Performance analysis of rolling bearing in conveyor belt idlers

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UNIVERSIDADE TECNOL ´

OGICA FEDERAL DO PARAN ´

A

PROGRAMA DE P ´

OS-GRADUAC

¸ ˜

AO EM ENGENHARIA

MEC ˆ

ANICA E DE MATERIAIS - PPGEM

BRUNA KOLCZYCKI BORGES

PERFORMANCE ANALYSIS OF ROLLING BEARING IN

CONVEYOR BELT IDLERS

MASTERS DISSERTATION

CURITIBA

2020

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BRUNA KOLCZYCKI BORGES

PERFORMANCE ANALYSIS OF ROLLING BEARING IN

CONVEYOR BELT IDLERS

Masters Dissertation presented to Programa de Pós-Graduação em Engenharia Mecânica e de Materiais - PPGEM from Universidade Tecnológ-ica Federal do Paraná as a partial requirement to obtain a Master’s degree in Mechanical Engineer-ing.

Supervisor: Tiago Cousseau

CURITIBA

2020

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Dados Internacionais de Catalogação na Publicação

_________________________________________________________________ Borges, Bruna Kolczycki

Performance analysis of rolling bearing in conveyor belt idlers [recurso eletrônico]/ Bruna Kolczycki Borges. -- 2020.

1 arquivo texto (114 f.): PDF; 7,31 MB. Modo de acesso: World Wide Web.

Título extraído da tela de título (visualizado em 10 mar. 2020). Texto em inglês com resumo em português.

Dissertação (Mestrado) - Universidade Tecnológica Federal do Paraná. Programa de Pós-graduação em Engenharia Mecânica e de Materiais, Curitiba, 2020.

Bibliografia: p. 84-87.

1. Engenharia Mecânica e de Materiais - Dissertações. 2. Lubrificação e lubrificantes. 3. Rolamentos. 4. Correia transportadora. I. Cousseau, Tiago, orient. II. Universidade Tecnológica Federal do Paraná - Programa de Pós-graduação em Engenharia Mecânica e de Materiais, inst. III. Título.

CDD: Ed. 23 -- 620.1 Biblioteca Ecoville da UTFPR, Câmpus Curitiba Bibliotecária: Lucia Ferreira Littiere – CRB 9/1271

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Ministério da Educação

Universidade Tecnológica Federal do Paraná Diretoria de Pesquisa e Pós-Graduação

TERMO DE APROVAÇÃO DE DISSERTAÇÃO Nº 374

A Dissertação de Mestrado intitulada ”Performance analysis of rolling bearing in conveyor belt idlers”, defendida em sessão pública pelo(a) candidato(a) Bruna Kolczycki Borges, no dia 5 de dezembro de 2019, foi julgada para a obtenção do título de Mestre em Engenharia Mecânica e de Materiais, área de concentração Engenharia de Materiais, e aprovada em sua forma final, pelo Programa de Pós-Graduação em Engenharia Mecânica e de Materiais.

BANCA EXAMINADORA:

Prof. Dr. Tiago Cousseau - Presidente - UTFPR Prof. Dr. Carlos Henrique da Silva - UTFPR Prof. Dr. Francisco José Profito - EPUSP

A via original deste documento encontra-se arquivada na Secretaria do Programa, contendo a assinatura da Coordenação após a entrega da versão corrigida do trabalho.

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ACKNOWLEDGEMENT

This dissertation becomes a reality with the support and help of many individuals. I would like to extend my sincere thanks to all of them.

First, I would like to thank Vale for the opportunity and financial support during the development of this dissertation combined with the research project: Study on Roller Sizing and Energy Consumption of Conveyors Belt - ROLOTOP (Estudo do Dimension-amento de Rolos e do Consumo Energético de Transportadores de Correia - ROLOTOP). I would like to express my special gratitude and thanks to my advisor, Dr. Tiago Cousseau for his guidance and imparting his knowledge and expertise in this study.

Finally, I am indebted to all my family for the encouragement which helped me in completion of this research and to all my friends and colleagues for their support.

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ABSTRACT

BORGES, Bruna Kolczycki. PERFORMANCE ANALYSIS OF ROLLING BEARING IN CONVEYOR BELT IDLERS. 114 f. Masters Dissertation – Programa de Pós-Graduação em Engenharia Mecânica e de Materiais - PPGEM, Universidade Tecnológica Federal do Paraná. Curitiba, 2020.

Nowadays, energy saving and environmental awareness are global requirements for creat-ing a sustainable society. Rollcreat-ing bearcreat-ings need to transmit load at a very low friction, therefore understanding internal friction losses in these elements is relevant for energy saving. Specifically for idler rolls of conveyor belts, rolling bearings represent one of the main sources of idler failure and power loss. Based on conveyor belt design it is possible to properly define operating conditions of rolling bearings and then use friction torque models to predict the idler’s rolling resistance needed to overcome frictional resistance on its bearings. Conveyor belt bearings are grease lubricated, their lubrication mechanisms are not yet well understood and there is no consensus on the correlation between grease properties and its performance. With the significant number of models aiming to predict film thickness and friction torque, few are valid for grease lubrication and the ones that are only consider base oil properties. Rheological measurements show the need to use grease apparent viscosity instead of base oil viscosity depending on the bearing operation conditions. This difference in viscosity promotes a significant difference in friction torque predictions and consequently, energy consumption.

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RESUMO

BORGES, Bruna Kolczycki. PERFORMANCE ANALYSIS OF ROLLING BEARING IN CONVEYOR BELT IDLERS. 114 f. Masters Dissertation – Programa de Pós-Graduação em Engenharia Mecânica e de Materiais - PPGEM, Universidade Tecnológica Federal do Paraná. Curitiba, 2020.

Atualmente, economia de energia e conscientização ambiental são requisitos globais para a criação de uma sociedade sustentável. Esta demanda gera desafios científicos e tecnológi-cos para os diversos setores da indústria. Um bom exemplo é a utilização em larga escala de rolamentos. Estes precisam transmitir carga com baixo atrito e apresentar alta dura-bilidade, portanto, entender as perdas internas por atrito nesses elementos é relevante para a economia de energia. Especificamente em correias transportadoras, os rolamentos representam uma das principais fontes de falha e perda de energia. Com base no projeto da correia transportadora, é possível definir adequadamente as condições de operação dos rolamentos e, em seguida, usar modelos de torque de atrito para prever a resistência ao rolamento do rolo necessária para superar a resistência ao atrito em seus rolamentos. Os rolamentos das correias transportadoras são lubrificados com graxa, seus mecanismos de lubrificação ainda não são bem compreendidos e não há consenso sobre a correlação entre as propriedades da graxa e seu desempenho. Há um número significativo de modelos para previsão da espessura do filme e do torque de atrito em rolamentos, porém poucos são válidos para a lubrificação com graxa e aqueles que são consideram apenas as propriedades do óleo base. Avaliações reológicas mostram a necessidade de usar a viscosidade aparente da graxa em vez da viscosidade do óleo base, dependendo das condições de operação do ro-lamento. Essa diferença de viscosidade promove uma diferença significativa nas previsões de torque de atrito e consequentemente, energia consumida.

