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Viscosity Index : Definition, Important Calculator (2025) Home Wiki Viscosity Index : Definition, Important Calculator (2025) Viscosity Index : Definition, Important Calculator (2025) Riya Veluri October, 21 2025 ASTM D2270 ASTM D567 VI viscosity index viscosity index calculator Table of Contents What is viscosity index? Calculate Viscosity Index ASTM D2270 and ISO 2909: ASTM D567 Method for Calculation of Viscosity Index from Viscosity at 100ºF and 210ºF. Viscosity Index Calculator VI modifiers: Classification: References: What is viscosity index? The;viscosity index;(VI) is an arbitrary, unitless measure of a fluid’s viscosity change relative to a temperature change. We can say that the it is the dimensionless number that shows how the temperature change can affect viscosity of an oil (engine oil and automatic gear oils, and power-steering fluids). The higher the VI, the smaller the change in fluid viscosity for a given change in temperature and vice versa. Thus, a fluid with a low viscosity index will experience a relatively large swing in viscosity as temperature changes. High-VI liquids, in contrast, are less affected by temperature changes. Viscosity Index was measured by a scale of 0 to 100; however, modern science of lubrication has led to the development of oils with very high VI. The best oils with the highest VI are stable and do not vary greatly in viscosity over a wide temperature range. In turn, this means consistent, high performance in the machine. Calculate Viscosity Index Standard ASTM D2270 Calculates Viscosity Index by Measuring the Kinetic Viscosity of Liquids at 40° and 100°C and ASTM D567 Method for Calculating Viscosity Index from Viscosity at 100ºF and 210ºF. Normally, all things being equal, highly refined mineral oils with few contaminants have high VIs and Synthetic oils generally have a higher VI than mineral oils. Below you will find a simple VI calculator. ASTM D2270 and ISO 2909: Oil viscosity (see ASTM D445) usually decreases with increasing temperature. If this reduction is significant, the system may not be sufficiently lubricated over the entire operating temperature range. The viscosity index describes this change – a high viscosity index indicates a slight viscosity change with increase in temperature compared to a low viscosity index. The standard covers procedures for calculating the viscosity index of petroleum products, such as lubricating oils, and related materials by their kinetic viscosities at 40°C and 100°C. The standard does not apply to petroleum products with a kinematic viscosity less than 2.0 mm2/s at 100 °C. This practice applies to that petroleum or lubricating products whose kinetic viscosity is between 2mm2/s and 70 mm2/s at 100°C. Equations are already provided for calculation of viscosity index for products like petroleum with kinematic viscosity above 70mm2/s at 100 °C. Values stated in SI units are considered standard. No other units are there for measurement in this standard. The values stated in SI units are to be regarded as the standard. For user reference, 1 mm2/s = 10-6m;2/s = 1 cSt. ASTM D567 Method for Calculation of Viscosity Index from Viscosity at 100ºF and 210ºF. The viscosity of oil usually decreases as the temperature increases. Viscosity index means that it measures the change in viscosity with temperature – a high viscosity index indicates a small viscosity change of a petroleum product with changes in temperature. This is the method that determines the viscosity index of lubricating oils. This method is considered obsolete by ASTM and replaced by ASTM D2270. Viscosity Index Calculator Here we are discussing the rule of calculating the viscosity Index. L = kinematic viscosity of an oil at 40 °C of 0 viscosity index having the same kinematic viscosity at 100 °C as the oil whose viscosity index needs to be calculated, mm2 /s, Y = kinematic viscosity at 100 °C of the petroleum product whose viscosity index needs to be calculated, mm2 /s. H = kinematic viscosity of an oil at 40 °C of 100 viscosity index having the same kinematic viscosity at 100 °C as the oil whose viscosity index needs to be calculated, mm2 /s. U = kinematic viscosity at 40 °C of the lubricant or petroleum product whose viscosity index needs to be calculated, mm2 /s. The viscosity index can be calculated using the following formula: ASTM D2270 table to get the L & H values for the calculations. Here is a simple VI calculator to calculate viscosity index from the temperatures at 40°C and 100°C: Viscosity Index (VI) Calculator