No full-text available
To read the full-text of this research,
you can request a copy directly from the authors.
Leonardo da Vinci's Friction Experiments: An Old Story Acknowledged and Repeated
Abstract
Leonardo da Vinci (1452-1519) is universally regarded as a brilliant polymath, designer, astronomer, artist, philosopher, and a visionary engineer of the Renaissance era. Interestingly, due to the delayed discovery of several caches of his notebook pages (as late as the 1960s), his immense contribution to the field of tribology has only recently surfaced. From these salvaged documents, da Vinci's three notable observations that preceded the development of the laws of friction were uncovered: (1) Friction is independent of apparent contact area, (2) the resistance of friction is directly proportional to applied load, and (3) friction has a consistent value of μ = 0.25. In this work, we have attempted to construct a nearly faithful recreation of Leonardo da Vinci's apparatus for measuring friction based on his notebook illustrations and investigate the conditions under which Leonardo da Vinci's experiments produced his findings. Our experiments, performed roughly 500 years later, reproduced Leonardo da Vinci's findings of friction coefficients with wood of μ = 0.25, but only under conditions of roughly cut and brusquely squared samples of dry wood that were handled and sullied by hand in a fashion typical of wood working but inconsistent with the modern laboratory practice. Thus, our interpretation of Leonardo da Vinci's findings is that these first tribological studies were actually performed on roughly cut and unpolished samples that had been handled extensively prior to and during testing; Such a procedure of sample preparation is entirely reasonable for the time period and suggests an active, dusty, and dynamic laboratory environment.
... The first quantitative studies on friction have been broadly attributed to Leonardo da Vinci [22]. He made three noteworthy observations that antedated the development of laws of friction: (a) friction does not depend on apparent contact area, (b) the frictional resistance is directly proportional to the applied load [23], and (c) friction is consistent, and its value is 0.25 [23]. Pitenis et al. [23] fabricated da Vinci's friction measuring apparatus (figure 7) to understand the experimental conditions that produced the findings above. ...
... The first quantitative studies on friction have been broadly attributed to Leonardo da Vinci [22]. He made three noteworthy observations that antedated the development of laws of friction: (a) friction does not depend on apparent contact area, (b) the frictional resistance is directly proportional to the applied load [23], and (c) friction is consistent, and its value is 0.25 [23]. Pitenis et al. [23] fabricated da Vinci's friction measuring apparatus (figure 7) to understand the experimental conditions that produced the findings above. ...
... He made three noteworthy observations that antedated the development of laws of friction: (a) friction does not depend on apparent contact area, (b) the frictional resistance is directly proportional to the applied load [23], and (c) friction is consistent, and its value is 0.25 [23]. Pitenis et al. [23] fabricated da Vinci's friction measuring apparatus (figure 7) to understand the experimental conditions that produced the findings above. The apparatus was made using the illustration (upper left inset of figure 7) from da Vinci's manuscript called Codex Arundel (date between CE 1478 and 1518). ...
The present review focuses on the progress of tribology from the prehistoric period to the contemporary interdisciplinary research trends. During the Paleolithic period, humans used sliding friction, generated inadvertently, to make fire. The Paleolithic inhabitants possessed the knowledge to wear the chloritolite blank to fabricate a bracelet using sophisticated material removal processes. Furthermore, they wore the tooth by making holes, filled them with fillings, intended as a pathologically motivated intervention. Humans wore the tooth by in vivo drilling in the Neolithic period, used as a remedial or soothing dental procedure. The Egyptians poured water on sand to ease the movement of the statue mounted on a sled, and recently, compared to the sled dragging on dry sand, the capillary water bridges easing the sled dragging on wet sand is experimentally observed. Bearings are proposed in the renaissance era, and Leonardo da Vinci initiated friction studies, which witnessed significant progress in the industrial revolution era. The industrial revolution ushered in the use of solid lubricants and lubricating oils and grease with additives. Studies in the scientific era discussed friction, wear, and lubrication problems and reported novel, proven solutions. The expansion of tribology research into different disciplines gave birth to novel interdisciplinary studies: the mimicking of biological structures to improve adhesion, use-wear patterns of ground stone tool surfaces, tribological behavior of artificial implants and medical devices, friction in oral processing, and lubricity of two-dimensional lamellar material. Green tribology is the recent focus and it promotes sustainable tribology research for the sustenance of the earth.
... Son modèle a été néanmoins validé dans de nombreux cas, même si certains paramètres ( notamment la valeur de la plus petite longueur d'onde à prendre en compte ) restent incertains pour une utilisation sur un cas réel. étudiés en utilisant un dispositif expérimental simple décrit et reproduit dans [5]. Selon ses observations, la force de frottement était proportionnelle à la force normale avec un coefficient de frottement µ = Force tangentielle/Force normale = 0.25, ce quelque soit l'état des surfaces. ...
... Friction forces between two solids have been studied for centuries. Leonardo Da Vinci studied wood on wood friction using a simple experimental setup (reproduced in [5]), stating that the friction force depended linearly on the normal load with a coefficient µ = tangential f orce normal f orce = 0.25. His findings were re-discovered by Amontons in the late 17 th century. ...
... 5 shows the evolution of the apparent shear modulus with the frequency of a typical tire material. At high frequencies rubber behaves like a stiff elastic solid, at low frequencies like a soft elastic solid. ...
