Optimizing Friction Losses of Conveyor Systems Using Large-Diameter Idler Rollers

Abstract

This study investigates the influence of idler roller diameter on indentation rolling resistance and idler rotating resistance in belt conveying systems, crucial for long-distance bulk material transport. It encompasses the impact on grease-lubricated rolling bearings, grease-filled labyrinth seals, and lip seals, with the aim of optimizing energy consumption. Experimental devices were used to refine predictive models, demonstrating that larger idler rollers reduce both resistances, leading to a 40% to 55% efficiency improvement. The study offers a detailed breakdown of friction losses under various operating conditions and provides valuable insights for lubricant selection and system enhancement, highlighting the significance of idler roller diameter in reducing energy costs and enhancing system performance.

Full text

Received: 16 December 2024
Revised: 29 January 2025
Accepted: 13 February 2025
Published: 26 February 2025
Citation: Cousseau, T.; O’Shea, J.;
Robinson, P.; Ryan, S.; Hoette, S.;
Badat, Y.; Carr, M.; Wheeler, C.
Optimizing Friction Losses of
Conveyor Systems Using
Large-Diameter Idler Rollers.
Lubricants 2025,13, 104.
https://doi.org/10.3390/
lubricants13030104
Copyright: © 2025 by the authors.
Licensee MDPI, Basel, Switzerland.
This article is an open access article
distributed under the terms and
conditions of the Creative Commons
Attribution (CC BY) license
(https://creativecommons.org/
licenses/by/4.0/).
lubricants
Article
Optimizing Friction Losses of Conveyor Systems Using
Large-Diameter Idler Rollers
Tiago Cousseau 1,* , Jayne O’Shea 2, Peter Robinson 1, Shawn Ryan 3, Stephan Hoette 4, Yusuf Badat 2,
Michael Carr 1and Craig Wheeler 1
1School of Engineering, University of Newcastle, University Drive, Callaghan, NSW 2308, Australia;
peter.w.robinson@newcastle.edu.au (P.R.); michael.j.carr@newcastle.edu.au (M.C.);
craig.wheeler@newcastle.edu.au (C.W.)
2TUNRA Bulk Solids, 70 Vale Street, Shortland, NSW 2307, Australia; jayne.oshea@newcastle.edu.au (J.O.);
yusuf.badat@newcastle.edu.au (Y.B.)
3Big Roller Overland Conveying Company, Spionkop Road, Grass Valley, WA 6403, Australia;
shawn@bigrollerolc.com
4ContiTech Australia, 7 Dunlop Court, Bayswater, VIC 3153, Australia; stephan.hoette@continental.com
*Correspondence: tiago.cousseau@newcastle.edu.au
Abstract: This study investigates the influence of idler roller diameter on indentation rolling
resistance and idler rotating resistance in belt conveying systems, crucial for long-distance
bulk material transport. It encompasses the impact on grease-lubricated rolling bearings,
grease-filled labyrinth seals, and lip seals, with the aim of optimizing energy consumption.
Experimental devices were used to refine predictive models, demonstrating that larger
idler rollers reduce both resistances, leading to a 40% to 55% efficiency improvement. The
study offers a detailed breakdown of friction losses under various operating conditions
and provides valuable insights for lubricant selection and system enhancement, high-
lighting the significance of idler roller diameter in reducing energy costs and enhancing
system performance.
Keywords: conveyor systems; indentation rolling resistance; idler rotating resistance;
large-diameter rollers; energy efficiency
1. Introduction
Belt conveying systems are highly effective for transporting large quantities of bulk
materials over long distances, offering continuous, cost-effective, and energy-efficient
solutions [
1
]. However, despite their efficiency, belt conveyors contribute significantly
to the overall operating costs of mines due to factors such as increasing transport route
lengths and rising electricity costs. Consequently, optimizing energy consumption in belt
conveying systems has become increasingly important.
Numerous solutions have been proposed in the literature to enhance the efficiency and
reliability of belt conveying systems. These solutions are rooted in early studies by Hager
and Hintz, which identified the main resistances in belt conveying systems, including
indentation rolling resistance (IRR), idler rotating resistance, flexure resistance, and sec-
ondary resistances [
2
]. While most recent studies align with [
2
]’s findings, variations in
resistance contributions have been reported depending on system characteristics, with idler
rotating resistance varying from 5% to 60% of the total [3,4].
Improvements in belt conveying systems range from disruptive technological solu-
tions like rail-running conveyors [
5
] to energy-efficient component designs such as rubber
Lubricants 2025,13, 104 https://doi.org/10.3390/lubricants13030104

Lubricants 2025,13, 104 2 of 26
bottom covers [
6
] and improved idler rollers [
7
–
11
]. However, existing predictions for eval-
uating idler rotating resistance often diverge significantly from experimental results [
12
],
hindering performance optimization. Current models also overlook the influence of grease
properties on rolling bearings [
13
], labyrinth seals [
14
], and lip seals [
15
], as detailed in
the next section. Furthermore, while some studies have explored the impact of idler roller
diameter on indentation rolling resistance [
9
,
11
], its effect on idler rotating resistance
remains unexplored.
In light of these gaps, this research investigates the effect of idler roller diameter on
both indentation rolling resistance and idler rotating resistance, aiming to provide insights
for optimizing friction losses in conveyor systems.
2. Background
The diameter of idler rollers directly impacts the indentation rolling resistance and
idler rotating resistance of conveying systems, while having minimal effect on flexure
resistances, which are primarily determined by conveying material physical and flow
properties, belt viscoelastic properties, and idler spacing [
4
]. As such, it is essential to
critically examine both experimental devices and theoretical models used to assess these
key components of friction. In this section, we provide an overview of indentation rolling
resistance and idler rotating resistance, focusing on the measurement techniques and
predictive approaches employed to quantify these frictional phenomena.
2.1. Indentation Rolling Resistance
Indentation rolling resistance arises from the contact behavior as the belt moves over
an idler surface. It results from the viscoelastic response of the belt cover to stress, with the
cover typically relaxing at a slower rate than the rate of indentation, based on belt velocity.
This difference leads to an asymmetric pressure distribution across the idler shell, resulting
in unequal contact lengths about the centerline of the idler roll. As depicted in Figure 1,
the majority of the load is located on the leading edge of the roller, generating a resistance
torque (Tind).
Figure 1. Mechanism of indentation rolling resistance: (left) Cyclic compression and recovery. (right)
Asymmetric pressure distribution. Adapted from [9].
Indentation rolling resistance is influenced by both component and operating variables.
Component variables such as idler roller diameter, belt cover thickness, the viscoelastic
material properties of the bottom belt cover, cord diameter, and pitch for steel cord belts
affect IRR. Additionally, operating conditions such as temperature, belt speed, and belt
load play a role [16].
Various test setups are used to measure indentation rolling resistance, including
methods described in the German standard DIN EN 16974 [
17
] and Australian Standard

Lubricants 2025,13, 104 3 of 26
AS 1334.13:2017 [
18
]. These methods typically measure IRR directly using an instrumented
idler roll, as a function of normal load, for specific parameters such as pulley cover com-
pound and thickness, belt speed, temperature, and idler roller diameter [
9
,
19
,
20
]. A detailed
explanation of the test method used in this work is provided in Section 3.1.
Prediction of IRR is facilitated by several numerical and analytical models. One widely
used model, developed by Jonkers in 1980 [
21
], was incorporated into the conveyor design
standard CEMA 6th edition. However, subsequent studies revealed that Jonkers’ equation
overestimates IRR due to its simplistic treatment of strain history [
6
]. This led to the
development of alternative predictive models [
22
,
23
]. A small sample IRR model was
developed and incorporated into the CEMA 7th Edition to calculate IRR for four specific
conveyor belt compounds. For this paper, the QC-N analytical model [
6
], known for its
accuracy and simplicity, has been utilised to predict IRR. This one-dimensional model
accounts for viscoelastic material properties determined from dynamic mechanical analysis
(DMA) testing and includes a ‘transient term’ to consider the contact stresses transient
response to indentation deformation, making it a preferred choice for predicting IRR [
24
].
The model is detailed in Appendix A.
2.2. Idler Roller Rotating Resistance
The primary function of a conveyor idler roller is to support and guide the conveyor
belt along the conveyor frame, ensuring smooth and efficient material movement. As de-
picted in Figure 2, it typically consists of a roller shell (1) connected to the shaft (4) through
rolling bearings (2), and a sealing system composed of grease-filled labyrinth seals (3)
and lip seals (5) that prevent lubricant leakage and contamination ingress. Depending
on the application, rolling bearings may be open, they may contain shields or seals, lip
seals may be disregarded or used in multiple locations, and labyrinth seal designs can
vary significantly. Generally, in applications where durability is essential, rolling bearings
with integral seals and lip seals are used along with labyrinth seals. In contrast, applica-
tions in cleaner environments focused on efficiency prefer shielded rolling bearings and
grease-filled labyrinth seals, with lip seals potentially omitted.
Figure 2. Schematic view of an idler roll.
The rotational resistance of an idler roller is the sum of the rotational resistance (friction
torque) of its rolling bearings, grease-filled labyrinth seals, and lip seals. As the friction
torque of these elements varies differently with load, temperature, and operating speed, it
is challenging to determine their individual contributions. However, a typical breakdown
of components contributing to conveyor idler roller rotating resistance is approximately
50% for the rolling bearings, 25% for labyrinth seals, and 25% for lip seals [12].

