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Spalling Damage: 3 Main Types, Causes & Prevention Guide Home Wiki Spalling Damage: 3 Main Types, Causes & Prevention Guide Spalling Damage: 3 Main Types, Causes & Prevention Guide ankitkumar September, 28 2025 Bearings Crack fatigue Flaking Hertzian Stress Pitting Spalling Stress Concentration Table of Contents Bearing Failure Modes Definition of Spalling Damage 3 Modes of Spalling Damage Pitting vs. Spalling Damage – Key Differences Causes of Spalling Damage Bearing Failure Modes Spalling damage is a common cause of bearing failure and occurs when cracks form in the running surfaces, causing flakes of material to detach. This progressive fatigue phenomenon impacts bearing performance, increases vibration, and signals the end of service life if left unaddressed. Understanding the modes of spalling damage, their causes, and prevention strategies is crucial to extending bearing life. Bearing damage, and ultimately, failure, can be caused by a variety of conditions, including improper mounting, poor lubrication, and overloading, to name a few. The mode of damage — what actually happened to the bearing as a result of detrimental conditions — is characterized by visible features, such as discoloration, wear marks, or pitting, on the rolling element and raceway surfaces. However, different modes of damage can produce visually similar results, although their causes and long-term effects may not be the same. This is why it’s important to understand the operating conditions when investigating bearing damage, as they can provide additional clues regarding the root cause of the damage. In this article , we will focus on the surface/subsurface initiated fatigue phenomena called spalling. The ISO standard 15243:2017, Rolling bearings – damage and failures – terms, characteristics, and causes, classifies failure modes for rolling bearings made of standard bearing steels. The standard defines six primary damage/failure modes, along with various sub-modes (Fig.1). Figure 1 :- Modes of damage/failure for rolling bearings according to ISO 15243. Image credit: SKF Definition of Spalling Damage Spalling damage is the result of surface or subsurface fatigue, which causes fractures to form in the running surfaces. When the rolling elements travel over these cracks, pieces, or flakes, of material break away. (Spalling is also referred to as “flaking,” “peeling,” or “pitting.”) In the ISO damage/failure modes, spalling occurs in the category of “Fatigue,” under both “Subsurface-initiated fatigue,” and “Surface initiated fatigue.” Spalling damage is progressive (Fig.2) and can indicate that a bearing has reached the end of its fatigue life. In general , Spalling is the pitting or flaking away of bearing material. Figure 2 :- Spalling in Ball bearings This primarily occurs on the races and rolling elements. The many types of primary damage referenced throughout this guide may eventually deteriorate into a secondary spalling damage mode. 3 Modes of Spalling Damage Three distinct modes classified are stated below : 1. Geometric stress concentration (GSC) spalling.:- The causes include misalignment, deflection or edge loading that initiates high stress at localized regions of the bearing. GSC occurs at the extreme edges of the race/roller paths, or it can also be the result of shaft or housing machining errors. 2. Point surface origin (PSO) spalling :- Very high and localized stress generates this type of damage. The spalling is typically from nicks, dents, debris, etching and hard-particle contamination in the bearing. It’s the most common type of spalling damage and often appears as arrowhead-shaped spalls, propagating in the direction of rotation. 3. Inclusion origin (IO) spalling .:- This damage, in the form of elliptically shaped spalls, occurs when there’s bearing material fatigue at localized areas of sub-surface, non-metallic inclusions following millions of load cycles. Due to improvements in bearing steel cleanliness in recent decades, encountering this type of spalling is unlikely. Figure 3 :- These images show representative rolling-element fatigue failure of an inner race (left) and ball (right) from 120-millimeter-bore ball bearings made of AISI M-50 steel. The failure manifests itself as a spall that is limited to the width of the running track and the depth of the maximum shearing stress below the contact surface. The spall can be of surface or subsurface origin. A spall originating at the surface usually begins as a crack at a surface defect or at a debris dent that propagates into a crack network to form spalling damage. A crack that begins at a stress riser, such as a hard inclusion below the running track in the region of the maximum shearing stress, also propagates into a crack network to form a spall. Fatigue failures that originate below the contacting surface are referred to as classical rolling-element fatigue. Failure by classical rolling-element fatigue is analogous to death caused by old age in humans. Spalling damage can occur on the inner ring, outer ring, or balls. This type of failure is progressive and once initiated will spread as a result of further operation. It will always be accompanied by a marked increase in vibration, indicating an abnormality. The remedy is to replace the bearing or consider redesigning to use a bearing having a greater calculated fatigue life. Figure 4 :- Moderately spalled area of bearing Image Credits :- Schaeffler.com Pitting vs. Spalling Damage – Key Differences Even when operating correctly, rolling element bearings will eventually fail as a result of a surface fatigue phenomenon. It starts after some variable time of service as embryonic particles that are liberated from the surface of a race or rolling element in the load zone. Surface fatigue leaves craters that act as stress concentration sites. Subsequent contacts at those sites cause progression of the spalling process. The duration of satisfactory performance depends largely on the durability of bearing surfaces. Generally, there are three types of surface contact damage that can occur under proper operational conditions: surface distress, fatigue pitting, and fatigue spalling. Other surface damage can occur due to improper mounting or improper operating conditions. Surface distress appears as a smooth surface resulting from plastic deformation in the asperity dimension. This plastic deformation causes a thin work-hardened surface layer (typically less than 10 µm). Pitting appears as shallow craters at contact surfaces with a depth of, at most, the thickness of the work-hardened layer (approximately l0 µm), as shown in Figure 5. Figure 5 :- Pitting and Spalling Spalling damage leaves deeper cavities at contact surfaces with a depth of 20 µm to 100 µm as shown in Figure 2. It must be noted here that no common definitions have been established to distinguish spalling from pitting in the literature. In most of the literature, spalling and pitting have been used indiscriminately, and in some other literature, spalling and pitting were used to designate different severities of surface contact fatigue. For instance, Tallian defined “spalling” as macroscale contact fatigue caused by fatigue crack propagation and reserved “pitting” as surface damage caused by sources other than crack propagation. One of the reasons for the confusing definitions is probably due to the fact that the physical causes of pitting and spalling damage have not yet been established. To discuss spalling and pitting on a common ground, the following discussion rests on the definitions according to the phenomena as described in the foregoing; that is, pitting is the formation of shallow craters by surface-defect fatigue, and spalling is the formation of deeper cavities by subsurface-defect fatigue. Figure 6 shows an example of advanced fatigue wear. The shaft in this tapered roller bearing was approximately 200 mm in diameter and some of the advanced spalling from multiple sites is 30 mm across. Figure 6:- Well-developed Fatigue Spalls on Bearing Inner Race Figure 7 shows a large single spall some 250 µm across. Initial spall particles are typically 30 µm to 50 µm, but it is common for several particles to be generated from individual spall sites. Note at the sharper crater wall (near the top edge of the spall in this micrograph) there are several cracks associated with the spall. Figure 7. Typical Spall Crater (Scale Bar = 400 µm) Though both spalling and pitting are the common forms of surface contact fatigue, spalling results in more rapid deterioration of surface durability when compared to pitting. Spalling damage often induces early failure by severe secondary damage. It has been repeatedly reported as the more destructive surface failure mode for gear contacts. Such secondary damage can result in roller or race breakage, initiated from a severe spall on the contact surface, as well as friction- or heat-induced surface seizure, or complete spalling over all of the contact surfaces. Causes of Spalling Damage Way’s hypothesis postulated that lubricating oil in a surface crack was trapped when the approaching contact reached the surface opening and pinched the crack closed. As a result, the crack tip was extended by the hydraulic pressure of the oil sealed between the crack surfaces. Subsequent work by Keer and Bryant found that the dominant mechanism for surface-breaking crack growth was Mode II (shear) propagation which contradicts Way’s assumption of Mode I (tension) crack propagation. Bower performed a fracture-mechanics analysis of crack propagation in the presence of lubricating oil. His results do not appear to support Way’s hypothesis, either. Furthermore, the experimental results obtained by Cheng and others showed that the surface crack growth was very slow. According to Ding and Kuhnell, surface crack growth can only be in Mode II and can result only in shallow craters. To better understand spalling/pitting mechanisms, many researchers have also studied the behavior of subsurface cracks under contact loads. Fleming and Suh used fracture mechanics methods to analyze the propagation of subsurface cracks parallel to the contact surface. Their results showed that the stress intensity factors (SIFs) for Mode I and Mode II were quite low. Kaneta and others studied the growth mechanism of subsurface cracks by numerically analyzing the behavior of a three-dimensional subsurface crack parallel to the contact surface. They concluded that the propagation of subsurface cracks is mainly by Mode II. More recently, Ding and others studied the behavior of subsurface cracks beneath the pitch line of a gear tooth, focusing on developing a fundamental understanding of the mechanisms of spalling in gears. Using the finite element method, the potential modes of crack propagation and failure were analyzed and the values of the stress intensity factors (SIFs) of the subsurface cracks were below the critical SIF, Kc. Consequently, ligament collapse at crack tips was hypothesized as the cause of spalling from subsurface cracks. Elastic-plastic finite element analysis was also performed to further evaluate the hypothesis as the failure mechanism of spalling in gears. According to Ding and Kuhnell, subsurface spalling by crack propagation mechanisms would be too slow. Stress intensity factors for