Tires are a key component for the handling and safety of personal vehicles. In this thesis a model of the contact between the tire tread and a dry road is described. It aims at understanding the different physical phenomena taking place in such a contact and their relative role in tire friction. Modeling the multiple scales of road roughness is difficult using a standard Finite Element Method. The hypothesis that the rubber of the tire tread is very large compared to the largest scale of surface roughness is made, so that it can be considered as a semi-infinite half-space. This way, the contact problem can be solved by discretizing the rubber surface only. The solver is a specific Conjugate Gradient iterative method, in which the matrix-vector products are performed with Fast Fourier Transforms. Transient viscoelasticity is accounted for with a step-by-step approach. The algorithm is able to model surface interactions such as Coulomb friction and adhesion. Results show the crucial role played by viscoelasticity. Coupled with the road roughness, it changes the contact surface during the different steps of tire sliding, which in turns impacts friction.
... Biotribology 13 (2018) [30][31][32][33][34][35] contact area remains small relative to the thickness of the sample, the contact mechanics of these high water content hydrogels have recently been shown to follow Hertzian behavior [28] for indentations lasting < 10 3 s [29][30][31]. This is an important finding for experimental studies, because performing in situ observations of contact area during sliding introduces significant experimental challenges [32]. ...
... In these experiments, we examine one of the oldest hypotheses in tribology: is friction force linearly dependent on the applied load? [33][34][35][36]. For these sphere-on-flat configurations, the expected behavior is the classic example of decreasing friction with increasing applied load if they follow the expected Hertzian mechanics and the dissipation is related to a shear stress at the surface of the gels that is not pressure-dependent. ...
... Biotribology 13 (2018) [30][31][32][33][34][35] As shown in Fig. 1b and c, the Gemini hydrogel configuration is capable of providing very low friction coefficients (μ < 0.01) at low contact pressures and low sliding speeds, which is in agreement with previous findings [1 -3]. For each of the eight normal forces in this study (0.1 to 20 mN), the full range of sliding speeds revealed speeddependent friction coefficient behavior, which is the subject of previous [3] and ongoing investigations [48]. ...
Health and physiology are critically dependent on the ability of soft, permeable, and aqueous materials (e.g. cartilage, cells, and extracellular matrix) to provide lubrication over a wide range of speeds and contact stresses. Living cells and tissues present tremendous handling and experimental challenges for fundamental biotribology studies. Synthetic high water content hydrogels, designed to share similar mechanical and transport properties of biomaterials, can provide fundamental insights into the basic dissipative mechanisms associated with aqueous lubrication. Recent studies investigating the response of self-mated (Gemini) hydrogels to a wide range of sliding speeds under constant load conditions revealed transitions in friction behavior that may be associated with polymer relaxation time and contact time for a surface mesh during sliding (mesh size divided by the sliding speed). Here, the extent to which contact pressure and contact area affect hydrogel friction behavior was explored by changing the applied load over two orders of magnitude (0.1–20 mN) and the sliding speed over four orders of magnitude (10 μm/s–100 mm/s). Oscillating pin-on-disk microtribological experiments were performed in ultrapure water for Gemini polyacrylamide hydrogels (average mesh size ~7 nm). Friction coefficient decreased across all ranges of sliding speed with increasing applied load, consistent with predictions of contact area scaling non-linearly with applied load and pressure-independent surface shear stresses. The contact area for Gemini hydrogel interfaces under these conditions has been shown to follow Hertzian contact mechanics theory, and supports the scaling of friction coefficient in the speed-independent regime that follows μ ~ Fn−1/3.
... It is very impressive to read the most recently published reproduction of Leonardo da Vinci's friction experiments [1]. In Table 1 of this paper, the authors reported measured average values of static friction coefficient for various roughness levels of three types of wood surfaces. ...
... Unfortunately, the values of the plasticity index were not provided for the experiments reported in Ref. [1]. However, an order of magnitude estimation of the parameters involved in Eq. (1) can be obtained as follows: From the information provided in Ref. [9], the elastic modulus of wood, E, is about 10 GPa, the hardness, H, is about 15 MPa, and the yield strength, Y, is about 5 MPa. ...
... In such a case, the plasticity index w = (E/H)(r/r) 1/2 is of order 10, and therefore, for rough wood surfaces, we may assume w [ 10. The range of the applied load (weight of the wood blocks) P as provided in [1] is between about 20-40N, and that of the apparent contact area A n is between about 150-420 cm 2 . Hence, the dimensionless load P * = P/(A n Y) is in the range of 10 -4 -10 -3 . ...
It is very impressive to read the most recently published reproduction of Leonardo da Vinci’s friction experiments [1]. In Table 1 of this paper, the authors reported measured average values of static friction coefficient for various roughness levels of three types of wood surfaces. These values are between 0.25 and 0.29 for rough (Ra > 3000 nm) surfaces, and they increase up to 0.72 for smooth (Ra = 200 nm) surfaces. Moreover, the lowest friction coefficient value of 0.25 is in agreement with da Vinci’s friction experiments from 500 years ago. In these experiments, da Vinci also found that the friction coefficient is independent of the apparent contact area and the applied load.An interesting question is whether such effects of surface roughness on friction coefficient can be predicted by a theoretical model. A first hint in this direction was probably provided by Greenwood and Williamson [2] in 1966. In this seminal paper, a model (known as the GW model) for the elastic contact of r ...
... Prior to present and analyze some of most relevant friction force models suitable to be utilized in multibody dynamics, it is opportune to revisit the scientific roots and milestones of this subject. Leonardo da Vinci (1452-1519) was pioneer in the study of friction, namely in terms of the required weight to be applied to different objects placed on horizontal and inclined planes in order to start their motion [142][143][144]. Based on experimental observations, da Vinci wrote, in his notebooks, two basic friction laws. ...
... Da Vinci also defined the concept of coefficient of friction, as the ration between friction force and weight of the moving object [144]. Lastly, da Vinci found a universal coefficient of friction equal to 1/4, independent of the material, and recognized the difference among sliding, rolling and viscous frictions [143]. Guillarme Amontons (1663-1705) developed his own experimental apparatus to investigate on friction and rediscovered the da Vinci friction laws [146]. ...