Lubricants 2025,13, 104 4 of 26
2.2.1. Rolling Bearing Rotating Resistance
Rolling bearing rotating resistance refers to the heat dissipated during bearing oper-
ation, resulting from resistance encountered as rolling elements move against lubricated
inner and outer races. Understanding such resistance in rolling bearings is crucial for
energy-saving and optimizing bearing performance in idler rollers. Efficient transmissions
generate less heat, wear, and power loss, reducing environmental impact from worn-out
mechanical components and lubricants.
Different setups are utilized to measure rolling bearing rotating resistance, which can
be divided into two groups: single contact measurements and full bearing tests. Single con-
tact measurements use a ball-on-disc device to measure the friction coefficient and predict
rolling bearing friction torque [
25
]. Although these tests offer a quick and cost-effective
approach for the initial development of low-friction grease formulations, it is important
to note that their applicability may vary, especially with aged lubricating greases [
13
].
On the other hand, full rolling bearing tests, which are widely accepted, directly measure
the rolling bearing rotating resistance using force or torque cells under specific operating
conditions [
12
,
19
,
26
]. A detailed explanation of the test rig used in this work is provided in
Section 3.2.
Numerous models can be found in the literature for estimating the internal friction
torque of rolling bearings [
27
–
31
]. While models provided by bearing companies like
Schaeffler and SKF are derived from extensive experimental data, accurately predicting
grease-lubricated rolling bearing friction torque remains a challenge due to uncertainties in
the thickness and properties of the lubricant film separating the surfaces [
32
]. Consequently,
there are various model proposals in the literature, with few showing good agreement with
experimental results [
33
], while the majority exhibit differences of up to 500% [
34
–
36
]. The
application of friction torque models to predict idler rolling bearings’ friction losses has
been limited, with discrepancies of three times between predictions and measurements
reported [
3
,
12
]. Due to uncertainties in predicting rolling bearing efficiency, especially
under idler roller operating conditions (low speeds and high loads), experimental results
were analyzed using a couple of friction torque models. The current SKF friction torque
model showed the best agreement, providing improved insights into bearing operating
conditions and enabling performance optimization. Details of the friction torque model are
provided in Appendix B.
2.2.2. Grease-Filled Labyrinth Seal Rotating Resistance
Labyrinth seals are essential for preventing water and dust from entering the bearing’s
rolling elements. In idler roller applications, these seals, typically packed with lubricating
grease, maximize sealing effectiveness while maintaining lower friction compared to contact
seals. The labyrinth seal design includes a stationary component fixed to the idler roller
shaft and a rotating element enclosed within the idler housing. Practical guidelines for
labyrinth seal design, along with detailed explanations of its function and geometrical
examples, are provided by Bosch [37,38].
The design of labyrinth seals results in viscous drag due to grease shearing between
the stationary and rotating surfaces. The resulting friction torque is primarily influenced
by the grease viscosity, as well as the specific geometry of the labyrinth seal and the idler
roll’s rotational speed. Laboratory setups for measuring labyrinth seal friction losses are
presented in [
37
]. The measurement principle involves applying rotational speed to one
part of the labyrinth seal and measuring the torque or force required to shear the grease in
the other part under controlled operating temperature and speed. Details of the test rig
used to measure labyrinth seal friction losses are provided in Section 3.2.

Lubricants 2025,13, 104 5 of 26
Friction losses in grease-filled labyrinth seals have not been extensively explored in
the literature. Only three approaches have been utilized. Wheeler solved the mass and
momentum equations, considering the grease’s apparent viscosity equal to its base oil
viscosity, resulting in a linear relationship between rotational speed (shear rate) and shear
stress [
12
]. Predictions were compared with experimental results, showing differences of
up to 100% in specific conditions. Augusto et al. [
14
] also solved the mass and momentum
equations but considered the shear-thinning behavior of the grease, modeling it using
the Herschel–Bulkley equation. Unfortunately, Augusto’s results were not compared to
experiments. Lastly, Bosch measured the friction losses of grease-filled labyrinth seals over
extended periods and observed the formation of an air gap within transparent labyrinth
seals due to grease leakage, leading to friction losses tending toward zero over time [
37
].
He concluded that even a small quantity of grease leakage from the labyrinth seal would
lead to negligible friction losses. Grease leakage and air gap formation were also observed
in [
39
]. In idler rollers, grease leakage may occur if labyrinth seals are not sealed with lip
seals, if the pressure generated due to thermal expansion of the grease within the labyrinth
seal exceeds the lip seal resistance, or if the lip seal wears off. The used grease-filled
labyrinth seal friction torque models are summarized in Appendix C.
2.2.3. Lip Seal Rotating Resistance
Lip seals play a crucial role in preventing grease leakage from labyrinth seals and
external contaminant ingress into the system. Typically made of elastomers, these soft
and flexible compounds minimize wear on contacting parts and operate with low friction
while effectively sealing the system. In most idler rollers, an outer lip seal is mounted
to the stationary shaft and makes contact with the labyrinth seal outer surface; the inner
lip seal, if included, contacts the shaft. However, the configuration of lip seals in idler
rollers varies depending on the application. Idler rollers designed for overland conveying
systems, aimed at reducing drag, often rely solely on grease-filled labyrinth seals, while
those intended to prevent dust and high-pressure water contamination may incorporate
multiple contacting lip seals. Figure 3illustrates common commercial solutions combining
labyrinth and lip seals in idler rollers with the same rolling bearing size.
Figure 3. Labyrinth and lip seal designs: radial labyrinth seal without a shaft lip seal (left), radial
labyrinth seal with one contacting lip seal (center), and axial labyrinth seal with two contacting shaft
lip seals (right). Contacting points highlighted in red.
As lip seals are vital for ensuring proper lubrication with minimal contamination in
many applications, extensive literature exists on measuring and predicting their perfor-
mance. Laboratory rigs for measuring lip seal friction losses of various types can be found
in [
40
–
42
]. Most devices assemble a static lip seal against a rotating shaft and measure the

Lubricants 2025,13, 104 6 of 26
rotation resistance of the sealing housing using load or torque cells. The specific device
used in this work will be detailed in Section 3.2.
Similar to rolling bearings, several models have been proposed in the literature to
predict lip seal friction losses [
15
,
42
]. These models generally agree on the dependence
of friction torque on contact pressure, contact area, friction coefficient, and the radius
of contact between surfaces. Calculations of contact pressure and contact area typically
involve finite element analysis for a given load, sample geometry, and material properties.
Elastic materials, such as the shaft, are described using the elastic modulus and Poisson‘s
ratio, while hyper-elastic materials, such as lip seals, are modeled using the Mooney–
Rivilin model [
42
]. The friction coefficient between contacting materials is often considered
constant under usual operating conditions, although some researchers incorporate grease
properties to account for EHL film formation on low-contact pressure-bearing seals [15].
These models are usually run for various operating conditions, and their results, along
with experimental data, are used to develop simpler diagrams and analytical equations.
The SKF seal friction torque diagram and model are one such example ([
27
,
43
], respectively).
This model considers an optimal contact pressure for a given lip seal type, ensuring proper
sealing without excessive friction or wear, and therefore depends only on the seal type and
the radius of contact. As demonstrated later, our measurements were independent of speed
and closely aligned with the diagram proposed in [
43
], and the model proposed in [
27
],
which is presented in Appendix B(Equation (A15)).
3. Materials and Methods
The effect of idler diameter on the overall efficiency was evaluated using two test
rigs operated by TUNRA Bulk Solids at The University of Newcastle, Australia: the
large indentation rolling resistance, and the idler rolling rotating resistance. These rigs
were chosen for their ability to provide comprehensive insights into the performance of
idler rollers under varying conditions. Details of the equipment and their operations
are presented in [
9
,
12
], respectively. Therefore, just a short description of the tests is
presented here.
3.1. Indentation Rolling Resistance Rig
The effect of idler diameter on IRR was evaluated in line with Australian Standard
AS 1334.13. Experiments were conducted using four different test idler sizes at three
operating temperatures, covering a range of belt loads and speeds typical of conveying
systems. The test conditions, summarized in Table 1, aimed to replicate real-world scenarios
to understand how idler diameter influences IRR. The tested belt main features, which are
required to run the QC-N model, are presented in detail in [24] as Compound A.
The test facility setup, depicted in Figure 4, featured idler rollers with diameters
of 152.4 mm and 400 mm. By varying idler size and operating conditions, the study
aimed to provide a comprehensive understanding of how idler diameter affects IRR. A full
description of the test rig is given in [4].
Table 1. Testing details for IRR measurements.
Parameter, Unit Value
Belt Bottom Cover Temperatures, °C 0, 20 and 40
Belt Bottom Cover Thickness, mm 9
Simulated Belt Sag, % 1.0
Idler Roller Diameters, mm 152.4, 219, 316 and 400
Belt Speeds, m/s 1.0 to 8.0
Load Per Belt Width, kN/m 1.0 to 8.0