Kinematic viscosity 40°C [cSt or mm^2/s] Kinematic viscosity 100°C [cSt or mm^2/s] Viscosity Index VI [ -] This calculator allows calculating kinematic viscosity at 100°C from the known VI and kinematic viscosity of the oil at 40°C: Kinematic Viscosity @ 100ºC Calculator Viscosity Index VI [-] Kinematic viscosity 40°C [cSt] Calculated Value [cSt] This calculator allows calculating kinematic viscosity at 40°C from the known VI and kinematic viscosity of the oil at 100°C: Kinematic Viscosity @ 40ºC Calculator Viscosity Index VI [-] Kinematic viscosity 100°C [cSt] Calculated Value [cSt] The common equation used to calculate the viscosity by interpolation between two reference points is with the Ubbelohde-Walther equation, which is adopted in ASTM D341. Here is a simple calculator to interpolate viscosity: Kinematic viscosity interpolation ASTM D341 Temperature and viscosity T1, v1 [ 0C ] 0C ]" id="fieldname2_4" name="fieldname2_4" step="1" class="field digits small" type="number" value="40" style=""> Temperature and viscosity T2, v2 [ 0C ] 0C ]" id="fieldname3_4" name="fieldname3_4" step="1" class="field digits small" type="number" value="100" style=""> Temperature and viscosity T3, v3 [ 0C ] 0C ]" id="fieldname4_4" name="fieldname4_4" step="1" class="field digits small" type="number" value="60" style=""> Kinematic Viscosity at T1, [cSt or mm^2/s] Kinematic Viscosity at T2, [cSt or mm^2/s] Kinematic Viscosity at T3, [cSt or mm^2/s] ; VI modifiers: VI modifiers are normally used in multi-grade engine oils, gear oils and automatic transmission fluids, power steering fluids, hydraulic fluids and greases. Widely used materials are, for example, olefin copolymers (OCP), polyalkyl methacrylates (PAMA), poly isobutylene (PIB), styrene block polymers, methylmethacrylate (MMA), polybutadiene rubber (PBR), cis-polyisoprene. (of a synthetic rubber), polyvinyl palmitate, polyvinyl caprylate, copolymers of vinyl palmitate with vinyl acetate, and various other materials used as viscosity index modifiers in a variety of petroleum oils. Below is the table of viscosity indexes of different petroleum products & fluids for ref: Oil / fluid types VI Mineral oil 95 – 105 Multi-grade oil 140 – 200 PAO oil 135 – 160 Ester 140 – 190 Vegetable oil 195 – 210 Glycol 200 – 220 Silicone oil 205 – 400 Classification: The VI scale was established by the Society of Automotive Engineers (SAE). The arbitrarily chosen temperatures for reference are 100 and 210 °F (38 and 99 °C). The scale was initially interpolated between 0 for naphthenic Texas Gulf crude and 100 for paraffinic Pennsylvania crude. Since the scale’s inception, better oils have also been produced, making VI over 100 (see below). VI-improving additives and high-quality base oils are widely used nowadays, allowing VI to be achieved over a value of 100. The viscosity index of synthetic oils ranges from 80 to over 400. Normally when we are talking about the synthetic oils, then there are normally two types of synthetic oil available for widely used in different critical & high temperature applications. PAO Based synthetic Oil (Polyalphaolefin) PAG based synthetic oil (Polyalkylene Glycol). Study shows that PAO based synthetic oils have better viscosity index compare to Group – i, group – ii or group – iii oils (Without addition of any index significantly better than PAO-based lubricants of the same viscosity grade. VI Classification Under 35 Low 35 to 80 Medium 80 to 110 High Above 110 Very high Conclusions: The viscosity index is an essential parameter indicating the flow properties related to the temperature of the oil. Selection of oil for a specific application without considering its VI, e.g. cause premature wear and costly machinery damage. As we have already discussed that normally in synthetic oil, Viscosity index is greater than the any kind of mineral oil. So, In critical applications or high temperature applications synthetic oil or grease is preferred rather than mineral oil based lubricants. References: BLAIR, G. Viscosity of Liquids and Colloidal Solutions.;Nature;156,;147–148 (1945). https://doi.org/10.1038/156147a0 http://ppapco.ir/wp-content/uploads/2019/07/ASTM-D2270-2016.pdf https://wiki.anton-paar.com/en/viscosity-index/ https://en.wikipedia.org/wiki/Viscosity_index Riya Veluri The article is written by Riya Veluri, an editorial team member of Industrial Lubricants. After her graduation, Riya works as a website developer & SEO specialist in Lubrication & Tribology Industry & writes technical articles on Lubricants, Lubrication, Reliability & sustainability. --> 4 Comments