both Mode I and Mode II never exceed the critical stress intensity of crack failure in their study. Therefore, spalling is not caused by crack propagation of subsurface cracks. Ding and others calculated the mean stress, sm, in a ligament region between the crack tip and the contact surface, and concluded that spalling results from ligament collapse at subsurface crack tips. The angles between the direction of the maximum shear stress and the crack line were 33 degrees at the trailing tip and 53 degrees at the leading tip of the subsurface crack. Therefore, a spall cavity should have a shallow wall at an angle of approximately 33 degrees at the trailing end and a steep wall of 53 degrees at the leading end of rolling direction. This finding was supported by the results of the experimental evidence as were the spall depth predictions. Figure 8 provides sectioned micrographs of three spall sites. Figure 8 :- Sectioned Micrographs of Spalling on Gear Teeth Surfaces Near Pitch Line Figure 8a shows a spall site with the material of the potential spall particle(s) still attached. Figure 8b is a spall which has progressed and a number of spall particles have detached. Figure 8c is a cross-section of a spall from which the particle(s) have been liberated. Note the cracks at the steep walls of Figure 8b, Figure 8c and Figure 7. These indicate the readiness for the spalling to continue on subsequent contacts at these sites. References https://www.tribonet.org/wiki/surface-fatigue/ https://www.linearmotiontips.com/whats-the-difference-between-brinelling-spalling-fretting/ https://www.pitandquarry.com/determining-types-of-bearing-damage/ https://www.machinerylubrication.com/Read/664/wear-bearings-gears/ Keer, L. M., and Bryant, M. D. (April 1, 1983). “A Pitting Model for Rolling Contact Fatigue.” ASME. J. of Lubrication Tech. April 1983; 105(2): 198–205. https://doi.org/10.1115/1.3254565 Way, S. (February 17, 2021). “Pitting Due to Rolling Contact.” ASME. J. Appl. Mech. June 1935; 2(2): A49–A58. https://doi.org/10.1115/1.4008607 Ding, Y. and Kuhnell B.T. “The Physical Cause of Spalling in Gears.” Machine Condition Monitoring, The Research Bulletin of the Centre for Machine Condition Monitoring, Vol. 9. Monash University, 1997. Lyu, Y., Bergseth, E. & Olofsson, U. Open System Tribology and Influence of Weather Condition.;Sci Rep;6,;32455 (2016). https://doi.org/10.1038/srep32455 BRUNTON, J., FIELD, J. & THOMAS, G. Deformation of Solids By the Impact of Liquids, and its Relation to Rain Damage in Aircraft and Missiles, to Blade Erosion in Steam Turbines, and to Cavitation Erosion.;Nature;207,;925–926 (1965). https://doi.org/10.1038/207925a0 ankitkumar Ankit works in the Mechanical Maintenance Division of Hot Strip Mill, Jindal Stainless in India. He has keen interest in HVAC , Hot Rolling Machinery & Equipment, and Industrial Hydraulics. -->
Elastohydrodynamic Lubrication: Theory, Types & Practical Guide Home Wiki Elastohydrodynamic Lubrication: Theory, Types & Practical Guide Elastohydrodynamic Lubrication: Theory, Types & Practical Guide Manoj Rajankunte Mahadeshwara September, 28 2025 calculate central film thickness definition EHD ehd meaning EHL elastohydrodynamic history lubrication minimum film thickness theory what is wiki wikipedia Table of Contents What is Elastohydrodynamic Lubrication (EHL)? History of Elastohydrodynamic Lubrication Theory & Equations of Elastohydrodynamic Lubrication Film Thickness in Elastohydrodynamic Lubrication Central and minimum film thickness: Online EHL film thickness calculator What is Elastohydrodynamic Lubrication (EHL)? Elastohydrodynamic lubrication (EHL) describes a lubrication regime where high pressure causes significant elastic deformation of the contacting surfaces, deeply affecting the shape and thickness of the lubricating film. EHL is essential in many machine elements like rolling bearings, gears, and cams to reduce friction and wear. This article explains the fundamentals of elastohydrodynamic lubrication, its theory, how film thickness is measured, and where it applies in engineering practice. Elastohydrodynamic Lubrication – or EHL – is a lubrication regime (a type of hydrodynamic lubrication (HL)) in which significant elastic deformation of the surfaces takes place and it considerably alters the shape and thickness of the lubricant film in the contact. The term underlies the importance of the elastic deflection of the bodies in contact in the development of the total lubricant film. EHL, the same way as HL, is used to decrease friction and wear in tribological contacts. It is achieved by the development of a thin lubricant film between rubbing surfaces, which separates them and decreases friction. EHL has characteristic features, such as constant film thickness and almost Hertzian contact pressure profile within the Hertzian contact area, as shown in the figure below. These features have been extensively used in construction of approximate solutions of EHL theory. Fig. 1. Hertz Contact Pressure Vs. Elastohydrodynamic Pressure. History of Elastohydrodynamic Lubrication Classical Hydrodynamic Lubrication (HL) theory assumes the bodies to be rigid. In 1916 Martin obtained a closed form solution of the Reynolds equation for a film thickness and pressure in a cylinder and plane geometry assuming rigid surfaces and isoviscous lubricant. But comparison with experimental data revealed significant discrepancy with the model predictions. Divergence of experimental and theoretical results leaded researchers to the conclusion that elastic distortion and pressure-viscosity effect play a significant role in lubrication. In 1949, Grubin obtained a first solution (approximate) for elasto-hydrodynamic lubrication problem assuming a cylinder on flat geometry. He was the first to include both elastic deformation and piezoviscous behavior of the lubricant into theoretical solution. Although his solution is only approximate, his analysis is quite accurate under certain conditions and it was recognized as a big step forward in EHL theory (since then the term EHL has been used). Moreover, Grubin’s assumptions are widely used in the modern tribology to build various approximate solutions under highly loaded contacts [1]. The derivation, Matlab code and detailed analysis of Grubin solution is considered here. Petrushevich (Petrusevich 1951) was actually first to obtain the exact solution of the line contact EHL problem by solving the corresponding equations numerically. He was also the first to observe a pressure spike at the outlet of the contact – a characteristic feature of EHL (see the figure above). For this reason the feature is sometimes referred to as “Petrushevich” spike. Obtained in 1951, his solution was first solution of combined elastic distortion, fluid flow and pressure-viscosity dependency equations. It should be emphasized, that the occurrence of the pressure spike is closely related to the variance of viscosity with pressure along with elastic properties of materials and relative speed. In 1959 Dowson and Higginson computed series of numerical solutions of EHL line contact problem for a range and obtained a regression formula for a minimum film thickness. Further information on the development of the EHL theory can be found in [2]. Theory & Equations of Elastohydrodynamic Lubrication A classical EHL system of equations consists of the system of Reynolds equation, film thickness and load balance equations: (1) ; where are hydrodynamic film thickness, pressure, viscosity, and and represent the velocity of the bearing surfaces. Variables represent the approach, macroscale geometry, elastic distortion of the surfaces and microscale geometry (surface roughness) correspondingly. This system of equations can be solved assuming appropriate boundary conditions to obtain unknown hydrodynamic pressure and film thickness in the contact. Typically, parameter is unknown (although sometimes it can be specified), therefore the last integral equation is needed to get the closed system of equations. is the normal load applied to the contact. The system of equations; shown above can be solved analytically in certain cases, however, in general it has to be solved using numerical methods. The problem in solving the Reynolds equation comes from the film thickness equation, when the elastic deflection of the surfaces is not negligible. For a 2-D case, this term can be calculated from the following equation: (2) ; where is the reduced elastic modulus. This equation is the analytical solution of the theory of elasticity equations for a semi-infinite body subjected to normal pressure (for the details of the derivation refer to [3]). The most robust and fast way (in terms of iterations at least) to solve EHL system is to use a fully coupled approach and Newton’s scheme. However, since the elastic distortion equation is given in the integral form, the Jacobian of the system is full which increases the demands in memory enormously. In addition, solution of the equations with full Jacobian is computationally significantly more intense compared to diagonally banded cases. Therefore, researchers worked hard to develop alternative solution methods. The two most common methods for solving EHL systems numerically are the Multilevel-Multigrid and Differential Deflection techniques. The former uses multiple grids and specific integration of the film thickness equation to build an iterative solver [5]. The latter solves a fully coupled system of equations, however, instead of using the original integral form of the film thickness equation, it considered the 2-nd derivative of it [4,6]. It turns out that the use of the derivative equation allows to construct a banded Jacobian and improve the efficiency of coupled approach significantly. Recently, a so called full system approach was proposed [7]. In this case, a Finite Element Methods are used to calculate both Reynolds and elasticity equations in a coupled manner. This method is computationally more demanding since the subsurface volume has to be discretized to calculate elastic distortions (the fully coupled approach based on differential deflection is faster than the FEM based full system technique). Nevertheless, the approach has the advantage of flexibility since it can be developed using commercial software such as COMSOL. A Matlab code for the solution of EHL system for the case of a cylinder-on-disk can be found here or for the cases of high pressures here. A fully coupled approach based on differential deflection technique was utilized. Newtons scheme was employed. Film Thickness in Elastohydrodynamic Lubrication Since the film thickness controls the separation of the rubbing surfaces and consequently friction, researchers developed several ways to measure the hydrodynamic film in the contact. One of the most frequently used techniques is based on optical interferometry. The instrument measures the lubricant film thickness in the contact formed between a steel ball and a rotating glass disc covered by a specific layer. T he lubricant film thickness at any point in the image can be accurately calculated by measuring the wavelength of light at that point. Film thicknesses down to 1 nm can be measured by this approach. You can see the measurement of the film in the video below (at first the disk is stationary and later on stats the motion): Central