Lubricants 2025,13, 104 7 of 26
Figure 4. Test facility setup with the 152.4 mm and 400 mm diameter test idlers.
3.2. Idler Roller Rotating Resistance Rig
To assess the impact of idler diameter on rotating resistance, a specialized roller was
designed and assembled to accommodate different rolling bearings, labyrinth seals, and lip
seals. Tests were conducted using the same idler roller but at varying speeds to account for
the effect of idler diameter on rotating resistance, as big rollers might use the same rolling
bearing and sealing package as standard rollers. Different loads and temperatures were also
employed to assess the impact of the operating conditions on the idler rolling resistance.
Figure 5presents the test rig and the idler roller of 152 mm in its two configurations,
one that accommodates grease-filled labyrinth seals and one for lip seals. A full description
of the test rig is given in [12].
Figure 5. (left) Idler rotating resistance measurement apparatus; (center) tested idler schematic view
with lip seals and (right) with labyrinth seals.
During the test, the desired vertical load is applied to the roller, which is gradually
accelerated to the belt speed. The test continues until a steady state condition, observed by
the stabilization of the measured force, indicating that the grease has reached its equilib-
rium temperature. This process is repeated twice across a range of ambient temperatures
measured at the rolling bearing inner race, based on the climate conditions in which the
conveyor will operate. Since both temperature and friction torque are mutually dependent,
all measured data are plotted in the Results Section. To assess the components’ individual
contributions, three sets of tests were conducted: (i) first, only the rolling bearings were
assembled in the idler roller; (ii) then, grease-filled labyrinth seals were mounted (Figure 5
right); and (iii) finally, the labyrinth seals were replaced by the lip seals (Figure 5center).
To assess the lip and grease-filled labyrinth seals’ individual contributions, the rolling
bearing friction torque is subtracted from the measurements performed in test sets i and ii.
It is important to mention that in prior testing, rolling bearings and lip seals ran for 12 h to
overcome the running phase and grease accommodation.
Tests were performed using SKF deep-groove ball bearings 6305-2RS1-C3 (SKF, New-
castle, Australia), as recommended by SANS 1313-3:2012 [
44
] for troughing and impact
rollers of series 25 (shaft diameter 25 mm). These rolling bearings are factory-lubricated

Lubricants 2025,13, 104 8 of 26
with a specific amount of the standard MT47 grease, a lubricant widely used in rollers
equipped with SKF rolling bearings, and were tested in a range of temperatures, speeds
and loads with and without one of the seals (RS) to assess the contribution of the seal to
rotating resistance.
Additionally, a radial grease-filled labyrinth seal, designed based on Bosch guide-
lines [
37
], was tested using Shell Alvania 2 grease at varying temperatures and speeds,
as load does not affect friction losses in labyrinth seals. This type of grease is commonly
used in grease-filled labyrinth seals [
15
] due to its NLGI 2 consistency, which prevents
grease leakage and contaminant ingress. Its low base oil viscosity and high flow index
minimize friction losses, and its inexpensive multipurpose formulation is suitable for ap-
plications where special properties, such as extreme pressure or anti-wear characteristics,
are unnecessary. To prevent grease leakage and excessive temperature rise during testing,
the labyrinth seals were re-greased before each test. Testing was conducted over very short
durations (10 min), as recommended in [12].
Lip seals, representative of common designs (see Figure 3), were tested against shaft
collars of various diameters to account for different contact pressures, and at different
rotational speeds.
The experimental procedures aimed to capture the impact of idler diameter and
operating conditions on rotating resistance. Table 2provides the tested operating conditions
for the rolling bearings, labyrinth seals, and lip seals. Rolling bearing and grease properties
relevant for the friction losses calculations are also provided.
Table 2. Operating conditions and grease properties used for rim drag tests.
Parameter, Unit Value
Belt Speed, m/s 1–4.2
Rotational Speed, rpm 150–600
Normal Load, N 250, 550
Ambient Temperature, °C 0–40
Idler Roller Diameter, mm 167
MT47 grease
Kinematic Viscosity at 40 °C, mm2/s 70
Kinematic Viscosity at 100 °C, mm2/s 7.3
Shell Alvania grease
Kinematic Viscosity at 40 °C, mm2/s 110
Kinematic Viscosity at 100 °C, mm2/s 11
4. Results
This section presents the experimental results of indentation rolling resistance (IRR) and
idler rotating resistance, with a focus on the effect of roller diameter and operating conditions.
4.1. IRR Results
The measured horizontal force during testing comprises the indentation rolling resis-
tance, the rotating resistance of the test idler due to bearings and seals, and belt flexure
forces resulting from the belt flexing between the hold-down rollers and measurement
roller to simulate a sag ratio of 1%. Direct measurement of the rotating resistance of the
test idler roller was conducted during testing, while the forces due to belt flexure were
determined using the method described in AS 1334.13 and detailed in [
9
]. After removing
both force components from the measured horizontal force results, only the indentation
rolling resistance force component remained.

Lubricants 2025,13, 104 9 of 26
Figure 6illustrates the measured indentation rolling resistance for the four idlers tested
at three temperatures, six speeds, and five loads, totaling 360 measurements. Additionally,
measurements were repeated twice for all rollers and temperatures at 5 m/s and 8 kN/m,
resulting in two additional sets of 12 measurements each. The standard deviation was
calculated for each roller diameter and temperature combination, yielding an average value
of 1.3 N. This aligns with the statistical analysis presented in [
45
], which demonstrated that
indentation rolling resistance can be determined with high repeatability and low standard
deviations (S < 2 N), making it suitable for validating simulation models.
Figure 6. IRR measurements in N/m.
The measurements reveal that the indentation rolling resistance performance of the
tested belt improves with increasing diameter and temperature, and decreasing load and
speed, although the effect of speed is minor and more significant at low temperatures.
This observation and the IRR values align with both on-site observations and recent
research [45–48].
It is logical to expect that a reduction in temperature causes the rubber to harden,
leading to smaller contact area, and thus a decrease in indentation. However, in reality,
the viscoelastic relaxation of the rubber slows with reduced temperature, exacerbating
the asymmetry (Figure 1, ratio
a/b
), and magnitude of the pressure distribution. This
phenomenon results in higher offset (
d
) and magnitude of the equivalent force (
Tind
),
leading to an increase in rolling resistance. The viscoelastic response of the conveyor belt
also depends on the operating speed, and therefore, the effect of speed is temperature-
dependent. The experimental data showed that IRR increases with speed at a very low rate
(0.1–0.2 N/m/s), with larger rates at lower temperatures.
Increasing idler diameter or reducing the load reduces IRR, albeit through a different
mechanism. Increasing idler diameter results in an increase in the contact area, and thus a
reduction in the magnitude of contact pressure. Meanwhile, reducing the load leads to a
direct reduction in contact pressure. In both cases, the pressure distribution profile (
a/b
)
remains the same. Therefore, the reduction in IRR primarily occurs due to a decrease in
the magnitude of the equivalent load. Experimental data showed that IRR decreases in a

