CRUSHING PLANT PERFORMANCE OPTIMIZATION

Per Svedensten, Plant Simulation Specialist

Sandvik Mining and Construction, Svedala, Sweden

per.svedensten@sandvik.com

ABSTRACT

The crushing plant system of crusher, screens, conveyors and other equipment can be difficult

to operate with the highest possible efficiency. To assist it the optimisation of the crushing

plant process a new computer tool has been developed. The normal procedure in a crushing

plant to study and improve the process is by means of measurements, rules of thumb, and

visual observations. These tools and methods are inadequate for a more advanced analysis of

the complex process that characterises many crushing plants. In order to improve the process,

both technical and economic factors must be taken into account. Normal simulation software

does not provide sufficient support for such tasks.

The developed optimisation method utilise both technical and economic calculations in order

to find the most profitable solution. The aim of the optimisation is to maximise the gross

profit of the crushing plant. The gross profit is calculated by subtracting the production costs

from the income. The production cost is calculated using the process accounting method. This

method is based on a fixed and variable operating cost for all machines. The production cost

of a product is calculated by adding the operating cost of all production units that has been

used. This result in a more accurate calculation of the production cost of all product. It is

important to be able to calculate the production costs of the products since this together with

the sales price gives a clear picture of the different products profitability.

In many crushing plant the particle shape is an important customer demand. A model that

predicts the particle shape of the final products has been developed and implemented. This

model predicts the particle shape over the entire gradation produced by a crusher. This allows

for the particle shape of the final product to be predicted. The model is mainly depending on

feed gradation and crusher setting. The optimisation routine will therefore be able to find the

best machine parameter settings in the plant. The optimum setting will maximise the gross

profit and produce products with the required quality.

From this work it can be concluded that it is important to be able to adjust the equipment

correctly. Viewing the crushing plant as an industrial process clearly shows that it is not the

individual machines that need to be optimised. In fact, just optimising a machine will not

necessarily be beneficial for the crushing plant. Automating the adjustment of the plant is

therefore crucial to ensure that the plant is operating at its peak performance. This is

especially important when product demand changes over time.

All methods were developed for use on a standard personal computer. The combination of

modelling, simulation and optimisation is useful for design and operation of a crushing plant.

The methods can also be used for education and training purposes. Optimisation generally

provides new insights into how to operate the crushing plant process more efficiently.

INTRODUCTION

The performance of a crushing plant is highly dependent on how the production units are

configured. Finding the optimal setting of the plant is very difficult without an optimisation

tool specially developed for crushing plants.

Today there are a number of simulation tools on the market. There are some simulation tools

with very simple optimisation features. The optimisation that can be conducted is

maximisation of one product. This type of optimisation is hard to utilise in most crushing

plants since maximisation of one product will not be optimal for the economic situation of the

plant. Usually there are more then one product that are profitable so maximising one product

will decrease the production of other profitable products giving a sub-optimal total production

of all products. Since the models used not take economics into account the maximisation of

one product might also increase the production cost.

MODELLING OF CRUSHING PLANTS

Crushing plant layout differs a great deal from site to site. Plants are designed differently due

to variation in the type of rock, the use of the products, the size of the quarry, plant history

and many other factors. The plant model is formed by connecting the various production unit

models to each other. The rock material feed is defined and used as input. In order to optimise

the plant it is necessary to have detailed information about the operating cost of each

production unit. Finally the product demand sequence, desired product quality, and product

price must be defined.

PRODUCTION UNITS

The plant design comprises a number of different production units. A production unit is

defined as a machine or larger arrangement used to move, store, separate or crush material in

the crushing plant. A production unit can be a crusher, screen, feeder, storage bin, stock pile,

or conveyor. Each production unit is represented by a model, which can be used to predict the

performance of the individual unit. The models are then connected, which means that the

predicted production of one of a production units serves as input for the following unit. The

crushing plant model forms a grid of production units connected to each other in accordance

with the plant layout. Connecting models places demands on the individual unit models.