... Many suggest Leonardo da Vinci as the archetype of the polymath; one of the greatest example of the Renaissance Man. In fact, he could work on projects where the artistic and the scientific research and practice merged, to the point that it was hard to discern the two or label the author as either an artist or scientist ( Figure 1) (Jones, 2012;Pitenis et al., 2014). Interestingly, many of the Leonardo Da Vinci's studies on anatomy, optics, perspectives, mechanics, production processes were aimed to the making of artworks, whether paintings, sculptures or architectures (Léonard de Vinci et al., 1997). ...
... There are, of course, examples of organizations that bring together the art and engineering worlds, through interdisciplinary teams and processes (i.e. MediaLab, Copenhagen Institute of Interaction Design, Interaction Design Institute of Ivrea, the Royal College of Art and some others) (Ortony, 2003)(Smith, 2007. For example, the now defunct Interaction Design Institute of Ivrea used to enrol students coming from both technical backgrounds, such as informatics, mathematics and engineering, and humanistic backgrounds, such as communication sciences, art and design. ...
As design practitioners researchers and educators, we constantly find ourselves shuffled between humanities and sciences. In fact, the design departments in the universities around the globe are sometimes placed under the formers, sometimes under the latters, thus becoming a meeting point for academics and professionals coming from both realms. The synergy resulting from the varieties of backgrounds and expertise creates a fertile ground for explorations on both a conceptual and a technical level. This paper reflects on the potential benefits of combining engineering and art research. The authors of this paper look at the increasingly delicate role that technicians, engineers and computer programmers play in developing technologies that impact our social, emotional and intimal lives, and advocate for art as a context and tool to help those professional developing their sensitivity and critical sense, besides their skills. In doing so, the paper makes a contribution to the STEM vs. STEAM conundrum, encouraging an education that merges arts and humanities disciplines with scientific and technical subjects. Art; Engineering; indisciplinarity; STEAM.
... These tabulated values are aggregated and they are shown in Fig. 2. As underlined by Blau, these values are far from applied problems and should be used carefully. Experimental data about wood-on-wood friction are scarce (e. g. [34][35][36][37][38]) and cover a wide variety of woods including balsa, cork or plywood. The experimental values shed doubt on the low value given by Bowden and Tabor of μ S = 0.2, which is only a typical value of friction. ...
... McKenzie [34] observed that the kinetic friction coefficient for wet wood decreases when the sliding speed increases. Pitenis et al. [38] found the friction coefficient is reduced by a specific surface preparation: sliding directions aligned with the grain, inclusion of wood dust, etc. Probably, the Egyptians had empirical methods to reduce the friction, but currently they remain hypothetical. ...
The transportation of a colossus painted in the ancient Egyptian tomb of Djehutihotep (Dayr al-Barsha) is known as an example of lubrication application. However the benefits and the nature of lubrication used by ancient Egyptians are controversial. In order to clarify this issue, the physical parameters involved in the transportation are carefully reviewed. The traction force is a key parameter, and is evaluated by simple physical models and the results of biomechanical and ergonomic studies. The results of this work suggest high traction force can be produced only with an excellent team coordination, and the friction coefficient between sledge and ground is efficiently reduced by hypothetical methods which exclude probably wood-on-wood or wood-on-sand surface contacts.
... It should be highlighted that these conclusions apply solely to an assembly of rigid and macroscopic granules, given that the impact of their deformation is negligible in this study since the stresses applied are significantly lower than the stiffness of the granules. Friction values close to ¼ appeared frequently over the history 3,4,43 , but our study is the first to generalize it and relate it to different physical systems of the same family. We show that such a value is characteristic to granular matter of perfectly spherical geometry and can be concluded from measurements of other granular media, including granular geometries that are far from spherical shapes and spanning over at least 5 orders of magnitude of the viscosity of the liquid between the granules. ...
The concept of friction was integrated into the broader field of tribology in the 20th century. Here, we revive the older friction coefficient concept and show that it is the defining parameter for a family of granular materials. We show, for the first time, that kinetic friction coefficients of such systems can be described as a function of the lubricating fluid and the shape of the granules, without any fitting parameters. With this, we define the value and conditions for the minimal friction of this system and show how it can increase depending on the properties of the system. This paper shows that the minimum possible friction for an assembly of granular media is the same universal constant of ¼ that da Vinci identified for kinetic friction between two rigid bodies.
Supplementary Information
The online version contains supplementary material available at 10.1038/s41598-024-83889-0.
... He examined the relationship between hydrostatic force and floating bodies in his notes. Yet, although he eventually noticed the equilibrium of fluids, his ideology of hydrostatics was still incomplete [8]. ...
Art is an important carrier of history. Through understanding art, scholars can know the ideas and theories of the people at that time and make all kinds of correlations and inferences. Leonardo da Vinci, a famous artist of the Renaissance era, has many surviving paintings and notebooks that contain a great deal of knowledge related to mechanical theories, and the topic of this paper is the relationship between Leonardo da Vinci’s works and the development of mechanics. This paper uses the method of literature analysis to read and find the relevant literature and makes the final conclusion: the science involved in Leonardo da Vinci's paintings has played a leading role in the development of some of the later mechanical development in both direct and indirect aspects, but at the same time it needs to be clear that the theories written in the notebooks and whether they are practically correct are irrelevant, and it is necessary to make a practical model of the theories before concluding Leonardo’s influence.
... As a real-life phenomenon, friction has been a topic of scientific and technological attention since ancient times [25]. The earliest characterisation of the friction force is attributed to Leonardo da Vinci [32], who suggested that the amplitude of the friction force F f might evaluated as: ...