Lubricants 2025,13, 104 10 of 26
power fashion with idler diameter (
≈
d
−2/3
), while it increases with load (
≈
Load
4/3
) for
usual operating conditions.
The benefits of using large idlers are illustrated in Figure 7, showing the percentage of
savings achieved by using 400 mm idlers compared to 153 mm idlers at all tested tempera-
tures (100
−(IRR400 /IRR153)×
100). The benefits range from 30% to 70%, with savings
of approximately 50% observed under typical operating conditions (5 kN/m and 5 m/s)
regardless of the operating temperature. However, it is important to note that at lower
loads (
≤
3 kN/m), where IRR values are low (refer to Figure 6), the savings exhibit signifi-
cant fluctuations.
Load per Belt Width, kN/m
Speed, m/s
IRR savings at 0°
C, %
2345678
2
4
6
8IRR savings at 20°
C, %
2345678
IRR savings at 40°
C, %
2345678
30
40
50
60
70
Figure 7. Percentage of IRR savings when using a 400 mm idler roller compared to 153 mm diameter
rollers. Values are indicated by the colored bar.
The QC-N model described in Appendix Awas applied and compared to the ex-
perimental results. To assess the model’s accuracy, Figure 8a presents a comparison for
idler rollers with diameters of 153 mm and 400 mm, tested at speeds of 4 m/s and 8 m/s,
temperatures of 0
◦
C and 40
◦
C, and loads ranging from 2 kN/m to 8 kN/m. Figure 8b
displays the measured versus predicted results and residuals for all tests. Consistent with
previous findings [
24
], the QC-N model demonstrates excellent performance for efficient
belts, with a correlation coefficient of R = 0.99 and a mean difference of 0.47%, although a
maximum difference of 23.8% was observed at very low speeds. This indicates that the
method is suitable for predicting IRR within the tested conditions.
2345678
Load per belt width, kN/m
0
5
10
15
20
25
30
35
40
IRR, N/m
Diamet.
153
400
Speed
4
8
Temp.
0
40
(a)
0 5 10 15 20 25 30 35 40
IRR Measurements, N/m
-5
0
5
10
15
20
25
30
35
40
IRR QC-N Model, N/m
Data
Residuals
(b)
Figure 8. (a) QC-N model (lines) versus measured data (points) for selected conditions. (b) QC-N
model versus experimental results and its residuals.
4.2. Rolling Bearing Results
Figure 9a depicts friction torque values as a function of the product of rotational
speed, operating viscosity, and mean diameter for three room temperatures, two loads
and two seal arrangements, which is typical for evaluating rolling bearings. Meanwhile,
Figure 9b presents a comparison between predictions and measurements, along with
the residuals.

Lubricants 2025,13, 104 11 of 26
12345678
n dm106
0
50
100
150
200
250
Rolling Bearing Friction Torque, Nmm
Temper.
10
20
40
Speed
150
300
450
600
Seal
1RS1
2RS1
Load
250
550
(a)
0 50 100 150 200 250
Rolling Bearing Friction Torque Measurements, Nmm
-50
0
50
100
150
200
250
SKF Friction Torque Model, Nmm
Data
Residuals
(b)
Figure 9. (a) SKF friction torque model (lines) versus measured data (points) as function of grease
viscosity and operating conditions. (b) SKF friction torque model versus experimental results and
its residuals.
In general, similar trends are observed between the predicted (continuous lines) and
measured (dots) friction torque values regardless of the operating temperature, speed, load,
or seal type. These data yield a correlation coefficient of R = 0.89, a mean difference of 8.7%,
and a maximum difference of 83.8%. Both measurements and predictions indicate that
friction torque losses increase with the product
n·ν·dm
, load, and contacting seals for the
tested operating conditions. This suggests that idler roller efficiency decreases under lower
temperatures (resulting in higher viscosity), higher speeds, higher loads, and when using
contact seals (RS1).
Figure 9b clearly demonstrates that the friction torque model is not sufficiently sensi-
tive to the product
n·ν·dm
. This aligns with previous literature suggesting the need for
model optimization for specific bearings and operating conditions [
35
]. However, experi-
mental data clearly indicate that as rotational speed decreases proportionally with idler
roller radius for a given belt speed, larger rollers will operate at lower rotation and therefore
be more efficient than standard idlers. Lighter dots, representing low rotational speeds,
consistently exhibit lower friction torque values than full-colored dots, representing higher
rotational speeds. The highest power consumption in these tests is 15 W, for the rolling
bearing 2RS1 operating at 600 rpm and presenting friction losses of 240 Nmm.
To illustrate the benefits of using larger rollers, Table 3presents the reduction in friction
torque achieved by a 450 mm idler roller compared to a 150 mm one for specific operating
conditions. This table also shows the viscosity ratio (k), which indicates the lubrication
condition of the rolling bearing. The viscosity ratio is defined as the ratio of the actual
lubricant viscosity to the reference viscosity, as detailed in [
28
]. It provides a measure of
the degree of surface separation, which is equivalent to lubricant specific film thickness,
and therefore, directly related to grease life.
Table 3. Rolling bearing friction torque measurements and their impact on force considering idlers of
150 mm and 400 mm.
Parameter, Unit Roller Diameter 150 mm Roller Diameter 450 mm
Tested Rotational Speed, rpm 450 150
Equivalent Belt Speed, m/s 3.53 3.53
Tested Load per Roller, N 250 250
Tested Temperature, C 10 20 40 10 20 40
Viscosity Ratio, k 10.3 5.0 2.2 6.4 2.3 0.8
Measured Torque per Roller, Nmm 131.6 94.7 69.3 83.5 55.0 55.2
Calculated Force per Roller, N 1.8 1.3 0.9 0.4 0.2 0.2
Force Reduction with Big Roller, % 78.9 80.6 73.5

Lubricants 2025,13, 104 12 of 26
The observed force reduction required to keep larger rollers running ranges from
73.5% to 80.6%. However, at low rotational speeds (150 rpm) and high temperatures (40 °C),
the specific film thickness (viscosity ratio, k) generated by the lubricating grease MT47,
standard for 6305DGBB, is lower than 1 (k = 0.8), indicating that the rolling bearing is
operating under boundary lubrication conditions. This explains the slight increase in
friction torque from 20 °C to 40 °C with the larger roller. Operations under boundary
lubrication conditions should be avoided, as they reduce rolling bearing life. Therefore,
larger rollers operating in warm environments, given their lower rotational speed, should
use more viscous lubricating greases in their bearings compared to standard rollers.
4.3. Labyrinth Seal Results
Figure 10a presents friction torque values as a function of the product of rotational
speed, operating viscosity, and mean diameter. Figure 10b provides a comparison between
predictions and measurements, along with the residuals.
0 2 4 6 8 10
n dm107
0
100
200
300
400
500
600
700
800
900
Labyrinth Seal Fricton Torque, Nmm
Temp.
10
20
30
40
Speed
250
500
750
(a)
0 100 200 300 400 500 600 700 800 900
Labyrinth Seal Friction Torque Measurements, Nmm
0
100
200
300
400
500
600
700
800
900
Newtonian Friction Torque Model, Nmm
Data
Residuals
(b)
Figure 10. (a) Newtonian friction torque model (lines) versus measured data (points) as a function of
grease viscosity and operating conditions. (b) Comparison of Newtonian friction torque model with
experimental results and residuals.
In general, similar trends are observed between the predicted (continuous lines) and
measured (dots) friction torque values regardless of operating temperature and speed.
The data show a correlation coefficient of R = 0.96, a mean difference of 161%, and a
maximum absolute difference of 602%. Both measurements and predictions indicate that
friction torque losses increase with the product (
n·ν·dm
) for the tested operating conditions.
This suggests that idler roller efficiency decreases under lower temperatures (resulting in
higher viscosity) and higher speeds.
However, Figure 10 clearly demonstrates that the Newtonian friction torque model [
12
]
underestimates the measured values. This occurs because lubricating greases are non-
Newtonian fluids that present shear thinning behavior and a limiting shear stress [
14
]. This
means that at low shear rates, lubricating greases with NLGI 2 consistently present much
higher shear stress values in comparison to their base oil (Newtonian), and that difference
decreases as shear rate increases, up to the point that it converges to the same values at
very high shear rates (
˙
γ≥
10
6s−1
). Therefore, the use of Newtonian models to predict
grease-filled labyrinth seals friction losses is only valid at ˙
γ≥106s−1.
As rotational speed decreases proportionally with idler roller radius for a given belt
speed, larger rollers will operate at a lower rotation and therefore are more efficient than
standard idlers. This is depicted by lighter dots in Figure 10a, representing low rotational
speeds, which consistently exhibit lower friction torque values than full-colored dots,
representing higher rotational speeds. To illustrate the benefits of using larger rollers,