and minimum film thickness: Online EHL film thickness calculator As it can be clearly seen from the Fig.1, the lubricant film thickness is more or less constant in the whole contact zone (where the pressure is large), except for the small area at the outlet, where the film thickness drops to its minimum value. Since the pressurized area is typically the most important for failure analysis, in practice engineers use only central film thickness and the minimum film thickness to describe the lubrication state (see this article for more details). An online film thickness calculator is available on tribonet for line and elliptical (point) contacts. The calculators allow calculating central and minimum film thicknesses using various equations. Exact equations are described on the calculator’s page. Here is the calculator for elliptical contact: <span data-mce-type="bookmark" style="width: 0px; overflow: hidden; line-height: 0;" class="mce_SELRES_start"></span><span data-mce-type="bookmark" style="width: 0px; overflow: hidden; line-height: 0;" class="mce_SELRES_start"></span> References [1] Ertel – Grubin methods in elastohydrodynamic lubrication – a review, G. E. Morales-Espejel and A. W. Wemekamp. [2] A Review of Elasto-Hydrodynamic Lubrication Theory, P. M. Lugt and G. E. Morales-Espejel. [3] Theory of Elasticity, Timoshenko, S.P., Goodier, J.N., 1970. [4] LUBRICATION AND WEAR AT METAL/HDPE CONTACTS , A. Akchurin [5] Multi-Level Methods in Lubrication, C.H. Venner, A. Lubrecht. [6] Evaluation of Deflection in Semi-Infinite Bodies by a Differential Method, Evans, H.P. Hughes, T.G. [7] A Full-system Finite Element Approach to Elastohydrodynamic Lubrication Problems: Application to Ultra-low-viscosity Fluids. PhD thesis, Habchi, W. Manoj Rajankunte Mahadeshwara I am a postgraduate researcher at the University of Leeds. I have completed my master's degree in the Erasmus Tribos program at the University of Leeds, University of Ljubljana, and University of Coimbra and my bachelor's degree in Mechanical Engineering from VTU in NMIT, India. I am an editor and social networking manager at TriboNet. I have a YouTube channel called Tribo Geek where I upload videos on travel, research life, and topics for master's and PhD students. -->
Stern Tube Sealing System: Design, Operation & Leak Prevention Guide (2025) Home Wiki Stern Tube Sealing System: Design, Operation & Leak Prevention Guide (2025) Stern Tube Sealing System: Design, Operation & Leak Prevention Guide (2025) Xavier Borras, PhD September, 28 2025 leakage lubricant seaing seals ship stern tube transport Table of Contents What Is a Stern Tube Sealing System? Key Components of a Stern Tube Sealing System How a Stern Tube Sealing System Operates Common Failure Modes in Stern Tube Sealing Systems Materials and Seal Design in Stern Tube Sealing Systems What Is a Stern Tube Sealing System? Stern tube sealing system is crucial for marine vessels to maintain lubrication in the stern tube bearings while preventing seawater ingress and oil leakage into the environment. It uses multiple rotary lip seals, oil-pressurized chambers, and corrosion-resistant materials to handle varying hydrostatic pressures, wear, and shaft rotation. In this article, we examine how a stern tube sealing system works, its components, challenges, and best practices for design and maintenance. Key Components of a Stern Tube Sealing System Most ships are driven by the engine-shaft-propeller arrangement shown in Figure 1. The stern tube is a metal tube welded to the hull of the ship connecting the engine chamber and the outside of the ship. The shaft driving the propeller and later transmitting its thrust to the hull goes through the stern tube. A couple of journal bearings are placed within the stern tube, carrying the weight of the shaft and the propeller while allowing rotation of the shaft. To decrease the frictional torque on the bearings the stern tube is flooded with lubricant so the bearings operate while fully immersed in oil. Finally, to ensure the lubricant stays within the stern tube, two sets of rotary lip seals are installed at each end of the tube, namely stern tube seals. The stern tube seal is one of the largest rotary lip seals, along with the seal used in hydropower turbines and wind turbines. Figure 1. Disposition of the stern tube oil tanks in a ship. How a Stern Tube Sealing System Operates The function of the stern tube seals is to prevent water entering the stern tube as well as to minimize the lubricant spillage to the marine environment and engine chamber. To increase the reliability of the system, a few sealing rings are mounted in line at both ends of the stern tube conforming the aft and forward stern tube seals packages shown in Figure 1. This special type of sealing rings constitutes the only barrier between the stern tube lubricant and the environment. The propeller of a ship is located below the sea water level, hydrostatically pressurizing the outermost sealing ring. Note that the draught of the ship varies between the loaded and unloaded situations impacting the operating conditions of the seal. Furthermore, the hydrostatic pressure at seal #1 oscillates with the sea waves [1]. To counteract the head of sea water on the outermost seal, the spaces between the stern tube seals are independently pressurized by a set of oil tanks, as shown in Figure 2. By filling each tank to a particular oil height the hydrostatic pressure at each space between seals can be set. The pressure difference over each seal differs from seal to seal according to its position (#1, #2, #3, #4 and #5 in Figure 1). The disposition of the oil tanks, together with the working pressures within the stern tube, is of relevance for the performance of the stern tube system. Figure 2. Disposition of the oil tanks feeding the chambers between the stern tube seals. Source: Wärtsilä. Although various seal dispositions exist, the arrangement shown in Figure 1 and Figure 2 is the most common one. Seal #1 faces the water side and works as a dirt excluder. This outermost seal is rapidly worn out, hence seal #2 also faces the water. Seals #3 and #4 face seal the oil in the header tank, i.e. the oil lubricating the stern tube bearings. Ultimately, seal #5 prevents the leakage of the lubricant into the engine chamber. Figure 3. Stern tube seal aft package. Common Failure Modes in Stern Tube Sealing Systems Typically, all the seals of a stern tube are of the same type, irrespective of their position. Additionally, some manufacturers use special compounds for the seals in contact with the sea water where lubrication is particularly difficult. The stern tube seals are mounted on the shaft liners, as shown in Figure 1 and Figure 2. This way, the shaft liner can be easily replaced when grooved or corroded, thus avoiding the disassembly of the shaft. Additionally, it is simpler to machine the shaft liners down to the required surface finish. Sometimes spacer parts are mounted between the housing rings and the hull, offsetting the position of the seal tip. This way, a fresh un-grooved surface is provided to the seal tip, allowing for an additional use of the shaft liner. To prevent disassembling the propeller when replacing the seals, stern tube seals are cut, mounted around the shaft and bonded. Using a specialized glue and a heating device the two cut surfaces are bonded together in such a way that the splitting line becomes almost unnoticeable. The life of stern tube seals usually spans two and five years depending on the operating conditions. However, to prevent costly unexpected failures while sailing the seals are replaced every time the ship is in dry dock. Figure 4. Stern tube seal profile. Materials and Seal Design in Stern Tube Sealing Systems Stern tube seals are usually made of fluoroelastomer compounds, specifically FKM compounds (see Figure 4). This saturated elastomer, often referred to by its trademark Viton®, stands out for its temperature resistance and inertness. The high bonding energy between the carbon and the bulky fluorine atoms shields the polymer back bond from chemical attacks. The inherent polarity resulting from bonding carbon and fluorine molecules makes fluoroelastomers extremely resistant to mineral oils and fats, i.e. non-polar media. Stern tube seals are generally manufactured via compression moulding although they can also be extruded. These production methods allow the manufacturing of complex geometries, decreasing the amount of tooling required. It is worth mentioning that rotary lip seals are not suitable for separating two liquids from each other. Therefore, even when several lip seals are installed in line, some of the lubricant is continuously spilled to the ocean. Furthermore, the loss of stern tube lubricant is considered an inevitable part of the normal operation of a ship [2]. Hence the lubricant tanks are periodically refilled to compensate for the amount of oil spilled to the ocean. The leakage of stern tube lubricant to the environment depends on elements such as seal design, vessel type, draught, shaft diameter and ship condition. As an example, the stern tubes of barge carriers, tankers and navy ships “consume” (i.e. spill) between 10 and 20 litres per day [2]. To the best of the author’s knowledge, there is no standard method for predicting the flow rate resulting from a particular stern tube arrangement. Check this video: https://www.youtube.com/watch?v=JFGJh-HsAmc&pp=ygUZc3Rlcm4tdHViZS1zZWFscyB0cmlib25ldA%3D%3D ; References S. Yamajo and I. Matsuoka, “Advanced Technology of Propeller Shaft Stern Tube,” in Advanced Naval Propulsion Symposium, 2008, pp. 1–14 D.S. Etkin, “Worldwide analysis of in-port vessel operational lubricant discharges and leakages.” Cortlandt Manor, pp. 2–9, 2008 Borras FX, “Rotary lip seal operation with Environmentally Acceptable Lubricants (EAL’s). Enschede: University of Twente, 2020. doi:10.3990/1.9789036550444 Borras FX, van den Nieuwendijk R, Ramesh V, de Rooij MB, Schipper DJ. Stern tube seals operation: A practical approach. Advances in Mechanical Engineering. 2021;13(2). doi: 10.1177/1687814021994404 Borras FX, Bazrafshan M, B De Rooij M, J Schipper D. Stern tube seals under static condition: A multi-scale contact modeling approach. Proceedings of the Institution of Mechanical Engineers, Part J: Journal of Engineering Tribology. 2021;235(1):181-195. doi:10.1177/1350650120925583 Borras, F.X.; De Rooij, M.B.; Schipper, D.J. Rheological and Wetting Properties of Environmentally Acceptable Lubricants (EALs) for Application in Stern Tube Seals. Lubricants 2018, 6, 100. https://doi.org/10.3390/lubricants6040100 Xavier Borras, PhD Industrial Engineer with focus on Tribology and Sealing Technology. Team player with an open-minded mentality author of several scientific publications and an industrial patent. Interested in Lean Management, Innovation, Circular Economy, Additive Manufacturing and Connected Objects Technology. --> 2 Comments Mr Singh says: 21.07.2023 at 14:03 What a great explanation. Really appreciate, could understand the topic in detail. Log in to Reply Lily says: 20.09.2023 at 15:23 Thanks for writing up such a good explanation Log in to Reply Leave a Reply Cancel reply You must be logged in to post a comment. Login using social account This site uses Akismet to reduce spam. Learn how your comment data is processed.
