us tha thatt the mod modifie ified d ene energ rgy y cal calcul culati ation on mod model el is easi ea sier er to us usee th than an IS ISO O 50 5048 48 an and d DI DIN N 22 2210 101 1 be beca caus usee of the rela relativ tively ely less param parameter eter requi requireme rements. nts. Furt Furtherm hermore, ore, this model is more accurate than JIS B 8805 or FDA because the compensat compe nsation ion leng length th var variabl iables es var vary y with the param parameter eterss the belt conveyor to fit different cases. P T T = gf (Lh + L01 )QV + gf (Lh + L02 )
IV.. T HE C OMPARATIVE S TUDY IV An inclined belt conveyor for conveying coal in a harbour is used for a comp comparat arativ ivee stud study y of thes thesee ener energy gy calc calculat ulation ion models. Its parameters are shown in Tab.I. A. Calcu Calculati lation on Results for the Specific Case
Using the same method, L02 is obtained as follows
F N F bA N bA + F f f + F w + F t . = = gf QG gf QG
calculation formulae of F bA bA , F f f and F w from [4] with (11), L02 is expressed as
(11)
In (11), F t is comparatively small and omitted [5]. F w is also small and does not vary much, so it is taken as a constant C F t . Ordinarily, the friction factor between material and belt equals equ als tha thatt bet betwee ween n mat materi erial al and ski skirt rt boa boards rds [4] [4].. In man many y cases, cas es, the input speed of the material material in the belt dir direct ection ion equal zero (V 0 =0). Under all these conditions, combining the
Seven energy calculation models are used to calculate the power po wer of the bel beltt con conve veyor yor und under er the spe specifi cificc con condit dition ion as shown sho wn in Tab ab.I. .I. The spe specia ciall res resist istanc ancee is cal calcul culate ated d usi using ng ISO 504 5048. 8. Fo Forr sim simpli plicit city y, we mak makee the con conve venti ntion on in the rest of the paper that I SO denot denotes es the accur accurate ate calc calculat ulation ion method of ISO 5048, I S O C denotes C coefficient method of ISO 5048, DI N denotes accurate calculation method of DIN 22101, D I N C denotes C coefficient method of DIN 22101, JIS denotes calculation method of JIS B 8805 standard, FDA
978-1-4244-3919-5/09/$25.00 ©2009 IEEE
3
IEEE AFRICON 2009 TABLE II ALCULATION TION RESULTS FOR THE C ALCULA
23 - 25 September 2009, Nairobi, Kenya 110
SPECIFIC CASE
100
Symbol
Description
Value (KW)
ISO
Accura Acc urate te cal calcul culati ation on met metho hod d of ISO 504 5048 8
141.58
ISO IS O C
C co coef effic ficie ient nt me meth thod od of IS ISO O 50 5048 48
151.46
DIN
Accura Acc urate te cal calcul culati ation on met method hod of DIN 221 22101 01
141.45
DIN DI N C
C co coef effic ficie ient nt me meth thod od of DI DIN N 22 2210 101 1
139.17
JIS
JIS B 8805 standard
144.55
FDA
FDA FD A’s ca callcu cullat atio ion n han and dbo boo ok
140.11
TwoL0
Modified energy calculation model
142.77
ISO ISO_C DIN DIN_C FDA JIS TwoL0
90 80 70 ) W 60 K ( P 50 40 30 20 10
denotes calc denotes calculat ulation ion meth method od in FDA FDA’’s handb handbook ook and TwoL0 denotes denot es the modi modified fied ener energy gy calc calculat ulation ion model we prop propose ose in thi thiss pap paper er.. The cal calcul culati ation on res result ultss are sho shown wn in Tab ab.II .II.. The seven energy calculation models draw similar results with smalll dif smal differe ferences nces except except ISO C. The ulti ultimate mate purpose of thes thesee ener energy gy calc calculati ulation on mode models ls discussed here is operating optimisation or scheduling for belt conve con veyor yors. s. So, it is nec necess essary ary to ana analyz lyzee and ev evalu aluate ate the influences on these models from certain parameters. Influences from fro m con conve veyin ying g dis distan tance, ce, bel beltt spe speed ed and tra transf nsfer er rat ratee are studied studi ed in the paper, paper, whil whilee the other design parameters parameters are considered constant as shown in Tab.I.