Besides predicting the performance of the individual machine and the amount of material that

will be produced, it must also predict information about the rock material that is of

importance for the subsequent units. In other words, it is essential that the models are

compatible with each other. There are many individual unit models that are good at predicting

the performance of the machine in question, but not well suited for implementation in a

crushing plant simulation program. Some types of screen models are a good example of this.

Production units such as crushers, screens and feeders can be configured differently, which

changes their performance and thereby crushing plant performance. This paper focuses on

parameters that can be easily changed during normal operation and that have a large influence

on plant performance. Crusher close side setting (CSS) and feed rate on feeders can be

changed within minutes and are therefore suitable for production scheduling. Other

parameters such as screen media, crusher throw and crusher mantle selection are decided in

advance and not included in the optimisation. Hence plant performance depends on the vector

of design parameters x. This vector has two main parts: variable parameters xij, and static

parameters yik. Here i is the unit number, j the variable parameter number and k the static

parameter number. The plant consists of n production units. The production unit has m

variable parameters and p static parameters. This forms the input vector x to the system:

1 2

1 2

1,1 1,2 1, 2,1 2,2 2, ,1 ,2 ,

1,1 1,2 1, 2,1 2,2 2, ,1 ,2 ,

, ,..., , , ,..., ,..., , ,..., ,...

..., , ,..., , , ,..., ,..., , ,...,

n

n

m m n n n m

p p n n n p

x x x x x x x x x

y y y y y y y y y

=x

ROCK MATERIAL

As mentioned in the previous section, information about the rock material is transferred

between the different production unit models and should include all details necessary to

predict production unit performance. Most important is the amount of material and its particle

size distribution, but the Bond work index, moisture content, abrasion index, clay content and

so on are also necessary.

ECONOMICS

As stated in the introduction, economics are essential for the optimisation. The whole purpose

of the plant is to earn a profit for its owner by supplying material to the customer. Economic

calculations are necessary in order to evaluate how effectively the plant operates. Predicting

the economic performance of a plant is difficult and an economic model is therefore needed.

Two different aspects must be borne in mind when designing such a model; simplicity, so that

the required information can be easily found or calculated and detail, as the model has to be

detailed enough to respond to any changes made in the plant. It was therefore decided to use

the process cost accounting model (Dearden, 1988), which consists of two costs; a fixed Chour

and a variable Cton(x). The main part of these costs have to be calculated manually. The

amount of material passing through the unit is also needed and denoted ( ),rock im x& . The total

production cost per ton Ctot,i(x) for unit i is calculated using the following equation:

( ) ( )( ),

, ,

,

hour i

tot i ton i

rock i

CC C

m= +x x

x&

CUSTOMER DEMANDS

The quality of the products is of great importance, as if they do not fulfil customer demands

they cannot be sold. The optimisation must produce solutions where all products meet the

quality demand, the most important of which is the limitation of misplaced particles. A

product with many particles outside the fraction limits cannot be sold, thus it is essential that

the optimisation model can predict this.

OPTIMISATION

To find the optimal performance of the crushing plant model an optimisation routine is

needed. This routine will with the information generated by the simulation routine the

solutions that will maximise the cost function. The optimisation problem can be classified as

large and discrete. It does not have a large number of parameters but there are a large number

of combinations of setting for the plant. There are a number of different optimisation routines

suited for these types of problems; simulated annealing, tabu search, genetic evolutionary

algorithms and more. They have all been used to solve optimisation problem similar to this. In

this work the Probabilistic global search Lausanne (PGSL) has been chosen. This was done

after a selection process where the PGSL algorithm was found to be one of the most suitable

with the best performance. The selection criteria for the optimisation algorithm are the

following:

• The main objective in the selection process was of course a good probability of

finding the global optimum.

• Good scalability, i.e. the optimisation routine must work without any changes for

different number of optimisation parameters.

• User independency, i.e. the optimisation routine does not depend on any start guess

or optimisation parameter change provided by the user.

• Optimisation iterations, number of runs before the optimal solution is found.