Hertz Contact Equations: Complete Guide for Elliptical, Spherical & Cylindrical Contacts (2025) Home Wiki Hertz Contact Equations: Complete Guide for Elliptical, Spherical & Cylindrical Contacts (2025) Hertz Contact Equations: Complete Guide for Elliptical, Spherical & Cylindrical Contacts (2025) TriboNet September, 25 2025 Cylinder contact Elliptical contact hertz contact Hertz contact equations Hertz contact theory hertz formula Line contact onlince calculator Point contact Spherical contact A theoretical background to the Hertz contact theory can be found here. Hertz contact equations for Line Contact (Cylindrical contact) Fig. 1. Contact of two cylinders In case of two cylinders in contact (with radii ), as shown in Fig. 1, the Hertzian radius of contact under applied normal load is given by the following equation: (1) ; where is the length of the cylinders. It is important to note here that the reduced elastic modulus is defined as follows:; . This definition is historically used in the field of hydrodynamic lubrication and it is different from the typical contact mechanics definition, where the reduced elastic modulus is given as . Therefore, the given equations may slightly differ from the classical Hertzian equations given in contact mechanics textbooks (but they are equivalent). Equivalent radius is given by the following relation: (2) ; The mean and maximum pressures are given by: (3) ; Corresponding Matlab code for Hertz contact equation and solution can be found here. The online Hertz contact calculator can be found here. Further details of the contact theory can be found in Contact Mechanics by James Barber. Fig. 2. Hertz radius of contact Hertz contact equations for Point Contact (Spherical contact) Fig. 3. Contact of two spheres For the case of two spheres in contact as shown in Fig.3, the Hertzian contact radius is given by the following equation: (4) ; , with is given by the following relation: (5) ; The elastic approach (also know as rigid body approach) is given by the following expression: (6) ; The mean and maximum pressures are given by: (7) ; Corresponding Matlab code for Hertz contact equations and solution can be found here. The online Hertz contact equations calculator can be found here. Further details of the contact theory can be found in Contact Mechanics by James Barber. Hertz contact equations for Elliptical Point Contact Fig. 4 Elliptical point contact For the case of two spheres in contact as shown in Fig.4. In this case the Hertzian contact is an ellipse and is described by major ( ) and minor; axes of the contact ellipse: (8) ; where . (9) ; The functions in the previous equations are approximated as follows: (10) ; The mean and maximum pressures are given by: (11) ; Load as a function of rigid body approach can be calculated as follows: (12) ; Stiffness of the contact is defined as follows: (13) ; Hence, for an elliptical contact, stiffness can be found from the following expression: (14) ; Corresponding Matlab code for Hertz solution can be found here. The online Hertz contact calculator can be found here. Further details of the contact theory can be found in Contact Mechanics by James Barber. Here is an online calculator for an elliptical point contact. <span data-mce-type="bookmark" style="display: inline-block; width: 0px; overflow: hidden; line-height: 0;" class="mce_SELRES_start"></span> TriboNet Administration of the project --> 11 Comments Owen says: 17.08.2018 at 18:19 I believe the formula for the b (width of contact) is incorrect in two ways, firstly if b is the whole width it contradicts the diagram of the two cylinders in contact which shows 2b. So if it is the full width it should be b=2*(sqrt((4*F*R)/(pi*L*E’))) with a 4 instead of a 2 in the formula, OR if b is the half width as implied by the diagram it should be b=(sqrt((4*F*R)/(pi*L*E’)) Log in to Reply Aydar Akchurin says: 20.08.2018 at 09:58 Hi Owen, Thank you for a comment. So b is the half-width, as shown in Figure 2. The equation for b that you posted in your comment assumes a different definition of the reduced elastic modulus (1/E’=…, while the equations posted in the wiki, assume 2/E’=…, see its definition after equation 1). If you substitute this formula to the equation in the article, you will get your equation. Log in to Reply geardyn.1 says: 06.12.2018 at 02:43 Hi, if we assume Steel material ,its ultimate strength is ~500MPa. if we calculate the contact pressure for a two sphere(0.1m) under contact in both elastic & plastic regime , the hertz contact pressure is reaching around 11.66E3 MPa. I have analytical & numerically(using abaqus) validated it. my concern is if the obtained contact pressure is so huge and crossing the ultimate strength of the material ,can i consider it for my design ? Should Contact pressure or hertz contact stress be LESS than Ultimate stress ? mat-reference: http://www.matweb.com/search/datasheet.aspx?MatGUID=abc4415b0f8b490387e3c922237098da Log in to Reply tribonet says: 07.12.2018 at 20:56 I believe, if the Hertzian stress exceeds the ultimate strength of the material in your design, it cannot be a good sign. You will get a lot of plastic deformation and probably a failure in a short term. So it is good to rethink the design. Log in to Reply kevin.stamp@live.co.uk says: 05.10.2022 at 23:37 A bit late to the party but, Hertz’s Contact Stress can be significantly greater than the ultimate stress, and not fail. Imagine that you are at the bottom of the ocean. In that case, you will be under considerable Stress from the water pressure, but you will not likely fail. All principal stress compression. It is similar to Hertz Stress, all three principal stresses are compression. The three principal stresses are not necessarily equal to each other. This sets up some shear internal to the component. So, it is the Shear Stress that is likely to fail your component rather than the compressible stresses. Thoughts anyone? Log in to Reply TriboNet says: 10.10.2022 at 22:35 Hi Kevin! Good point! I think you are right, its the difference in stresses in different directions that cause the failure. And in Hertz stress that’s also the case. You have pressure gradient along the cross section in any direction. Here is how the pressure profile looks like: https://www.tribonet.org/calculators/hertz-pressure-calculator/. Log in to Reply Jamie says: 26.04.2020 at 22:30 Hi, Are there any places that the derivation for the elliptical point contact equations are published? I’ve looked through some of the references and couldn’t find the exact equations. Many thanks. Log in to Reply Olga AFiyan says: 12.07.2023 at 10:30 in case we have a pin within the hole-cylinder in cylinder contact, convex, and concave, respectively, should I put a negative value for R2 since it is a concave shape? Log in to Reply TriboNet says: 12.07.2023 at 16:05 Olga, yes, you are right, as long as the resultant radius is positive! Log in to Reply SD says: 22.08.2023 at 18:58 Hi could you provide me the references for the above used equations. Thanks. Log in to Reply kishore Kumar says: 17.05.2024 at 07:11 Can you please tell me, How to find the stiffness formula for cylinder-cylinder contact? Log in to Reply Leave a Reply Cancel reply You must be logged in to post a comment. Login using social account This site uses Akismet to reduce spam. Learn how your comment data is processed.