Friction damping is commonly used in engineering structures for dissipating energy and reducing vibrations. However, friction can also introduce undesired effects such as the periodic or permanent sticking between the contacting parts or the magnification of the response amplitude. These behaviours need to be accounted for during the early design stages, where these structures are modelled as discrete single (SDOF) or multi-degree-of-freedom (MDOF) systems. However, even when Coulomb friction and simplified mechanical models are considered, the dynamic analysis of these systems is complicated by the nonlinearity of the friction forces.
In this thesis, the dynamic response of different lumped mechanical systems including a Coulomb friction contact and subjected to harmonic excitation is investigated analytically, numerically and experimentally, aiming at establishing how their response features and motion regimes are affected by the presence of multiple DOFs and by the motion of the contacting components.
Exact solutions are derived for the continuous steady-state response of these systems and validated numerically. These solutions enable the exploration of the Coulomb friction effects on response features such as resonant, low- and high-frequency behaviours, the presence of invariant points and inversions of the transmissibility curves. Moreover, the analytical boundaries among continuous, stickslip and permanent sticking regimes are represented in a two-dimensional parameter space, allowing for a quick prediction of the motion regimes during the design stage.
An experimental investigation of the response of SDOF and MDOF systems is carried out by using a base-excited shear frame setup with a brass-to-steel contact, leading to the validation of the theoretical results and the evaluation of different metrics for measuring friction from the dynamic response.
The main findings of this thesis are that: (1) MDOF systems exhibit significantly different behaviours depending on whether the friction and the harmonic forces are applied to the same or different masses; (2) the friction generated by a contact between oscillating components can magnify the response of the system at high frequencies; (3) Coulomb friction model is generally suitable for describing the dynamic behaviour of structures with a metal-to-metal contact.
... 9 The earliest scientific methodology for investigation of sliding friction is generally attributed to Leonardo da Vinci (1452-1519). 10 According to his notebook pages, the resistance of friction is directly proportional to applied load. In around 1699, Amontons carried out a series of experiments and established the friction laws. ...
Solid-liquid interfaces exist widely in a variety of physical and chemical fields. The coupling of friction and electric fields at solid-liquid interfaces is a common concern in many cases, such as in corrosive wear or charged lubrication. In most cases, it is hardly to identify whether characteristics of the charged interfaces affect frictional behavior or friction affects the charged solid-liquid interfaces. They often entangle with each other. In this article, we will discuss the interactions between friction and charged solid-liquid interfaces.
... This reflects the fact that this force is a single scalar which is the outcome of a complex spatiotemporal process of slip nucleation across a typically heterogeneous interface, and as a result depends on a large variety of factors, both controlled [1][2][3][4][5][6][7][8][9][10] and uncontrolled (such as wear) [9,10]. Even in well-designed, rigorous laboratory experiments static friction can vary significantly and unpredictably between successive measurements with the same two bodies [9,11]. This stochasticity largely stems from one inconvenient truth about frictional interfaces: Even using the same bulk solids, a new system is formed after each slide. ...
Classically, the quantity of contact area AR between two bodies is considered a proxy for the force of friction. However, bond density across the interface—quality of contact—is also relevant, and contemporary debate often centers around the relative importance of these two factors. In this work, we demonstrate that a third factor, often overlooked, plays a significant role in static frictional strength: The spatial distribution of contact. We perform static friction measurements, μ, on three pairs of solid blocks while imaging the contact plane. By using linear regression on hundreds of image-μ pairs, we are able to predict future friction measurements with three to seven times better accuracy than existing benchmarks, including total quantity of contact area. Our model has no access to quality of contact, and we therefore conclude that a large portion of the interfacial state is encoded in the spatial distribution of contact, rather than its quality or quantity.
... More systematic approaches to understanding and controlling friction are thought to start during the Middle Ages. The highly methodical work of Leonardo da Vinci and his explicit drawings depicting a range of friction experiments attest themselves to be extremely ingenious even today and conform to modern days' treatment of friction (Pitenis et al., 2014). Further analyses of friction by Guillaume Amonton during the 1600s and Charles-Augustin de Coulomb in the 1700s have laid the foundation of many other scientific studies on friction by Desaguliers, Reynolds, Hardy, Holm, Bowden and Tabor, and many other scientists during the 19th and 20th centuries (Dowson, 1998;Ludema, 2001). ...
Superlubricity is a terminology often used to describe a sliding regime in which the adhesion leading to friction or resistance to sliding literally vanishes. For improved energy security, environmental sustainability, and a decarbonized economy, achieving superlubric sliding surfaces in moving mechanical systems sounds very exciting, since friction adversely impacts the efficiency, durability, and environmental compatibility of many moving mechanical systems used in industrial sectors. Accordingly, scientists and engineers have been exploring new ways to achieve macroscale superlubricity through the use of advanced materials, coatings, and lubricants for many years. As a result of such concerted efforts, recent developments indicate that with the use of the right kinds of solids, liquids, and gases on or in the vicinity of sliding contact interfaces, one can indeed achieve friction coefficients well below 0.01. The friction coefficient below this threshold is commonly termed the superlubric sliding regime. Hopefully, these developments will foster further research in the field of superlubricity and will ultimately give rise to the industrial scale realization of nearly-frictionless mechanical systems consuming far less energy and causing much-reduced greenhouse gas emissions. This will ultimately have a substantial positive impact on the realization of economically and environmentally viable industrial practices supporting a decarbonized energy future. In this paper, we will provide an overview of recent progress in superlubricity research involving solid, liquid, and gaseous media and discuss the prospects for achieving superlubricity in engineering applications leading to greater efficiency, durability, environmental quality, and hence global sustainability.
