two variable real-time algorithm for cone crusher control abstract ...

TWO VARIABLE REAL-TIME ALGORITHM FOR CONE CRUSHER CONTROL Erik Hulthén, M.Sc. and C Magnus Evertsson, Ph.D. Department of Product and Production Development Chalmers University of Technology, SE 41296 Göteborg, Sweden

ABSTRACT Cone crushers are used in the mineral, mining, and aggregate industry for fragmentation of rock materials. Control systems for cone crusher setting (CSS) are widely used to compensate for wear and to protect the crusher. With a frequency converter the eccentric speed in a cone crusher can be adjusted in real-time. The eccentric speed of the main shaft affects the number of compressions the material is exposed to and thus the capacity and the particle size distribution of the product. By applying mass-flow sensors to the process, a feedback of the different product yields is obtained in every moment. In this paper, a model and an algorithm are presented. The algorithm takes the incrementally increasing CSS into account and compensates for this with a successively changing eccentric speed. In order to implement the algorithm, a monitoring and control system is developed, including the online algorithm for selection eccentric speed. The different product flows from the crushing plant are continuously monitored by mass flow meters. The fitness function is set by the plant management depending on production targets and market situation. An earlier developed Finite State Machine (FSM) Algorithm is also implemented and evaluated in the system. The developed algorithm has been validated and verified at a crushing plant for aggregates with a production of around 400 kton a year. The new algorithm is shown to increase the crushing stage throughput with 6.9 %. The FSM algorithm, on the other hand, increases the throughput with 5.3 %, which is a confirmation of the magnitude of its benefits demonstrated in an earlier paper. Keywords: Cone Crusher, Control Algorithm, Eccentric Speed, CSS

INTRODUCTION Cone crushers are widely used for the size reduction of rock materials, such as aggregate products or ores, into finer fractions. Their main operating principle is the same today as when developed, a century ago. As the mantle and the concave get worn, the distance between them must be adjusted in order to maintain the reduction ratio and control the top size and particle size distribution of the product. Control systems for cone crushers, introduced in the 1960ths, are therefore widely used to compensate for wear and to protect the machines from overloads. However, several crusher types, e.g. Symons 7’, HP, etc., are often not equipped with this kind of system, and even if they are, these systems require the feed to be stopped before the adjustment of the CSS can take place. During this time, no material is produced. This is the main reason why the CSS is adjusted anything between four times a day to once a week. In the time between each adjustment, the crushers are thus run at non-optimal, incrementally increasing CSS. D.1

The speed of a cone crusher can typically be adjusted by changing the pulleys of the belt drive. This is both labour- and time-consuming, and is therefore not done unless necessary. Moreover, most crushing plants have no accurate nor reliable way of monitoring the changes in production which is implied by speed changes. While taking repeated belt cuts is one test strategy, this is nevertheless very time-consuming. It requires additional sieving, and is nonetheless still just a single sample that must be combined with further samples for an accurate assessment. However, the eccentric speed does have a significant impact on the product of a cone crusher. The speed affects the number of compressions that the material is exposed to and thus affects the particle size distribution of the product. Similarly, the speed also affects the shape of the product. This issue is however beyond the scope of this work. Capacity, on the other hand, is also directly affected by the speed. Figure 1 shows a comparison between different closed side settings (CSS) and eccentric speeds. While the CSS tend move the particle size distribution of the product horizontally, the eccentric speed tends to rotate it.

Figure 1 – Resulting particle size distribution of a cone crusher with different parameters, varying a) the closed side settings and b) the speed.

By applying a frequency converter, it has become possible to continuously adjust the eccentric speed of the cone crusher. Frequency converters have decreased in cost during the last years, making them more available for use in standard cone-crushing operation. By using sensors to gain feedback on the process, the crusher can be adjusted to run optimally at each and every moment. A conveyor-belt scale, for instance, can easily retrieve and transmit information about the mass flow to a computer. A cost-effective alternative is to monitor the current capacity by measuring the power draw on an inclined conveyor belt that is performing a lifting work. Such a sensor can be obtained for about one-tenth of the cost of a traditional belt scale. This principle is described by Hulthén and Evertsson [3]. By directly monitoring the sellable products after a screen, the control system can control the output particle size distribution of a crushing stage (Figure 2).