Scanning Electron Microscope (SEM): Principles, 6 Components & Powerful Applications Home Wiki Scanning Electron Microscope (SEM): Principles, 6 Components & Powerful Applications Scanning Electron Microscope (SEM): Principles, 6 Components & Powerful Applications Manoj Rajankunte Mahadeshwara September, 22 2025 miscroscope scanning electron miscroscope Surface characterization surface imaging Table of Contents Introduction to Scanning Electron Microscope (SEM) Definition of Scanning Electron Microscope (SEM) Working Principle of Scanning Electron Microscope (SEM) 6 Components of Scanning Electron Microscope (SEM) Advantages and Disadvantages of Scanning Electron Microscope (SEM) Applications of Scanning Electron Microscope (SEM) Introduction to Scanning Electron Microscope (SEM) A Scanning Electron Microscope (SEM) is an advanced microscopy tool that overcomes the resolution limits of optical microscopes by using electrons instead of light. SEM have been commercialised for about 40 years; since then, the SEM has been developed for various applications. SEM is used in fields that deal with observing the features of specimens in micro- and nano-sized particles. Fig. 1 shows the SEM instrument by Hitachi. Fig. 1;Scanning;Electron Microscope (SEM) instrument by Hitachi [1] Definition of Scanning Electron Microscope (SEM) SEM is an advanced electron microscope that is used to observe specimens by irradiating the fine beam of high-energy electrons on the specimens. The variety of signals that are emitted from the surface of the specimen reveals information about the specimen. Information such as external morphology, chemical composition, and crystalline structure of the specimens can be obtained from this technology. The data that is collected from the surface of the specimen is generated as a 2-dimensional image, which describes the spatial variations in the surface properties of the specimen. The schematic representation of SEM is shown in Fig. 2. Fig-2 Schematic diagram of Scanning Electron Microscope (SEM) [2] Working Principle of Scanning Electron Microscope (SEM) SEM works by directing a fine beam of high-energy electrons onto the specimen surface, generating various signals that reveal its properties. The electron-specimen interaction produces secondary electrons, backscattered electrons, diffracted electrons, photons, light, and heat. Among these, secondary and backscattered electrons are mainly used to form images — the former showing surface morphology and topography, and the latter highlighting compositional contrast in multiphase samples. The schematic of this process is shown in Fig-3. Fig-3 Working principle of Scanning Electron Microscope (SEM) [3] 6 Components of Scanning Electron Microscope (SEM) SEM is a very complex structure with a variety of components operating in it to analyze the data of the specimen surface. The essential components in the SEM constitute an electron gun, condenser and objective lens, specimen stage, secondary electron detector, image display, recording, and vacuum system. Electron gun: The electron gun is used to produce the electron beam that mostly uses thermionic emission from the cathode source (tungsten filament). The filament is heated to a very high temperature (2800K) and the emitted thermoelectric is focused through a metal plate which acts like an anode. This is done in order to focus the current of the electron beam at the desired point. Condenser and objective lens: These lenses are used to enable the adjustment of the diameter of the electron beam. A condenser lens helps in strengthening the electron beam and adjusting the diameter of the electron beam when it passes through this lens. An objective lens is used to focus the electron beam onto the specimen surface and it determines the final diameter of the electron beam. Specimen stage: This acts as the supporting base of the specimen which stably supports the specimen by moving smoothly in vertical, horizontal, and rotational ways. Secondary electron detector: This is used to detect the secondary electrons emitted from the specimens and it is placed above the objective lens. Magnetic fields are utilized in detecting secondary electrons. Image display and recording: The output signals obtained from the secondary electron detector are amplified and sent to the display unit. Initially, cathode ray tubes were used for the display units however now the liquid crystal display is being used. Recording of these images is obtained in digital format. Vacuum system: The electron optical system and the specimen chamber should be in vacuum condition and hence the components are evacuated by diffusion pumps. In the case of an oil-free environment, then, turbo molecular pumps are used. Fig. 4 Components of Scanning Electron Microscope (SEM) [4] Advantages and Disadvantages of Scanning Electron Microscope (SEM) The image processing and data analysis of the topographical characteristics of any material specimen is very easy in the case of SEM. Using different techniques such as the backscattered electron beam technique, and diffracted backscattered electron techniques then various information such as crystal structure orientation and chemical compositions of the specimens can be obtained. SEM is one of the most used techniques in material surface analysis. The disadvantages of the SEM include the sizing of the specimen, which should be fitted inside the specimen chamber. The specimen compositions also play an important role as the specimens which oxidize at low pressure or the specimens that are wet, such as organic materials, cannot be determined in this technique. Also, the materials should be electrically conductive or conductive coatings in order to analyze the data. Applications of Scanning Electron Microscope (SEM) The application of SEM is in various fields, it is used to determine high-resolution images of the material’s shapes and determine the chemical compositions by acquiring the elemental maps. SEM is used in identifying the phases based on qualitative chemical analysis or by crystalline structure. Backscattered electron images can be used to determine the discrimination of phases in multiphase specimens. Whereas diffracted backscattered electron detectors are used to determine the micro fabric and crystallographic orientation in specimens. Do check Transmission electron Microscope ; Reference [1] https://analyticalscience.wiley.com/do/10.1002/imaging.6389 [2] https://www.britannica.com/technology/scanning-electron-microscope [3]https://www.thermofisher.com/blog/materials/what-is-sem-scanning-electron-microscopy-explained/ [4] https://www.jove.com/v/5656/scanning-electron-microscopy-sem Manoj Rajankunte Mahadeshwara I am a postgraduate researcher at the University of Leeds. I have completed my master's degree in the Erasmus Tribos program at the University of Leeds, University of Ljubljana, and University of Coimbra and my bachelor's degree in Mechanical Engineering from VTU in NMIT, India. I am an editor and social networking manager at TriboNet. I have a YouTube channel called Tribo Geek where I upload videos on travel, research life, and topics for master's and PhD students. --> 1 Comment Ramesh K says: 18.09.2023 at 16:52 Good Log in to Reply Leave a Reply Cancel reply You must be logged in to post a comment. 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Hertz Contact Theory: Key Concepts Explained Home Wiki Hertz Contact Theory: Key Concepts Explained Hertz Contact Theory: Key Concepts Explained TriboNet September, 20 2025 contact stress contact theory Cylindrical contact Elliptical contact example Hertz contact pressure Hertz contact stress Hertz contact theory hertzian contact stress calculation Line contact Matlab code online calculator Point contact Spherical contact Fundamentals of Hertz Contact Theory Hertz Contact Theory describes the stresses and deformations that occur when two curved surfaces come into contact. It is widely used in mechanical engineering to calculate contact pressures and predict material behavior under load. Hertzian contact theory is a classical theory of contact mechanics and is a very useful tool for engineers and researchers. Even though the derivation of the theory is relatively difficult, the final solution is a set of simple analytical equations relating the properties of the system to the developed stress. Hertz theory was also successfully applied to get a first analytical solution of Elastohydrodynamic lubrication theory (this solution is known as Grubin’s solution). Here, the main equations of the theory are considered, while the full derivation and the description can be found in the classical contact mechanics books [1,2]. Hertz contact theory is derived from the analytical solution of elasticity theory equations (as discussed by Timoshenko and Goodier in [2]) under half-space approximation: Surface are infinitely large half-spaces. Pressure profile is parabolic (which assumes that the shape of the bodies in contact can also be approximated well with parabolic shapes, e.g., sphere, ellipse or a cylinder) All the assumptions of the classical theory of elasticity apply (small strain, homogeneous material). Equations and Stress Calculations in Hertz Contact Theory If there are only vertical forces acting on the surface, elastic deflection of the surface under applied pressure is given by the following relation: (1) ; Here is the elastic deflection, is the reduced elastic modulus, are the Poisson’s ratio and Young’s modulus of the bodies, is the contact pressure. If the pressure profile is arbitrary, this equation does not lead to the analytical solution. However, Hertz solution is obtained under the assumption of a parabolic pressure distribution, which is a very good approximation for spherical,elliptical or cylindrical bodies in contact: (2) ; where is the distance to the arbitrary point on the surface and; is the unknown parameter (which is called Hertz contact radius). Parameter is also unknown (it is called maximum Hertz pressure). Substituting this into the equation for deflection leads to the following expression for Hertzian pressure; [3]: (3) ; Fig. 1. Sphere in contact with flat. For a rigid sphere penetrating an elastic half-space as shown in Fig.1, the elastic deformation of the initially flat surface within the contact is given by the following equation: (4) ; where the local curvature of the sphere is approximated by the expression . By equating this expression to the expression for obtained earlier, the equations for the unknown parameters are obtained: (5) ; where is the applied load. Hertz theory briefly described is applicable for the case of spherical, cylindrical and elliptical contacts. List of all expressions of the Hertz contact theory is given here (this list includes solution for spherical, elliptical (point) contacts and cylindrical (line) contact). A Matlab code of Hertz solution is given here. The online calculators to obtain Hertz solution for a spherical (elliptical) case is given here, for a cylinder (line) contact case is given here. Further overview of the case of contact of two spheres can be found here. Conclusion of Hertz Contact theory Understanding Hertz Contact Theory is essential for engineers working with bearings, gears, and other components under load. By applying these principles, you can predict contact stresses, prevent material failure, and optimize designs. Use the equations and examples provided to apply Hertz Contact Theory effectively in real-world mechanical engineering problems. Check the Guide for tribology ‘Tribonets guide to Tribology‘ Dowload the pdf version. Here is an tool for calculating the Hertzian stress in an elliptical/point contact: <span data-mce-type="bookmark" style="display: inline-block; width: 0px; overflow: hidden; line-height: 0;" class="mce_SELRES_start"></span> References Contact Mechanics, K. Johnson, http://www.ewp.rpi.edu/hartford/~ernesto/S2015/FWLM/Books_Links/Books/Johnson-CONTACTMECHANICS.pdf Theory of Elasticity, S.P. Timoshenko, J.N. Goodier, https://engineering.purdue.edu/~ce597m/Handouts/Theory%20of%20elasticity%20by%20Timoshenko%20and%20Goodier.pdf Contact Mechanics and Friction, V. Popov. TriboNet Administration of the project --> 2 Comments geardyn.1 says: 06.12.2018 at 02:48 Should Contact pressure/hertz contact stress be less than Ultimate stress of a material ? Log in to Reply alpay says: 09.12.2018 at 02:17 ı think, the hertzian contact ( principal ) stresses should be less than the yield stress of material, otherwise some permanent damages will be occurred on the contact surface of two elastic bodies. Log in to Reply Leave a Reply Cancel reply You must be logged in to post a comment. Login using social account This site uses Akismet to reduce spam. Learn how your comment data is processed.
