Catenary Analysis and Calculation Method of Track Rope of Cargo Cableway with Multiple Loads

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4 MATEC Web of Cofereces 8, (016) DOI: / mateccof/ DME Cetralized load i1 d y d x Ai 1 i B i Ai 1 i 1 d y i d x Bi p i Figure 3. Forcig Aalysis at Actio Poit of Cetralized Load Show as figure 3, from the force o the actio poit betwee every rope sectio, the force balace coditios at every load poit is obtaied: i i 1 0 (9) dy dy i i 1 pi (i=1,,, -1) (10) dx B dx i Ai 1 It is kow from the balace coditios that the horizotal force of every rope sectio i is same, which is marked as. Ad equatio (10) ca be writte as pi t[sih( bi) sih( ai 1)] (i=1,,, -1) (11) q ere t=/q 0, a i =sih -1 (V Ai /), b i =sih -1 (V Bi /) (i=1,,, ) Legth of suspesio rope Durig operatio of the cableway, the rope legth of the track rope betwee the cetralized load (heavy objects) is fixed ad uchaged, iitial legth s i of every rope sectio appears i the equatio as the kow quatity, the horizotal spa l i ad height differece h i of the rope sectio will chage followig differet loads ad differet positios. Therefore, whe iitial rope legth of every rope sectio s i (i=1,,, ) is kow, the rope sectio legth equatio is obtaied accordig to equatio (7): t[sih( a ) sih( b)] s (i=1,,, ) (1) i i i 3.3 Compatibility coditio 1) Every sectio of the track rope shall meet with the compatibility equatio of the whole horizotal spa l i i1 l, accordig to equatio (5), it ca be obtaied: ( i i) [sih( i) sih( i)] i1 i1 (13) t a b a b l ) Accordig to deformed compatibility equatio i height hi h ad equatio (6) i1 4

5 MATEC Web of Cofereces 8, (016) DOI: / mateccof/ DME 016 ere K=q 0 /(EA 0 ). t a b a b h [cosh( i) cosh( i)] [cosh ( i) cosh ( i)] i1 i1 (14) 3.4 Noliear equatio set Summarizig the above equatios, the oliear equatio set of the elastic track rope uder multiple cetralized loads is obtaied: pi t[sih( bi) sih( ai 1)] 0 ( i 1,,, 1) q0 t[sih( ai) sih( bi)] si 0 ( i 1,,, ) t( ai bi) [sih( ai) sih( bi)] l 0 i1 i1 t a b a b h [cosh( i) cosh( i)] [cosh ( i) cosh ( i)] 0 i1 i1 (15) The equatio set icludes +1 oliear equatios, +1 ukow umber ai, bi(i=1,,, ) ad t, therefore the oliear equatio set is closed, which ca be expressed as: FX ( ) 0 (16) I which X=[a 1, a,, a, b 1, b,, b, t] T. After X is calculated, the vertical compoet V x ad tagetial tesio T x at ay rope legth s x poit of the track rope are obtaied respectively: m Vx tq0sih( am) q0sx si (17) i1 I which, m is umber of cetralized load i the [0,s x ]. x T tq V (18) 0 x 4 Examples I order to validate calculatio accuracy of the cargo cableway track rope, testig data i the referece documet [1] ad calculatio data i referece documet [8] are applied for compariso. Load weight i the referece[1] is P=6130N. The cross area of the track rope is A 0 =89.95mm, weight of uit legth is q 0 =7.0N/m, elastic module E=90GPa. The cableway set up for testig is two spa with sigle track rope. Testig data are complete i the first spa of the cableway. The horizotal spa of first spa is l=70.9m, height differece h=15.m. This paper selects the testig data with deflectio coefficiet S f =f/l=0.05 for compariso ad validatio. Table 1. Testig Compariso ad Validatio Compariso items Test value Calculatio value Error % 5

7 MATEC Web of Cofereces 8, (016) DOI: / mateccof/ DME Coclusios The track rope is a importat weight bearig member i the cargo cableway, its shape ad tesio calculatio relatioship is directly related to speciatio ad model selectio of the track rope, etc. This paper establishes the balace equatios of the elastic track rope uder the multiple cetralized loads based o the cateary equatio of the elastic track rope. The formatio of equatios is brief ad the structure is clear. The Newto iteratio method is applied to calculate the equatios, i which calculatio quatity is small, ad accuracy of result is high. Through compariso with result data i other referece documets, reliability of the calculatio method i this paper is validated, which ca meet with requiremet of desig ad egieerig safety i the cargo cableway. Refereces 1. Zheg Lifeg. Theory study of cableway o the cateary method [J]. Fujia: Fujia Agriculture ad Forestry Uiversity CEN Chagsog, CEN Zhegqig, YAN Doghuag. Accurate iteratio method to calculate the iitial [J]. Egieerig Mechaics, 006, 3(8): 6~ QIN Jia, XIA Yogju. The matrix iteratio method for aalysis of suspesio cable based o segmetal cateary theory [J]. Chiese Joural of Egieerig Desig, 013, 0(5): 404~ Qia Chagzhao, Che Chagpig, Che Zili. Direct solutio procedure obtaiig the lie shape of cable with segmetatio parabolic fuctio [J]. Joural of Xiame Uiversity of Techology, 01, 0(3): 71~ Zhou Xiia, Zha Zhegyi. The system of multi-spa cableway desig based o parabola method (JIA SI) [J]. Joural of Zhejiag Forestry College, 000, 17(1):50~ Ahmadi-Kashai, K. Represetatio of cables i space to uiformly distributed loads [J]. Iteratioal Joural of Space Structures, 1988, 3(4): 1~ Zhag Qili, Zhag Li, Zhou Dai, U.Peil. Fem with Splie Fuctio for Noliear Aalysis of Cotiuous Log Cables [J]. Egieerig Mechaics, 1999, 16(1): 115~1. 8. Tag Jiami, Zhao Yi. A Euler Geometrically No-liear Fiite Elemet Method with Twoode Cable Elemet for the Aalysis of Cable Structure [J]. Shaghai Joural of Mechaics, 1999, 0(1): 89~ Yua Xigfei, Dog Shili. A two-ode curved cable elemet for oliear aalysis [J]. Egieerig Mechaics, 1999, 16(4): 59~ Yag Meggag, Che Zhegqig. Noliear aalysis of cable structure usig a two-ode curved cable elemet of high precisio [J]. Egieerig Mechaics, 003, 0(1):4~ Zhag Zhiguo, Ji Migju, Zou Zhezhu. Static solutio of suspesio cables uder tare load [J]. Chia Railway Sciece, 004, 5(3): 67~ Bai Xuesog, Miao Qia. Research o calculatio model based o suspesio cable theories i costructio cargo cableway [J]. Power System Techology, 008, 3(0): 90~94. 7

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