... The Amontons-Coulomb law can be considered the first empirical friction law. It was originally deduced by observing the initiation of sliding of objects in stationary contact (Pitenis et al., 2014), and still is the one used in most studies concerning the analytical and computational aspect of dynamic ...
This study aims at assessing the predictive performance of the Amontons-Coulomb law to reliably predict the cyclic response, inclusive of stick–slip, of a single degree of freedom system in contact with the ground through two versions (steady-state and rate-and-state) of a regularised Dieterich-Ruina law. The assessment is carried out by defining a cost function and a physics-based constraint that enable the identification of the corresponding optimal coefficients of the Amontons-Coulomb law through a multi-start constrained non-linear optimization. The comparative study starts with a sensitivity analysis, aimed at first identifying the most meaningful model parameters for the Dieterich-Ruina law. Subsequently, the cyclic dynamic responses provided by both friction laws are analyzed for varying model parameters, and characteristic features are observed within the dynamic forcing-displacement graph and the friction force - velocity plot, that could be directly linked to one friction model or the other. The sensitivity analysis led to the definition of a cost function expressed in terms of the displacement and velocity response differences and a constraint based on the phase difference. The optimization study identified areas of the Dieterich-Ruina’s parameter space for which the Amontons-Coulomb law can reliably be used to predict a cyclic stick–slip response. The relevance of these results with respect to problems of modelling and identification of friction are discussed.
... As soon as the weight is large enough, the block is set in motion. Based on the weights, the friction value at which the movement begins, is calculated [2]. This results in the stick-slip condition: |F F |≤ µ s F N , where µ s is the static friction coefficient, if the formula is satisfied. ...
Friction is one of the variables that have a far-reaching influence on forming processes. In the past, less attention was paid to static friction than to sliding friction in forming processes. In this paper, a test stand for the determination of static friction under load in metal forming is presented. The results are discussed using the example of an oscillating cold forming process. It could be shown that the expected influence of static friction is low in this application.
Graphical abstract
... Friction is a tribological phenomenon which takes place at the interface between two contacting bodies, representing a resistance to the local relative tangential motion. The first investigation on friction dates back to the sixteenth century, when Leonardo da Vinci, based on experiments, postulated that the frictional force is proportional to the normal contact force, opposes the tangential motion, and does not depend on the apparent contact area [1]. Subsequently, Amontons [2] and Coulomb [3] validated the work by da Vinci and demonstrated that friction is independent of the relative tangential velocity. ...
The LuGre friction force models are amongst the most popular and powerful approaches to treat frictional contact in modeling, simulation and control of mechanical systems. However, these friction force models have some numerical difficulties related to physical inconstancies, when the systems under analysis include frictional contacts with significant variations in the normal loads. The LuGre friction force models can exhibit some problems resulting in the ratio between the friction and normal contact forces exceeding the friction coefficients. Another limitation deals with the drift problem which might occur during sticking periods. Thus, this work is aimed at presenting a new investigation based on the LuGre friction foundation capable of overcoming those limitations. In a simple manner, the new solution for the LuGre friction force model includes a stiffness coefficient to adjust and accommodate the variations of the normal contact forces in dynamical systems. In this study, two LuGre friction force models are revisited to facilitate the description of the proposed solution. Finally, several numerical application examples regarding a block of mass on a horizontal plane are presented to compare and examine the advantages and potentials of the original, amended and proposed models.
... Da Vinci (and, centuries later, Guillaume Amontons and Charles-Augustin de Coulomb) observed that in most cases (e.g., macroscale experiments, simple machines, and various material pairs like wood on wood) the force of friction, F f , was proportional to the normal load, F n , and independent of the apparent contact area [45][46][47][48]. These early observations led da Vinci to conclude that the coefficient of friction (μ, the proportionality of the friction force and the normal force) was constant and equal to ¼, possibly due to an active laboratory environment [45,49,50]. Over 200 years later, Amontons independently concluded that the coefficient of friction was 1 / 3 , although all his experimental surfaces were greased in old pork fat, and thus he was actually studying boundary lubrication [45]. ...
Biology largely manages tribological challenges either by eliminating sliding altogether or by protecting sliding interfaces with soft aqueous gels. In the body, aqueous gels are often thin (thickness, t < 100 μm), soft (elastic modulus, E < 10 kPa), lubricious (friction coefficients, μ < 0.01), and cover compliant surfaces, including cell membranes, pleura, cartilage, and the eye. These characteristics provide a natural defense against wide ranges of applied loads. In this work, hydrogel samples (7.5 wt% polyacrylamide, 0.3 wt% N,N′-methylenebisacrylamide) were prepared with spherically-capped shell probe geometries, which have been previously determined to provide constant contact pressures during indentation measurements against flat hydrogel disks. In a self-mated (“Gemini”) sliding configuration, this geometry is capable of load-independent friction over a range of low normal loads spanning 0.5 to 2.0 mN. This friction behavior is consistent with da Vinci-Amontons' friction law (Ff = μFn) due to the large compliance of the spherically-capped shell probe geometry enabling the area of contact to increase in proportion with the applied load and due to low shear stresses reacted across the sliding interface for high water content aqueous gels. Future bio-inspired lubrication strategies involving aqueous gels may benefit from leveraging contact geometry for constant, load-independent friction.
... Many suggest Leonardo da Vinci as the archetype of the polymath; one of the greatest examples of the Renaissance Man. In fact, he could work on projects where the artistic and the scientific research and practice merged, to the point that it was hard to discern the two or label the author as either an artist or scientist ( Figure 1) [1,2]. Interestingly, many of the Leonardo Da Vinci's studies on anatomy, optics, perspectives, mechanics, production processes were aimed towards the making of artworks, whether paintings, sculptures or architectures. ...