CONSTRAINTS

For the optimisation of a crushing plant there are constraints that will restrict the solutions

space. The type of constraints can be divided into two types. There are constraints that can be

checked without a simulation and those that need a simulation to be carried out. Most

constraints related to production unit adjustment can be checked without performing a

simulation, although model constraints such as feed size restrictions on some units will

require a simulation, as it will prevent the preceding crusher from running with a large CSS.

All constraints will yield the admissible set of parameter values, which are denoted Ωx.

COST FUNCTION

The cost function used for the optimisation calculates the plant performance during operation.

The aim of the optimisation is to maximise the gross profit. The gross profit is calculated as

the difference between the income from product sales and production cost. To calculate the

income per operating hour for product h the sales price sh and produced amount ( ),rock hm x& are

used. The production cost was derived earlier and the gross profit for product h is formed as

the following equation:

( ) ( )( ) ( ),h h h init rock hP s C C m= − − ⋅x x x& (1)

The gross profit for the plant is calculated by adding the profit from all products together. The

total gross profit per operating hour will be:

( ) ( )1

q

h

h

P P=

=∑x x (2)

The statement of the optimisation problem will be to maximise the gross profit subject to all

constraints imposed on the variable parameters x. The statement of the problem is formulated

in the following way:

( )max P∈Ω

xx

x (3)

The obtained solution *x of the problem represents the most profitable setting of the crushing

plant. This setting will give the global optimum ( )*P x , generating the highest gross profit per

operating hour, provided all products are sold.

EXAMPLE: OPTIMISATION WITH AND WITHOUT PARTICLE SHAPE DEMANDS.

To demonstrate the optimisation method, a three stage crushing plant designed for aggregate

production was studied. The flow sheet is presented in Figure 1.

Figure 1. Three stage aggregates production plant used in the example. The thicker connection

lines represent conveyors. (Screen shot from the developed software)

Both the primary and secondary crushers operate in an open circuit, while the tertiary crusher

is installed in a closed circuit configuration. In addition to size reduction, the primary stage

also extracts a low quality natural fines product from the feed material, which is most suitable

for applications where the demands on the product are low, for example different types of

land fill, covering or road base. If the feed material contains any moisture the major part will

follow the natural fines product. This will make the rest of the process insensitive to any

moisture in the feed material. The main part of the material processed in this stage is

conveyed to the secondary stage where it is crushed again. The secondary stage is only for

size reduction and no final products are produced. All material is transferred to the tertiary

stage where the high quality final products are made. The tertiary stage also produces a fines

product (0-2 mm) that is considered to be waste. It cannot be sold and is thus transported back

to the quarry where it is deposited.

The selected optimisation parameters are throw and CSS on the secondary and tertiary

crusher. The feed rate of the feeders for the 11-16 mm and 16-22 mm product is also selected

as an optimisation parameter. The aim is to find the value of all optimisation parameters that

will maximise the gross profit of the plant.

The used production unit models are all based on the models used in PlantDesigner (Sandvik).

To these models additional sub-models have been added but the original models has not been

changed so the prediction of particle shape distribution, capacity and so on remains the same

as the original.

One of these sub-models is a particle shape module that is added to the crusher models. This

model was developed by Bengtsson (2006) and predicts the flakiness index for material larger

than 4 mm. The flakiness index is not defined for particles of less than 4 mm. It should also be

noted that the model is still under development. The product flakiness of the rock size p

depends on the average feed size x , crusher CSS and three constants α1, α2, and α3. The

numeric value of the constants depends on the type of crusher and chamber. The following

formula is used to predict flakiness:

( )2 2

22 3 2 312, ,

x xF x CSS p p p x

x CSS CSS

α α α ααα

⋅ + ⋅ + = ⋅ − ⋅ + ⋅

(4)

The particle shape is optimal for particles with the same size as the CSS. The flakiness index

is higher for both larger and smaller particle sizes. An increasing average feed size results in a

higher flakiness index. This is also illustrated in Figure 2.

Fla

kin

ess

ind

ex [

%]

Fla

kin

ess

ind

ex [

%]

Particle size [mm] Particle size [mm]

Increasing CSS

Increasing Feed size x

Figure 2. Illustration of the effect of process parameters on the flakiness index.