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LIST OF FIGURES

Figure 1.1 – Work Flow Diagram . . . 13

Figure 2.1 – Rulmeca scheme of belt conveyor . . . 15

Figure 2.2 – Conveyor belt and idler rolls. . . 15

Figure 2.3 – Typical scheme of idlers . . . 16

Figure 2.4 – Work Flow Diagram - Operating Conditions . . . 16

Figure 2.5 – Possible Conveyor Power Loss Breakdown . . . 18

Figure 2.6 – Angles of surcharge and repose as function of transported material . . . 19

Figure 2.7 – Physical Properties of Materials . . . 19

Figure 2.8 – Maximum speeds advised . . . 20

Figure 2.9 – Factor of feeding regularity . . . 21

Figure 2.10–Factor of inclination K . . . 21

Figure 2.11–Loaded volume with 3 roll troughing sets . . . 22

Figure 2.12–Maximum advised pitch of troughing sets. . . 23

Figure 2.13–Roller diameter advised . . . 23

Figure 2.14–Maximum speed and number of roller revolutions . . . 24

Figure 2.15–Service factor . . . 24

Figure 2.16–Environment factor . . . 24

Figure 2.17–Impact factor . . . 25

Figure 2.18–Speed factor(CEMA, 2002) . . . 25

Figure 2.19–Participation factor Fp - loaded rate on the most loaded roller . . . 26

Figure 2.20–Central and lateral loads on roller . . . 26

Figure 2.21–Bearings loads . . . 27

Figure 2.22–Force distribution for different rates of material transported . . . 27

Figure 3.1 – Work Flow Diagram - Grease Properties . . . 29

Figure 3.2 – Analogy of grease working as a sponge . . . 29

Figure 3.3 – Laminar flow between two plates . . . 31

Figure 3.4 – Variation of shear stress with shear rate for generalized newtonian fluids 31 Figure 3.5 – Percentage increase in film thickness of the grease in comparison to the base oil as function of the ration between thickener concentration (ϕ) and average volume of thickener particle (V). . . 35

Figure 3.6 – Apparent viscosity versus shear rate for (a) newtonian fluid and (b) non-newtonian grease . . . 36

Figure 3.7 – Operation conditions inside a rolling bearing . . . 37

Figure 3.8 – Schematic representation of the apparent viscosity versus shear rate for lubricating greases . . . 38

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Figure 3.9 – Geometries for shear rheometer (a) concentric cylinder, (b) Vane-cylinder

(c) parallel plates and (d) cone-plate . . . 39

Figure 3.10–Modelled curve of viscosity at 60◦_C _{versus shear rate . . . 41}

Figure 3.11–Modelled curve of viscosity at 40◦_C_{, 60}◦_C _{and 80}◦_C _{for greases . . . . 44}

Figure 3.12–Modelled curve of viscosity at 60◦_C _{versus shear rate for greases . . . . 45}

Figure 4.1 – Work Flow Diagram - Film Thickness . . . 46

Figure 4.2 – Planes and radii of curvature for a pontual hertzian contact . . . 47

Figure 4.3 – Example of Stribeck curve . . . 49

Figure 4.4 – Lubrication conditions . . . 49

Figure 4.5 – Elastohydrodynamic lubrication . . . 50

Figure 4.6 – Log-log plot of lubrication mechanisms for greases . . . 51

Figure 4.7 – Iterative calculation of film thickness . . . 56

Figure 4.8 – Film thickness versus bearing rotation . . . 57

Figure 4.9 – Specific film thickness versus bearing rotation . . . 58

Figure 4.10–Operating viscosity for rotations between 300 and 700 rpm at 60◦ C . . 59

Figure 4.11–Operating viscosity for rotations between 300 and 700 rpm at different temperatures . . . 60

Figure 5.1 – Work Flow Diagram - Frictional Power Loss . . . 61

Figure 5.2 – Inlet shear heating reduction factor . . . 64

Figure 5.3 – Typical variation of the weighting factor Φbl and coefficient of friction µsl with operating parameter (nν)1.4dm . . . 66

Figure 5.4 – Rolling and sliding components of frictional moment for SKF model . . 66

Figure 5.5 – Total frictional moment for SKF model . . . 67

Figure 5.6 – Frictional moment Shell AS2 central 40◦_C _{and 80}◦_C _{. . . 68}

Figure 6.1 – Work Flow Diagram - Bearing Life . . . 71

Figure 6.2 – Effect of viscosity, contamination and load on rolling bearing life . . . . 73

Figure 6.3 – Guideline values for factor ηc for different level of contamination . . . . 74

Figure 6.4 – Viscosity ratio k . . . 74

Figure 6.5 – Rated Viscosity . . . 75

Figure 6.6 – Viscosity ratio k - lubrication condition . . . 77

Figure 6.7 – Lubrication condition . . . 77

Figure 6.8 – Frictional moment for different lubrication conditions . . . 78

Figure 6.9 – Grease life for deep groove ball bearings . . . 79

Figure 7.1 – Work Flow Diagram - Bearing Performance . . . 81

Figure A.1 – Curves of viscosity at 40◦_C _{versus shear rate for greases . . . 88}

Figure B.1 – Specific Film Thickness at 40◦_C _{versus rotation for greases . . . 91}

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Figure B.3 – Specific Film Thickness at 80◦_C _{versus rotation for greases . . . 93}

Figure C.1 – Frictional moment Shell AS2 central 40◦_C _{and 60}◦_C _{. . . 94}

Figure C.2 – Frictional moment Shell AS2 laterals 60◦_C _{. . . 95}

Figure C.3 – Frictional moment Shell AS2 central 80◦_C _{and Mobil Polyrex central} 40◦_C _{. . . 96}

Figure C.4 – Frictional moment Mobil Polyrex central and lateral 60◦ C . . . 97

Figure C.5 – Frictional moment Mobil Polyrex lateral 60◦_C _{and central 80}◦_C _{. . . . 98}

Figure C.6 – Frictional moment SKF LGMT central 40◦_C _{and 60}◦_C _{. . . 99}

Figure C.7 – Frictional moment SKF LGMT laterals 60◦_C _{. . . 100}

Figure C.8 – Frictional moment SKF LGMT central 80◦_C _{and GLi central 40}◦_C _{. . 101}

Figure C.9 – Frictional moment GLi central and lateral 60◦_C _{. . . 102}

Figure C.10–Frictional moment GLi lateral 60◦_C _{and central 80}◦_C _{. . . 103}

Figure C.11–Frictional moment SKFLEGE central 40◦_C _{and 60}◦_C _{. . . 104}

Figure C.12–Frictional moment SKF LEGE laterals 60◦_C _{. . . 105}

Figure C.13–Frictional moment SKF LEGE central 80◦ C and Gadus 1 central 40◦C 106 Figure C.14–Frictional moment Gadus 1 central and lateral 60◦_C _{. . . 107}

Figure C.15–Frictional moment Gadus 1 lateral 60◦_C _{and central 80}◦_C _{. . . 108}

Figure D.1–Schematic view of the Rolling bearing power loss rig - RBPLr . . . 110

Figure D.2–Schematic view of the Rolling bearing power loss rig - RBPLr . . . 111

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LIST OF TABLES

Table 2.1 – Radial and axial forces components on bearings . . . 27

Table 3.1 – NLGI grades . . . 30

Table 3.2 – Piezoviscosity coefficients for different base oils (GOLD et al., 2001) . . 33

Table 3.3 – Greases used by Vale . . . 39

Table 3.4 – Greases recommended for conveyor belt application . . . 39

Table 3.5 – Greases properties . . . 40

Table 3.6 – Cross model constants for greases at 40◦_C _{. . . 42}

Table 4.1 – Lubrication Regimes (SEABRA; CAMPOS, 2003) . . . 54

Table 4.2 – Values of Λ0 and Λ1 for rolling bearings (SEABRA; CAMPOS, 2003) . . 54

Table 4.3 – Material and geometry parameters for contact in 6310 rolling bearing . . 55

Table 4.4 – Contact pressures and contact dimensions for 6310 bearing . . . 55

Table 4.5 – Operating Viscosity at 500 rpm and 60◦_C _{. . . 58}

Table 5.1 – Power loss at 500 rpm and 60◦_C _{. . . 69}

Table 6.1 – Viscosity, Power loss and Bearing life at 500 rpm and 60◦_C _{. . . 78}