Fig. 2.
0
60
80
100 L(m)
120
140
160
180
200
1600 ISO ISO_C DIN DIN_C FDA JIS TwoL0
1400 1200 1000 ) W K 800 ( P
600 400 200 0
1) The accurate calculation calculation method method of ISO 5048 and that of DIN 22101 yield quite similar results; the power curves of the two are nearly parallel with small differences. 2) With sho short rt con conve veyin ying g dis distan tances ces and lo low w bel beltt spe speeds eds (V ≤ 2 m/s m/s), ), the calcula calculatio tion n res result ultss of JIS and FD FDA A are larger larger tha than n tho those se of ISO or DIN DIN.. Ho Howe weve verr, whe when n conveying distances are quite long, JIS and FDA yield smaller results than ISO and DIN. These indicate that JIS and FDA can not satisfy all these cases quite well using usin g just one or few compensatio compensation n leng length th const constants ants.. Furthermore, the four values for the compensation length consta con stant nt of FD FDA A pre presen sentt an in inve verse rse rel relati ation on wit with h the convey con veying ing dist distance ance,, so FD FDA A’s abso absolute lute error incre increases ases in direct proportion to conveying distance. 3) Withi Within n short conveying conveying distance distance ( L ≤80 m), ISO C and DIN C hav havee unce uncertai rtain n C coef coefficie ficient nt [4], [4],[5]. [5]. Thus they cannot yield satisfactory results under this condition. 4) IS ISO O C an and d DI DIN N C ar aree ea easy sy to use, use, but show show lo lowl wly y accuracy.
40
Power Pow er curves curves for L=10-200 L=10-200 with with V=3.15 V=3.15 m/s and T=2000 T=2000 t/h
B. Variable Conveying Conveying Distance
With constant belt speed and transfer rate, the correlation between power and conveying distance are calculated by the previous pre viously ly ment mentione ioned d sev seven en ener energy gy calc calculat ulation ion mode models. ls. The resulting curves for short conveying distances ( L=10-200 m) with V =3.15 m/s and T =2000 t/h are shown in Fig.2, while the resulting curves for medium to long distances 200-4000 m are shown in Fig.3. Using ISO as the baseline, the relative errors of the other models are obtained as shown in Fig.4. By analyzing calculation results of diffident combinations of belt speedss tran speed transfer sfer rate ratess and con convey veying ing dista distances, nces, the foll followi owing ng conclusions are drawn.
20
Fig. 3.
0
500
1000
1500
2000 L(m)
2500
3000
3500
4000
Power Pow er curves for L=200-4 L=200-4000 000 with V=3.15 V=3.15 m/s and T=2000 T=2000 t/h 10
5
) 0 % ( E −5
ISO_C DIN DIN_C FDA JIS TwoL0
−10
500
Fig. 4.
1000
1500
2000 L(m)
2500
3000
3500
4000
Relative Relat ive errors errors for L=50-400 L=50-4000 0 with V=3.15 V=3.15 m/s and T=2000 t/h
5) The mod modifie ified d ene energ rgy y cal calcul culati ation on mod model el fol follo lows ws ISO quite well with relatively small differences during whole domain of conveying distance. C. Variab ariable le Belt Speed
Power curves for V =1.5-6 m/s with L=1000 m and T =1200 t/h are shown in Fig.5, and the relative error curves for the samee cas sam cases es are sho shown wn in Fig Fig.6. .6. The cal calcul culati ation on res result ultss of other combinations of belt speed ranges, conveying distances and tra transf nsfer er rat rates es are als also o stu studie died d to dra draw w the fol follo lowin wing g conclusions. 1) When When bel beltt spe speed ed is lo low w, ISO and DIN’s DIN’s cal calcul culati ation on results resul ts are smallest smallest amon among g all the sev seven en mode models. ls. Wi With th increase in belt speed, they yield higher values relative
978-1-4244-3919-5/09/$25.00 ©2009 IEEE
4
IEEE AFRICON 2009
23 - 25 September 2009, Nairobi, Kenya
330
to other models. With very high belt speed, they yield the largest values comparing to other models. 2) When belt belt speed is relati relatively vely high, high, DIN C and FDA result in large values. so, they can just be used within low to medium belt speed where the secondary resistances are quite small comparing to primary resistance [5]. 3) Withi Within n the whole belt speed speed domain, the modified modified energy model follows ISO and DIN quite well too.
