Aplicación Práctica / Practical Issues

Recibido: 15-09-2023, Aprobado tras revisión: 15-12-2023

Forma sugerida de citación: Paredes, J.; Cepeda, J.; Lozada, J.; “Parameters for the Grinding Process in Vertical Mills Using

Optimization Methods”. Revista Técnica “energía”. No. 20, Issue II, Pp. 90-97

ISSN On-line: 2602-8492 - ISSN Impreso: 1390-5074

Doi: https://doi.org/10.37116/revistaenergia.v20.n2.2024.594

© 2024 Operador Nacional de Electricidad, CENACE

Esta publicación es de acceso abierto bajo una licencia Creative Commons

Parameters for the Grinding Process in Vertical Mills Using Optimization

Methods

Parámetros para el Proceso de Molienda en Molinos Verticales Usando

Métodos de Optimización

J. Paredes1 0009-0002-2256-3018 J. Cepeda1 0000-0002-2488-6796

J. Lozada2 0009-0009-0016-0913

1Escuela Politécnica Nacional, Quito, Ecuador

E-mail: jorge.paredes01@epn.edu.ec ; jaime.cepeda@epn.edu.ec

2Unión Cementera Nacional, Riobamba, Ecuador

E-mail: jlozada@ucem.com.ec

Abstract

Vertical roller mills, (VRM), are widely used for

grinding raw materials in factories engaged in the

extraction and processing of minerals. Any machine

used for grinding or crushing consumes around 30 to

40% of the energy of a factory. The loading pressure,

table rotation speed, moisture content, outlet

temperature and pressure rollers are variables that can

be controlled to decrease the specific energy

consumption Ecs. This paper poses an optimization

problem in order to reduce the energy consumption of a

VRM used to produce cement and to find the optimal

parameters of the operating variables. Several packages

are used to solve the nonlinear programming problem,

with very good results in terms of accuracy and speed

of convergence, but those provided by the Pyomo

package are used because it obtains more accurate

results. Comparing the result of the objective function

with the energy consumption of a well-known cement

company in Ecuador, it is concluded that the optimized

parameters are able to reduce by 25% the energy

consumption guaranteeing a minimum production of

2200 tons of cement per day, so the model is correctly

validated.

Resumen

Los molinos verticales de rodillos (VRM), son

máquinas muy utilizadas para moler materia prima en

fábricas dedicadas a la extracción y procesamiento de

minerales. Cualquier máquina ocupada para moler o

triturar consume alrededor del 30 o 40% de la energía

de una fábrica. La presión de carga, la velocidad de

rotación de la mesa, el contenido de humedad,

temperatura de salida del molino y presión de los

rodillos son variables que se pueden controlar para

disminuir el consumo de energía especifica (Ecs). Este

trabajo plantea un problema de optimización con el fin

de reducir el consumo energético de un VRM utilizado

para producir cemento y encontrar los parámetros

óptimos de las variables de operación. Se utilizan varios

paquetes para resolver el problema de programación no

lineal, obteniendo resultados muy buenos respecto a la

precisión y velocidad de convergencia, pero se usan

aquellos proporcionados por el paquete Pyomo ya que

obtienen resultados más exactos. Comparando el

resultado de la función objetivo con el consumo

energético de una empresa cementera en Ecuador se

concluye que los parámetros optimizados son capaces

de reducir en un 25% el consumo energético

garantizando una producción mínima de 2200 toneladas

de cemento diarias por lo que el modelo se valida

correctamente.

Index terms−−

efficiency, grinding process,

optimization, vertical mill.

Palabras clave −−

eficiencia, proceso de molienda,

optimización, molino vertical.

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Edición No. 20, Issue II, Enero 2024

1. INTRODUCTION

Minning is an economic activity that has been

growing since the beginning of the 20th century. From

1920 to 2018 the rate of exploitation of each mineral has

varied from 1.48% to 7.3% measured in megatons (Mt)

[1]. Since the end of the 1990s, mineral exploitation has

advanced at a much higher rate than in previous years,

which has caused an accelerated depletion of mineral

resources [2]. Among the largest industries that make use

of the exploited minerals, metallurgy, oil and cement can

be named. The cement industry complies with providing

the main material for construction, which is cement and

which has been key to the process of human civilization

[3].