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Figure 2 – Illustration of a mass-flow meter, e.g. a conveyor-belt scale, which is attached to the different outputs from the screens. The computer then estimates the particle size distribution (PSD). PSDs at six different times are shown here. As evident the reduction decreases as the liners wear.

In earlier papers, [4] and [2], have worked with one variable at the time, namely eccentric speed and CSS, respectively. Then a simple model is assumed: ‫ݕ‬ො ൌ ܽ ൅ ܾ‫ݔ‬ଵ ൅ ܿ‫ݔ‬ଵ ଶ

Equation 1

where ‫ݕ‬ො is the crushing stage output, ‫ݔ‬ଵ the studied variable and ܽ, ܾ and ܿ are constants, respectively. The form of this equation was chosen because of the behaviour of the process with a re-circulating load; a combination of reduced crusher capacity and increased crushing, or verse vice. In order to find an optimum (although momentary) and maintain the found optimal setting for that moment, an algorithm based on a Finite State Machine (FSM) is used. In the 1970’s, Karra [5] performed a large number of tests on cone crushers with different parameter settings, including various eccentric speeds. However, those tests did not show any significant effect from the eccentric speed on the particle size distribution, nor on the capacity. The lack of effect can possibly be attributed to a number of reasons; one being that the effects from other parameters were much larger. The lack of an accurate procedure for long-term evaluation is another explanation.

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There are, however, models where the eccentric speed is predicted to affect both the particle size distribution and the capacity, e.g. [1]. Nonetheless, studies to find the best constant speed for cone crushers are rare. Studies of continuous regulation of crushers during operation are even rarer. No reference regarding online speed optimization has thus been found. The objective of this paper is to introduce a model and a speed selection algorithm, which considers the continuously increased CSS on some crushers.

A TWO VARIABLE MODEL Similar to the earlier papers, [4] and [2], the output for the applied model is the mass flow of the products coming out of the crushing stage, i.e. it is assumed that the crusher is operated in closed circuit. This implies that all particles that are not crushed to a small enough size will be re-circulated back to the crusher and will thus affect the overall capacity negatively. For a given CSS, the model in Equation 1 is a good approximation of the crushing stage output. In the same way, for a given speed the same model appropriately describes the behaviour of the crushing stage at varying CSS. For a crusher without a continuously working control system, on the other hand, the CSS is not a fully operational parameter, i.e. it naturally increases over time and costs production capacity for adjusting it. In order to model something directly measurable, while assuming that the CSS adjustment results in the same CSS every time, the time since last adjustment can be the studied variable. The assumed model is then ‫ݕ‬ො ൌ ܽ ൅ ܾ‫ݔ‬ଵ ൅ܿ‫ݔ‬ଶ ൅ ݀‫ݔ‬ଵ ଶ ൅ ݁‫ݔ‬ଶ ଶ ൅ ݂‫ݔ‬ଵ ‫ݔ‬ଶ

Equation 2

where ‫ݕ‬ො is the crushing stage output, ‫ݔ‬ଵ the eccentric speed, ‫ݔ‬ଶ the time since last CSS adjustment and ܽ െ ݂ are constants, respectively, see (Figure 3).

Figure 3 – The suggested and fitted model for the crushing stage performance looks like a loaf. The parameters are speed and time since last Closed Side Setting (CSS) adjustment.