ISO ISO_C DIN DIN_C FDA
320 310 300
JIS TwoL0
290 ) W280 K ( P 270 260 250
D. Variable Transfer Transfer Rate
240 230 1.5
Fig. 5.
2
2.5
3
3.5 4 V(m/s)
4.5
5
5.5
6
Power Pow er curves curves for V=1.5-6 V=1.5-6 m/s with L=1000 L=1000m m and T=1200 T=1200 t/h 4
2
) % ( E
0 ISO_C DIN DIN_C FDA JIS TwoL0
−2
−4
−6 1.5
Fig. 6.
2
2.5
3
3.5 4 V(m/s)
4.5
5
5.5
6
Relative Relat ive errors errors for V=1.5-6 V=1.5-6 m/s with L=1000m L=1000m and T=1200 T=1200 t/h 420 400 380 360 340 ) W320 K ( P 300
ISO ISO_C DIN DIN_C FDA JIS TwoL0
280 260 240 220 1000 1000 1100 1100 1200 1200
Fig. 7.
1300 1300 1400 1400
1500 1500 1600 1600 1700 1700 1800 1800 1900 1900 2000 2000 T(t/h)
Power Pow er curves curves for T=100-2000 T=100-2000 t/h with with L=1000 m and V=3.15 V=3.15 m/s 4 ISO_C DIN DIN_C FDA JIS TwoL0
3
2 ) % 1 ( E
0
−1
−2 1000 1000 1100 1100 1200 1200
Fig. 8.
1300 1300 1400 1400
1500 1500 1600 1600 1700 1700 T(t/h)
1800 1800 1900 1900
2000 2000
Relativ Rela tivee errors for T=100-20 T=100-2000 00 t/h with L=1000 L=1000 m and V=3.15 m/s
It is als also o nec necess essary ary to stu study dy the influence influence on the energy energy calculation calculat ion mode models ls from transfer transfer rate rate.. The resul resulting ting curves for T =100 =1000-200 0-2000 0 t/h with V =3. =3.15 15 m/s and L=10 =1000 00 m are shown in Fig.7. The relative errors under the same condition are shown in Fig.8. With constant belt speed and conveying distance, power increases in direct proportion to transfer rates. Unlike Unli ke con convey veying ing dist distance ance and belt speed, the var variati iations ons in transfer rate do not change the relative positions of the result curves of all these energy models. According to Fig.8, the new model results in smaller errors relative to other models except DIN. Hence, the new model shows quite good accuracy within the domain of transfer rate. V. APPLICATION A ND C ALIBRATION A. Appli Applicati cations ons of The Modified Energy Energy Calc Calculat ulation ion Model
The modified energy calculation model is formulated into three integrated analytic equations. While the resistance based models consist of many equations for all kinds of resistances. Moreover, the empirical compensation lengths within the models based on energy conversion methodology are determined mainly main ly by expe experien riences. ces. All these issues make the modi modified fied modell more suitable mode suitable for the operational operational opti optimisa misation tion of the belt conveyors than other models. The ultimate purpose is to use this model for the optimisation of energy efficiency of belt conveyor. The goal is achieved by using this energy calculation model for the belt conveyor design or for the improvement of the efficiency of the existing belt conveyors. During the design phase of a belt conveyor, the modified energy model is built using usi ng the design design par parame ameter ters. s. The Then n it wil willl be use used d to ve verif rify y the design of the drive system. For exi existin sting g belt conveyor conveyors, s, this model will be used to improve their energy efficiency by optimizing the transfer rates and belt speeds, and it will also be used for load shifting or operation scheduling. B. Calib Calibrat ration ion of The Modified Energy Energy Calcu Calculati lation on Model
Nowad No wadays ays,, mos mostt of the exi existi sting ng bel beltt con conve veyor yorss ope operat ratee at the non non-op -optim timal al ope operat rating ing poi points nts bec becaus ausee of equ equipm ipment ent aging, agin g, main maintena tenance nce or re-a re-adjust djustment ment.. As a resu result, lt, the actual operating points always deviate from the design points. Hence, the energy calculation model, calibrated by field experiment, must be more accurate than those totally calculated through design desi gn para paramete meters. rs. The modi modified fied ener energy gy calc calculat ulation ion mode modell provides the mechanism for calibration of its parameters by field experiment. According to ISO 5048, the special resistances F S for an
978-1-4244-3919-5/09/$25.00 ©2009 IEEE
5
IEEE AFRICON 2009
23 - 25 September 2009, Nairobi, Kenya
existing belt conveyor, including F fr fr , F sb sb , F c and F p , has the following relation with T and V
model and the actual energy consumption of the corresponding belt conveyor.