For the cement grinding process, two machines can

be used, which are: a ball mill or a VRM vertical roller

mill. The ball mill makes use of grinding bodies and they

have been the main tool for more than 100 years,

although they have a low efficiency, while the vertical

mills are much more modern tools that are capable of

saving between 45 to 70% of the power consumed [4].

It is important to know that the cement classification

process in a VRM can be carried out by air sweep or by

overflow the use of the overflow model suggests more

energy savings than the sweep model, however it is

useless in certain conditions operation (VRM motor at

full load or rater load pressure) such as particle size,

moisture or hardness [5]. This directly influences energy

consumption and the characteristics and quality of the

cement.

Some methods to improve the grinding process vary

one parameter at a time such as the loading force, the rate

of revolution or the fractional filling [6]. Some studies

also try to predict energy consumption taking into

account the characteristics of the material to be ground in

the VRM [7]. An energy and exergy analysis are used to

compare the ball mill and the VRM, finding that the

VRM is more efficient and consumes less energy,

maintaining the quality parameters of the product, so its

use is recommended [8]. The grinding performance has

been improved by increasing the grinding surface, in

addition, it has been compared with other processes such

as jaw crushing and the ball mill, finding the VRM with

better characteristics in product quality and energy

efficiency [9]. A model of material failure can provide

different energy levels, which can help improve energy

efficiency [10]. With the above, it is observed that no

research makes use of optimization methods to find

adequate operating parameters in vertical mills.

Crushing processes consume about 3 to 4% of the

electricity generated worldwide and about 70% of the

energy required in an industry dedicated to mineral

processing [11]. That is why it is important to optimize

the cement grinding process, in order to obtain better

efficiency with the lowest consumption of electrical

energy, in addition, it is necessary to take into account

certain operating parameters to guarantee a quality

product.

Most of the works related to energy consumption

vary a single parameter at a time, propose models, make

comparisons between grinding processes or perform

various energy analyses. The present work takes into

account five important parameters in the operation of any

VRM such as the load pressure, humidity, the speed of

rotation of the motor, outlet temperature and pressure

roller [12].

This document is structured by: section one presents

the introduction, in the second section is presented the

related work, the third section explains the milling

process in vertical mills, the methodology used is

explained in the fourth section, while in the fifth section

all the results obtained are presented and finally, in the

last section, the conclusions that were obtained.

2. RELATED WORKS

The search for optimal operating parameters in

vertical milling processes is essential to guarantee a

product under all quality standards and that unplanned

shutdowns are considerably reduced. However, the

complexities of the models or the handling of proprietary

software make this task difficult.

There are several optimizations works related to

vertical roller mills. The one proposed by [13] proposes

the design of the lower rocker arm body that supports the

roller and take as optimization objective function the

mass of the rocker arm and as constraint conditions the

stresses and displacements generated by the roller in the

rocker arm in order to decrease the mass while

conserving the resistance and deformation. In this way,

the design is optimized and the cost is reduced by saving

material.

A VRM in its normal operation undergoes cyclic

bending stresses due to the roller load which can cause

fractures in the mill table so [14] makes use of artificial

neural networks to solve the multi-objective optimization

problem by determining the maximum and minimum

stresses to which the vertical mill can be subjected.

High vibration in a VRM can considerably reduce

productivity, using the 7 quality tools and together with

a vibrational analysis, an optimization model is obtained

that achieves improved productivity and reduced

downtime [15].

To predict the vibrations in the upper case of the

VRM, use can be made of the fruit fly optimization

algorithm (FOA). It shows better precision in

simulations. As a result, a vibration pattern can be

predicted which will help to understand the state of the

VRM and take new safety precautions [16].

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Paredes et al. / Parameters for the Grinding Process in Vertical Mills Using Optimization Methods

Another way to optimize the load and the quality of

the cement is by using expert PID controllers, increasing

the production of the cement in vertical roller mills [17].

Although there are already some optimization works

in the field of VRMs, there are still few or almost none

those works that aim to optimize key parameters in the

operation in order to reduce electricity consumption.

