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.

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 secondary 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 solutions like rail-running conveyors [5] to energy-efficient component designs such as rubber bottom covers [6] and improved idler rollers [7,8,9,10,11]. However, existing predictions for evaluating 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 ($T_{ind}$).

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 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 compound 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 depicted 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, applications in cleaner environments focused on efficiency prefer shielded rolling bearings and grease-filled labyrinth seals, with lip seals potentially omitted.

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].

2.2.1. Rolling Bearing Rotating Resistance

Rolling bearing rotating resistance refers to the heat dissipated during bearing operation, 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 contact 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 [27,28,29,30,31]. 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% [34,35,36]. 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.

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 3 illustrates common commercial solutions combining labyrinth and lip seals in idler rollers with the same rolling bearing size.

As lip seals are vital for ensuring proper lubrication with minimal contamination in many applications, extensive literature exists on measuring and predicting their performance. Laboratory rigs for measuring lip seal friction losses of various types can be found in [40,41,42]. Most devices assemble a static lip seal against a rotating shaft and measure the 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. 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

, 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].

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 5 presents 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].

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 equilibrium 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 5 center). 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, Newcastle, 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 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 guidelines [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 applications 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 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

provides 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.

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 resistance, 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.

Figure 6 illustrates 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.

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 [45,46,47,48].

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 ($T_{ind}$), 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 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 temperatures ($100-(IR{R}_{400}/IR{R}_{153})\times 100$). 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 significant fluctuations.

The QC-N model described in Appendix A was applied and compared to the experimental 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.

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.

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 $n·\nu ·d_m$, 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 sensitive to the product $n·\nu ·d_m$. This aligns with previous literature suggesting the need for model optimization for specific bearings and operating conditions [35]. However, experimental 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 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

presents 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.

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.

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 ($n·\nu ·d_m$) 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 ($\dot{\gamma }\ge {10}^6{s}^{-1}$). Therefore, the use of Newtonian models to predict grease-filled labyrinth seals friction losses is only valid at $\dot{\gamma }\ge {10}^6{s}^{-1}$.

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,

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

presents 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.

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 (${30}_{-0.89}^{+0.08}$). 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 predictions 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 B also 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.

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 Appendix B and Appendix C. The SKF friction torque model optimization 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 ($M_{rr}$) was adjusted from ${(n·\nu )}^{0.6}$ to ${(n·\nu )}^{0.65}$ to accelerate the rate of torque increase as a function of $n·\nu ·d_m$. 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 ($k\ge 1$), as it significantly reduces bearing life [50]. Additionally, Equation (A13) also shows that the reduction in the EHL friction coefficient (${\mu }_{EHL}$) 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 ($k,n,{\tau }_y$) optimized to fit the experimental results. Although rheological 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 (${\tau }_y$). This occurs because non-Newtonian fluids (${\tau }_y\ne 0;n\ne 1$) exhibit viscosity variations that follow the power of $n-1$ in relation to shear rate (${\tau }_y/\dot{\gamma }$), 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 friction loss perspective only, the efficiency increases by reducing labyrinth radius and increasing the gap, which lead to low shear rates $\left({\displaystyle \frac{\omega \overline{r}}{h}}\right)$ 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 experiments, 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.

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. 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
40 °C
	Indentation Rolling Resistance (N)
10 °C
40 °C
	Rolling Bearing Resistance (N)
10 °C
40 °C
	Labyrinth Seal Resistance (N)
10 °C
40 °C
	Lip Seal Resistance (N)
-	1.52	0.46	1.06

. 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 Table 1 and Table 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 5 also 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 predominant 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.

6. Simplified Case Study

Some case studies based on the conveying systems described in [53] are presented to allow for comparison. The parameters of these case studies are given in

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

, with the predicted installed power breakdown for such systems presented in Figure 13, based on installed idler diameter. The following simplifications and assumptions 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 operate 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 physical 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 (≈$Loa{d}^{4/3}$). 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 parameters, 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, end caps, bearings, and shafts. Shell wall thickness, abrasion design allowances, and component 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.

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 $Loa{d}^{4/3}$ 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 (${\tau }_y$), and low base oil viscosity ($\eta$), or by reducing the labyrinth radius and increasing its gap $\left({\displaystyle \frac{\overline{r}}{h}}\right)$;
• Rolling bearings’ friction losses can be reduced by selecting lubricating greases formulated with synthetic base oils (${\mu }_{EHL}^{syn}<{\mu }_{EHL}^{min}$), and a base oil viscosity that leads to a viscosity ratio of $k\approx 2$;
• 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.