T 2 T + k2 + k3 , (14) 2 V V where k1 , k2 and k3 are constant coefficients which relate to the structure parameters of the belt conveyor. Combining (12) (13) and (14), and denoting
For belt con convey veyors ors with perm permanen anentt inst instrume ruments nts for P T T , T and V , an adapt adaptiv ivee para paramete meterr ident identifica ification tion scheme can be developed to adjust the model automatically to guarantee the accuracy of this energy calculation model.
1 , 6.48b21 ρ θ2 = gf (Lh + L01 )Q + k3 + C F t , θ3 = k 1 , gH + gf Lh θ4 = + k2 , 3.6
This paper proposes a modified energy calculation model for belt conveyors. It is expected to be useful in the optimisation of operating efficiency, load shifting and operation scheduling of belt conveyors. This model is proposed by interlinking two existing categories of the energy calculation models. The first category is complicated because it needs many parameters of the belt conveyor. The second one introduces the compensation length constants into the models to make itself easy to use. The modified energy calculation model employs two compensation length variables L01 and L02 , which vary with design parameters and operation parameters to adapt all the cases. Its applicability and validity are proven by the comparative study of all these energy energy mod models els.. Thi Thiss mod model el wil willl be use used d eit either her for belt conveyor design or for the improvement of operating efficiency of existing belt conveyor. A calibration method and its procedure are also proposed to guarantee the applicability of the newly proposed energy calculation model.
F S = k1
θ1 =
(15)
the total power P T T is expressed as follows
V 2 T T 2 + T 2 V θ1 + V θ2 + (16) θ 3 + T θ4 , V 3.6 where θ1 , θ2 , θ3 and θ4 are constant coefficients for a certain belt conveyor, but they cannot keep constant all through for a long time span. In (15), L01 is related to the structure parameters of the belt conveyor, which guarantees the invariability of θ2 . Then, θ1 , θ2 , θ3 and θ4 in (16) can be calibrated by field experiment. Some measurement instruments must be installed to measure P T T , V and T during the experiment. For the belt convey con veyor or with fixed speed, the transfer transfer rate is cont controll rolled ed to operate it at different operating points to get different equations according to (16). For belt conveyor with variable speed and vari va riabl ablee tra transf nsfer er rat rate, e, eit either her spe speed ed or tra transf nsfer er rat ratee can be controlled to get different equations. At least four equations are needed to obtain four coefficients θ1 , θ2 , θ3 and x4 . The working states of belt conveyor change slowly due to abrasion, aging and some environme environmental ntal issues, which resu results lts in the time-variations time-var iations in θ1 , θ2 , θ3 and θ4 . So So,, it is necess necessar ary y to calibrate the energy calculation model periodically, for example once a week, to guarantee its accuracy. The recommended calibration procedure for this model is shown as follows. 1) Inst Install all measurement measurement instruments instruments for P T T , V and T . In many cases, there are permanent instruments for those. If so, this step is not necessary. 