Derjaguin, Muller, and Toporov (DMT) – Adhesion theory ;Derjaguin, Muller, and Toporov (DMT) – Adhesion theoryManoj Rajankunte Mahadeshwara ; ; ; March, 25 2025 ; ; Table of ContentsIntroductionChallengesDMT – ModelReferenceIntroductionAdhesive contact mechanics has become an important area of study in nano- and biosciences. There are various methods developed over the past 75 years to address adhesive interactions in elastic contact problems. The emphasis is on connecting the local physical mechanisms of adhesion with macroscopic mechanical loading, with particular attention given to the contact equations. Adhesive contacts are crucial in various technological fields. Efficient manufacturing processes, like wafer cleaning in semiconductor technology, require tight control over surface contamination. Energy-efficient mechanical devices and reliable micromechanical systems depend on better management of friction and lubrication. Understanding key phenomena, such as particle immobilization or release in filtration, controlled positioning in reproduction devices, and the settling of bioorganisms on surfaces in health and biotechnology, is essential for further advancements. ChallengesThe first issue concerns the physical and chemical properties of surfaces and how two surfaces interact, along with how these interactions can be engineered through surface modification.The second issue addresses the impact of surface interactions on the overall mechanical response of a particle: for a given load, will the particle be captured, or can it be released?DMT – ModelThe Derjaguin, Muller, and Toporov (DMT) adhesion theory applies to elastic contact with adhesion between two locally spherical bodies under a normal force, without friction. It builds on the Hertz theory of contact but incorporates adhesion by assuming that the Hertz deformation profile remains unchanged by adhesion. The DMT theory is suitable for small values of the Tabor parameter, which corresponds to small radii, low adhesion, and high modulus materials. The DMT theory can also be applied to the adhesive contact of two elastically deformable spherical particles. It is generally considered suitable for small particles that have a high elastic modulus and low work of adhesion. Figure-1 The geometry of the DMT adhesive contact involves attractive interactions that act over the cohesive zone, which is an annulus with radius c surrounding the contact zone with radius a. The DMT model applies if c is greater than a. The pull-out force for the DMT theory is Fpullout = -2 πRw Where w is the adhesion energy and R is the contact radius As these more general results demonstrate, the DMT model depends on the interaction potential and the punch shape. Unlike the Derjaguin 1934 model, which assumes the pull-out force is controlled by the creation or destruction of the contact area, the DMT model suggests that the pull-out force is influenced by the motion of the punch in the long-range interaction potential. In this model, the adhesion energy w (which is coupled to the contact area) is not the relevant concept. Instead, the key parameter for adhesion is the amplitude of the interaction potential V₀. In the DMT theory, the punch displacement directly couples to the interaction potential. Figure-2 The schematic illustration shows the formation of a neck at the contact edge. In a thought experiment, an adhesionless contact is initially formed. When adhesion is introduced, the contact area begins to spread out (a). If a (negative) flat punch displacement is applied, it restrains the growth of the contact area, preserving the contact radius (b). Reference[1] Barthel, E., 2008. Adhesive elastic contacts: JKR and more. Journal of Physics D: Applied Physics, 41(16), p.163001. Manoj Rajankunte Mahadeshwara I am a postgraduate researcher at the University of Leeds. I have completed my master's degree in the Erasmus Tribos program at the University of Leeds, University of Ljubljana, and University of Coimbra and my bachelor's degree in Mechanical Engineering from VTU in NMIT, India. I am an editor and social networking manager at TriboNet. I have a YouTube channel called Tribo Geek where I upload videos on travel, research life, and topics for master's and PhD students.
A mechanical view of wear – The third body approach A mechanical view of wear – The third body approachManoj Rajankunte Mahadeshwara ; ; ; March, 14 2025 ; ; A mechanical view of wear – The third body approachTable of ContentsIntroductionThird Body approach Properties of the third bodyBoundary conditionsReferenceIntroductionSurface roughness is an inherent property of any material, and it is established when two surfaces come in contact, it was assumed that these asperities were rounded than spiky. Further, the clean surfaces adhere to each other increasing adhesion hence artificial screening is performed on the industrial surfaces to avoid friction. Key challenges in this domain include predicting particle detachment during contact (relevant to both material science and mechanical engineering), understanding the mechanical conditions lead to screen destruction, and investigating the kinetics of screen regeneration. The behavior of detached particles is influenced by mechanical factors like velocity fields, while their composition and transformations fall under materials science. Third Body approach Any contact consists of two primary surfaces i.e. first body and an intermediate layer known as the third body. The third body can be defined in two ways: by its material composition, which differs from the first bodies, or by its role in accommodating velocity differences between the first bodies. Contacts are categorized as either “full,” where the space between first bodies is completely filled by the third body (e.g., in elastohydrodynamic lubrication), or “empty,” where the third body acts as struts to separate the first bodies, common in the initial rubbing of hard materials. Third bodies are introduced into the contact either tangentially (via the motion of the first bodies) or normally (through wear of the first bodies). Normal feeding involves wear, whereas tangential feeding helps prevent it. Lubricants, whether solid or liquid, are typically tangentially fed, while wear debris, such as from rubbing plastics, is fed normally. In multi-pass systems, both feeding methods can occur simultaneously, as newly formed debris mix with previously deposited particles, forming traces that are recirculated after being destroyed and reprocessed. Figure-1 Schematic showing variables which may influence wear when using the particle approach [2]. To achieve efficiency comparable to lubrication theory, the Third Body Approach (TBA) must predict load and friction for specific operating conditions and materials. For the simplest cases, such as full contacts, this requires: Understanding the properties and behavior of the third body.Analyzing how the third body interacts with the first bodies under load.Modelling the effects of these interactions on friction and wear.Accounting for the dynamics of third-body formation, destruction, and regeneration.Properties of the third bodyUnderstanding the rheological behaviour of the material acting as the third body is essential. This is straightforward when the third body is a material available in sufficient quantities, like a solid lubricant, as it can be studied directly. However, challenges arise when the third body is produced in minute amounts, such as from normal feed during the rubbing of plastics. In such cases, third bodies are extremely thin (less than 1 µm thick) and small in area, making them difficult to analyze with existing microrheometric techniques. Additionally, the behaviour of these third bodies cannot be directly inferred from the properties of the original material (first body), as compacted wear particles exhibit different characteristics. This complicates the understanding of third-body rheology and its relationship with the materials involved. Boundary conditionsTo fully understand the behaviour of third-body contacts, detailed information is needed about both longitudinal boundary conditions (entry and exit) and transverse boundary conditions (interfaces between the first body and third body). Unfortunately, very little data exists on these topics. Studies of two-body contacts indicate no clear relationship between tangential and normal stresses, and the situation is even more complex in three-body contacts. Observations suggest that particles in three-body interactions may adhere, roll, or slip on the counter face, but the exact boundary kinematics remain uncertain and are not yet well-defined. Developing a comprehensive theory of thin film mechanics that accounts for all possible rheological conditions is essential but challenging. This difficulty arises primarily from the high aspect ratio of the contact, where the film thickness is extremely small compared to the other contact dimensions. To address this, either generalized equations or advanced numerical discretization methods are needed. These approaches would provide an integrated understanding of contact behaviour, which is critical for making significant advancements in this field.Reference[1] Godet, M., 1984. The third-body approach: a mechanical view of wear. Wear, 100(1-3), pp.437-452. [2] Cowie, R.M. and Jennings, L.M., 2021. Third body damage and wear in arthroplasty bearing materials: a review of laboratory methods. Biomaterials and Biosystems, 4, p.100028. Manoj Rajankunte Mahadeshwara I am a postgraduate researcher at the University of Leeds. I have completed my master's degree in the Erasmus Tribos program at the University of Leeds, University of Ljubljana, and University of Coimbra and my bachelor's degree in Mechanical Engineering from VTU in NMIT, India. I am an editor and social networking manager at TriboNet. I have a YouTube channel called Tribo Geek where I upload videos on travel, research life, and topics for master's and PhD students.