Bryan Miller says: 16.08.2022 at 21:24 Is there a way to calculate the Viscosity at -40C for Dexron 75W-90 pour point is -57C Log in to Reply TriboNet says: 18.08.2022 at 22:20 Hello Bryan! You can use the Ubbelohde-Walther calculator. To use it you would need viscosity at 2 different temperatures. I hope this helps! Log in to Reply Chris says: 23.10.2023 at 13:57 Hi there! Great article but it didn’t explain what’s the difference (if any) between ASTM D2270 and ISO 2909, as we could see on many engine oil manufacturers technical sheets. Could you please explain that? Best of luck and keep up the good work you are doing! Chris Log in to Reply CHRISHAN says: 21.01.2024 at 11:24 Hi, Could you please tell me PAG base oil is good for a slow RPM gearbox that is lubricated by splash lubrication? 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.
Types of Lubrication Systems – Complete Guide and its Benefits (2025) Home Wiki Types of Lubrication Systems – Complete Guide and its Benefits (2025) Types of Lubrication Systems – Complete Guide and its Benefits (2025) Riya Veluri October, 21 2025 Dry Sump Lubrication System Grease Lubrication System lubricant Lubrication system Oil Lubrication System Progressive Lubrication systems Wet Sump Lubrication Table of Contents Introduction to Types of Lubrication system Types of Lubrication system:;Lubricants and Friction What are the types of lubrication system? Types of lubrication systems Benefits of using types of lubrication systems Introduction to Types of Lubrication system There are many types of lubrication systems used across mechanical systems and industrial machinery. From traditional oil and grease systems to modern approaches like MQL (Minimum Quantity Lubrication), each system offers unique benefits and trade-offs. In this guide, we explore each type in detail, explain how they work, and help you choose the right system for your application. Types of Lubrication system:;Lubricants and Friction Lubricants act to reduce friction. Now, this makes it easier to keep machines running smoothly, and it cuts down on the amount of heat and wears caused by friction. A machine’s moving parts generally experience three types of friction. Sliding Friction Rolling Friction Fluid Friction Sliding friction occurs when two surfaces in contact slide past each other. This type of friction offers the most resistance to motion. So machinery is usually built to minimize or eliminate it. Building a machine to minimize sliding friction is to place rolling elements between the moving surfaces. This is the principle behind rolling contact bearings. Rolling contact bearings experience rolling friction that is considerably less severe than sliding friction. Still, they must be properly lubricated to reduce heat and wear. The useful life of a rolling contact bearing or anti-friction bearing would be drastically shortened if the bearing were operated dry. Another way to build a machine to reduce friction is to separate two sliding surfaces by a lubricant film. As long as the surfaces do not touch, sliding friction is eliminated. There’s still some fluid friction within the lubricant, but it’s much less than sliding friction. Fluid friction is the resistance to motion within a fluid, and it’s not as obvious as other types of friction. Lubricants are made from one of four groups of materials or medium. Animal Vegetable Mineral Synthetic Originally animal and vegetable lubricants were the most widely used. Still, they’ve been almost completely replaced by mineral and synthetic types. But whatever lubricant you use, to get maximum benefits from lubricants we need to use a proper lubrication system. What are the types of lubrication system? An automatic lubrication system, also known as a centralized lubrication system, is defined as a controlled and precise amount of a specific lubricant that is delivered to a specific location at a specific time when the machine is running. Reasons for using the types of lubrication system The study says that in plant maintenance, lubrication cost is approx. 