Lubricants 2025,13, 104 13 of 26
Table 4presents the reduction in friction torque achieved by a 450 mm idler roller compared
to a 150 mm one for the tested operating conditions presented below.
Table 4. Labyrinth seal friction torque measurements and their impact on force considering idlers of
150 mm and 400 mm.
Parameter, Unit Roller Diameter 150 mm Roller Diameter 450 mm
Tested Rotational Speed, rpm 764 255
Equivalent Belt Speed, m/s 6.0 6.0
Tested Temperature, C 10 20 30 40 10 20 30 40
Measured Torque per Roller, Nmm 773.7 415.8 278.9 255.3 436.8 302.6 221.1 200.0
Calculated Force per Roller, N 10.3 5.5 3.7 3.4 1.9 1.3 1.0 0.9
Force Reduction with Big Roller, % 81.2 75.7 73.6 73.9
The observed force reduction required to keep larger rollers running ranges from
73.6% to 81.2%. The current model does not provide any insights for grease selection,
as it only used its base oil. However, it does show that reducing the shear rate leads to
lower friction losses. That can be achieved by increasing the gap between labyrinth seals,
or by reducing the radius of the seals, which is more difficult as it is limited by external
geometries of shaft and housing.
4.4. Lip Seal Results
Figure 11a presents measured friction torque values (dots) of a radial shaft lip seal as a
function of rotational speed for five shaft diameters within the required tolerances (30
+0.08
−0.89
).
The friction torque value obtained from SKF diagram for lip seals [
43
] is shown as a black
line, and the SKF rolling bearing seal (RS1) friction torque model is presented as a grey
line (Appendix B, Equation (A15)). Figure 11b provides a comparison between SKF lip seal
friction torque predictions and measurements, along with the residuals.
The increase in contact pressure due to shaft diameter variance within its tolerances
leads to a maximum torque loss variation of 606%. Such variation clearly indicates the
significant impact of contact pressure on lip seal friction losses. In the same figure, the pre-
dictions using the SKF friction torque model for lip seals are presented. The predicted
values are conservative, leading to similar results as the measured ones for a shaft diameter
of 30.08 mm. In contrast, the SKF friction torque model for the springless contact seal
(RS1) presents lower values, between those observed for shaft diameters of 29.81 mm and
29.88 mm. The RS1 friction torque model accuracy was verified by testing rolling bearings
with one and two RS1 seals, presenting maximum differences of 10%. As mentioned in
Section 2.2.3, idler rollers might contain radial shaft lip seals and grease seals (without
spring loading). Radial lip seals in contact with the shaft are expected to lead to much
higher friction losses compared to springless lip seals.
The measured and predicted values present the same trends concerning speed. For the
tested operating conditions (low tangential speeds of 0.4 to 1.2 m/s), the friction losses of
lip seals are independent of speed. Therefore, no differences are expected between large
and standard rollers regarding lip seal friction torque. However, due to the larger roller
diameter, the friction force required to overcome the torque will decrease proportionally
to the idler diameter. A closer look at the lip seal friction torque model presented in
Appendix Balso shows that the friction losses are independent of temperature or the
load applied on the roller. Therefore, a rough estimation of the friction losses of radial
shaft lip seals and RS1 lip seals can be performed using the diagram provided in [
43
] and
Equation (A15), respectively. Once more, due to the wide range of lip seal designs and
configurations used by various manufacturers, and the sensitivity of the friction losses to
contact pressure, these equations should only be considered rough approximations.

Lubricants 2025,13, 104 14 of 26
300 400 500 600 700
Rotational Speed, rpm
0
20
40
60
80
100
120
140
160
180
200
Lip Seal Fricton Loss Measurements, Nmm
Diameter
29.81
29.88
29.95
30.01
30.08
SKF Lip Seal
30.00
30.00
SKF RS1 Seal
(a)
0 20 40 60 80 100 120 140 160 180 200
Lip Seal Friction Torque Measurements, Nmm
-50
0
50
100
150
200
SKF Lip Seal Friction Torque Model, Nmm
Data
Residuals
(b)
Figure 11. (a) SKF RS1 and lip seal friction torque model (lines) versus measured data (points)
as a function of operating conditions. (b) Comparison of SKF lip seal friction torque model with
experimental results and residuals.
5. Discussion on Measured and Predicted Values
Except for IRR, the current predictive models used to estimate the friction losses for
idler rollers [
3
,
7
,
8
,
12
] did not perform well, showing differences up to 83.8% for rolling
bearings and up to 602% for labyrinth seals, and could not easily assess lip seals, as they
depend on lip seal geometry, material and contact pressure, which are not standardized
for idler rollers. Therefore, estimating rotating resistance from these models might lead
to significant inaccuracy. This clearly indicates the need to further develop the current
models used to predict rim drag losses. Although such development is not in the scope of
this paper, a numerical optimization of the SKF friction torque model and an optimization
of a non-Newtonian model for the labyrinth seals used in idler rollers were performed.
The optimization is detailed in Appendices Band C. The SKF friction torque model opti-
mization followed the procedure previously applied by several researchers [
35
,
49
], in which
model constants were adjusted to fit the experimental data. In this case, the rolling torque
component (
Mrr
) was adjusted from
(n·ν)0.6
to
(n·ν)0.65
to accelerate the rate of torque
increase as a function of
n·ν·dm
. The optimized model clearly indicates that the use of
lubricating greases with low base oil viscosity will lead to lower friction torque values at
the tested operating conditions, although the viscosity should be big enough to prevent
a boundary lubrication regime (
k≥
1), as it significantly reduces bearing life [
50
]. Addi-
tionally,
Equation (A13)
also shows that the reduction in the EHL friction coefficient (
µEH L
)
increases rolling bearing efficiency. This is achieved by using lubricating greases formulated
with ester or polyalphaolephin base oils instead of mineral base oil [
34
]. Therefore, selecting
a lubricating grease viscosity yielding a viscosity ratio
k
higher than 1, formulated with
ester or PAO base oil, will ensure durability with low friction losses.
The labyrinth seal friction torque model developed by [
14
] was used with the grease
rheological parameters (
k
,
n
,
τy
) optimized to fit the experimental results. Although rheolog-
ical measurements could not be performed with the tested grease, the obtained values are
within the ones reported for NLGI 2 greases [
15
] (see Appendix C), indicating the need to
use non-Newtonian models to properly predict labyrinth seal friction losses. A closer look
at this model clearly indicated that labyrinth seals’ efficiency can be improved by using
lubricating greases with a low flow index (
n
) and low limiting shear stress (
τy
). This occurs
because non-Newtonian fluids (
τy=
0;
n=
1) exhibit viscosity variations that follow the
power of
n−
1 in relation to shear rate (
τy/˙
γ
), resulting in decreased viscosity as shear
rate increases. As a result, the viscous torque increases at a slower rate since viscosity
diminishes with higher rotational speeds. When it comes to labyrinth geometry, from a

Lubricants 2025,13, 104 15 of 26
friction loss perspective only, the efficiency increases by reducing labyrinth radius and
increasing the gap, which lead to low shear rates
(ωr
h)
and consequently lower shear stress
and lower friction torque.
Finally, the lip seal friction torque losses will be considered constant as a function of
throughput (load per idler roll), belt speed (idler roller rotational speed), and temperature,
varying only with material type and counterface diameter, as shown for radial shaft lip
seals [43], and Equation (A15) for springless lip seals, and as verified in our experiments.
Such optimizations allow for the prediction of rim drag and IRR friction losses under
different operating conditions than those tested, overcoming the limitations of the experi-
ments, such as the low loads (in comparison to field use) used to evaluate rolling bearing
friction losses. Additionally, it allows the integration of IRR and rim drag to perform studies
with different conveyor belt settings and visualize the separate impact of each component
on the total losses of the system under different operating conditions, in particular the
effect of idler roller diameter.
The optimized models were applied and compared to the measured data, as shown
in Figure 12. The rolling bearing and labyrinth seal optimized friction torque models
presented a correlation factor of R = 0.95 and R = 0.98, respectively.
12345678
n dm106
0
50
100
150
200
250
Rolling Bearing Friction Torque, Nmm
Temper.
10
20
40
Speed
150
300
450
600
Seal
1RS1
2RS1
Load
250
550
(a)
0 50 100 150 200 250
Rolling Bearing Friction Torque Measurements, Nmm
-50
0
50
100
150
200
250
Optimized SKF Friction Torque Model, Nmm
Data
Residuals
(b)
0 2 4 6 8 10
n dm107
0
100
200
300
400
500
600
700
800
900
Labyrinth Seal Fricton Torque, Nmm
Temp.
10
20
30
40
Speed
2
4
6
(c)
0 100 200 300 400 500 600 700 800 900
Labyrinth Seal Friction Torque Measurements, Nmm
-100
0
100
200
300
400
500
600
700
800
900
Non-Newtonian Friction Torque Model, Nmm
Data
Residuals
(d)
Figure 12. (a) Optimized SKF friction torque model (lines) versus measured data (points) as function
of grease viscosity and operating conditions. (b) Optimized SKF friction torque model versus
experimental results and its residuals. (c) Optimized non-Newtonian labyrinth seal friction torque
model versus experimental results and its residuals. (d) Optimized non-Newtonian labyrinth seal
friction torque model versus experimental results and its residuals.