Table 6.2 – Viscosity, Power loss, Bearing life and Grease life at 500 rpm and 60◦_C _{. 80} Table D.1–Rolling bearing dimensions . . . 111

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CONTENTS

1 INTRODUCTION . . . 11

1.1 Aim and Thesis Outline . . . 12

2 CONVEYOR BELT ROLLERS . . . 15

2.1 Introduction . . . 15

2.2 Conveyor Belts Operation . . . 17

2.3 CEMA standard . . . 18

3 GREASE COMPOSITION AND PROPERTIES . . . 28

3.2 Grease Definition . . . 28

3.2.1 Grease Base Oil . . . 30

3.2.1.1 Definition of Viscosity . . . 30

3.2.1.2 Base Oil Types . . . 34

3.2.2 Grease Thickener . . . 34

3.2.3 Grease Additives . . . 35

3.3 Characterization of Lubricating Greases . . . 36

3.3.1 Flow Tests . . . 36

3.4 Experimental Characterization of Lubricating Greases . . . 38

4 CONTACT MECHANICS AND EHD LUBRICATION . . . 46

4.2 Hertz Theory . . . 46

4.3 Lubrication Theory . . . 49

4.4 Film Thickness . . . 51

4.5 Lubrication Regime for Greases . . . 54

5 ROLLING BEARING FRICTION TORQUE . . . 61

5.2 SKF Friction Torque Model . . . 62

5.2.1 SKF Model Adaptation . . . 67

6 BEARING LIFE . . . 71

6.1.1 SKF grease rating life . . . 79

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7.1 Future Work . . . 82

Bibliography . . . 84

A GREASE VISCOSITY . . . 88

B SPECIFIC FILM THICKNESS . . . 91

C FRICTIONAL MOMENT GREASE . . . 94

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11

1 INTRODUCTION

Energy consumption in machine design has become ever more important since the machines are required to be economical and have high productivity. Because friction is a major component of power loss, controlling and reducing it becomes significant. One type of machine element that is present in many mechanical systems is the rolling bearing. This element has the function to transmit power at very low friction, therefore, understanding its lubrication behavior under different conditions contributes to evaluate their overall efficiency.

The majority of rolling bearings use grease as a lubricant because its formulation -base oil and thickener - provides some benefits over lubricating oils, such as its consistency, which minimizes leakage. In a rolling bearing, the primary role of grease is to lubricate the contact between the rolling elements and the raceway, since it generates a large portion of the overall friction (LAURENTIS et al., 2017). Lugt states that grease lubricating mechanisms are not well understood in comparison to oil lubrication mechanisms due to the complex composition of greases. Therefore, film thickness and friction prediction remains a challenge (LUGT, 2012).

Since the coefficient of friction depends on the lubrication regime, most of the research efforts have been made to understand film formation. For oil lubrication, the lube films can be reasonably well predicted using classical elastohydrodynamic (EHL) lubrication theory. However, for greases, there are several aspects to be considered, such as rheology, thickener type, bleeding characteristics, starvation and others.

During the last decades intensive research work has been done regarding the tribological and structural changes that take place on lubricating greases under some influencing parameters (temperature, speed, shear stress, grease formulation, contamina-tion, etc.) (LUNDBERG; HöGLUND, 2000; CANN et al., 2001; HURLEY; CANN, 2001; BALY et al., 2006; DELGADO et al., 2008; GONÇALVES et al., 2017b; GONÇALVES et al., 2017a). There have been significant advances and the assumption that grease rolling contacts operating under high shear rates are lubricated mostly by the grease base oil on the top of a thin sheared thickener layer is well-accepted by many researchers (LUGT, 2012). As a consequence, most of the analytic tools developed to predict grease film thickness (CANN et al., 1992; ZOELEN et al., 2010), traction behaviour (YANSHUANG; BOYUAN, 2006; LU; KHONSARI, 2007) and rolling bearing friction torque (SKF, 2018; ESPEJEL, 2006) only take into account the grease base oil properties and neglect the interaction between thickener, additives and base oil.

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Chapter 1. Introduction 12

carries information regarding the thickener-additive-base oil interaction, can possess sig-nificantly different properties from the base oil (COURONNé et al., 2003; GONÇALVES et al., 2017b; COUSSEAU et al., 2012). Furthermore, film thickness, friction coefficient and friction torque measurements performed with grease and its base oil showed different results (COURONNé et al., 2003; GONÇALVES et al., 2017b; COUSSEAU et al., 2012). This suggests that a different approach should be used in order to characterize the grease behaviour (durability and efficiency) in an EHL contact.

One application in which grease lubricated rolling bearings are of utmost impor-tance is conveyor belts. Conveyor belts are commonly used to transport bulk material due to their low maintenance, operation costs, reliability and capacity. Basically, they are composed by thousands of idler sets supporting the belt over long distances. Almost as much as the belt itself, grease lubricated rolling bearings affect the behavior of con-veyed material, durability, power loss and the overall suitability of the conveyor (REICKS, 2008). Therefore, understanding grease lubricated rolling bearing life and friction losses of idler rolls allows for improving conveyor belt durability and efficiency. To do so, it is important to properly define the operating conditions of the rolling bearings based on the conveyor belt design, such as: spacing between rollers set, number of rollers in each set, tons of iron ore transported per hour, etc.

1.1 AIM AND THESIS OUTLINE

The main purpose of this work is to investigate the influence of grease formulation on rolling bearing performance (durability and efficiency) of conveyor belt idlers in the early stages of grease life. The work is also directed at increasing knowledge on the field of greased lubricated radial rolling bearings, thereby contributing to the understanding of grease lubrication mechanisms and to the development of predictive tools, in particular those related to film formation and rolling bearing friction torque.

The specific objectives of this thesis are:

• To define and characterize the grease properties that are relevant for film thickness formation and friction torque losses;

• To optimize the friction torque models presented in the literature including grease properties;

• To integrate the optimized friction torque model with the loading model of conveyor belt idlers;

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Figure 1.1 presents a work flow diagram with the main tasks carried out to analyse the performance of rolling bearings in conveyor belt idlers. First it is needed to evaluate the operating conditions of the conveyor belt and the grease properties. Using this data it is possible to predict film thickness that dictates the separation of rolling surfaces on the bearing, the power loss due to the frictional moment and the bearing life. With these results one can evaluate the best grease to provide a greater life with lower energy consumption in a given system of conveyor belts.

Figure 1.1 – Work Flow Diagram

Source: Autor

This figure will be presented at the beginning of each chapter to situate the reader on what is being studied and the relation to the dissertation outline.

This Dissertation consists of seven chapters including this Introductory Chapter, which justifies the importance of increasing our knowledge on grease lubrication in radial rolling bearings, and consequently of this work. It also briefly presents an overview of current knowledge of grease lubrication mechanisms, identifies areas needing improvement and, lastly, presents a strategy for understanding grease formulation influence on the early stages of bearing performance.

Chapter 2 Conveyor Belt Rollers describes a methodology to quantify the load and rotational speed of rolling bearings from conveyor belts design and operating conditions, such as: spacing between rollers set, number of rollers in each set, tons of iron ore transported per hour, etc. These forces are going to be used in the friction torque model described in chapter 5 in order to compare the performance of different lubricating greases.

Chapter 3 Grease Composition and Properties presents a general study of lubricating greases and their components (base oil, additives and thickener), mostly related to the typical physico-chemical properties and rheological response of greases and their base oils. Finally, the base oil, thickener and additive types and main characteristics

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are briefly described. All the description is focused on their influence on film formation and friction response.

Chapter 4 Contact Mechanics and EHD lubrication presents the con-tact mechanics and elastohydrodynamic lubrication theories applied to grease lubricated rolling bearings. Here it is proposed that grease apparent viscosity should be used to pre-dict EHL film thickness in rolling bearings operating at low to moderate speed, while the current practice is to use the base oil viscosity.