3% of the total cost of maintenance budget, but lubrication-related activities could reach up to 40% of the total maintenance budget. If one needs to achieve optimum reliability & maximum benefits from the Lubrication system, the following factors must be considered. The Right Lubricant The proper lubricants selection for proper application is vital to get maximum benefits from the lubrication system. Normally right lubricants selection can depend on four factors of applications. Speed Ambiance Load Temperature Right Quantity Neither less quantity of grease is good nor high quantity. An increase qty of grease can increase temperature & friction inside the bearing & can decrease the efficiency or lifetime of bearing lead to failure. Only measured lubricant qty reached to lubrication point so, no wastage of lubricants hence lubrication cost reduce. At Right Time Lubricants will effectively reduce friction & wear if supplied at the right timing with proper re-lubrication interval. At Right Point Grease or oil should reach the right point where friction & wear is high. If it does not reach the friction point, then it will be of no use. Types of lubrication systems Different types of lubrication systems have been designed and developed over the years based on the specific requirements of the instrument and the different industrial sectors. We are talking about the most popular and beneficial lubricant systems used by different plants in different industrial sectors. Oil Lubrication System The oil lubrication system is also known as the loss lubrication system. In this system, oil or liquid grease produces a thin oil film that protects the parts. It is renewed at regular intervals by an automatic lubrication system with an electric oil pump. The main systems used in oil lubrication are single-line systems and 33V systems. Splash Lubrication System In these types of lubrication systems, the lubricating oil accumulates in an oil sump. Most small four-stroke petrol engines use splash lubrication. On horizontal crankshaft engines, a dipper on the bottom of the connecting rod scoops up oil from the oil sump for the bearings. When the engine runs, the dipper dips in the oil once in every crankshaft revolution and causes the oil to splash on the cylinder walls. Recirculating Oil System The purpose of oil recirculation is to supply lubrication and provide cooling to bearings and gears. An electric pump ensures that an appropriate lubricant pressure is available in the mainline, where the oil flow is also measured and regulated. Air-Oil Lubrication System This system consists of a controlled air-oil stream utilized to cool and carry small quantities of air-oil particles to the lubrication points. It is suitable for large machines in heavy industry and machine tools. Air Oil lubrication system is the optimal solution for economical and reliable lubrication of bearings. The bearings have a longer service life, and thus high production availability is attained. Grease Lubrication System In this system, the greasing pumps provide a proper amount of grease to the lubrication points. The main systems used for grease lubrication are Dual Line and Progressive systems. Dual Line Lubrication Systems The dual-line system has a modular design that allows easy configuration and expansion of the system. It is suitable for industries with large machines and many lubrication points. SKF has developed a Dual Line Lubrication system. These flexible systems are simple to design and can be reduced easily by removing metering devices or extended by installing additional metering devices. You can know more about the Dual Line Lubrication system by watching the video. Progressive Lubrication systems For small to medium-sized machines that require continuous lubrication, a progressive lubrication system will best suit them. Progressive systems provide uninterrupted lubrication as long as the pump is turned on. Once the pump is turned off, the pistons of the progressive metering device will stop at their current position. When the pump starts supplying lubricant again, the pistons will move to where they were left. MQL (Minimum Quantity Lubrication) System & Near Dry Machining An innovative new technology that replaces traditional and pure oil-liquid systems in a machining environment. A controlled compressed air flow carries minimal cutting oil in an “aerosol” format to the cutting surface by external or internal (through equipment lubrication). MQL is a little bit bigger of an umbrella than near dry machining. MQL can be applied to multiple manufacturing operations like sheet metal forming operations, blanking, forming, cutting, etc. Near dry machining is more specific to machining operations such as mills, drills, turning operations, and tapping. Wet Sump Lubrication System In wet sump lubrication systems, the oil is transported to different engine parts with the help of a sump strainer, and the oil pressure is about 4 to 5 kg / cm2. After lubrication, the oil is again taken to the oil sump. In this case, the oil is present in the samp. Therefore, it is called