Lubricants 2025,13, 104 16 of 26
5.1. Implications for Conveyor Design
To demonstrate the impact of idler diameter and operating conditions on total friction
losses for the center roller (as wing roller operating conditions were not tested), the sum of
indentation rolling resistance and rim drag losses, along with their individual contributions,
is presented in Table 5. The table also illustrates the predicted benefits of using a larger roller
(500 mm) compared to a standard roller (150 mm) by showing the difference in friction
resistance values in the last column. Each row represents the friction losses of a specific
combination at a specific temperature. The calculations were performed using the same
conveyor belt, rolling bearings, labyrinth seals, and lubricants detailed in
Tables 1and 2
.
The setup includes two springless lip seals in contact with the grease-filled labyrinth seal at
its internal and external diameters to prevent grease leakage. These seals were modeled
using Equation (A15).
The total force required to keep idlers rotating shows a similar trend regardless
of temperature or diameter. The highest friction resistance occurs at high loads, high
speeds, and low temperatures, while the lowest occurs at low loads, low speeds, and high
temperatures. By increasing the idler diameter from 150 mm to 500 mm, reductions from
8.3 N (2.1
×
) to 28.6 N (4.0
×
) at 10 °C and from 5.6 N (1.8
×
) to 16.8 N (2.6
×
) at 40 °C are
expected within the calculated operating conditions. An analysis of each component shows
that most of the absolute benefits (force in N) come from the indentation rolling resistance
with reductions ranging from 0.8 N to 11.5 N at 10 °C and from 0.6 N to 7.8 N at 40 °C. This
is followed by the labyrinth seals, with reductions ranging from 3.4 N to 8.7 N at 10 °C and
from 1.1 N to 4.0 N at 40 °C, and by rolling bearings, with reductions ranging from 1.3 N to
5.6 N at 10 °C and from 1.1 N to 2.2 N at 40 °C. Finally, lip seals present a reduction of 1.1 N.
Table 5also clearly shows the effect of operating conditions. In general terms, IRR is
mostly affected by load and temperature, rolling bearings are similarly affected by load,
speed, and temperature, and labyrinth seals are affected only by speed and temperature.
As a consequence, whatever the temperature or idler diameter, IRR losses become predomi-
nant at high loads, while rim drag losses, which are the sum of rolling bearings, labyrinth
seals, and lip seals, are predominant at low loads.
These calculations assume grease leakage does not occur and lip seal wear is minor, so
it does not affect the friction losses. This situation is representative of the early usage of
idler rollers but might not be representative of most of the idler rollers’ lifespan. Opasiak
measured the rotating resistance of 10 idler rollers as new and after one, two, and three
years of use in a hard coal mine [
51
]. The rotational resistance consistently reduced over
time, presenting an average reduction of 45% (from 3.1 N to 1.7 N) after three years of
use. Although Opasiak et al. did not discuss the reason for this reduction, it can be
inferred that it comes from grease leakage in the labyrinth seals, as previously discussed
by [
37
,
39
], and the reduction in the contact pressure of lip seals due to wear [
52
]. Rolling
bearing friction torque is expected to be higher in the first hours of operation due to grease
accommodation and surface smoothing. However, after a few hours or days, the friction
torque stabilizes and should not change much over time. Possible changes due to grease
aging might lead to either a reduction or an increase in friction torque depending on the
aging intensity [
13
]. In fact, no publications could be found comparing measurements of
friction torque over long periods or for new and used rolling bearings. However, rolling
bearing monitoring techniques show stable temperatures over years, indicating the rolling
bearing friction torque does not change significantly over time. Therefore, it is likely that
only the friction losses from labyrinth seals and lip seals are significantly reduced over time.
To the interested reader, the influence of bearing clearance and provider, not discussed in
this work, were reported in [
10
], showing that rim drag friction losses in conveying systems
were reduced when using rolling bearings with C4 clearance instead of C3.

Lubricants 2025,13, 104 17 of 26
Table 5. Rotating resistance as a function of belt speed and load per belt width at 10C and 40C for
150 mm and 500 mm idler rollers, and the impact of each component of the friction losses.
150 mm 500 mm Benefits of Big Roller (N)
Total Friction Resistance (N)
10 ◦C
12345678
Belt Speed, m/s
2
3
4
5
6
7
8
9
10
11
Load per belt width, kN/m
15
20
25
30
35
40
12345678
Belt Speed, m/s
2
3
4
5
6
7
8
9
10
11
Load per belt width, kN/m
4
5
6
7
8
9
10
11
12
13
14
12345678
Belt Speed, m/s
2
3
4
5
6
7
8
9
10
11
Load per belt width, kN/m
10
12
14
16
18
20
22
24
26
28
40 ◦C
12345678
Belt Speed, m/s
2
3
4
5
6
7
8
9
10
11
Load per belt width, kN/m
10
12
14
16
18
20
22
24
26
28
12345678
Belt Speed, m/s
2
3
4
5
6
7
8
9
10
11
Load per belt width, kN/m
3
4
5
6
7
8
9
10
11
12345678
Belt Speed, m/s
2
3
4
5
6
7
8
9
10
11
Load per belt width, kN/m
6
7
8
9
10
11
12
13
14
15
16
Indentation Rolling Resistance (N)
10 ◦C
12345678
Belt Speed, m/s
2
3
4
5
6
7
8
9
10
11
Load per belt width, kN/m
2
4
6
8
10
12
14
16
18
20
12345678
Belt Speed, m/s
2
3
4
5
6
7
8
9
10
11
Load per belt width, kN/m
1
2
3
4
5
6
7
8
9
10
12345678
Belt Speed, m/s
2
3
4
5
6
7
8
9
10
11
Load per belt width, kN/m
1
2
3
4
5
6
7
8
9
10
11
40 ◦C
12345678
Belt Speed, m/s
2
3
4
5
6
7
8
9
10
11
Load per belt width, kN/m
2
4
6
8
10
12
14
16
12345678
Belt Speed, m/s
2
3
4
5
6
7
8
9
10
11
Load per belt width, kN/m
1
2
3
4
5
6
7
8
12345678
Belt Speed, m/s
2
3
4
5
6
7
8
9
10
11
Load per belt width, kN/m
1
2
3
4
5
6
7

Lubricants 2025,13, 104 18 of 26
Table 5. Cont.
150 mm 500 mm Benefits of big roller (%)
Rolling Bearing Resistance (N)
10 ◦C
12345678
Belt Speed, m/s
2
3
4
5
6
7
8
9
10
11
Load per belt width, kN/m
2
2.5
3
3.5
4
4.5
5
5.5
6
6.5
12345678
Belt Speed, m/s
2
3
4
5
6
7
8
9
10
11
Load per belt width, kN/m
0.5
0.6
0.7
0.8
0.9
1
1.1
1.2
12345678
Belt Speed, m/s
2
3
4
5
6
7
8
9
10
11
Load per belt width, kN/m
1.5
2
2.5
3
3.5
4
4.5
5
5.5
40 ◦C
12345678
Belt Speed, m/s
2
3
4
5
6
7
8
9
10
11
Load per belt width, kN/m
1.6
1.8
2
2.2
2.4
2.6
12345678
Belt Speed, m/s
2
3
4
5
6
7
8
9
10
11
Load per belt width, kN/m
0.47
0.48
0.49
0.5
0.51
0.52
0.53
0.54
0.55
0.56
0.57
12345678
Belt Speed, m/s
2
3
4
5
6
7
8
9
10
11
Load per belt width, kN/m
1.2
1.3
1.4
1.5
1.6
1.7
1.8
1.9
2
2.1
Labyrinth Seal Resistance (N)
10 ◦C
12345678
Belt Speed, m/s
2
3
4
5
6
7
8
9
10
11
Load per belt width, kN/m
5
5.5
6
6.5
7
7.5
8
8.5
9
9.5
10
12345678
Belt Speed, m/s
2
3
4
5
6
7
8
9
10
11
Load per belt width, kN/m
1.2
1.3
1.4
1.5
1.6
1.7
1.8
12345678
Belt Speed, m/s
2
3
4
5
6
7
8
9
10
11
Load per belt width, kN/m
3.5
4
4.5
5
5.5
6
6.5
7
7.5
8
8.5
40 ◦C
12345678
Belt Speed, m/s
2
3
4
5
6
7
8
9
10
11
Load per belt width, kN/m
1.5
2
2.5
3
3.5
4
4.5
12345678
Belt Speed, m/s
2
3
4
5
6
7
8
9
10
11
Load per belt width, kN/m
0.35
0.4
0.45
0.5
0.55
0.6
0.65
12345678
Belt Speed, m/s
2
3
4
5
6
7
8
9
10
11
Load per belt width, kN/m
1.5
2
2.5
3
3.5
4
Lip Seal Resistance (N)
- 1.52 0.46 1.06
6. Simplified Case Study
Some case studies based on the conveying systems described in [
53
] are pre-
sented to allow for comparison. The parameters of these case studies are given in
Table 6
, with the predicted installed power breakdown for such systems presented