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FULL SCALE TESTS The developed algorithms were tested at a crushing plant in Uddevalla, 80 km north of Gothenburg. The crushing plant is owned and operated by NCC Roads. The plant produces high quality aggregates products, ranging from 0-2 mm to 16-32 mm size fraction in its tertiary crushing stage. The applied crusher is a Nordberg HP4 equipped with a fine chamber. The feed size to this tertiary crushing stage is 16-70 mm. The crusher is equipped with a system for manual adjustment of the CSS. The cone crusher was also equipped with a Control Techniques Unidrive SP frequency converter, which allowed step-less changes of the eccentric speed of the crusher. After the crusher, the screens are classifying the product into the size fractions of 0-2 mm, 2-5 mm, 5-8 mm, 8-11 mm, 11-16 mm, 16-22 mm and +22 mm. The +22 mm material is always returned to the crusher in a closed circuit. All products at sizes from 5 mm and upwards can be returned in a closed circuit at 0, 50 or 100% re-crushing. During the final test runs, 100 % of the product 8-11 mm was re-circulated back to the crusher. An outline of the plant can be seen in Figure 4. In total, ten conveyor belts have mass-flow meters monitoring the electrical power draw. The power is measured with power transducers (Carlo Gavazzi WM-14 adv DIN) which can deliver information to a computer, where the actual capacities are calculated. The algorithm was implemented in a computer that could communicate with the frequency controller, retrieve data from ten mass-flow meters in the process, and also interact with the operator. To this an HMI/Scada system was developed for convenience and for communication with users, see Figure 5. Thanks to the ten mass flow sensors, all materials flows can be monitored by the operators in real-time.

Figure 4 - Tertiary crushing stage at NCC Roads' plant in Uddevalla. The plant has six profitable products. The oversize particles are re-circulated to the crusher.

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Figure 5 – An HMI/Scada system for the monitoring and control system was developed for convenience.

Test period The early pre-test experiments were conducted during the first half of 2009. The final tests were done from October 23rd to November 13th 2009. During this period of time, all operation of the crushing stage was recorded, resulting in 680 short evaluation periods each lasting for 120-400 s. The performance of the plant is here defined as the crushing stage throughput, i.e. the crusher throughput reduced with the circulating load.

Finite State Machine Algorithm The Finite State Machine (FSM) algorithm described by [4] was implemented. It is simple variant of FSM called the Mealy machine [6], in which actions only take place on the entry of a state. The exit of a state is conditioned but brings no actions. The FSM was developed manually (in contrast to a computer-generated algorithm) to find a speed close to the optimal value and to maintain at that speed for a time period.

Function adaption The coefficients in Equation 2 were fitted to the test results from the first half of the test period (441 evaluation periods) with a genetic algorithm (GA), described by Wahde in [7]. ିଵ The fitness for the GA was taken as ݁௥௠௦ ., where ݁௥௠௦ is the root mean square of the error D.6

between the function, ‫ݕ‬ො, and the measurements. The adapted function can be seen in Figure 3. The coefficients ܽ െ ݂ were 235.7932, 149.0957, 57.7275, -149.6255, -0.8789 and -65.6250 respectively.

The “Loaf” Algorithm The FSM algorithm assumes that the optimal speed for every CSS forms a “loaf”-like landscape, and “walks” on top of this loaf back and forth, trying to stay as close to the top as possible. However, this search for the maximum performance costs in term of nonoptimal operation. Therefore, by identifying the maximum of the function at every CSS, the optimal eccentric speed path can be determined.

Best fixed speed During the trial runs with the FSM algorithm, the results from different eccentric speeds were recorded. Thus, to compare the FSM algorithm and the so called “loaf” algorithm (described below), these trial results were sorted according to speed. The CSS of the tested crusher is typically adjusted every two hours. Thanks to the amount of obtained data during the trial tests, complete data series of two hours operation at fixed eccentric speeds could be assembled. The speeds, which were then compared with one another as well as the algorithms, were 838, 876, 914 and 952 rpm.

RESULTS The results in this chapter refer to the 7200 s operation if not stated otherwise, which implies a calibration at every two hours. The results from the first 441 runs, ordered according to the eccentric speed, can be found in Table 1. It is evident that if one fixed drive shaft speed had to selected, it should be around 876 rpm. The average result from operations at this speed, i.e. 245.5 tph, is 10.8 % better than the original eccentric speed, i.e. 221.5 tph. Table 1- The results from the trial test runs ordered according to the eccentric speed. Average performance up to Speed