As design practitioners researchers and educators, we constantly find ourselves shuffled between humanities and sciences. In fact, the design departments in the universities around the globe are located within the faculties of engineering, architecture, visual art, liberal are or environmental sciences, thus becoming a meeting point for academics and professionals coming from both the humanities and sciences. The synergy resulting from the varieties of backgrounds and expertise creates a fertile ground for explorations on both a conceptual and a technical level. By briefly compiling and analysing a review of literature and creative works spanning from the renaissance to contemporary art, this paper reflects on the potential benefits of combining engineering and art research. The authors of this paper look at the increasingly delicate role that technicians, engineers and computer programmers play in developing technologies that impact our social, emotional and intimal lives, and advocate for art as a context and tool to help those professional developing their sensitivity and critical sense, besides their skills. In doing so, the paper makes a contribution to the STEM vs. STEAM conundrum, encouraging an education that merges arts and humanities disciplines with scientific and technical subjects.
Doi: 10.28991/HIJ-2021-02-01-04
Full Text: PDF
... 70 The first observations of friction were recorded by Leonardo da Vinci between 1480 and 1518, later described by G. Amontons in 1699, and again confirmed by C. Coulomb in 1785. 71,72 The simple laws of friction, derived from Amontons' publications, state that the friction force F f is proportional to the applied load F n and independent of the contact area, represented by the equation ...
Aqueous surface gels are fragile yet resilient biopolymer-based networks capable of sustaining extremely low friction coefficients despite tribologically-challenging environments. These superficial networks are ubiquitous in natural sliding interfaces and protect...
... The static friction coefficient decreased with an increase in the phenol formaldehyde resin concentration. Pitenis et al. [11] measured friction for various wood blocks sliding on a wood surface. The values of the static friction coefficient were in the range of 0.35 to 0.72. ...
... Which were in fact first discovered by da Vinci(Pitenis, Dowson, and Gregory Sawyer, 2014;Hutchings, 2016). ...
All mechanical systems, naturally occurring or human-produced, are subjected to friction and wear at the interface of solid constituents. Large portions of energy dissipation and loss of material, in every-day life and industrial applications alike, are due to friction and wear. Mitigating their effects could save between 1% and 2% of the GDP of a developed country. Some systems governed by friction and wear can have an even more important bearing on human lives, such as earthquakes nucleating from the sliding of tectonic faults. Despite the tremendous impact of tribological phenomena on society, their understanding has remained empirical, and to this day no predictive model has emerged. Interface processes such as friction and wear are difficult to investigate because of the large number of underlying physical phenomena (e.g. adhesion, fracture, etc.) and the difficulty of observing them at contact interfaces.Although research endeavors into friction and wear have not produced predictive models, they have identified key components of tribological systems necessary to build such models. Central among them is the idea that solids may not be in contact across their apparent interface area, but instead a much smaller "true contact area." This true contact area is the result of the surfaces in contact being inevitably rough. In addition, contact pressures on roughness peaks are expected to cause plastic flow of material, drastically changing the properties of the contact interface, and the role it plays in tribological processes. Therefore, the aim of this PhD thesis is to develop tools for the modeling of elastic-plastic rough contact interfaces, and to study the applicability of knowledge of the contact state to the modeling of interface phenomena.The first part of this objective is the development of a novel computational approach to volume integral methods, which are used to solve elastic-plastic rough surface contact. Volume integral methods have the advantage over the finite-element method in that they can represent exactly elastic constitutive behavior and semi-infinite bodies, which are commonly used in rough contact applications. This thesis develops a new fundamental solution used in a volume integral approach, which drastically improves computation times and required memory over previous approaches. Derived directly in the Fourier domain, this fundamental solution makes optimal use of the fast-Fourier transform while retaining the advantages of classical volume integral methods.In the second part, this numerical approach is used to study the so called "Archard's wear coefficient", and to up-scale known micro-scale adhesive wear mechanisms to the macro-scale via rough contact simulations. These show that wear is an emergent process dependent on the interaction of micro-scale mechanisms: they demonstrate the role of plastic deformations in the crack nucleation process, and the necessity to look beyond the true contact area to understand tribological phenomena.While this thesis remains quite fundamental, the tools and codes developed can be used outside the realm of elastic-plastic contact, and the up-scaling approach to wear that we have established is a first step towards predictive models.
... Friction is an integral part of life and has been used and studied since ancient civilization. The first documented scientific characterization of the friction forces comes from Leonardo da Vinci [48]. He modeled friction force F f in the direction opposite to motion according to the following equation, ...
This survey provides an insight into the modeling and testing of uniaxial friction dampers. The focus is on attenuating the linear relative movement along planar surfaces for frequencies between 10 Hz and 1 kHz. An overview of the different approaches seen in the literature concerning friction damping is provided. Examples and evaluation of such dampers excited over a wide range of frequencies are presented. The information required to develop models of friction dampers is covered. To that end, different modeling approaches are presented for dry friction. Dynamic friction models with an internal state are covered, and their advantages are described. Other modeling approaches are reported for complete systems with friction dampers. Both numerical and analytical models are covered. Experimental configurations from a selection of authors are also included. Finally, a series of suggestions for the numerical modeling and experimental testing of a friction damper are given.
... A set of slabs in dissimilar orientations on a plane. b) a block on a horizontal surface connected by a string which passes over a cylinder to a hanging weight, and a horizontal cylinder placed in a hemi-cylindrical cavity with a string supporting to a hanging weight c) Bodies rolling and sliding on horizontal planes [17,18]. -11-In France, in 1699, Guillaume Amontons formulated the rules of friction after investigating dry sliding between two flat surfaces. ...