Chapter 5 Rolling Bearing Friction Torque presents the new SKF friction torque model. Then the model is explored by adding the knowledge obtained in Chapters 3 and 4. Finally, the rolling bearing power loss rig is being developed in partnership with our research group to measure the friction losses in rolling bearings is described in detail. Chapter 6 Bearing Life presents the rolling bearing and grease life equations. Then these models are explored by evaluating rolling bearings of idlers with different type of seals and for all the studied greases.

The Chapter 7 Final Considerations discusses the main conclusions of this work and presents the research plan to conclude this dissertation.

This work resuletd in two reports sent to VALE; a paper was accepted for the 24th ABCM International Congress of Mechanical Engineering - COBEM 2017; an ex-panded abstract was accepted for the 3rd International Brazilian Conference on Tribology – TriboBR2018; and a paper was accepted for the 13th International Conference on Bulk Materials Storage, Handling and Transportation (ICBMH) 2019;

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15

2 CONVEYOR BELT ROLLERS

2.1 INTRODUCTION

A belt conveyor system schematized in Figure 2.1 is a medium to continuously transport a wide range of materials (Figure 2.2). It consists of two or more pulleys that move the belt and the material on the belt forward. The drive pulley is responsible to provide the power to move the system.

Figure 2.1 – Rulmeca scheme of belt conveyor

Source: (RULMECA, 2015)

Figure 2.2 – Conveyor belt and idler rolls.

Idlers rolls and their assembly in sets are a integral part of belt conveyors. Almost as much as the belt itself, they affect the behavior of conveyed material, the power loss and the overall suitability of the conveyor (REICKS, 2008). Even though idlers have been developed to perform adequately for various installations over the years, to select the most appropriate one is not that clear. This is observed by the variety of solutions with different technical specifications available for the same application.

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Chapter 2. Conveyor Belt Rollers 16

Figure 2.3 presents a typical arrangement of rollers, consisting of a central one and two lateral ones.

Figure 2.3 – Typical scheme of idlers

Source: Autor

Understanding the conveyor belt operating conditions is important to determine the loads and rotational speed of the bearings, providing information to further analyse the bearing performance (Figure 2.4).

Figure 2.4 – Work Flow Diagram - Operating Conditions

Source: Autor

Furthermore, idler design is relatively neglected in the academia. As shown by Vieroslav et al. (MOLNÁR et al., 2015), there are several studies on conveyors, such as: test rigs for quality control of conveyor belt idlers based on vibration (BARTELMUS et al., 1999), idler wear due to ore particles entrapment (FISET; DUSSAULT, 1993), rolling resistance between idler and belt (KINOSHITA et al., 2013), stress state of idler rolls and deformation of the belt (PANG; LODEWIJKS, 2013); power consumption as function of idler space (HE et al., 2010), load distribution on pipe conveyor (ZAMI-RALOVA; LODEWIJKS, 2015), dynamic load analysis on idler rolling bearing (FUR-MANIK, 2009), material and components of conveyor belt analysis (numerical and ex-perimental) (BOCKO et al., 2014). However there is a lack of research on idlers design and performance of its rolling bearings as function of the lubricant and the operating conditions.

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Few of the published work in the topic is purely experimental (KRÓL et al., 2017; KRÓL et al., 2015; KROL et al., 2017), and they accentuated the importance to predict energy consumption on idler rolls. Kroll estimated annual energy savings (at 60 euro/MWh) of up to 159 thousands euros for one branch of a copper mine transportation system of 11.9 km length assuming 6000 working hours (KROL et al., 2017).This shows the importance to develop an integrate model to predict the load distribution and the the power loss in rolling bearings from conveyor belt idlers.

2.2 CONVEYOR BELTS OPERATION

In terms of performance, the main sources of energy loss depend on the conveyor characteristics and operational conditions. For the iron ore transportation, which accounts for a significant part of conveying system in operation in Brazil, such operating conditions are summarized below 1_:

Load

• up to 4.000 tons per hour (10%)

• between 4.000 and 8.000 tons per hour (15%) • between 8.000 end 12.000 tons per hour (65%) • between 12.000 and 20.000 tons per hour (10%)

Speed

• approximately 300 rpm (10%) • approximately 500 rpm (80%) • approximately 700 rpm (10%)

Operating Temperature

• average operating temperature of 30ºC (10%) • average operating temperature of 50ºC (50%) • average operating temperature of 65ºC (60%)

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Even thought the operating conditions are approximately well known, the power loss breakdown for each condition remains a challenged to be estimated or measured. However, according to Shinde and Patil (SHINDE; PATIL, 2012), for most long over land conveyors (> 4km), which are the reality for the iron ore transportation in Brazil, rolling bearing losses account for about 20% of the total losses. Figure 2.5 shows an example where idler friction losses account 16% (REICKS, 2016).

Figure 2.5 – Possible Conveyor Power Loss Breakdown

Source: (REICKS, 2016)

These data will be used as boundary conditions for the power loss predictions presented ahead.

2.3 CEMA STANDARD

Rulmeca (RULMECA, 2015) is an Italian manufacturer of conveyor belt com-ponents that provides a methodology to select idler rolls based on the conveyor belt characteristics, and currently used by the VALE engineers. This methodology is based on the scheme presented in Figure 2.1, and it will be introduced using data from one of the conveyor belts of VALE. The inputs are: iron ore with density of 2.4 t/m3 and lump

size of 300 mm as the material to be transported at a rate of lV M = 5, 000m3/h, which is

equivalent to 12,000 t/h. The belt conveyor has a length of 800 m and a height variation of 55 m, and is used 16 hours a day in a very abrasive environment. The troughing sets are composed by 3 idler rolls.

For iron ore transportation, the surcharge angle of 25o _{and repose angle of 35}o _are

obtained from Figure 2.6. However, these values may differ from the standard depending on the iron ore properties.

Considering the iron ore a irregular material (stringy, interlocking, mats together), the material class is E. From Figure 2.7 one also defined that iron ore have high abrasive-ness ("C") and low corrosiveabrasive-ness ("A").

Another important design factor that needs to be calculated is the maximum speed of the conveyor. It depends on the physical and geometrical properties of the con-veyed material. Lightweight materials enable high speeds while heavy materials demand

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Figure 2.6 – Angles of surcharge and repose as function of transported material

Figure 2.7 – Physical Properties of Materials

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low speeds. In Figure 2.8, using lump size of 300 mm and class D for abrasive material (defined in Figure 2.7) as input, the recommended maximum speed and minimum belt with are 2.65 m/s and 1,200 mm, respectively. Thus, a maximum speed of v = 2.6m/s and a minimum width of 1,800 mm will be assumed for the first run, since it is an iterative procedure.

Figure 2.8 – Maximum speeds advised

With the conveyor dimensions and speed defined, it is necessary to check if these values satisfy the loaded volume used by VALE (lV M = 5, 000m3/h). Equation 2.1 gives

the required value of the theoretical loaded volume for v = 1 m/s. The parameters v,

K and K1 are the maximum speed and the factors for inclination and irregularity of

conveyor feeding, respectively. In this case, it is considered an irregular feed, K1 = 0.95

(2.9), and δ = 3.933o_{, thus K = 0.98, (Figure 2.10). The inclination angle is derived from}

belt conveyor length of 800 m and height variation of 55 m. It is important to mention the input values were provided by VALE.

lV T =

lV M

v.K.K1

[m3

/h] (2.1)

From Equation 2.1, the loaded volume required is lV T = 2, 065.6m3/h. It is now

necessary to check the proper width of the belt to satisfy the tabulated value of lV T using

Figure 2.11. For surcharge angle of 25o _{and idler roll angle of 35}o_{, the minimum width of}

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Figure 2.9 – Factor of feeding regularity

Source: (RULMECA, 2015) Figure 2.10 – Factor of inclination K

It is now necessary to determine the maximum pitch for troughing sets in relation to belt width (2,200mm) and the specific weight of the conveyed material (2.4 t/m3₎

using Figure 2.12 to maintain belt deflection with safe values. The deflection between 2 consecutive carrying troughing sets should not be more than 2% of the pitch itself, because this could cause a discharge of the material during the loading and promote excessive frictional forces.