As discussed in the introduction, model compatibility is an issue when combining production

unit models. The particle shape model is a good example of why this is so. The model predicts

crusher performance with satisfying accuracy in the example considered. In many plants

where different rock materials are processed, it has been observed that particle shape also

affects screen performance. The screen performance may be fine when processing a rock

material that mostly generates cubical material, but when more flaky or elongated material is

processed, it drops significantly and most of the products do not fulfil customer demands.

This implies that, for a full implementation of particle shape prediction, the other production

unit models must be changed so that they both predict product shape and respond correctly to

feed material shape.

To further assist the economic cost calculation, a sub-model for power draw model has been

added to the production unit models (Hulthén, 2004), thus part of the variable costs can be

automatically calculated together with the energy price.

OPERATING CONDITIONS

The plant is assumed to operate in a market where it can expect to sell all of its final products

with the exception of the by-product. The plant is fed with blasted rock defined as granite,

with a particle size distribution denoted medium blasted rock, see the curve in Figure 1. The

hauling capacity of the available trucks limits the feed rate to 270 tonnes per hour.

Two different optimisations were done to demonstrate the influence of particle shape on the

operation. The first had no demands on particle shape, while in the second, four of the

products had to fulfil customer shape demands.

In the given example all crushers and screens have been assigned a fixed and a variable cost

in accordance with Figure 3. All products are assigned a sales price as well as quality

demands for particle shape and a limited proportion of misplaced particles.

Figure 3. The fixed and variable costs assigned to the different production units. (Screen shot from

the developed software)

A routine to calculate the wear part consumption of the crushers was also implemented, which

estimates the crushing chamber life time, thus allowing the wear part cost to be determined.

The installed cone crushers are equipped with a control system that compensates the effect of

mantle wear. This system aims to keep the crusher performance constant with respect to wear.

In the example the variable crusher costs were set to zero. The energy and wear part cost was

automatically calculated by the crushing models and no additional variable costs were

assigned.

OPTIMISATION RESULTS

The first optimisation led to the result shown in Figure 4 and Table 2. It maximises plant

profit without activating any shape constraints. As can be seen in the figure, the secondary

crusher was operated with a large CSS. The reduction ratio in the crusher was quite small

while the capacity was large. There was no need to use a larger throw on the crusher since the

capacity was sufficient. The optimisation algorithm has therefore found the small throw to be

the best. Since a smaller CSS will generate more fines, the crusher was kept as open as

possible. 50 mm is the maximum CSS for this crusher.

Figure 4. Results from the optimisation without any restrictions on particle shape. Note that all

production rate values are average values if nothing else is specified. (Screen shot from the

developed software)

Table 1. Production cost of the final products.

Product Production cost [SEK/ton]

2-5 mm

5-8 mm

8-11 mm

11-16 mm

16-22 mm

44.49

44.49

41.38

41.38

41.38

Table 2 Results from the optimisation without any customer demands for product shape

Parameter Optimal value

Cone Crusher S-type 4800 C

Throw

CSS

25 mm

50 mm

Cone Crusher H-type 4800 M

Throw

CSS

28 mm

33 mm

Cone Crusher H-type 4800 MF

Throw

CSS

28 mm

33 mm

Feeder, 11-16 mm 0 tph

Feeder, 16-25 mm 0 tph

At the tertiary stage the crushers are also set with a large CSS, for the same reason as the

secondary crusher, namely to generate as little fines as possible. The CSS of the tertiary

crushers is not limited by the crushers themselves. If a larger CSS were to be selected, more

material would be larger than 22 mm and returned to the crushers. Too much material in the

closed loop is negative, as it generates extra cost. The throw of the tertiary crushers is set

quite low, since they do not require any extra capacity.

The two feeders were set to zero. This is to be expected, as returning the final product to the

plant will not generate more profit. Instead, it will lead to additional costs, as the material will

have to be crushed again, leading to the production of even more fines. The production costs

of the high quality final products are shown in Table 1.The generated gross profit is 14810

SEK/h.