3. GRINDING PROCESS IN VERTICAL ROLLER

MILLS (VRM)

A vertical roller mill is suitable equipment for

grinding and drying wet materials, which can be carried

out in the same equipment [18]. Some of the materials

that can be processed in a VRM are:

1) Clinker for cement manufacturing

2) Raw materials for cement manufacturing

3) Pozzolan

4) Metal dross

The grinding process in a VRM is carried out by

placing a certain amount of material on a horizontal

surface that is in motion, at a pressure sufficient to

fracture the materials on the bed. The bed materials are

considerably smaller, so it is necessary to form a stable

grinding bed between the rollers and the grinding table to

withstand the pressure without the material being ejected

from the grinding pressure zone. [19].

A vertical roller mill can be divided into 3 sections.

1) Motor and gears

2) Grinding

3) Drying and separation.

In the grinding process, the material is fed to the

grinding table and due to its speed, the material is

directed towards the rollers where it is milled. This

process is one of the most efficient in the cement industry

[15].

The drying process consists of a stream of

recirculated gases, which can come from the clinker kiln

or from hot gas generators. Drying usually occurs on the

mill table and in the vertical sections towards the

separator [20].

Finally, the pressure exerted by the rollers on the table

causes the material to rise towards the separator which

together with fixed plates and the cage separates the

material to the desired size. The rejected coarse material

is recirculated back to the mill [20].

In Fig. 1, shows a vertical roller mill in which the

three sections mentioned above can be easily

distinguished. The motor, grinding table, rollers and

separator are clearly visible. The material and hot gas

inlet ducts and the material outlet can also be seen.

Figure 1: Vertical Roller Mill

4. METHODOLOGY

4.1 Mathematical Model

In grinding processes, it is common to use the specific

energy [21]as observed in (1).

𝑬𝒄𝒔 =𝒌𝑾𝒉

𝒕𝒐𝒏 (1)

The ratio between the kilowatt hour, which is the unit

of measurement for accounting for electricity

consumption, and the kilogram, which is the unit of

measurement for mass, is also known as energy

efficiency and is widely used in the field of mineral

processing. This allows the performance of the grinding

process to be evaluated as well.

In vertical roller mills there are several factors that

influence the performance of the grinding process [22]

which are moisture content (mc), grinding table rotation

speed (s), load pressure (P), outlet temperature (T) and

the pressure rollers (Pr).

The specific energy model [23] can be seen in (2).

The resulting model is non-linear, so some variables,

such as roller pressure and speed, are of degree two and

other variables can be multiplied by others. There is only

one independent term.

The model was developed using the Box-Behnken

method, using historical data on the energy consumption

of the VRM and the number of tons of cement produced.

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Edición No. 20, Issue II, Enero 2024

𝑬𝒄𝒔 = 𝟎. 𝟎𝟏𝟕𝟔𝟖 + 𝟎. 𝟎𝟏𝟕𝟔𝟓𝒔

−𝟎. 𝟎𝟎𝟑𝒎𝒄 − 𝟎. 𝟎𝟑𝑻 + 𝟎. 𝟎𝟏𝟕𝟑𝑷𝒓

−𝟎. 𝟎𝟎𝟒𝑷 ∗ 𝑷𝒓 + 𝟎. 𝟎𝟏𝟕𝒔 ∗ 𝑻

−𝟎. 𝟎𝟐 𝑻 ∗ 𝑷𝒓 + 𝟎. 𝟎𝟏𝟓 𝒔𝟐+ 𝟎. 𝟎𝟎𝟒 𝑷𝒓𝟐

(2)

Taking into account the above, the formulation of the

optimization problem is as follows:

𝑴𝒊𝒏𝒊𝒎𝒊𝒛𝒆 𝒁 = 𝟎. 𝟎𝟏𝟕𝟔𝟖 + 𝟎. 𝟎𝟏𝟕𝟔𝟓𝒔

−𝟎. 𝟎𝟎𝟑𝒎𝒄 − 𝟎. 𝟎𝟑𝑻 + 𝟎. 𝟎𝟏𝟕𝟑𝑷𝒓

−𝟎. 𝟎𝟎𝟒𝑷 ∗ 𝑷𝒓 + 𝟎. 𝟎𝟏𝟕𝒔 ∗ 𝑻

−𝟎. 𝟎𝟐 𝑻 ∗ 𝑷𝒓 + 𝟎. 𝟎𝟏𝟓 𝒔𝟐+ 𝟎. 𝟎𝟎𝟒 𝑷𝒓𝟐

Subject to:

(3)

𝟐𝟐 ≤ 𝑷 ≤ 𝟐𝟖 𝒎𝒃𝒂𝒓 (3a)

𝟖𝟖𝟔 ≤ 𝒔 ≤ 𝟏𝟏𝟗𝟖 𝒓𝒑𝒎 (3b)

𝟎 ≤ 𝒎𝒄 ≤ 𝟑 % (3c)

𝟎 ≤ 𝑻 ≤ 𝟗𝟕 ˚𝑪 (3d)

𝟏𝟎𝟎 ≤ 𝑷𝒓 ≤ 𝟏𝟗𝟎 𝒃𝒂𝒓 (3e)

The restriction data are obtained using a Pffeifer

vertical roller mill. Parameter intervals documented in

articles, manuals and INEN standards were taken into

account. To guarantee a desired fineness of less than 45

microns in the case of cement, a charge pressure between

22 and 28 mbar [24] as observed in restriction (3a), a

pressure of the rollers between 100 and 190 mbar [24]

defined in the restriction (3e), speed between 886 and

1198 rpm [25] as indicated in the restriction (3b) the

moisture content between 0 and 3% [26] as observed in

restriction (3c), and the outlet temperature between 0 and

97 ˚C [26] be used as indicated in the restriction (3d).

4.2 Model Optimization

The objective function of the proposed model clearly

presents non-linear terms, so it must be solved using non-

linear programming methods. To choose the appropriate

method it is necessary to check certain characteristics of

the objective function.

As a first step it is necessary to check the convexity

or concavity of the function. For this it is necessary to

obtain the gradient (4) and Hessian of the objective

function (5).

𝜵𝒇(𝑷, 𝒔, 𝒎𝒄, 𝑻, 𝑷𝒓

)= [−𝟎. 𝟎𝟎𝟒 ∗ 𝑷𝒓,

𝟎. 𝟎𝟑 ∗ 𝒔 + 𝟎. 𝟎𝟏𝟕 ∗ 𝑻 + 𝟎. 𝟎𝟏𝟕𝟔𝟓,

−𝟎. 𝟎𝟎𝟑,

𝟎. 𝟎𝟏𝟕 ∗ −𝟎. 𝟎𝟐 ∗ 𝑷𝒓 +𝟎. 𝟎𝟏𝟕𝟑

−𝟎. 𝟎𝟎𝟒 ∗ 𝑷 − 𝟎. 𝟎𝟐 ∗ 𝑻 + 𝟎. 𝟎𝟎𝟖 ∗ 𝑷𝒓]

(4)

𝑯𝒇(𝑷, 𝒔, 𝒎𝒄, 𝑷𝒓, 𝑻

)=

[

𝟎 𝟎 𝟎 𝟎 𝟎

𝟎 𝟎. 𝟎𝟑 𝟎 𝟎 𝟎

𝟎 𝟎 𝟎 𝟎 𝟎

𝟎 𝟎 𝟎 𝟎 𝟎

𝟎 𝟎 𝟎 𝟎 𝟎. 𝟎𝟎𝟖]

(5)

From the Hessian matrix, its eigenvalues (6) are

obtained, which are equal to or greater than zero, so it is

a positive semi-definite matrix.

𝝀 = [𝟎, 𝟎. 𝟎𝟑, 𝟎, 𝟎. 𝟎𝟎𝟖, 𝟎

] (6)

Taking into account the considerations that the

gradient is greater than zero and the Hessian matrix is

positive semidefinite, the objective function presents

convexity.

With this in mind, we proceed to solve the

optimization problem proposed in (3). In this case, in

addition to the Python programming language, nonlinear

programming solvers from the Pyomo and Scipy

packages are uses. Both solvers are used to ensure the

accuracy and speed of convergence of the model and to

select the model that yields parameter values that meet

the constraints of the optimization problem.

The Pyomo package uses the ipopt solver [27] to

solve nonlinear programming problems. Table 1 shows

the optimal values for each variable and the objective

function.

Table 1: Optimized values obtained using Pyomo

Variables Optimized Value

P 28

s 886

mc 3

T 0

Pr 100

Z 11.82

Finally, the Scipy package makes use of sequential

least-squares programming [28], which is a widely used

solver for non-linear programming problems. In Table 2,

you can see the optimized values using Scipy.