Lubricants 2025,13, 104 19 of 26
in
Figure 13
, based on installed idler diameter. The following simplifications and as-
sumptions were made to perform the calculation: (i) all systems are considered flat
to observe the direct benefit of IRR and for consistency with [
2
]; (ii) all systems op-
erate with the same belt, with bottom cover thickness and properties as described in
Section 5.1
, and a belt mass of 81 kg/m; (iii) a three-idler trough is used for the carry
side; (iv) a two-idler trough is used for the return side; (v) return idler spacing is twice
the carrying idler spacing; (vi) the system operates at an ambient temperature of 20 ºC;
(vii) rolling bearings, seals, and lubricants are as described in Section 5.1; (viii) secondary
resistances are given by ISO5048 [
54
] and are based solely on the length of the system,
equal to 2.5% for a conveyor more than 1.5 km long; (ix) flexure resistance is considered
as one-third of the total indentation rolling resistance calculated for the 150 mm roller
for consistency with Hager’s observation [
2
]. This assumption is based on the fact that
flexure resistance is barely affected by idler diameter, being mostly dependent on the physi-
cal and flow properties of the bulk material being conveyed, belt viscoelastic properties,
and idler spacing.
Overall, the use of larger-diameter idler rollers can lead to substantial energy savings,
ranging from 40% to 55% in the studied cases. The absolute savings (kW) come mostly
from IRR, as its share of the total losses is the highest, at approximately 41%.
It is also relevant to observe that the early predictions of of Hager [
2
], where IRR
represented about 60% of total friction losses in overland conveying systems, were not
observed for any of the systems presented below, with mean values of 41%. Several reasons
can justify such differences. As presented in the previous section, the calculations do not
take into account grease leakage from labyrinth seals and lip seal pressure reduction due
to wear. In fact, if labyrinth seal losses alone were not considered, the average IRR would
represent 58% of total losses. Additionally, IRR can vary up to 200% depending on the
bottom cover’s viscoelastic properties [24]. All tests were performed with a conveyor belt
with a high-efficiency bottom cover.
These findings suggest that upgrading to larger-diameter idler rollers can be a practical
and effective solution for industries seeking to improve their energy efficiency. Furthermore,
the use of larger idlers also permits other design changes to be incorporated. A key
consideration when selecting idler diameter and spacing is the contact stresses on the
bottom cover of the belt. The use of a larger idler reduces these stresses and therefore
permits idler spacings to be increased accordingly. From Figure 6, it can be seen that the
IRR varies with load exponentially (
≈Load4/3
). While increasing the idler span for a given
idler diameter will not directly reduce IRR, it will reduce other drag forces like rim drag
through a reduction in the gross number of idler sets, which also leads to a reduction in
roller replacement. Finally, due to their larger perimeter, lower rotational speed, and lower
contact pressure, larger idlers are expected to wear less than standard rollers over the same
operational period.
Increasing the span between idler stations containing larger-diameter rollers can
enable the optimization of changes to roller rotating mass and inertia within the system.
The impact on the dynamic response of the belt due to the span increase also needs
further consideration.
It is noteworthy that the costing implications of upgrading to larger-diameter idler
rollers cannot be determined solely based on the optimization of energy efficiency. A more
detailed optimization process, considering factors such as spacing, wear, and other parame-
ters, would be necessary to accurately assess the costing implications of such an upgrade.
Given idler roller mass constraints and the available materials of construction, there
will be a trade-off between increasing roller diameters and increased spans for the best
efficiency versus the material strengths and weights for roller components such as shells,

Lubricants 2025,13, 104 20 of 26
end caps, bearings, and shafts. Shell wall thickness, abrasion design allowances, and com-
ponent design life expectations will also have a major bearing on the practical limits for
roller diameters. Additionally, larger rollers introduce greater inertia, which affects startup
dynamics and related phenomena [55], necessitating further studies.
Table 6. Selected system details for simplified power loss calculations.
Conveyor Yandi Escond Overb Ingwe Zisco Overland Curragh Impum Los P
Material Iron ore Copper Ore Overburden Coal Iron ore Copper Ore Coal Coal Copper Ore
Tonnage, ton/h 4000 6000 20,000 1800 500 6000 2500 2400 11,000
Belt Speed, m/s 5.5 5 3.15 5 4.5 5 7.5 6.5 7
Belt Width, m 1.2 1.5 2.8 1.05 0.75 1.5 1.2 1.2 1.8
Through angle, º 45 35 35 45 25 35 45 45 40
Conveying Length, km 4 10 2 8.9 15.6 10 20 27 12.8
Carry idler spacing, m 2.5 2 1 4.5 5 2 5 4.5 1.5
Yandi
Escond
Overb
Ingwe
Zisco
Overland
Curra
Impum
Los P
0
1000
2000
3000
4000
5000
6000
7000
8000
Power Consumption, kW
IRR
Labyrinth
Lip Seal
Rolling Bearing
Flexure
Secondary
(a) (b)
Figure 13. Calculated power consumption for selected conveying systems considering (a) all idlers of
150 mm, and (b) considering carrying idlers of 500 mm and return idlers of 150 mm.
7. Conclusions
The study presented in this paper highlights the energy efficiency benefits of using
larger-diameter idler rollers in belt conveying systems through experiments and predictions.
The results demonstrate the following key points:
Indentation Rolling Resistance:
•
IRR decreases as the idler diameter increases, following an exponential relationship of
d−2/3 for usual overland operating conditions;
•
IRR decreases as the load decreases, following an exponential relationship of
Load4/3
for usual overland operating conditions;
•
Higher temperatures can lead to a decrease in IRR due to the ability of the rubber
compound to relax faster, depending on the belt bottom cover’s viscoelastic properties;
•
IRR increases with speed at a very low rate (0.1–0.2 N/m/s), with a higher rate at lower
temperatures, as it also depends on the belt bottom cover’s viscoelastic properties;
•
Increasing the idler diameter from 152.4 mm to 400 mm can lead to a significant
reduction in IRR, up to 50%, due to the reduced contact stresses.
Rim Drag Resistance:
•
Labyrinth seals presented the highest contribution to the rim drag, followed by the
rolling bearings and lip seals. This ranking is highly dependent on grease properties;
•
Labyrinth seals’ friction losses can be reduced by selecting lubricating greases with
low flow index (
n
), low limiting shear stress (
τy
), and low base oil viscosity (
η
), or by
reducing the labyrinth radius and increasing its gap (r
h);

Lubricants 2025,13, 104 21 of 26
•
Rolling bearings’ friction losses can be reduced by selecting lubricating greases formu-
lated with synthetic base oils (
µsyn
EH L <µmin
EH L
), and a base oil viscosity that leads to a
viscosity ratio of k≈2;
•
Lip seal friction losses were shown to be independent of the operation, being a function
of material, geometry, and assembly load;
•
Increasing the idler diameter from 152.4 mm to 400 mm can lead to a significant
reduction in rim drag force losses, of up to 80%, due to the reduced rotational speed
and increased lever arm. This benefit assumes the use of the same sealing package
design and rolling bearings. This is feasible because rolling bearing selection depends
on load, which is influenced by the idler span rather than the roller diameter.
Predictive models:
•
The QC-N analytical model provides a good prediction of the impact of idler diameter
on indentation rolling resistance compared to experimental data under the temperature
and operating conditions considered;
•
The models used to predict rolling bearing and grease-filled labyrinth seal friction
losses in idler rollers were outdated, showing differences of up to 3
×
and 6
×
compared
to experimental measurements, respectively;
•
Updated models were applied and optimized for the measured data, allowing the
assessment of the individual contributions of each component to the friction losses
under a broad range of operating conditions;
•
IRR contribution can be as low as 10% in applications with low load per belt width,
while for high loads, values around 50% to 60% are observed;
•
Lip seals can be roughly estimated using Equation (A15), which serve as a guide to
estimate the resistances.
These findings suggest that upgrading to larger-diameter idler rollers is a practical
and effective solution for improving energy efficiency in conveying systems. Additionally,
the use of larger idlers allows for other design changes, such as increased idler spacing,
which further enhances system efficiency.
Author Contributions: Conceptualization and methodology, all authors; IRR experiments, J.O. and
P.R.; rim drag experiments, T.C. and Y.B.; formal analysis and investigation, T.C., P.R. and J.O.; data
curation, T.C.; writing—original draft preparation, T.C.; writing—review and editing, P.R., C.W.
and J.O.; funding acquisition, S.R. and S.H. All authors have read and agreed to the published version
of the manuscript.
Funding: This paper received no external funding.
Data Availability Statement: Data is contained within the article.
Acknowledgments: We would like to extend our gratitude to Big Roller Overland Conveying
Company for supporting this research. We are also grateful to ContiTech Australia Pty Ltd. for
supplying the conveyor belt used in our experiments.
Conflicts of Interest: Jayne O‘Shea and Yusuf Badat are employed by TUNRA Bulk Solids. Shawn
Ryan is employed by Big Roller Overland Conveying Company. Stephan Hoette is employed by
ContiTech Australia. The remaining authors declare that the research was conducted in the absence
of any commercial or financial relationships that could be construed as a potential conflict of interest.
Appendix A. Indentation Rolling Resistance
Appendix A.1. QC-N Model
To understand the role of the idler roller diameter on indentation rolling resistance,
the QC-N model was used. This model also quantifies the influence of load, speed, tempera-
ture, and the properties and thickness of the belt bottom cover on the IRR. A full description

