by J GOTTVALD · Cited by 16 — Abstract: – Tangential digging force is one of the basic descriptive parameters of bucket wheel excavators. (BWE). Knowledge of factors that influence its
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Variance-Based Sensitivity Analysis of Tangential Digging Forces of the Bucket Wheel Excavator SchRs 1320 JAKUB GOTTVALD Vítkovice ÚAM a.s. Mezírka 775/1, 602 00 Brno CZECH REPUBLIC jakub@gottvald.eu http://www.vitkovice.com ZDENEK KALA Department of Structural Mechanics Brno University of Technology, Faculty of Civil Engineering Veveí Str. 95, Brno CZECH REPUBLIC kala.z@fce.vutbr.cz http://www.vutbr.cz Abstract: – Tangential digging force is one of the basic desc riptive parameters of bucket wheel excavators (BWE). Knowledge of factors that influence its value is necessary for correct design of bucket wheel and its motors with gearbox. Presented paper deals with sensitivit y of vary parameters during mining to total tangential force. Analyses were made for BWE SchRs 1320. On th is BWE parameters were measured during mining that were used to sensitivity analyses. Key-Words: – Sensitivity analysis, Digging force, Bucket wh eel Excavator, Measurement, SchRs 1320, Sobol 1 Introduction The new coal brown pockets are not so well mineable as the previous ones. Pockets are usually covered by huge mass of overburdens, which are very hard for mining. Subsequently the rate between mined coal and overburden increases. Geologic conditions change to worse, too [1, 2]. These facts are of a big influence on costs of mined products. It is desirable to focus on optimisation of energy needed to mining and on optimisation of maintenance and operations of BWEs [3, 4]. Consequences of failures [5-7] of BWEs are huge and repairs of machineries are connected with big investments and substantial loss of profit. Failures of steel structures and components of BWEs are mainly caused by fatigue. Steel structures are loaded by vibrations that are produced by digging forces. While designing BWE and consequential process of tuning of dynamical behaviour possible resonation of natural frequencies of BWE with frequency of mining forces are solved [8, 9]. For proper design of motors with gearbox of bucket wheel right values of digging forces are needed. Digging forces depend on geological parameters of mined overburden, on design of BWE, on mining method and parameters (dimensions) of terraces in working faces. In this paper results of sensitivity analyses of varying parameters during mining to total tangential force are presented. Analyses were made for BWE SchRs 1320 that works in Tuıimice open pit in the Czech Republic, see Fig. 1. Fig.1: Bucket wheel excavator SchRs 1320 2 Calculation of Tangential Digging force The calculation of tangentia l digging force is based on calculation of power of drive of bucket wheel:
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kgrgesgrgrgesRPF (1) Where Pgr is power which is needed to overcoming of tangential component of digging resistance; grges is effectivity of digging process; is angular velocity of bucket wheel and Rk is radius of bucket wheel over the bucket. Power Pgr we can calculate by: Lzh grPPPPP (2) Where Ph is power which is needed to transport of material to place where buckets are emptying; Pz is power needed to overcoming of friction of thrust journal; PL is power to overcoming of friction between soil and ring of bucket wheel. Drive of BWE SchRs 1320 is consisting of two motors Siemens ARNR 630Y-6. Total power of these motor is: pm mp PP cos (3) Were Pp is sum of incoming power of both motors of bucket wheel; is m effecivity of electro motors; cosm is power factor of electro motors; p is effecivity of gearbox of bucket wheel. Power Ph [10] for transport of material is possibly calculated by: thF PhhgF h (4) Where FgF is lifting force; hh is median height of material lifting; h is effecivity of lifting and tis time of lifting. The lifting force FgF by [10] can by calculated by: hsbF gF (5) Where s is cutting depth; b is cutting width and h is height of terrace and is specific weight of soil. Lifting time t is calculated from parameters of gearbox and measured revolutions of motors of bucket wheel. On BWE SchRs 1320 we do small inaccuracy by this access because in this case resulting revolutions can be influenced by fluid couplings Rexnord that are