Table 2: Optimized values obtained using Scipy

Variables Optimized Value

P 27.99

s 885.99

mc 2.99

T 0

Pr 99.99

Z 11.82

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Paredes et al. / Parameters for the Grinding Process in Vertical Mills Using Optimization Methods

5. DISCUSSION

The benefits of optimizing any process or model are

many, such as better tuning the parameters of a particular

controller or reducing associated costs by making it more

efficient. The grinding process optimized in this work is

important because it provides the optimum operating

parameters. Optimized parameters avoid potential

damage to machine components, such as preventing

VRM rolls from breaking due to out-of-range operating

parameters or high energy consumption with low

production.

Grinding in the cement industry is a critical process

as it is the last step before the finished product is

obtained. There are other sub-processes involved in

grinding, such as material transport or separation, but this

work focuses on the actual grinding process that takes

place within the VRM.

In Ecuador, there are several companies dedicated to

the production of cement. In the center of the country

there is a well-known cement industry from which the

energy consumption data for the grinding process could

be obtained. For reasons of confidentiality, the name of

the company is withheld.

The company's grinding process consists of a VRM,

which will replace a ball mill previously used for cement

production in 2021. The current VRM has a capacity of

100 tons per hour. This process also includes the raw

material feeding sub-process, which is carried out by

means of dosing tables, the finished product separation

sub-process and transport to the finished product silo.

The company also has two other VRMs, one for the

production of raw meal, which is heated to 1200 ˚C to

produce clinker, the main ingredient of cement, and the

other for the production of Petcoke powder, the main fuel

for the clinker kiln.

Taking this into account, the average consumption

data obtained is 78,408.5 kWh per day. Similarly, the

average cement production is 2228 tons. Dividing the

consumption value by the number of tons produced gives

a value of 34.39 kWh/tons, which means that it takes

34.39 kWh to produce one tons of cement. The Ecs value

obtained takes into account all the processes involved,

such as raw material dosing, separation of the final

product and transport. However, if only the VRM

grinding process, which accounts for 40%, is specifically

analyzed, the value obtained is 13.75 kWh/tons.

The packages used to optimize the problem proposed

in this work provide very similar data. The Pyomo

package provides optimized values of the operating

values within the given constraints, but Scipy packages

provide optimized values very close to the constraints,

which, by applying rounding methods, are equal to the

values provided by Pyomo. Taking this into account, for

further comparisons with the production data presented

above, the values optimized by the Pyomo package will

be used, which are considered to be the most accurate and

reliable values for this work.

The value of the objective function after the

optimization process is 11.82 kWh/tons, while that of the

normal process without optimization of the operating

parameters is 13.75 kWh/tons. This reduction

corresponds to 14.03% of the energy consumption of the

grinding process carried out by the VRM. To achieve

this, it is necessary to change the values of the current

mill parameters to the optimized values, which are: for a

feed pressure of 28 mbar, the table speed should be set to

886 rpm, the moisture content of the material should be

0% the outlet temperature should be 0 and the pressure

roller should be 100 bar. This ensures low energy

consumption and a minimum cement production of over

2200 tons per day. Table 4 summarizes the results

obtained.

Table 4: Comparison of the results obtained

Variable Ecs (kWh/ton)

Actual 13.75

Optimized 11.82

Difference 1.93

It is important to know the savings in dollars of the

consumption of the milling process. Currently, in the year

2023, the cost per KWh in Ecuador is $0.105 for voltages

between 351V and 500V [29]. Considering this, before

the optimization process, the consumption was $3216 for

a production of 2228 tonnes of cement per day, and with

the optimized parameters, the consumption is $2686 for

the same production of cement. This represents a saving

of $530 per day.

5.1. Effect of the parameters in Ecs

When comparing the loading pressure P with the

pressure roller Pr, the specific energy Ecs increases if the

loading pressure and pressure roller also increases due to

the features of the raw material. Due to this increase in

ECS, it is necessary to carry out optimal quality control

of the raw material used in the cement manufacturing

process. By increasing the loading pressure and the

pressure roller to their maximum levels, the maximum

Ecs can be obtained as shown in Fig 2.

Figure 2: Change of Ecs by varying loading pressure and pressure

roller

94