a wet sump lubrication system. The advantage of the wet sump system is its simplicity. And machine parts are near where the lubrication will be applied through lubricating oil, there are not many parts required, and it is relatively safe to make in the car. Dry Sump Lubrication System A dry-sump lubrication system is particularly used in racing cars, and it has additional components to the wet-sump lubrication system. These components include an oil tank with a breather tank. Furthermore, the dry-sump lubrication has a cyclone separator and a multi-stage pump. Check out the video to know more about the Dry Sump Lubrication system. So, we have covered different types of lubrication systems used in different applications to achieve the maximum benefit of lubrication. Except achieving max benefit, there are multiple benefits are there of the automatic lubrication system. Benefits of using types of lubrication systems Easy access: All important components of the machine can be oiled, regardless of criticality and location. This ensures safe machine operation and reduces the risk of undefined lubricating components by maintenance personnel. Increase the machine’s efficiency: In a centralized lubrication system, lubrication occurs when the machine is running so that the lubricant is distributed evenly across all friction points and increases the efficiency of the overall machine performance, less breakdown, less downtime, and replacement cost. Reduced energy consumption: In centralized or automatic lubrication, the system as lubricant reaches the friction point at the right time, in the right amount so low friction, energy consumption is lower, and overall machine operation cost is lower. Cleanliness: Lubricant contamination with the effect of foreign particles carries the overall performance and life. Avoiding grease contamination in manual lubrication systems can be a challenge for every maintenance person. However, through an automatic lubrication system, we can avoid contamination of lubricants and achieve cleanliness. In an automatic lubrication system, an automatic lubricant can provide an uninterrupted and accurate flow of fresh and clean lubricant at the lubrication points. Reference: [1] https://onlinelibrary.wiley.com/doi/abs/10.1002/9783527645565.ch20 [2] https://www.academia.edu/download/121935517/Maintenance_4_25p_merged.pdf Riya Veluri The article is written by Riya Veluri, an editorial team member of Industrial Lubricants. After her graduation, Riya works as a website developer & SEO specialist in Lubrication & Tribology Industry & writes technical articles on Lubricants, Lubrication, Reliability & sustainability. -->
Pour Point Definition & Testing Standards: Complete Guide 2025 Home Wiki Pour Point Definition & Testing Standards: Complete Guide 2025 Pour Point Definition & Testing Standards: Complete Guide 2025 Riya Veluri October, 21 2025 ASTm standard for pour point common values for pour point measurement tools measuring pour point pour point definition pour point depressant pour point table Table of Contents Pour point definition How to Measure Pour Point of Lubricants? What is Pour Point Depressant? Pour Point of Various Lubricants and Oils Pour point definition The pour point is the lowest temperature at which oil flows in a specified lab test. Specifically, the pour point is 3℃ (5℉) above the temperature at which the oil shows no movement when a lab sample container is held horizontally for 5 seconds. Pour point is an indication of the cold temperature properties of oil. But we should not select a lubricant product based solely on its pour point. The cloud point is also a very important factor for choosing any lubricant for any application. Cloud point is approximately the low temperature at which the oil becomes cloudy due to the formation of wax crystals within the oil. ASTM D97 (ISO 3016 or IP 15) covers the standard methods to measure the pour point of petroleum products. In addition, several methods are used to determine cloud points, including ASTM D5772. How to Measure Pour Point of Lubricants? The Seta Cloud and Pour Point Bath give the required cold bath to liquid to take them to the necessary stage. It utilizes the current and with the help of conditioners and couples present in them. They cool the fluids up. They hold four test positions. They can supply the temperature range from 9°C to -69°C. The equipment identifies the minimum safe operating temperature. The bath accommodates four jackets and a steel cover, and a drain tap. Methods of pour point : These are the most common methods that