Using belt width and conveyor speed as input in Figure 2.13, an idler roll diameter of 194mm is obtained. For this diameter, the rotational speed that provides the desired speed of 2.6 m/s is ≈ 254 rpm.

The determined parameters now have to be checked with the maximum limits defined by in Figure 2.14. As one can see, the set diameter is acceptable. Choosing the right idler roll diameter bring several advantages, such as: less cycles per minute and therefore higher rolling contact fatigue, and reduced wear between the roller and the belt.

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Figure 2.11 – Loaded volume with 3 roll troughing sets

Finally, with the conveyor belt geometry defined the load on the carrying trough-ing set can be calculated. First it is necessary to calculate the static load on the carrytrough-ing troughing set using equation 2.2:

Ca= a0(qb+

lV M · ρ

3.6.v )9.81[N] (2.2)

where a0 = 0.7m is the upper pitch of sets (2.13), qb = 9.9kg/m is the belt weight

(which is based on the belt width and material carried density), lV M = 5000m3/h, is the

volume of transported material, ρ = 2.4t/m3 _{is the iron ore density and v = 2.6m/s is}

the belt speed. The calculated value of Ca is 8,872 N.

By multiplying Ca by the work factors (equation 2.4) one determines the dynamic load (Ca1). The work factors are standardized and presented in Figures 2.15 to 2.18.

Ca1 = Ca · F s · F m · F d · F v[N] (2.3)

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Figure 2.12 – Maximum advised pitch of troughing sets.

Figure 2.13 – Roller diameter advised

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Figure 2.14 – Maximum speed and number of roller revolutions

Figure 2.15 – Service factor

Figure 2.16 – Environment factor

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Figure 2.17 – Impact factor

Figure 2.18 – Speed factor(CEMA, 2002)

three idler rolls in the set, the load in the central roll is obtained from a participation factor (see Figure 2.19). This results in a dynamic load, according to Equation 2.4, of

Ca1center = 7, 568N for the central idler roll.

Ca1 = Ca.F p[N] (2.4)

Notice that the RULMECA standard does not provide a participation factor for the lateral idler rolls, since the central one carries most of the weight, and therefore is the critical idler. However, in order to predict the efficiency of the troughing sets, the load in the lateral idler rolls is required. In this sense, the participation factor for lateral rollers was defined as F pl = (1 − F p)/2 in order to total 1. Thus F pl = 0.165, and the lateral

idler load is Ca · 0.165 = 1, 248 N.

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de-Chapter 2. Conveyor Belt Rollers 26

Figure 2.19 – Participation factor Fp - loaded rate on the most loaded roller

composed into radial and axial loads in the rolling bearings by considering the idler roll angle as 35o_.

Recalculating the load for a speed of 2.5m/s, which is slight lower than the max-imum, using the same operating conditions, it is found that the dynamic load Ca1 =

11744N. Therefore, using the participation factor, the load in the central roller is Fc =

7868.91N and on each of the lateral rollers is Fl = 1937.87N, as shown in Figure 2.20.

Figure 2.20 – Central and lateral loads on roller

Source: Author

To know the forces on each rolling bearing, the forces Fc and Fl on Figure 2.20

are applied on the center of mass of each of the three sections of the cross sectional area related to each roller. These forces need to be decomposed on each of the two bearings of each roller. In the central roller, the load can be equally distributed in the two bearings. However for the lateral rollers, the cross sectional area of the load was modeled and the center of mass found, on which the load is applied. The force was decomposed using the size of the roller and the position of the bearings. Figure 2.21 shows the free body diagram of the loads on the bearings.

The values of the radial and axial components on the bearings are shown on Table 2.1.

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Figure 2.21 – Bearings loads

Source: Author

Table 2.1 – Radial and axial forces components on bearings

Force Position Value

Flr1 = Flr6 Upper Lateral 1414.90 N

Flr2 = Flr5 Lower Lateral 522.96 N

Flr3 = Flr6 Central 3934.45 N

Fa1 = Fa2 = Fa5 = Fa6 Axial Lateral 555.76 N

The structural loads on the central roller are without a doubt the most significant ones. However, the lateral forces also need to be analysed in order to evaluate the influence of the axial component.

Figure 2.22 shows the relation between the forces on the rolling bearings and the volume of material transported in tons per hour.

Figure 2.22 – Force distribution for different rates of material transported

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28

3 GREASE COMPOSITION AND PROPERTIES

3.1 INTRODUCTION

The main reason lubricants are used is to reduce friction and wear between sur-faces in relative motion. Theoretically, any substance - solid, liquid or gas – placed between two surfaces to facilitate their relative slip is a potential lubricant. However, other char-acteristics are often demanded from lubricants, such as separation of the surfaces, low shear strength, good thermal conductivity, good oxidation and corrosion protection abil-ities and, because of environmental concerns, biodegradability and low toxicity. Some of these characteristics are inherent, such as low shear strength, while others are related to surface contact, such as protection against corrosion or film formation.

In an elasto-hydrodynamic contact the lubricant flows through the contact in a very small period (≈ 1ms), with contact pressure in the order of 1GPa or higher, being submitted to deformation rates up to 107_s−1 _{and temperature rises above 100}◦_C_.

These conditions of high and rapid variations in pressure and temperature inside the contact affects dramatically the properties of the lubricant. Therefore, characterization of physical, chemical, rheological and tribological behaviors of the lubricant inside the contact is challenging.

Such characterizations are even more complex when greases are used as lubri-cants, since their lubrication mechanisms are yet not as well understood as oil lubrication mechanisms (LUGT, 2012). This complexity can be expressed by the significant number of standard and nonstandard test methods used to qualify lubricating greases and their constituents (more than 100)/ (COUSSEAU, 2013).

Therefore experimentally understanding grease properties is an essential input to evaluate bearing performance in conveyor belt rollers (Figure 3.1).

3.2 GREASE DEFINITION

The most common definition of lubricating grease is the one from the American Society for Testing and Materials (ASTM D 288): "A solid to semi fluid product of a thickening agent in a liquid lubricant, other ingredients imparting special properties may be included" (ASTM, 1978). This definition means that a lubricating grease is a thickened - and not a thick - oil. So, it is a multi-phase system consisted of at least two well defined components, namely a thickener and a lubricating oil. The other ingredients refer to additives and co-thickeners. Usual distribution of this components on commercial greases is 65 to 95 wt % base oil, 5 to 35 wt % thickener and from 0 to 10 wt % additives

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Chapter 3. Grease Composition and Properties 29

Figure 3.1 – Work Flow Diagram - Grease Properties

Source: Author (DRESEL; HECKLER, 2000).

This multi phase structure of a grease can be compared to a wet sponge 3.2. The thickener works as the structure of the sponge and the lubricating oil permeates this structure like the water. The thickener gives consistency, but the oil is the lubricating agent.

Figure 3.2 – Analogy of grease working as a sponge

Source: Author

This complex composition provides semi-plastic behaviour that gives it some advantages over other lubricant fluids. But the lubricating ability depends on the com-ponents interactions and manufacturing process, which makes it difficult to characterize their individual influence on grease performance.

Lubricating greases are classified according to their consistency, which is defined by the National Lubricating Grease Institute (NLGI) grade based on a penetration test. The cone penetration test was standardized by ASTM D217 and ASTM D1403 for un-worked and un-worked greases, respectively. Table 3.1 shows the nine NLGI grades.