2) Con Contro troll V or T to operate the belt conveyor at different operating points and record the readings of P T T , T and V . At least four operating points are needed. Running the empty belt (T=0) with certain speed is considered as the specific operating point. It is not mandatory to execute this specific operating point during the calibration. However, if permitted by the condition, this specific operating point is recommended because it has rather good ability to obtain θ2 directly by single experimental procedure. That is θ2 = P V , where P T e and V e are the readings of power and speed of the belt conveyor operating with empty belt respectively. 3) All these readings readings are used used by (16) to calibrate calibrate θ1 , θ2 , θ3 and θ4 . 4) Th Thee ab abov ovee st step epss sh shou ould ld be ca carr rrie ied d ou outt pe peri riod odic ical ally ly to minimize the errors between the energy calculation P T T =
Te e
V I . C ONCLUSION
R EFERENCES Solids ds [1] A. G. Tapp, “Energy saving troughing troughing idle idlerr techn technolog ology y,” Bulk Soli Handling , vol vol.. 20, no. 4, pp. 437-449, 437-449, Oct. 2000. [2] M. Hager and A. Hint Hintz, z, “The ener energy-s gy-savi aving ng design of belts for long conveyor conve yor systems, systems,”” Bulk Solids Handling , vo vol. l. 13, no. 4, pp. 749-75 749-758, 8, Nov. 1993. [3] A. Z. Dalgleish and L. J. Grobler, “Measurement “Measurement and verification of motor motor sequencing controller on a conveyor belt,” Energy, vol vol.. 28, pp. 913-927, 913-927, 2003. [4] Continuous Mechanical Handling Equipment-Belt Cconveyors With Carrying Idlers- Calculatio Calculation n of Operating Power and Tensile Forces , 2nd ed., ISO 5048, 5048, 1989 1989.. Continuous us Conveyors-Belt Conveyors Conveyors for Loose Bulk Materials-B Materials-Basis asis for [5] Continuo Calculation and Dimensioning , DIN 22101, 2002 2002.. [6] C. Spaans, “The calculation calculation of the main resistance resistance of belt con convey veyors, ors,”” vol.. 11, no. 4, pp. 809-820, 809-820, Nov. Nov. 1991. Bulk Solids Handling, vol [7] Rubber Belt Conve Conveyors yors with Carrying Idlers-Calcul Idlers-Calculation ation of Operating 1992.. Power and Tensile Forces , JIS B 8805, 1992 [8] Handbook of Conveyor & Elevator Belting , The Goodyear Tire & Rubber Company Comp any,, Akro Akron, n, Ohio, USA, USA, 1975. [9] A. W. W. Roberts, J. W. W. Hayes and O. J. Scott, “Optimal design of continuous continuous conveyors,” Bulk Solids Handling , vol vol.. 1, no. 2, pp. 255-264, 255-264, 1981. [10] I. Kusumaningtyas and G. Lodewijks, “Toward “Toward intelligent power consumption optimization in long high-speed passenger conveyors,” in Proc. of the 2007 IEEE Intelligent Transportation Systems Conference , Seattle, WA, USA, 30 Sept.-3 Oct., 2007, pp. 597-602. [11] [1 1] A. T. de Al Almei meida, da, F. J. T. E. Fer Ferrei reira ra and D. Bo Both, th, “Techn “Technica icall and economical considerations in the application of variable-speed drives with electric motor systems,” IEEE Trans. Ind. Appl. , vol. 41, no. 1, pp. 188199, Jan./Feb. 2005. [12] D. J. L. Marx and J. E. Calmeyer, Calmeyer, “A case study of an integrated integrated conveyor belt model for mining industry,” IEEE AFRICON 2004, Gaborone, 15-17 Sept. 2004, pp. 661-666. [13] D. J. L. Marx and J. E. Calmeyer, “An “An integrated conveyor conveyor energy energy model Transactions sactions of the South African Institute of Electrical methodology,” Tran Engineers, vol vol.. 95, pp. 256-264, 256-264, 2004. 2004. [14]] H. Lau [14 Lauho hoff ff,, “Sp “Speed eed con contro troll on bel beltt con conve veyor yors-d s-dose ose is rea really lly sav savee engery?” Bulk Solids Handling , vol vol.. 25, no. 6, pp. 368-377, 368-377, 2005.
978-1-4244-3919-5/09/$25.00 ©2009 IEEE
6