are used to determine the pour point of a product: D97 – Pour Point of Petroleum Products D5853 – Pour Point of Crude Oils; D5949 – Pour Point of Petroleum Products (Automatic Pressure Pulsing Method) Measuring the pour point of petroleum products Manual method: ASTM D97, Standard Test Method for Pour Point of Crude Oils. The specimen is cooled inside a cooling bath to allow the formation of paraffin wax crystals. At about 9 °C above the expected pour point, and for every subsequent 3 °C, the test jar is removed and tilted to check for surface movement. When the specimen does not flow when tilted, the jar is held horizontally for 5 sec. If it does not flow, 3 °C is added to the corresponding temperature, resulting in the pour point temperature. Automatic method: ASTM D5949, Standard Test Method for Pour Point of Petroleum Products (Automatic Pressure Pulsing Method) is an alternative to the manual test procedure. It uses automatic apparatus, and yields pour point results in a format similar to the manual method (ASTM D97) when reporting at a 3 °C. Under ASTM D5949, the test sample is heated and then cooled by a Peltier device at a rate of 1.5±0.1 °C/min. At either 1 °C or 3 °C intervals, a pressurized pulse of compressed gas is imparted onto the sample’s surface. Multiple optical detectors continuously monitor the sample for movement. The lowest temperature at which motion is detected on the sample surface is the pour point. Test Objective/Summary Applications Typical results High/Low Pour Point ( ASTM D97 – 96a) 1) This is the test to determine the lowest temp at which oil will flow under the influence of gravity. 2) The oil sample is placed in a beaker along with a thermometer, sealed with a cork, heated to 46℃ (115℉), and then progressively cooled. The jar is removed at progressive 3℃ (5℉) intervals & tilted to determine fluidity. 3) The pour point is 3℃ (5℉) above the temperature at which the oil shows no movement when a lab sample container is held horizontally for 5 seconds. All lubricants exposed to cold start or cold operating temperatures. -10℃ or -32℃. Low is better What is Pour Point Depressant? Pour ​​point depressant is an additive (polymer) that allows oils and lubricants to flow at very low temperatures without the heavy wax formation at these cold temperatures and enables the oil to remain pumpable (flowable). They are typically used in paraffinic base oils in applications where extremely low machine startup temperature conditions are possible. Most paraffinic motor oils use pour point depressors. Pour Point Depressants work as modifiers & modify the interface between the crystallized wax and the oil. Pour Point of Various Lubricants and Oils Pour points for Crude oils range from 32 °C to below −57 °C (90 °F to below −70 °F). Some typical values of Pour Point are provided below in the table: Liquid Pour Point Multi-grade engine oil -35 Deg. C Monograde engine oil -23 Deg. C Turbine Oil -18 Deg. C Synthetic Polyol ester -32 Deg. C Castor Oil -33 Deg. C Coconut Oil 21 Deg. C Groundnut Oil 3 Deg. C Mustard Oil -18 Deg. C Sunflower Oil -18 Deg. C Olive Oil -9 Deg. C Kerosene -69 Deg. C Table: Typical Pour Point Values for Oils Typical properties of commonly used classes of synthetic lubricants (oils). Lubricants Thermal stability, (◦C) Specific gravity at 20◦C Flash point (◦C) Pour point (◦C) Mineral oils 135 0.86 105 −57 Diesters 210 0.9 230 −60 Neopentyl polyol esters 230 0.96 250 −62 Phosphate esters 240 1.09 180 −57 Silicate esters 250 0.89 185 −65 Disiloxanes 230 0.93 200 −70 Silicones Phenyl methyl 280 1.03 260 −70 Fluoro 260 1.2 290 −50 Polyphenyl ethers 4P-3E 430 1.18 240 −7 5P-4E 430 290 +4 Perfluoropolyethers Fomblin YR 370 1.92 none −30 Fomblin Z-25 370 1.87 none −67 Adapted from PRINCIPLES AND APPLICATIONS OF TRIBOLOGY, Bharat Bhushan, 2013 Due to the presence of high molecular weight components, such as wax, asphaltene, and resin, heavy and extra-heavy crude oils usually have higher pouring points. The pour point of the liquid can be improved by using depressants like polymethacrylates, alkylated wax fennel, alkylated wax naphthalene, etc. References Pour Point - Wikipedia PRINCIPLES AND APPLICATIONS OF TRIBOLOGY, Bharat Bhushan, 2013 Riya Veluri The article is written by Riya Veluri, an editorial team member of Industrial Lubricants. After her graduation, Riya works as a website developer & SEO specialist in Lubrication & Tribology Industry & writes technical articles on Lubricants, Lubrication, Reliability & sustainability. --> 2 Comments Dattatray J. Gharge says: 14.04.2023 at 12:38 very good information , easy to understand . Log in to Reply Vijay Painter says: 23.10.2023 at 07:43 nice information provided. Thanks. 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.