The NLGI grade alone is not sufficient for specifying a grease, but in combination with other properties it can quite well determine the suitability of greases for a specific application.

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Table 3.1 – NLGI grades

NLGI grade _{penetration at 25°C (0.1 mm)}ASTM worked (60 strokes) Appearance

000 445-475 fluid 00 400-430 semi-fluid 0 355-385 very soft 1 310-340 soft 2 265-295 "normal" grease 3 220-250 firm 4 175-205 very firm 5 130-160 hard 6 85-115 very hard

The lower the NLGI number, the softer the grease is. Most commonly rolling bearing greases have consistency between 1 and 2, because if it is not consistent enough it may leak and therefore do not provide the necessary lubrication on the contact; but if it is too consistent, it can leave the contact and not flow back.

3.2.1 GREASE BASE OIL

Lubricating greases typically contain 65 to 95 % in weight of base fluid. Since this represents a considerable portion of the grease, it has a large influence of the behavior of the finished grease. In order to fulfill its role in a certain application, the base oil needs to contain a combination of properties such as: solubility, oxidation stability, low evaporation loss, low temperature properties and viscosity. From this properties, the one that can influence the most rolling bearings performance is the viscosity, because different levels of base oil viscosity lead to different film thickness and friction response.

3.2.1.1 Definition of Viscosity

The viscosity of a fluid is a measure of a fluid’s resistance to internal shear defor-mation from a flow. This resistance can be determined with simple shear flow represented here by a laminar flow in permanent regime between a mobile surface with velocity V and a fixed fixed surface as shown in Figure 3.3. Considering a no-slip boundary condition, the fluid velocity ranges from 0 to V .

The behavior is consistent with the definition of a fluid, where if a shearing stress is applied to a fluid, it will deform continuously. The fluid between the plates moves with a velocity v = v(y). At any distance y from the fixed surface, the speed of the fluid is v; at y + dy the speed will be v + dv. Thus the shear stress, represented by τ is represented

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Figure 3.3 – Laminar flow between two plates

Source: Author by Newton’s formula in Equation 3.1.

τ = ηdv

dy (3.1)

where η is the dynamic viscosity and dv

dy is the variation of fluid speed with height,

referred as shear rate ˙γ. The equation 3.1 is the model for the generalized newtonian fluid. For any given fluid, viscosity can be a function of temperature, pressure, shear rate and time. If the viscosity is constant, curve 1 from Figure 3.4 presents a constant slope and the fluid is said to be Newtonian. If η = η( ˙γ), the fluid is a generalized non-Newtonian fluid (curves 2 to 4 from Figure 3.4).

Figure 3.4 – Variation of shear stress with shear rate for generalized newtonian fluids

Source: Author

A Newtoninan fluid has a constant viscosity; a pseudoplastic fluid is shear thin-ning (viscosity decreases with increasing shear rate); a dilatant fluid is shear thickethin-ning (viscosity increases with increasing shear rate); and a viscoplastic presents a "solid like" behavior with low shear rates, showing no deformation until a critical stress is reached, followed by a shear thinning behaviour. Lubricating greases are pseudoplastic fluids.

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Dynamic viscosity η in the International System is given in P a.s. Kinematic viscosity ν can be calculated from the dynamic viscosity with Equation 3.2.

ν = η

ρ (3.2)

where ρ is the density of the fluid in kg/m3 _{and ν is the kinematic viscosity in}

m2_/s_{, most commonly represented in mm}2_/s _{or cSt (centistoke).}

Viscosity dependence on temperature Thermoviscosity represents the variation

of viscosity with temperature. For lubricating oils, the viscosity decreases as the temper-ature increases. This dependence of the viscosity on tempertemper-ature is significant in EHD lubrication because of the observed temperature increase in the contact (inlet, high pres-sure and outlet zone).

One of the simplest thermoviscosity law is given in Equation 3.3 (CROUCH; CAMERON, 1961).

η= η0e−β∆T (3.3)

where η is the dynamic viscosity, η0 is the viscosity on the reference temperature,

∆T is the variation on the temperature from the reference and β is a constant experi-mentally determined with two temperatures and their respective viscosities. However, this equation is only valid for small variations of the reference temperature.

Another method more accurate is the one given by ASTM D341 standard (ASTM, 2009) shown in Equation 3.4.

loglog(ν + a) = n − mlog(T ) (3.4)

where ν is the kinematic viscosity, T is the temperature in Kelvin and m, n and

a are experimentally determined lubricant dependent constants.

There are other laws such as Vogel’s equation (equation 3.5)

ν= KeT +cb (3.5)

where ν is the kinematic viscosity, T in the temperature in Celsius and K, b and

c are constants determined experimentally.

Vogel’s equation is said to be a more realistic approximation for viscosity variation with temperature since it requires three experimental points to calculate the constants.

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But it gives a similar result as ASTM D341, which requires only two experimental points, that usually are provided on the lubricant data sheet.

Viscosity dependence on pressure Piezoviscosity represents the change in

vis-cosity with pressure. For lubricating oils, an increase in pressure results in an increase in viscosity. This behavior is important for predicting film thickness on EHD lubrication.

Barus (BARUS, 1893) proposed a simple law that describes the variation of vis-cosity with pressure shown in Equation 3.6 or in Equation 3.7 when the thermo viscous effect is also included.

η= η0Teαp (3.6)

η= η0eαp−β∆T (3.7)

where α is the pressure-viscosity coefficient given in P a−1_{, β is the thermoviscosity}

coefficient and p is the pressure on the lubricant.

The piezoviscosity coefficient can be approximated using Equation 3.8 (GOLD et al., 2001).

α= s · νt (3.8)

Where ν and t are constants given in Table 3.2.

Table 3.2 – Piezoviscosity coefficients for different base oils (GOLD et al., 2001)

Mineral PAO Ester

s 9.9040 7.3820 6.6050

t 0.1390 0.1335 0.1360

Viscosity dependence on shear rate In lubricating greases, the viscosity

depen-dence on shear rate is evident as described by Cousseau (2013) and shown in Section 3.4. The base oil presents a newtonian behavior under moderate pressures and shear rates. However under the more extreme conditions of an EHL lubrication, it can present a non-newtonian behavior.

This transition occurs up to the point where stress reaches a limiting shear stress. If the lubricant behavior on the contact was truly newtonian, considering a exponential increase of viscosity with pressure and very high shear stresses, significant coefficients

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of friction would have to be observed. But this does not happen, since relatively low coefficient of frictions like 0.05 are measured in these conditions.

The shear rate dependency in this situation is commonly defined in terms of the critical shear stress τ∗ that represents the newtonian limit. One frequently used model, given by equation 3.9, is the Ree-Eyring model (EYRING, 1936).

η η∗ = _{τ ∗} τ −1 sinh _{τ ∗} τ (3.9) Whereby, the viscosity is found to be temperature, pressure and shear rate de-pendent.

3.2.1.2 Base Oil Types

Base oils can be either mineral or synthetic. Mineral oils contain a variety of compounds because it undergoes a series of processes that depend on the crude and the technology used for refining. On the other hand, synthetic oils are prepared by the re-action of chemical compounds, so their properties can be tailored to the need. Typical applications for greases based on synthetic oils are those requiring a wide range of op-erating temperatures or enhanced chemical resistance. Environmental concerns such as biodegradability also lead to their use, however the cost is considerably higher.

Lubricating greases studied here have either synthetic or mineral oil as will be shown in section 3.4. There are several differences between mineral and synthetic oils, but the most important one for this study is the fact that mineral oil has a higher friction coefficient than synthetic ones as shown by Brandão et al. (2012). According to SKF (2018), the sliding friction coefficient in full film conditions is 0.05 for mineral oils and 0.04 for synthetic oils.