situated between motors and gearbox. But this inaccuracy is not so significant in this case. Equation for lifting time is: 26205.17260 mnt (6) Where nm is average revolutions of motors. Median height of material lifting in accordance with [10] is calculated by: 2maxyhh Eh (7) Where height ymax is value from equation (9) for maximum angle which determinate from equations: for kRh iskkRhR arccosmax (8a) for kRh is 90max (8b) for kRh is kkRRh arcsin90 max (8c) cos2 sRRy kk (9) The total height hE [10] of lift establish from equation: 1, 180cos vvkE RRh (10) Where Rv is internal radius of the bucket wheel and1, v is angle of the point where starting emptying of the bucket [11]. BWE SchRs 1320 mining overburden that consist of clays. These clays form blocks during mining so in this case we use equations (13) and (14) for determining angle that is delay of emptying of bucket. This angle we added to angle v,1, see equations (11) and (12) and Fig. 2 [11]. Fig.2: Geometry of emptying of bucket 1,1, vv (11)
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gRvv21, arccos180 (12) vvzRacos.2 arcsin2 (13) zvvvvgR 111, 1, 2tansinarctan90 (14) Where az is size of blocks of mined material; is angle of tilt of bucket wheel boom; z is friction angle of soil. Angular velocity of the bucket wheel we calculate from measured revolutions of bucket wheel motors. Is a same case as calculation of lifting time (6). For BWE SchRs 1320 can be calculated by: 05.17260 mn (15) Mutual relation between angular velocity and tangential speed of bucket wheel is: kR (16) The power Pz in our case was establish by experiment. It was measured input power of motors of bucket wheel during free rotation of bucket wheel. For measured values same calculation is valid as (3): pm mZpZ PP cos (17) Where Pzp is measured input power of motors of bucket wheel during free rotation of bucket wheel. Power PL we can calculated from equation from [10]: fhbsP L (18) Where f is coefficient of friction. 3 Measurement on the BWE On the BWE a lot of data for needs of operative system about operating and behaviour of machine or his devices are measured. For needs of sensitivity analysis of tangential digging force values that are shown in Table 1 were used. On the BWE SchRs 1320 was held up logging of these operating parameters to hard disk of PC of operative unit. Frequency of data logging was 1 s that was determined by data bus line on BWE. Table 1: Measured values Value Dimension Input power of bucket wheel motor 1 [kW] Input power of bucket wheel motor 2 [kW] Revolutions of bucket wheel motor 1 [min-1] Revolutions of bucket wheel motor 2 [min-1] Horizontal situation of bucket wheel boom [°] Vertical situation of bucket wheel boom [°] Distance moved by BWE [m] Data saving was held during one month. For our sensitivity analysis one day measure was selected. Fig. 3 illustrates plotted data on horizontal and vertical situation of bucket wheel boom and on distance moved by BWE. During this day whole block was mined out by terrace cutting method. Massive block was about a size of 20.5 m. This block was mined out in four terraces. Dimension of particular terraces was 7.19 m, 5.08 m, 5.28 m and 3.17 m, see Table 3. Fig.3: Day record of mining 4 Sensitivity Analysis The sensitivity analysis studies the relationships between information flowing in and out of the model [12]. The information on problems, methods and applications of the sensitivity analysis of steel structures and stability is presented, e.g. in [13-22]. For calculation of influence of random inputs X i to tangential digging force Y (output quantity) sensitivity analysis by Sobol was used [23, 12]. Sobol™s first order sensitivity indices may be written in the form: YV XYEV Sii (19) Analogously as (19) we can write the second order sensitivity indices:
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ji ji ijSS YV XXYEV S , (20) Sensitivity index Sij expresses the influence of doubles on the monitored output. Other Sobol™s sensitivity indices enabling the quantification of higher order interactions may be expressed similarly [12]. The Monte Carlo method was applied. The variance V(Y) of tangential digging force is calculated under the assumption that all the input imperfections are consider ed to be random ones; one million simulation runs were applied. The conditional random arithmetical mean iXYE was evaluated for N=20000 simulation runs; the variance iXYEV was calculated for N=20000 simulation runs, as well, i.e. the numerical demanding difficulty of the calculation is N2. It was preceded similarly when calculating the second order indices (20). Other Sobol™s sensitivity indices enabling the quantification of higher order interactions may be expressed similarly. 1123 MiijjkijkiijijiiSS SS (21) The number of members in (21) is 2 M-1, , i.e., for M=3 obtain 7 sensitivity indices S1, S2, S3, S12, S23, S13, S123; for M=8 obtain 255 sensitivity indices. It is so much for practical usage. The main limitation in the determination of all members of (21) is so much high numerical demand of their computation. 4.1 Inputs In Table 2 constant parameters are presented that were used in calculation of tangential digging force of BWE SchRs 1320. Table 2: Constant parameters of BWE SchRs 1320 Symbol Value Dimension grges 90 [%] m 96.5 [%] p 95 [%] h 90 [%] cosm 0.85 [-] f 0.5 [-] Rk 6.25 [m] Rv 5.45 [m] g 9.81 [m.s-2] Height of terrace h and angle of tilt of bucket wheel boom are values that are constant during terrace. See Table 3 for details. Table 3: Values of h and for terraces Terrace h [m] [°] First 7.185 3.972 Second 5.084 -2.866 Third 5.278 -9.707 Fourth 3.172 -14.900 4.1.1 Input random variables Results of statistical evaluation of measured values are written in Table 4 (results for first terrace), Table 5 (results for second terrace), Table 6 (results for third terrace) and Table 7 (results for forth terrace). In tables statistical values of z, az and that were measured during power testing of BWE SchRs 1320 are mentioned. Result of this test is available by owner of BWE. Table 4: Random variables for first terrace SymbolDimension Distribution Mean valueStd. deviation nm [min-1] Gauss 797.799 3.498 Pp [W] Gauss 820641 143621 PZp [W] Uniform 49500 6639.53 b [m] Gauss 0.158 0.053 z [°] Uniform 30 5.77 [N.m-3] Gauss 19559 875.77 az [m] Lognormal 0.4 0.15 s [m] Hermit 0,377 0.094 Skewness Kurtosis -1.66 5.44 Table 5: Random variables for second terrace SymbolDimension Distribution Mean valueStd. deviation nm [min-1] Gauss 978.733 4.536 Pp [W] Gauss 1227430 151649 PZp [W] Uniform 75500 18186.5 b [m] Gauss 0.155 0.047 z [°] Uniform 30 5.77 [N.m-3] Gauss 19559 875.77 az [m] Lognormal 0.4 0.15 s [m] Hermit 0.506 0.138 Skewness Kurtosis -1.224 3.445 Table 6: Random variables for third terrace SymbolDimension Distribution Mean valueStd. deviation nm [min-1] Gauss 997.694 10.890 Pp [W] Gauss 1244370 219840 PZp [W] Uniform 75500 18186.5 b [m] Gauss 0.185 0.052 z [°] Uniform 30 5.774 [N.m-3] Gauss 19559 875.77 az [m] Lognormal 0.4 0.15 s [m] Hermit 0.367 0.104 Skewness Kurtosis -1.860 6.929
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Table 7: Random variables for forth terrace Symbol Dimension Distribution Mean value Std. deviation nm [min-1] Gauss 997.46 10.74 Pp [W] Gauss 1313200 223770 PZp [W] Uniform 75500 18186.5 b [m] Gauss 0.148 0.041 z [°] Uniform 30 5.773 [N.m-3] Gauss 19559 875.77 az [m] Lognormal0.4 0.15 s [m] Hermit 0.587 0.174 Skewness Kurtosis -1.826 6.098 5 Sensitivity Analysis Results The results of the tangential digging force sensitivity analysis are presen ted in Fig. 4, Fig. 5, Fig. 6 and Fig. 7. Fig.4: Sensitivity analysis for first terrace Fig.5: Sensitivity analysis for second terrace Fig.6: Sensitivity analysis for third terrace Fig.7: Sensitivity analysis for forth terrace 6 Conclusion The results have shown that input power of motors of bucket wheel have dominant influences to tangential digging force. For better analyses of influence of other parameters it will be better to think the input power as non random variable and it will order as constant. We achieve high transparency in description of influence of other variables by this access. Result of analysis for second terrace cutting depth s and cutting width b are of higher influence. Influence of these parameters b and s will be subjects of other analyses of different heights of terrace h. In this case heights correspond with those actually measured while mining, these heights of terraces are very different and subsequent mutual comparison of these results between terraces is difficult. The article was elaborated within the framework of projects of AVR IAA201720901 and MSM0021630519.
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