Mechanism of Metallic Friction as described by Bowden and Tabor Table of ContentsIntroductionFiction of metal in hard on soft surfaceEffect of contaminating film with frictionEffect of intermittent motion on frictionFriction of metallic films ReferenceIntroductionKinetic friction is not merely a surface phenomenon but rather depends on the bulk properties of the interacting materials, such as their relative hardness and melting points. Experimental investigations indicate that friction primarily arises from shearing or adhesion of the softer material in contact with the harder surface. Even highly polished surfaces, which may appear smooth at the macroscopic level, possess microscopic irregularities that contribute to friction. The temperature rise at the interface is not the primary cause of friction, as friction can still occur at cold asperity contacts due to localized adhesion and welding under high pressure. However, when sliding occurs at high loads and speeds, the resulting temperature increase at the interface may give the impression that elevated temperatures directly cause higher friction. Importantly, this relationship does not imply that higher ambient (room) temperatures always lead to increased friction. Instead, the frictional behavior is influenced by temperature generated during sliding, which depends on parameters such as load and speed, rather than the initial room temperature. Fiction of metal in hard on soft surfaceThe relationship between frictional force, contact area, and applied load has been extensively studied. Coulomb and Amontons formulated two key laws: (i) frictional force is independent of the apparent contact area, and (ii) it is proportional to the applied load. While these laws initially lacked a theoretical basis, studies on the real area of contact have provided explanations. With respect to the first law, various experiments revealed that the real area of contact between metals was measured using electrical conductance techniques. The findings revealed that contact occurs primarily at the summits of surface asperities, resulting in a real contact area that is significantly smaller and largely independent of the apparent contact area. This insight helps to explain why the frictional force is unaffected by changes in the apparent contact area, as the real contact area—and consequently the frictional force—remains consistent under similar loading conditions. Amontons’ second law, which states that frictional force is proportional to the applied load, initially posed challenges because it was assumed that the surfaces deformed elastically. Elastic deformation would predict the contact area, and thus the frictional force, to vary with the two-thirds power of the load, not linearly. However, conductivity measurements revealed that the surface deformation is predominantly plastic. Under plastic deformation, the material flows until the contact area becomes proportional to the applied load, resolving this inconsistency. Effect of contaminating film with frictionUnder most experimental conditions the metallic surfaces are covered with thin oxide layers and contaminating films. During sliding, these films are withered, allowing some metallic contact leading to penetration of surface irregularities through them. However, the adhesion and shear strength at these junctions are lower than those of pure metal. Earlier experiments confirm this, showing that removing surface films by outgassing in a high vacuum significantly increases friction (e.g., for nickel or tungsten, the coefficient of friction rises from ~0.3 to 6). Similarly, adding lubricants reduces contact and adhesion strength, though metallic adhesion still occurs as surface irregularities tear through the film. Lubricants significantly reduce the area of metallic seizure, primarily by lowering both the coefficient of friction and the shear strength at the junctions.Effect of intermittent motion on frictionIt has been studied that when any moving system has significant elastic freedom, this motion may become intermittent progressing via “stick-slip” behavior. This occurs because the kinetic friction during slipping is lower than the static friction during sticking. The type of sliding is strongly influenced by the properties of the metals and lubricant films, as well as the mechanical characteristics of the system, such as natural frequency, moment of inertia, and damping. Researchers have replicated these experiments, confirming that the elastic properties of the system play a key role in determining the motion. Stick-slip behavior is common in systems with elastic freedom or surfaces capable of slight elastic deformation, provided the surface and operating conditions are conducive to such motion. Friction of metallic films In earlier experiments, Amontons’ Law was observed because changes in the load naturally caused proportional changes in the area of contact, preventing independent variation of these factors. This limitation can be overcome by using a hard steel substrate coated with a thin layer of soft material, such as indium. When a hemispherical slider is placed on this surface and different loads are applied, the slider sinks into the indium until the load is supported by the underlying steel. Since the steel deforms minimally under further increases in load, the contact area between the slider and the indium remains largely unaffected, enabling independent control of load and contact area. Reference[1] Bowden, F.P. and Tabor, D., 1942. Mechanism of metallic friction. Nature, 150(3798), pp.197-199. [2] https://physics.aps.org/articles/v17/s120 Manoj Rajankunte Mahadeshwara I am a postgraduate researcher at the University of Leeds. I have completed my master's degree in the Erasmus Tribos program at the University of Leeds, University of Ljubljana, and University of Coimbra and my bachelor's degree in Mechanical Engineering from VTU in NMIT, India. I am an editor and social networking manager at TriboNet. I have a YouTube channel called Tribo Geek where I upload videos on travel, research life, and topics for master's and PhD students.
Adhesive Wear Modelling Methods Table of ContentsIntroductionWear Models Phenomenological approachAsperity Level ApproachRough surfaceSmooth surface SurfaceReferencesIntroductionWear in dynamic systems significantly impacts performance, efficiency, operational costs, and safety. Predicting wear using computer simulations, empirical data, or theoretical frameworks is crucial for determining system reliability and durability. Haibo et al. [1] Reviewed wear modelling methods and depicted that wear modelling could be on macro, micro, or atomic scales. In light of this, wear modelling could be divided into a phenomenological approach or real contact conditions; the former utilizes physical understanding and experimental observation, i.e., macroscale level. In phenomenological technique, assumptions must be made, and empirical coefficients must be determined. Those models are constrained by their assumptions and lack generality, even though they provide accurate predictions for a specific range of operations and rely on the constraints of the empirical coefficients. Archard’s theory [2] and Rabinowicz’s criterion [3] These are examples of such models. The second method, such as asperities contact models, implements advanced numerical techniques to find the wear at micro- or atomic levels under relaxed assumptions and more realistic conditions; however, analytical models have been utilized for material and fracture estimation, and the actual surface characteristics may need to produce specific and accurate results. In the next section, microscale modelling techniques have been introduced. Wear Models Phenomenological approachAn example of this approach is Archard’s wear model which is a famous model to evaluate adhesive wear. Theoretically, the Archard wear model estimates the adhesive wear volume of softer material. The model is named after Archard publicizes his work [2]; He said that the wear volume depends on the normal load and sliding distance and is inversely proportional to the hardness of the softer material.The wear volume (W) is defined as [4]: W = (K*P*S)/H – Equation-1 Where P is the normal force, S is the sliding distance, H is the softer material hardness, and is the dimensionless wear coefficient, and commonly used is the dimensional wear coefficient which is found experimentally and its value depending on lubricity condition and wear severity 1e-2 to 1e-9 [4] depending on the type of surface and lubricity condition. It’s commonly explained the wear rate is wearing volume per sliding distance (w) which is defined by [4]: w = (K * P) – Equation-2Asperity Level ApproachAsperity-level models for wear prediction offer valuable insights into wear phenomena, allowing for the estimation of wear volume and particle morphology. A prominent model developed by A. Greenwood and J. Williamson (GW model) [5], describes contact between rough, deformable surfaces, assuming that each asperity is loaded independently as shown in Figure 1. In this model, all asperities are hemispherical, with a constant radius of curvature distributed at different heights above mean surfaces. Figure-1 : GW model, contact of two rough surfaces [5] Numerical methods such as the Finite Element Method (FEM) and Boundary Element Method (BEM) are frequently employed to analyze complex dynamic systems. These methods transform model geometries into finite elements, making them particularly useful for studying rough surface contact—for example, Hu et al. [6] used asperity-level models to evaluate contact responses in such systems, and his FEM model is shown in Figure 2 which the rough surface has meshed with fine gird to capture the asperities contact. Figure-2 : Finite element mesh required for asperity level models as illustrated by Hu et al. [6] Rough surfaceSmooth surface SurfaceOne of the critical advantages of asperity modelling is its ability to predict wear particle formation. H. Zhang and I. Etsion [7] utilized FEM to study spherical contact and the initiation of wear particles due to adhesive wear, finding the friction coefficient and wear volume for both elastic and plastic deformations. They also formulated wear particles resulting from these deformations as illustrated in Figure 3. Figure-3 : Wear particle formulation as different sliding instants as predicted by H. Zhang and I. Etsion model [7] At a smaller scale, atomic-level contact models have gained attention for providing detailed insights into contact phenomena. However, these models are limited to primary cases due to the need for extremely fine discretization. For instance, J. François et al. [8], using similar principles of asperity contact as depicted in Figure 4 and implemented the BEM mode, shown in Figure 5, to study asperity contact at the atomic scale and identified junction growth as a critical factor in wear particle formation. Despite the depth of understanding these models provide, they are constrained by the need for highly dense finite element models, which limit their broader application. Figure-4 : Schematic for atomistic simulations. (a) single-asperity surface (b) Interlocking asperities surface, J. François et al [8] Figure-5 : BEM model results which determined two wear mechanisms at the microscale level. (a) the plastic deformation without wear particle formulation. (b) the plastic deformation with wear particle formulation, J. François et al .BEM model [8] Moreover, asperity contact models require a failure criterion to simulate crack initiation and propagation for surface fracture. They also necessitate material models for plastic flow. Author: Shenouda Adel MSc in machine design References1. Zhang, H., R. Goltsberg, and I. Etsion, Modeling Adhesive Wear in Asperity and Rough Surface Contacts: A Review. Materials (Basel), 2022. 15(19). 2. Archard, J.F., Contact and Rubbing of Flat Surfaces. Journal of Applied Physics, 1953. 24(8): p. 981-988. 3. Rabinowicz, E., The effect of size on the looseness of wear fragments. Wear, 1958. 2(1): p. 4-8. 4. Bhushan, B., Principles of Tribology. Modern Tribology Handbook. Vol. 1. 2001: CRC Press LLC. 5. Greenwood, J.A. and J.H. Tripp. The Contact of Two Nominally Flat Rough Surfaces. in Proceedings of the Institution of Mechanical Engineers. 1967. 6. Hu, G.-D., et al., Adaptive finite element analysis of fractal interfaces in contact problems. Computer methods in applied mechanics and engineering, 2000. 182(1-2): p. 17-37. 7. Li, M., G. Xiang, and R. Goltsberg, Efficient Sub-Modeling for Adhesive Wear in Elastic–Plastic Spherical Contacts. Lubricants, 2023. 11(5). 8. Molinari, J.-F., et al., Adhesive wear mechanisms uncovered by atomistic simulations. Friction, 2018. 6(3): p. 245-259. ; TriboNet Administration of the project