3.2.2 GREASE THICKENER

The thickener of a grease is a matrix that holds the base oil by mechanical en-trapment and a combination of Van der Waals and capillary forces. The system must offer a solid structure until operating conditions such as load, shear and temperature -initiate a viscoelastic response in the grease. In rolling bearings, the solid structure of the grease forms a lubricant reservoir and provides a sealing action by attaching to seals and cage.

Grease thickeners are usually classified as metal soaps or non-soap thickener. There are several types of thickeners for formulating greases, but in this work the soap thickeners evaluated are Lithium (Li) and Polyurea (Pu) ones, since they are the ones used in greases used to lubricated rolling bearings from conveyour belt idlers. It is important

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pointing out that the thickener influence on film formation and friction coefficient is not well understood. However, recently Cyriac et al. (CYRIAC et al., 2016) showed that the thickener morphology and concentration impact film thickness as shown in Figure 3.5. Based on Cyriac et al. observations, one conclude that greases formulated with Polyurea and ester oil present higher film thickness increase due to the thickener properties than greases formulated with lithium and mineral oil. In these study the lubricating greases were either Polyurea with ester oil or Lithium with mineral oil.

Figure 3.5 – Percentage increase in film thickness of the grease in comparison to the base oil as function of the ration between thickener concentration (ϕ) and average volume of thickener particle (V).

Source: (CYRIAC et al., 2016)

Figure 3.5 shows that grease film thickness is always greater than its base oil film thickness due to the interaction of grease composition. The amount of this increase depends on the type on grease.

However, it is important pointing out that grease properties, besides to depend on its constituents, also depend on their interaction and the manufacturing process. Therefore properties based on thickener and base oil type do not necessarily translate to grease performance.

3.2.3 GREASE ADDITIVES

Other components are added to the grease besides the base oil and thickener. Additives are used to enhance various aspects of lubricant performance. Some additives need to be available at the metal surface when others need to be thoroughly dispersed in the base oil or even in the thickener system.

The most common additives used in lubricating greases are: extreme pressure, corrosion inhibitors, anti-wear and friction modifiers which are surface active and antiox-idants and viscosity modifiers which are bulk active.

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Formulation of additives is a manufacturing secret and are difficult to find out by the end user. This makes it harder to associate additive effect on grease performance.

3.3 CHARACTERIZATION OF LUBRICATING GREASES

Rheology is defined by Macosko e Larson (1994) as the study of flow and defor-mation of materials. Therefore, it is essential for understanding and characterizing fluids submitted to flow. On this study, the focus is to obtain curves of viscosity as function of shear strain rate for greases.

3.3.1 FLOW TESTS

Flow curves usually describe the shear stress τ and the apparent viscosity η be-haviour between a large range of shear rates and temperatures at low pressure. Flow curves are taken on permanent regime, so no time-dependent characteristics can be as-sumed. Non-newtonian fluids such as lubricating greases show a non-linear relation be-tween shear stress and apparent viscosity. An example of viscosity versus shear rate for greases compared to a newtonian fluid such as lubricating oil is shown in Figure 3.6. Figure 3.6 – Apparent viscosity versus shear rate for (a) newtonian fluid and (b)

non-newtonian grease

Source: Author

The effect observed for greases is shear thinning, that is, the viscosity decreases with increasing shear rate.

Inside a rolling bearing, there are several components in contact, such as ball, inner and outer raceways, cage and seal. Figure 3.7 helps visualize several regions on a lubricated bearing. Since each component has a different type of movement, each region is subjected to different operation conditions.

With different pressures, temperature and shear rates, the lubricating grease presents different viscosity on each region. This makes it difficult to predict film thickness

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Figure 3.7 – Operation conditions inside a rolling bearing

Source: Author

and overall friction on a bearing. In this work, the apparent viscosity will be used to predict film thickness formation in the contact region (Zone B - Figure 3.7).

There are several models for predicting shear stress and apparent viscosity of lubricating greases. These models are important to extrapolate measures for very low and high shear rates due to the difficulty to measure them.

An example of viscosity behavior for lubricating greases is shown again in Figure 3.8. At very low shear rates (Zone 1) lubricating greases do not depend significantly on shear rate and the viscosity is very high. Increasing shear rate, shear thinning starts to occur, reducing viscosity orders of magnitude (Zone 2). As shear rate continues to increase, shear thinning becomes less significant and the viscosity reaches a second plateau, where this approximate newtonian behavior is believed to approach the base oil viscosity (Zone 3) (HURLEY, 2000).

A model that fits the viscosity behavior for lubricating greases reasonably well is the Cross model for pseudoplastic flow (CROSS, 1965).

η= η0− η∞

1 + (K ˙γ)m + η∞ (3.10)

where η0 is the viscosity at very low shear rates, η∞ is the viscosity at very high

shear rates and K and m are model constants.

By far the most frequently used method for measuring grease rheology is shear rheometry. Rheometers are equipment that can control either or both shear stress or shear rate to evaluate fluid properties. Sample fluids can be tested in several geometries, such as the ones shown in Figure 3.9.

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Figure 3.8 – Schematic representation of the apparent viscosity versus shear rate for lu-bricating greases

Source: (COUSSEAU, 2013)

to very rough surfaces. The selection of the appropriate shear rheometer, geometry type, surface finishing and operating conditions depend on the desired outputs and sample characteristics.

To characterize greases a large range of shear rate (10−6 _≤ _{˙γ ≤ 10}7_{) is essential to}

better characterize the range of viscosity expected in the three different zones presented in Figures 3.7 and 3.8. However, there are errors associated with range extremes. In low shear rates, wall slip is often observed while in high shear rates, leakages and edge effects can occur. Regarding geometries, parallel plates have some advantages over others in grease testing: they are less sensitive to grease leakage and edge effects due to the geometry and they are the only ones that allow control of gap-height that provides wider range of shear rates. As to surface finishing, rough surfaces are preferred over smooth as they are less sensitive to wall slip. However, extremely rough surfaces can promote secondary flows or not be reliably filled, altering results.

3.4 EXPERIMENTAL CHARACTERIZATION OF LUBRICATING GREASES

The selection of the greases for the conveyor belt bearing application can be very challenging since there is no consensus on the ideal type of grease. Table 3.3 presents some of the greases currently used by Vale on their conveyor belt idlers. On the other hand, Table 3.4 presents the greases recommended by SKF and Petrobras online tools.

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Figure 3.9 – Geometries for shear rheometer (a) concentric cylinder, (b) Vane-cylinder (c) parallel plates and (d) cone-plate

Source: (BAART, 2011) Table 3.3 – Greases used by Vale

Manufacturer Grease ν at 40 ◦C (mm2_{/s) ν at 100} ◦_{C (mm}2_/s)

Mobil (NSK) Polyrex EM 115 12.2

Shell (NSK) Gadus S2 (Alvania) 130 18

SKF MT33 100 10

Schaeffler (FAG) GA14 - Arcanol Multi2 68 7

Table 3.4 – Greases recommended for conveyor belt application Manufacturer Grease ν at 40 ◦C (mm2_{/s) ν at 100} ◦_{C (mm}2_/s) SKF LGWA2 EM 185 15 SKF LGHB2 420 26.5 Petrobras CGS-2-EP * 252 18.7 SKF LGMT2 * 110 11 SKF LGMT3 * 130 12 HP2 LGHP2 * 96 10.5

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In Table 3.4 the greases highlighted by a * were found by entering the application of conveyor belt idlers (general application - non mining industry) and the others were obtained as a function of the operating conditions data presented in section 2.3.

It is important to emphasize a significant difference between the viscosities of the recommended greases. There can be a difference of more than four times on the viscosity at 40◦_C_.