Archard Wear Equation: Importance and Formula (2025) Home Wiki Archard Wear Equation: Importance and Formula (2025) Archard Wear Equation: Importance and Formula (2025) Manoj Rajankunte Mahadeshwara October, 21 2025 archard equation wear coefficient wear equation wear model wear volume formula Introduction to Archard wear equation The Archard wear equation is a fundamental empirical model in tribology that relates wear volume to load, sliding distance, and material hardness. The importance of wear losses leads to considerable effort in establishing theories and predictive models of wear. Meng and Ludema; [1] have identified 182 equations for different types of wear. Among them were empirical relations, contact mechanics-based approaches, such as Archard wear model, and equations based on material failure mechanisms, which were found to get more popular recently according to authors. In this review, empirical equations won’t be considered, as they are applicable for very specific range of parameters. No unified fundamental theory of wear was established so far, and as a consequence, there is no unique wear model, applicable in all cases. Archard wear equation Derivation One of the most famous and frequently used wear equations was developed by Holm and Archard in 1953[2]. The Archard wear equation model considers adhesive wear and assumes the sliding spherical asperities to deform fully plastically in contact. The area of contact then is circular with the contact area equal to , where is the radius. The mean contact pressure in this case equal to hardness of the softer material, and thus, . After the asperity slides a distance of , it is released from the contact and there is a probability , that debris will form. It is assumed, that if debris is formed, it is formed as a hemisphere with the radius , having a volume of . Then the wear volume per sliding distance; ; is , and hence, as , . Introducing , the total wear volume for a sliding distance , equals to . The coefficient ;is known as a wear coefficient and is frequently used to compare the material wear resistance[2,3]. Most of the times, it is estimated experimentally. Although the Archard’s equation was developed for the adhesive wear, it is widely used for modeling of abrasive, fretting and other types of wear[4]. It should be noted that Archard wear equation is often applied on a local level. For that, the Archard equation is first formally divided by the area : (1) ; h = k *P_c/H*s \end{eqnarray*} " title="Rendered by QuickLaTeX.com" data-src="https://quicklatex.com/cache3/7c/ql_3221f18a274f582325609d585785867c_l3.png"> h = k *P_c/H*s \end{eqnarray*} " title="Rendered by QuickLaTeX.com" data-eio="l"> where are the local wear depth and contact pressures. Further, this equation is differentiated in time and the equation takes the following form: (2) ; \frac{\partial h}{\partial t} = k *P_c/H*v \end{eqnarray*} " title="Rendered by QuickLaTeX.com" data-src="https://quicklatex.com/cache3/72/ql_0b8f38db42dbbc21e5d9ddb0b336d272_l3.png"> \frac{\partial h}{\partial t} = k *P_c/H*v \end{eqnarray*} " title="Rendered by QuickLaTeX.com" data-eio="l"> where is the sliding speed. This equation can be used to calculate wear locally if the contact pressure is known and is also applied to track the evolution of the surface roughness in rough contacts. This approach was implemented in Tribology Simulator (a stand-alone free to download software). A chart linking the specific wear coefficients and friction is given below: Friction coefficients and specific or volumetric wear rate map of tribological materials, [5] References [1] Expressing Wear Rate in Sliding Contacts Based on Dissipated Energy. Huq, M.,Z., Celis, J.-P. s.l. : Wear, 2002, Vol. 252. [2] Wear Patterns and Laws of Wear – A Review. Zmitrowicz, A. 2006, Journal of Theoretical and Applied Mechanics, pp. 219-253. [3] Classification of Wear Mechanisms/Models. Kato, K. 2002, Journal of Engineering Tribology, pp. 349-355. [4] On the Correlation Between Wear and Entropy in Dry Sliding Contact. Aghdam, A.,B., Khonsari, M.,M. s.l. : Wear, 2011, Vol. 270. [5] Achieving Ultralow Wear with Stable Nanocrystalline Metals, John F. Curry et al.,https://doi.org/10.1002/adma.201802026 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. -->
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.
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