The main objective of the thesis was to study the triboelectric behavior of dry sliding contacts between polymeric materials (ABS, PE, PP, PS and two types of PVC), including the possibility to control and optimize the results in terms of either surface charge generated or wear. A linear tribometer with tribocharging capabilities was designed and built, to enable the study of the sliding contact between solids and to allow the adjustment of main tribocharging control variables: normal force, sliding speed, time and stroke. This device also provided measurement data to characterize the friction condition: the variations of the normal and tangential forces, as well as the relative displacement between the specimens. Furthermore, the electric charge generated and temperature raise due to rubbing on the surface of the polymer were measured, so that to investigate the relationship between the tribological properties. The experiments showed that the level and distribution of the charge generated by dry friction depends on the normal force applied, friction time (cycle), sliding speed, material mechanical properties and surface roughness or texture. Corona discharge may be used to provide initial charge on the surfaces before sliding. Modelling of tribocharging processes was done using the design of experiments methodology. The models can be used to predict and optimize the tribocharging. Control charts were used to monitor the process and detect the special causes of variation in the charge generated by triboelectric effect.
... Engineering had few papers on the subject but demonstrated a high level of continued interest on da Vinci's work, showing 6.89% of the papers on da Vinci that are very recent and published during 2017. This result was confirmed by a study in tribology displaying friction experiments (Pitenis et al. 2014), noting that his immense contribution to the field of tribology has only recently surfaced. Figures 1, 2, and 3 visualize the number of publications, citations. ...
The article evaluates the body of literature on Leonardo da Vinci using for the first time bibliometric and altmetric methods for data processing. The question of whether the literature on Leonardo da Vinci reflects his interdisciplinarity as scientist and artist is addressed. We argue that the medical and material sciences show a high number of citations to the respective publications, and much higher number of citations to publications ratio than the humanities and social sciences fields. We also found that there is no relationship between the number of publications for each research area and the citations (between productivity and quality). The largest category of papers, in terms of citations and in terms of the number of subfields, discussing da Vinci’s contribution to the various sciences, belongs to exact sciences. This finding is surprising as Leonardo da Vinci has become a synonym for the mysterious artist whose paintings consist of many messages that are difficult to explain. Therefore it seems natural that Leonardo the artist would get a lot of research attention. Nevertheless, the bibliometric findings show that the academic community has interest in his contributions to science, no less than in his work of art.
... One of the basic laws of friction dictate "force of friction is independent of the apparent area of contact" and was already noticed by Leonardo da Vinci (Pitenis et al 2014). The geometry of Leonardo's experiments is still of interest after 500 years, since we are still trying to understand what happens to the "contact area" by measuring it with a different resolutions. ...
Jacobs and Martini (JM in the following) give a nice review of direct measurement methods (in situ electron microscopy), as well as indirect methods (which are based on contact resistance, contact stiffness, lateral forces, and topography) for measurement of the contact area, mostly at nanoscale. They also discuss simulation techniques and theories from single-contact continuum mechanics, to multi-contact continuum mechanics and atomistic accounting. As they recognize, even at very small scales, "multiple-contacts" case occurs, and a returning problem is that the "real contact area" is often an ill-defined, "magnification" dependent quantity. The problem remains to introduce a truncation to the fractal roughness process, what was called in the 1970's "functional filtering". The truncation can be "atomic roughness", or can be due to adhesion, or could be the resolution of the measuring instrument. Obviously, this also means that the strength (hardness) at the nanoscale is ill-defined. Of course, it is perfectly reasonable to fix the "magnification" and observe the dependence of contact area, and strength, on any other variable (speed, temperature, time, etc).
... The nature of friction has been widely investigated since Leonardo's studies, recently commented in [1,2]. However, its prediction still remains a difficult issue. ...
An experimental investigation on the friction coefficient in line contacts under mixed and boundary lubrication regimes is described. Rectangular contacts between cylindrical specimens and the flat surface of discs of different material and surface roughness combinations were analyzed. Very low Stribeck numbers have been considered, resulting also in low dimensionless film thickness, so that the morphology of the surfaces and the material had a remarking role. In this work, the theoretical procedure for assessing the friction coefficient in the tested cases is described and compared to experimental results. Additionally, wear effects obtained in boundary lubrication conditions are shown. The surface conditions are put in relation with some particular trends of the friction coefficient obtained for certain combinations of materials and roughness.
... Although for each test person an individual set of new test surfaces was used, sebum might have also remained on the test surfaces. The effect of fingerprints on contact mechanics has been recently demonstrated in a tribological study repeating Leonardo da Vinci´s friction experiments (Pitenis et al., 2014). Our measurements showed that in real life the combined effect of these variables causes high differences in the human adhesive strength that have to be seriously taken into account when tuning haptic properties of surfaces in technical products. ...
Fingertip friction is a rather well studied subject. Although the phenomenon of finger stickiness is known as well, the pull-off force and the adhesive strength of human finger tips have never been previously quantified. For the first time, we provided here characterization of adhesive properties of human fingers under natural conditions. Human fingers can generate a maximum adhesive force of 15 mN on a smooth surface of epoxy resin. A weak correlation of the adhesive force and the normal force was found on all test surfaces. Up to 300 mN load, an increase of the normal force leads to an increase of the adhesive force. On rough surfaces, the adhesive strength is significantly reduced. Our data collected from untreated hands give also an impression of an enormous scattering of digital adhesion depending on a large set of inter-subject variability and time-dependent individual factors (skin texture, moisture level, perspiration). The wide inter- and intra-individual range of digital adhesion should be considered in developing of technical and medical products.