Six lubricating greases that could be used in rolling bearings of conveyor belt idlers were rheologically evaluated. The main properties provided by the grease manufacturer are presented in Table 3.5.

Table 3.5 – Greases properties

Grease SHELL_AS2 _POLYREX _LEGESKF GLi _LGMTSKF GADUS_{S2 1} Grease

Manufacturer Shell Mobil SKF Moly-grafit SKF Shell

Consistency 2 2 2 1 2 1

Base oil Mineral Mineral Ester Mineral_{+ ester} Mineral Mineral Thickener Lithium Poliurea Lithium Lithium Lithium Lithium

ν at 40C

(mm2_/s₎ 130 115 25 460 110 220

ν at 100C

(mm2_/s₎ 18 12.2 4.9 36 11 19

Of the many grease properties that can be evaluated, the most important for this work is the viscosity for several shear rates, so flow tests were performed.

All rheometry tests were performed with assistance of the CERNN Rheology Laboratory situated in UTFPR, using the rheometer Haake Mars III with parallel smooth plates with 35mm of diameter and three temperatures ( 40◦ _{C, 60}◦ _{C and 80}◦ _{C). To load}

the geometry, an excessive amount of grease was used to ensure fully filling the gap between plates. After setting the desired gap, the excess of grease was carefully removed from the edges of the geometry. Before the experiments, a temperature control and shear were executed to ensure all samples were in the same initial conditions. This pre-shear was performed to remove internal stresses that arise from manipulating the sample, as recommended for grease rheology evaluation (BAART, 2011).

After the pre-shear, tests were performed with a lower gap between the plates because leakage was observed and it is necessary to fully fill the geometry. The sample excess was removed after lowering gap. The lower gap also allows higher shear rates to be achieved in lower rotational speeds which prevents leakage.

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Separate tests were performed at 40◦_C _{, 60}◦_C _{and 80}◦_C _{to evaluate the}

temper-ature influence.

The sequence of steps is described below:

1. Temperature control at either 40◦_C_{, 60}◦_C _{or 80}◦_C _{for 600s with null stress}

2. Pre-shear with 250 µm gap

a) Shear rate ramp from 0.1 to 10s−1 _{during 120s}

b) Shear rate ramp from 10 to 0.1s−1 _{during 120s}

3. Rest for 10 minutes to ensure strain stabilization

4. Shear rate steps up to 1000s−1 _{with 25 steps logarithmic distributed and a 175 µm}

gap. To ensure the test has reached steady conditions on each step, the gradient of the stress response was analyzed. If the variation on stress between two measures is lower then 5% after seven seconds, proceed to the next step.

Larger shear rates than 103 could not be achieved because leakage was observed.

For these conditions, the tests were repeated twice. Figure 3.10 presents an example of the main results of viscosity as a function of shear rate for one grease.

Figure 3.10 – Modelled curve of viscosity at 60◦_C _{versus shear rate}

Source: Author

In Figure 3.10 and on the other data collected from the rheological tests, it is possible to observe the trend of the Cross Model Equation and how it fits the data. In low shear rates, the difference between the two measurements can be significant, but in the scope of this work it is not very relevant since the shear rates the bearings operate are about ˙γ ≈ 105_s−1_{. In this higher shear rate, the difference between the two fitted curves}

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In Appendix A it is presented the experimental data and the curves for all six greases studied in the three temperatures. Constants for the Cross model for greases were fitted on the experimental results and are shown in Tables 3.6, 3.7 and 3.8. The experimental data from Figure 3.10 reached low shear rates ˙γ ≈ 10−5_{, which provides}

data to evaluate viscosity at low shear rates necessary in Cross model (Equation 3.10) as an average of the first measured data. The η∞ was estimated as the base oil viscosity. For

speeds over ≈ 106_{, grease viscosity can be approximated by base oil viscosity, although}

some researchers disagree with this method. There are studies ((COUSSEAU, 2013)) that show that grease bled oil, which is the oil extracted from the grease contains information about the thickener and can behave differently from the base oil. Here, grease base oil provided by the grease manufacturer will be considered for the calculations regarding high shear rates.

Table 3.6 – Cross model constants for greases at 40◦_C

Grease Viscosity η0 (P a.s) Base Oil Viscosity η∞ (P a.s) Constant K (s) Constant m(-) SHELL AS2 2.07 · 105 117 · 10−3 _{2.52 · 10}3 0.779 POLYREX 0.73 · 105 _{104 · 10}−3 _{0.399 · 10}3 _0.851 SKF LEGE 4.99 · 105 _{22.5 · 10}−3 _{0.263 · 10}3 _0.998 GLi 2.28 · 105 _{414 · 10}−3 _{2.34 · 10}3 _0.818 SKF LGMT 2.49 · 105 _{99.0 · 10}−3 _{1.84 · 10}3 _0.838 GADUS 1 3.06 · 105 198 · 10−3 _{4.96 · 10}3 0.767

Grease Viscosity η0 (P a.s) Base Oil Viscosity η∞ (P a.s) Constant K (s) Constant m(-) SHELL AS2 1.54 · 105 _{42, 7 · 10}−3 _{5.00 · 10}3 _0.759 POLYREX 0.68 · 105 _{40.0 · 10}−3 _{0.355 · 10}3 _0.887 SKF LEGE 7.58 · 105 11.4 · 10−3 _{0.682 · 10}3 0.960 GLi 2.10 · 105 144 · 10−3 _{2.83 · 10}3 0.827 SKF LGMT 1.50 · 105 _{37.1 · 10}−3 _{1.58 · 10}3 _0.838 GADUS 1 4.91 · 105 _{70.4 · 10}−3 _{1.60 · 10}3 _0.766

No relationship between the Cross Model constants from Tables 3.6, 3.7 and 3.8 and the temperature was found. Therefore, to know the behavior of the viscosity in a different grease, a new rheological test would have to be performed.

On the other hand, overall the behavior of decrease in viscosity with increase of temperature was observed, such as shown in Figure 3.11.

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Grease Viscosity η0 (P a.s) Base Oil Viscosity η∞ (P a.s) Constant K (s) Constant m(-) SHELL AS2 1.42 · 105 _{19.9 · 10}−3 _{5.82 · 10}3 _0.783 POLYREX 0.11 · 105 _{19.4 · 10}−3 _{0.992 · 10}3 _0.864 SKF LEGE 7.49 · 105 6.7 · 10−3 _{1.54 · 10}3 0.911 GLi 1.18 · 105 _{62.7 · 10}−3 _{1.15 · 10}3 _0.869 SKF LGMT 1.17 · 105 _{17.6 · 10}−3 _{6.14 · 10}3 _0.774 GADUS 1 1.02 · 105 _{31.9 · 10}−3 _{2.55 · 10}3 _0.797

In Figure 3.11, it is possible to see that the measurements in low shear rates is not accurate since the viscosity doesn’t decrease with temperature. But for higher shear rates - scope of this work - the behavior of viscosity with temperature is as expected and essential for further calculations of film thickness and friction torque.

In Figure 3.12, it is possible to compare apparent viscosity curves for the studied greases. Each grease viscosity has a different behavior with changes in shear rate: not always the grease with lower base oil viscosity is the one with lowest viscosity for any shear rate. For example, SKF LEGE has the lowest base oil viscosity at high shear rates, but presents the highest viscosity at low shear rates.

Since film thickness and traction coefficient depend on the lubricant viscosity, the apparent viscosity is the most adequate value to use, instead of the commonly used base oil viscosity. That assumption for EHL contacts is based on the fact that in most cases shear rate values are above 106 _s−1_{, and in this condition grease performance can}

be described by its base oil performance. But for lower shear rates, this may not be an accurate approximation, as it will be shown in chapeter 4.

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Figure 3.11 – Modelled curve of viscosity at 40◦

C, 60◦C and 80◦C for greases