Lubricants 2025,13, 104 22 of 26
is given in [
6
,
24
], and only summarized below. The expression for the horizontal force (see
Figure 1,FQ=Tind
R) resulting from indentation rolling resistance is formulated as
FQ=sin δDQ(π/4)4/3h/¯
GR21/3W4/3 (N/m), (A1)
where
h
is the bottom cover thickness of the belt,
W
represents the normal load per belt
width, accounting for the weight of both the material and the belt itself,
R
is the ra-
dius of the roller, and
δ
is the bottom cover loss angle.
¯
G
,
DQ
, and
A(α)
are defined by
Equations (A2)–(A4).
¯
G=qG′(ω)2+G′′(ω)2, (A2)
where the shear elastic (
G′
) and shear loss (
G′′
) moduli are derived from the
master curve.
DQ=(1/2)sin α∗[A(α∗)−cos α∗]+1
4[2α∗+sin(2α∗)] −Zα∗
0A(α)cos αdα
cos δ−cos(α∗+δ)−sin δZα∗
0A(α)dα−4/3 (A3)
A(α) = 0.6520 exp(−α/0.4843)−0.0544α+0.3480 (A4)
The phase angle is defined as
α=ωt
, where
ω
represents the frequency and
t
denotes
time. The term
α∗
is given by Equation (A5), where
b/a
is the ratio of the asymmetric
deformation between belt and roller as presented in Figure 1.
α∗= (π/2)[1+b/a](A5)
Operational parameters are listed in Table 1, while the belt bottom cover properties are
given in [
24
]. Although this paper does not address the impact of viscoelastic properties
on indentation rolling resistance (IRR), the QC-N model explicitly illustrates this relation-
ship through the equation
sin δ/G(1/3)
. This relationship facilitates quick comparisons of
rubber compounds.
Appendix B. Rolling Bearing Friction Torque Model
The SKF model takes into account several factors contributing to the total frictional
moment: the moment generated by the rolling elements (
Mrr
), the moment resulting from
the sliding of the elements (
Msl
), the moment created by the seals (
Mseal
), and the moment
due to viscous drag (
Mdrag
). These components are combined in Equation (A6) to calculate
the total frictional moment
(Mt)
. A detailed explanation of this model and its limitations is
given in [28].
Mt=Mrr +Msl +Mseal +Mdrag (A6)
The friction torque from hydrodynamic drag (
Mdrag
) is negligible for grease-lubricated
rolling bearings. The other components are detailed below. Except for Equation (A7), which
was modified to reflect a higher increase rate of friction torque with the product
(vn)
, all
equations adhere to the original source.
Rolling friction torque is calculated using Equations (A7)–(A10), which incorporate
the correction factors “inlet shear heating” (Equation (A9)), and “kinematic replenishment”
(Equation (A10)).
Mrr =Φish ΦrsGrr(vn)0.65 (A7)
Grr =R1dm1.96F0.54
r(A8)

Lubricants 2025,13, 104 23 of 26
Φish =1
1+1.84 ×10−9(ndm)1.28 v0.64 (A9)
Φrs =1
eKrs vn(d+D)rKZ
2(D−d)(A10)
The rolling torque is primarily influenced by the lubricant’s viscosity at operating
temperature (base or bleed oil viscosity for grease) and the rotational speed. It basically
follows the film thickness increase, thus rising with speed as a result of a significant
hydrodynamic effect. As a higher increase rate of friction torque with the product
(vn)
was
observed, Equation (A7) was adjusted based on experimental data, increasing the exponent
from
(vn)0.6
to
(vn)0.65
. The (
Φish Φrs
) product diminishes as operating speed increases,
requiring no further adjustment.
Sliding torque can be determined using Equations (A11)–(A14). Unlike
Mrr
, sliding
friction torque decreases with
(vn)
to a minimal value as the lubrication regime transi-
tions, reducing surface asperity interactions. Equation (A14), (‘load weighting factor’)
dictates the proportion of boundary/mixed lubrication (
µbl
) to full-film lubrication (
µEH D
),
increasing as specific film thickness decreases. Since most tests were under full-film lubri-
cation
(k>> 1)
, the sliding torque component was minimal, making further adjustments
unnecessary.
Msl =Gsl µsl (A11)
Gsl =S1dm−0.26 F5/3
r(A12)
µsl =Φbl µbl +(1−Φbl)µEH L (A13)
Φbl =1
e2.6×10−8(nv)1.4 dm(A14)
Friction torque from contact seals generally exceeds that from the bearing, as seen in
all tested conditions. It can be estimated using Equation (A15), where
SealN
indicates the
number of contacting seals in the bearing: zero for no contacting seals; one for sealed on
one side; or two for sealed on both sides.
Mseal =0.5 SealN.KS1dβ
s+KS2(A15)
The constant parameters for a 6305-2RS1 lubricated with MT47 grease are
Krs =
6.8
×
10
−8
,
KZ=
3.1,
R1=
3.7
×
10
−7
,
S1=
2.84
×
10
−3
,
KS1=
0.023,
ds=
36.6,
β=2.25, and KS2=2.
Appendix C. Labyrinth Seal Friction Torque Model
Grease-filled labyrinth seals were modeled following the approach in [
14
]. This model
assumes grease flow in the labyrinth gap as laminar drag flow, treating the axial regions (
Ta
)
as flow between concentric cylinders and the radial regions (
Tr
) as flow between parallel
plates, while disregarding the effects of corners. These equations can be simplified to
represent Newtonian fluids, as used in [12], by setting τyand Kto zero and nto 1.
Ta=τy+Kω¯
r
bn
+η∞ω¯
r
b2πR2
oL(A16)

Lubricants 2025,13, 104 24 of 26
Tr=2πR3
o−R3
i
3





τy+3K
3+nωRo
bn




1−Ri
Ro3+n
1−Ri
Ro3





+
η∞ωRo
4b





1−Ri
Ro4
1−Ri
Ro3










(A17)
In this context,
ω
represents the rotational speed,
L
is the cylinder length,
¯
r
is the average
radius, and
Ro
and
Ri
denote the outer and inner radii of the radial labyrinths, respectively.
The total viscous torque for each labyrinth is calculated by summing the contributions from
both the axial and radial regions:
T=
q
∑
j=1
Taj +
l
∑
j=1
Trj (A18)
In this equation,
q
is the number of concentric cylinders, and
l
represents the parallel plates.
For the axial labyrinth,
q=
2
m+
1 and
l=
2
m
; for the radial configuration,
q=
2
m
and
l=2m+1.
Since the rheological properties of the lubricating grease Shell Alvania 2 could not
be directly measured, these values were optimized to match the experimental results.
The adjusted values, presented in Table A1, align with the rheological properties of NLGI2
lubricating greases as reported in the literature [
14
,
15
]. The base oil viscosity (
η∞
) was
obtained from the grease’s technical data sheet.
Table A1. Rheological parameters for different temperatures [15].
Temp. [◦C] τy[Pa] n [-] K [Pa·s] η∞[Pa·s]
10 30 0.500 35 0.76
20 27 0.495 22 0.33
30 25 0.490 15 0.16
40 25 0.485 12 0.09
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