The particle shape constraints were activated for the second optimisation. As seen in Figure 5

and Table 3, the results differ from those of the first optimisation. Since no final products are

produced in the secondary crushing stage, the crusher’s only task is to provide a good feed to

the tertiary crushers. The setting of the secondary crusher is therefore adjusted so that the

tertiary crusher can operate with a feed that offers the best trade-off between cost and ability

to generate correctly shaped final products. This is achieved by providing the crusher with the

optimum average feed size x .

Figure 5. Results from the optimisation with restriction on particle shape. Note that all production

rate values are average values if nothing else is specified. (Screen shot from the developed

software)

Table 3. Results from the optimisation with the customer demands for product shape. The results

from the previous optimisation is also presented as a reference.

Parameter Optimal value

with shape requirements

Optimal value

without shape requirements

Cone Crusher S-type 4800 C

Throw

CSS

25 mm

43 mm

25 mm

50 mm

Cone Crusher H-type 4800 M

Throw

CSS

32 mm

20 mm

28 mm

33 mm

Cone Crusher H-type 4800 MF

Throw

CSS

32 mm

17 mm

28 mm

33 mm

Feeder, 11-16 mm 16 tph 0 tph

Feeder, 16-25 mm 54 tph 0 tph

The feed material size to the tertiary crushers is one of the most interesting parts of this

optimisation. Both feeders for the two final products are now used, the reason being to

generate a better feed to the two tertiary crushers. Trials were made with these two feeders

turned off, but the optimisation routine failed to identify any solutions. The main problem

seemed to be with the larger products. Unless some of the final products were returned, the

shape of the larger products failed to meet customer demand.

Since a whole range of final products with a good shape are produced, it is important to

operate both tertiary crushers so that the combined product from the two units is optimal. The

mix of these products should have good shape over the whole range of sizes. This is normally

achieved by operating the two crushers at different CSSs and is another result of the

optimisation. The left crusher with the slightly coarser M chamber is operated at 20 mm and

yields a good particle shape for the coarser products, while the right crusher with the finer MF

chamber is operated with a CSS at 17 mm, which ensures that the finer products are of good

shape. The shape and gradation curves of the two crushers and the mix between them are

presented in Figure 6.

Figure 6. Product size distribution and flakiness index from H-4800 M and H-4800 MF. Both the

individual crusher production and the mixed product are shown. (Screen shot from the developed

software)

The generated gross profit is 13013 SEK/h this value can be compared to the previous result

of 14810 SEK/h. When doing the comparison one must remember that the prices of all

products have remained the same even though the product quality has been improved. The

production costs of the final products are compared to the previous results in Table 4.

Table 4. Production costs of the final products.

Product Production cost [SEK/ton]

with shape

Production cost [SEK/ton]

without shape

2-5 mm

5-8 mm

8-11 mm

11-16 mm

16-22 mm

49.15

49.15

46.88

46.88

46.88

44.49

44.49

41.38

41.38

41.38

RESULTS

Computer simulation and optimisation can assist the study and improvement of the crushing

plant operation. It has been found that it is important to combine both technical and economic

aspects when the plant is studied. This type of combined study is now available by using the

developed methods.

The result from the two cases also show the importance of total plant optimisation. To achieve

optimal plant performance it is not possible to make single machine optimisation. It is

important to study all production units in order to achieve a beneficial adjustment of the plant.

By comparing the two cases this is even more obvious. The setting of the production units

must be optimised together in order to find the best solution that both will generate the highest

gross profit and ensure that the final products will all fulfil the customer requirements. It is

Flakiness index

therefore also important to have equipment and plant control system that allow the equipment

to be adjusted.

The developed method is all developed with the aim to be implemented in a computer

software. The implantation has already started with parts of the developed method

implemented in PlantDesigner. Simulation and optimisation is useful in many situations. In

the design it is useful to be able to do these types of combined economic and technical

calculations. When the plant has been built and is in operation optimisation is a powerful tool

to determine how to operate the plant in order to meet the current market demand. Finally

simulation and optimisation is useful to educate personnel on all level in the crushing plant.

REFERENCES