Mechanism of Metallic Friction as described by Bowden and Tabor HomeWikiMechanism of Metallic Friction as described by Bowden and Tabor ;Mechanism of Metallic Friction as described by Bowden and TaborManoj Rajankunte Mahadeshwara ; ; ; January, 15 2025 ; ; Table of ContentsIntroductionFiction of metal in hard on soft surfaceEffect of contaminating film with frictionEffect of intermittent motion on frictionFriction of metallic films ReferenceIntroductionKinetic friction is not merely a surface phenomenon but rather depends on the bulk properties of the interacting materials, such as their relative hardness and melting points. Experimental investigations indicate that friction primarily arises from shearing or adhesion of the softer material in contact with the harder surface. Even highly polished surfaces, which may appear smooth at the macroscopic level, possess microscopic irregularities that contribute to friction. The temperature rise at the interface is not the primary cause of friction, as friction can still occur at cold asperity contacts due to localized adhesion and welding under high pressure. However, when sliding occurs at high loads and speeds, the resulting temperature increase at the interface may give the impression that elevated temperatures directly cause higher friction. Importantly, this relationship does not imply that higher ambient (room) temperatures always lead to increased friction. Instead, the frictional behavior is influenced by temperature generated during sliding, which depends on parameters such as load and speed, rather than the initial room temperature. Fiction of metal in hard on soft surfaceThe relationship between frictional force, contact area, and applied load has been extensively studied. Coulomb and Amontons formulated two key laws: (i) frictional force is independent of the apparent contact area, and (ii) it is proportional to the applied load. While these laws initially lacked a theoretical basis, studies on the real area of contact have provided explanations. With respect to the first law, various experiments revealed that the real area of contact between metals was measured using electrical conductance techniques. The findings revealed that contact occurs primarily at the summits of surface asperities, resulting in a real contact area that is significantly smaller and largely independent of the apparent contact area. This insight helps to explain why the frictional force is unaffected by changes in the apparent contact area, as the real contact area—and consequently the frictional force—remains consistent under similar loading conditions. Amontons’ second law, which states that frictional force is proportional to the applied load, initially posed challenges because it was assumed that the surfaces deformed elastically. Elastic deformation would predict the contact area, and thus the frictional force, to vary with the two-thirds power of the load, not linearly. However, conductivity measurements revealed that the surface deformation is predominantly plastic. Under plastic deformation, the material flows until the contact area becomes proportional to the applied load, resolving this inconsistency. Effect of contaminating film with frictionUnder most experimental conditions the metallic surfaces are covered with thin oxide layers and contaminating films. During sliding, these films are withered, allowing some metallic contact leading to penetration of surface irregularities through them. However, the adhesion and shear strength at these junctions are lower than those of pure metal. Earlier experiments confirm this, showing that removing surface films by outgassing in a high vacuum significantly increases friction (e.g., for nickel or tungsten, the coefficient of friction rises from ~0.3 to 6). Similarly, adding lubricants reduces contact and adhesion strength, though metallic adhesion still occurs as surface irregularities tear through the film. Lubricants significantly reduce the area of metallic seizure, primarily by lowering both the coefficient of friction and the shear strength at the junctions. Effect of intermittent motion on frictionIt has been studied that when any moving system has significant elastic freedom, this motion may become intermittent progressing via “stick-slip” behavior. This occurs because the kinetic friction during slipping is lower than the static friction during sticking. The type of sliding is strongly influenced by the properties of the metals and lubricant films, as well as the mechanical characteristics of the system, such as natural frequency, moment of inertia, and damping. Researchers have replicated these experiments, confirming that the elastic properties of the system play a key role in determining the motion. Stick-slip behavior is common in systems with elastic freedom or surfaces capable of slight elastic deformation, provided the surface and operating conditions are conducive to such motion. Friction of metallic films In earlier experiments, Amontons’ Law was observed because changes in the load naturally caused proportional changes in the area of contact, preventing independent variation of these factors. This limitation can be overcome by using a hard steel substrate coated with a thin layer of soft material, such as indium. When a hemispherical slider is placed on this surface and different loads are applied, the slider sinks into the indium until the load is supported by the underlying steel. Since the steel deforms minimally under further increases in load, the contact area between the slider and the indium remains largely unaffected, enabling independent control of load and contact area.Reference[1] Bowden, F.P. and Tabor, D., 1942. Mechanism of metallic friction. Nature, 150(3798), pp.197-199. [2] https://physics.aps.org/articles/v17/s120 Manoj Rajankunte Mahadeshwara I am a postgraduate researcher at the University of Leeds. I have completed my master's degree in the Erasmus Tribos program at the University of Leeds, University of Ljubljana, and University of Coimbra and my bachelor's degree in Mechanical Engineering from VTU in NMIT, India. I am an editor and social networking manager at TriboNet. I have a YouTube channel called Tribo Geek where I upload videos on travel, research life, and topics for master's and PhD students.
Prandtl-Tomlinson friction model HomeWikiPrandtl-Tomlinson friction model ;Prandtl-Tomlinson friction modelManoj Rajankunte Mahadeshwara ; ; ; January, 8 2025 ; ; Prandtl-Tomlinson friction modelTable of ContentsIntroductionHistorical perspectiveExplanationsLimitations of PT modelIntroductionThe Prandtl–Tomlinson model was introduced in 1928 as a conceptual framework for single-atom contact friction, described as a point mass dragged over a sinusoidal potential by a spring. Although it remained largely overlooked for decades, recent experimental validations have demonstrated its relevance for contacts involving tens to hundreds of atoms. Today, the Prandtl–Tomlinson model is widely recognized as a highly insightful mechanical analogue for understanding atomic-scale phenomena at sliding interfaces. Historical perspectiveThe field of nanotribology emerged in the late 1980s which was a significant leap in friction research by enabling the study of nanoscale contacts with tools like the atomic force microscope (AFM). Among its notable breakthroughs was the observation of individual atomic “hopping events” over a corrugated interface potential with atomic periodicity. These events revealed a “stick-slip” motion that revitalized interest in the Prandtl−Tomlinson (PT) model, an older conceptual framework. Historically, the PT model is often attributed to G. A. Tomlinson’s 1929 paper, which led to its alternate name, the “Tomlinson model.” However, the theory underlying the PT model was first presented in Ludwig Prandtl’s 1928 paper, which was initially inaccessible to much of the scientific community due to its publication in German. This oversight was corrected in 2012, when an English translation of Prandtl’s seminal work was published, finally clarifying its foundational role in modern nanotribology. ExplanationsThe PT model today forms the cornerstone of our understanding of atomic-scale friction. In this model, a point mass moves over a periodic potential (illustrated in Figure 1), explaining a wide range of experimental observations. Figure-1 Schematic drawing illustrating the basic principles of the Prandtl−Tomlinson model.This schematics in Figure-1 a) and b) shows the basics of PT model, where a point mass is connected to a supporting body M via a spring with an effective spring constant ceff​. The mass interacts with a periodic potential V(xt​) with a periodicity ‘a’. During sliding, the supporting body M moves with a velocity vS​ in the x-direction. If the spring is sufficiently soft, the resulting motion exhibits characteristic “stick-slip” behavior. The point mass remains in a potential minimum (“stick”) until the spring tension reaches a critical value, at which point it jumps (“slips”) to the next minimum. The model also predicts temperature effects, which can be introduced by considering thermal oscillations of the mass. Figure-2 Graphs showing the scan position with lateral force wit changes in temperature Figure-2 c and d show at zero temperature (T=0K), the lateral force is a sawtooth-like function, with the mass jumping only when the critical force Fc for that potential and spring constant is reached. The lateral force is measured by tracking the spring tension as a function of the position of the supporting body M along the x-axis (“scan position”), which differs from the tip’s position xt. At higher temperatures, thermal activation allows the mass to jump at forces lower than Fc, due to thermal energy kB​T (where kB is Boltzmann’s constant). As a result, the maxima of the lateral force and the overall frictional force decrease, and thermal noise becomes visible on the “rising leg” of the sawtooth pattern. Figure-3 ketch of a mechanical model designed by PrandtlThe schematics of Figure 3 shows a macroscopic mechanical model created by Prandtl to demonstrate stick-slip behavior same as that of the atomic-scale model, illustrating the generalizability of the concept. The PT model has successfully explained friction phenomena across various systems, including flat surfaces, surfaces with different atom types, velocity and temperature dependence, atomic-scale steps, and ions in a trap. Notably, despite its origins as a single-atom model, the PT model provides intuitive explanations for many fundamental properties of dry friction. Limitations of PT modelExtrapolation to Macroscopic Scale: While the PT model effectively explains friction at the atomic scale, it remains challenging to extrapolate its findings to larger, macroscopic contacts. Scaling up from nanometre-sized contacts to macroscopic rough interfaces has not yet been fully resolved. This limitation stems from the difficulty in translating atomic-scale behaviours into statistical models for complex, rough contact surfaces. Complexity of Real-World Surfaces: The PT model primarily addresses idealized, single-atom contacts. In real-world applications, surfaces are often non-ideal, featuring defects, surface steps, impurities, and varying chemical activities. These factors influence friction and are not adequately captured by the simple model, limiting its applicability to more complex systems. Structural Lubricity and Super-Lubricity: Although phenomena like “structural lubricity” or “super-lubricity” have been observed at atomic and small-scale contacts, the PT model does not fully account for how friction behaves in the presence of these phenomena when the contact area is large. The scaling of friction with contact area remains a significant challenge, and the model’s predictions for real, rough contacts are still incomplete. References: [1] Schwarz, U.D. and Hölscher, H., 2016. Exploring and explaining friction with the Prandtl–Tomlinson model. Acs Nano, 10(1), pp.38-41. [2] Tomlinson, G.A., 1929. CVI. A molecular theory of friction. The London, Edinburgh, and Dublin philosophical magazine and journal of science, 7(46), pp.905-939. [3] Tomlinson, G.A., 1928. LXVII. Molecular cohesion. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science, 6(37), pp.695-712. Manoj Rajankunte Mahadeshwara I am a postgraduate researcher at the University of Leeds. I have completed my master's degree in the Erasmus Tribos program at the University of Leeds, University of Ljubljana, and University of Coimbra and my bachelor's degree in Mechanical Engineering from VTU in NMIT, India. I am an editor and social networking manager at TriboNet. I have a YouTube channel called Tribo Geek where I upload videos on travel, research life, and topics for master's and PhD students.
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