3600 s

7200 s

838 rpm

236.3 tph

233.6 tph

876 rpm

246.7 tph

245.5 tph

914 rpm

243.0 tph

236.4 tph

952 rpm

225.1 tph

221.5 tph

The result from the evaluation test runs can be seen in Figure 6. In Table 2 these three results are compared with the calculated results from trial period. The fixed speed was tested during one hour operation, which resulted in 258.5 tph which is about 5 % better than the corresponding result from the 441 periods from the trial runs. The implementation of the FSM algorithm resulted in 258.4 tph, which is 5.3 % better than the best fixed speed, i.e. 876 rpm. Already in the function adaption, Figure 3., it can be seen that the optimal speed during the continuous wear of the crushing chamber is not fixed. The virtual “loaf” is D.7

not in parrallel with the t time axxis. The te est with this algorithm m gave the e result of 262.5 tph, which is 6.9 % bettter than the t best fixed speed d and also o 1.6 % b better than n the FSM M algorithm.. Table 2 - Th he results fro om the all tesst runs, the tw wo first are from fr the trial runs and the e rest from th he final evaluation runs. r Average e performan nce up to Method Calculated 952 9 rpm (orig ginal) Calculated 876 8 rpm (besst fixed) Fixed 876 rp pm FSM algoritthm Loaf algorith hm

3 3600 s 225.1 tp ph 246.7 tp ph 258.5 tp ph 271.7 tp ph 285.0 tp ph

7200 s 221.5 tph 245.5 tph 258.4 tph 262.5 tph

f the diffe erent final tessts. The lines s with diamo onds, boxes a and triangles s represents Figure 6 – The results from a the e Finite State e Algorithm (FSM) ( algoritthm and consstant speed 876 rpm, the runss of the loaf algorithm, respectively y.

CONCLU USIONS In this pap per, it has been show wn that a fixed f eccentric speed d in a cone e crusher is far from m optimal. The T explan nation for this t is that the crusher mangan nese linerss wear con ntinuously. One mustt thus ask the questtion: How could c a fix xed eccenttric speed ever be th he best? Iff so, it musst be selectted after on n-site trialss and evalu uation. Succh on-site trials have e obviouslyy

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not been carried out correctly at this site, since the performance at the original speed was significantly poorer. The earlier presented FSM algorithm, [4], performed 5.3% better than the best fixed speed, which confirms the old result (4.2 %). The new “loaf” algorithm performed even better, 6.9 %. Long time test of the new algorithm is, however, still desirable. Future work includes a CSS adjustment alarm to an operator or a control system in order to optimise the CSS adjustments.

ACKNOWLEDGEMENTS The authors wish to thank the Development Fund of the Swedish Construction Industry (SBUF), the Swedish Mineral Processing Research Association (MinFo), the Ellen, Walter, and Lennart Hesselman Foundation for Scientific Research and the Swedish national research program MinBaS (Minerals, Ballast and dimensional Stone) MinBaS for financial support. NCC Roads and their personnel in Glimmingen, Uddevalla are gratefully acknowledged for all their support.

REFERENCES [1] [2] [3]

[4]

[5]

[6] [7]

C. M. Evertsson, Cone crusher performance, Ph.D. thesis, Chalmers University of Technology, Goteborg, Sweden, 2000, pp. 1-49. E. Hulthén and C. M. Evertsson, Algorithm for dynamic cone crusher control, Minerals Engineering, 22 (2009), pp. 296-303. E. Hulthén and C. M. Evertsson, A Cost Effective Conveyor Belt Scale, 11th European Symposium on Comminution, The Hungarian Chemical Society (MKE), Budapest, 2006. E. Hulthén and C. M. Evertsson, On-line Optimization of Crushing Stage using Speed regulation on Cone Crushers, XXIV International Mineral Processing Congress, Beijing, China, 2008, pp. 2396-2402. V. K. Karra, Process performance model for cone crushers, XIV International mineral processing congress, CIM, Montreal, Que, Canada, Toronto, Canada, 1983, pp. III 6.1 - III 6.14. G. H. Mealy, A Method for Synthesizing Sequential Circuits, Bell System Technical Journal, 34 (1955), pp. 1045–1079. M. Wahde, An introduction to adaptive algorithms and intelligent machines, Göteborg, 2002.

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