... The friction data with contaminated spheres in pH-neutral solution have also been plotted in Figure 6. In this case, the coefficient of friction (μ dirty = 0.26) corresponds to the typical values for contaminated surfaces 54 and the values reported for contaminated silica microsphere pairs by Ling et al. 44 Polymer-Brush-Coated Particles. The copolymer that has been used is known to adsorb on the surface via calcium bridging of its phosphate anchors, forming a hydrophilic polymer brush and reducing the coefficient of friction. ...
Friction between microscopic objects controls many macroscopic phenomena. For instance, the friction between micro-asperities determines the tribology of rough surfaces in contact and in relative motion. Additionally, the friction between micro-particles is responsible for many aspects of the rheological response of granular media, ranging from micro-scale contacts at the single-particle level to macroscopic flow properties of sheared, dry granular systems and non-Brownian suspensions. We propose a new, precise and robust method, based on lateral force microscopy, to measure the coefficient of friction between microspheres quantitatively and without complex data processing. We have successfully applied this method to the contact between silica spheres in liquid with and without polymer coating.
... The effectiveness of boundary lubrication for the reduction in friction and wear can be demonstrated through a recreation of Leonardo da Vinci's friction experiments, which was recently reported [3]. The authors attempted to construct a nearly faithful recreation of Leonardo da Vinci's apparatus for measuring friction based on his notebook illustrations, and investigated the conditions under which Leonardo da Vinci conducted his experiments. ...
A complete understanding of the mechanism of boundary lubrication is a goal that scientists have been striving to achieve over the past century. Although this complicated process has been far from fully revealed, a general picture and its influencing factors have been elucidated, not only at the macroscopic scale but also at the nanoscale, which is sufficiently clear to provide effective instructions for a lubrication design in engineering and even to efficiently control the boundary lubrication properties. Herein, we provide a review on the main advances, especially the breakthroughs in uncovering the mysterious but useful process of boundary lubrication by adsorption film. Despite the existence of an enormous amount of knowledge, albeit unsystematic, acquired in this area, in the present review, an effort was made to clarify the mainline of leading perspectives and methodologies in revealing the fundamental problems inherent to boundary lubrication. The main content of this review includes the formation of boundary film, the effects of boundary film on the adhesion and friction of rough surfaces, the behavior of adsorption film in boundary lubrication, boundary lubrication at the nanoscale, and the active control of boundary lubrication, generally sequenced based on the real history of our understanding of this process over the past century, incorporated by related modern concepts and prospects.
... Accurate understanding of this problem has eluded physicist, engineers and scientists since the first well-known experiments conducted by Leonardo da Vinci (ca. 1500) [2]. While the simplistic versions of Amontons-Coulomb laws of friction were sufficient until the late 1950s, it was not until the following developments of Bowden and Tabor [3] and Rabinowicz [4], who discussed the importance of plasticity in contact, Archard [5] and Greenwood and Williamson [6], who characterized the surface roughness and interactions using statistical mechanics, that contacts along the multicontact interface (MCI) were shown to form in three mechanical constitutive behaviors: (I) elastic; (II) elasto-plastic; and (III) fully plastic [7]. ...
A pressure-sensitive film was used to characterize the asperity contacts along a polymethyl methacrylate (PMMA) interface in the laboratory. The film has structural health monitoring (SHM) applications for flanges and other precision fittings and train rail condition monitoring. To calibrate the film, simple spherical indentation tests were performed and validated against a finite element model (FEM) to compare normal stress profiles. Experimental measurements of the normal stress profiles were within -7.7% to 6.6% of the numerical calculations between 12 and 50 MPa asperity normal stress. The film also possessed the capability of quantifying surface roughness, an important parameter when examining wear and attrition in SHM applications. A high definition video camera supplied data for photometric analysis (i.e., the measure of visible light) of asperities along the PMMA-PMMA interface in a direct shear configuration, taking advantage of the transparent nature of the sample material. Normal stress over individual asperities, calculated with the pressure-sensitive film, was compared to the light intensity transmitted through the interface. We found that the luminous intensity transmitted through individual asperities linearly increased 0.05643 ± 0.0012 candelas for an increase of 1 MPa in normal stress between normal stresses ranging from 23 to 33 MPa.
This study aims to investigate the impact of faithfully reconstructing the experiments in the history of science on the academic success and word association levels of secondary school students. It uses the one-group pretest-posttest weak experimental design, which is one of the mixed experimental designs. It was carried out for six weeks with 13 students in seventh grade in the physics group for the Development of Special Talents in a Science and Art Center located in Istanbul in the 2021-2022 academic year. During the practice, three experiments were performed by the students. Academic Success Test and Word Association Test, formed by the investigators, were applied to the students as a pretest and a posttest. A significant difference was found between the students’ pretest and posttest academic success scores, which was in favor of the posttests. It was seen that new relationships were established between the concepts after the practice.
Wood friction welding is a green and pollution-free wood processing technology. Research on wood friction welding mainly focuses on the influence of wood type, welding process, and welding interface additives on welding interface strength. However, studies on the tribological properties of wood friction welded interface and its effect on the strength of the welded interface are few. In this article, chemical additives in wood were added to the interface. The frictional force, normal force, microstructure, and chemical composition of the welding interface, and their effects on the strength of the welding interface were studied. In the rotating friction welding of wood, frictional force increased gradually with friction welding. Approximately 2 s after welding, the frictional force achieved a stable state. Normal force increased and then gradually decreased. No considerable changes in frictional force and interface strength were observed and interface strength increased with normal force. The interface strength of glucose and rosin increased, whereas that of N2 protection showed little change. The interface strength of tung oil, cellulose, and guaiac decreased. This study provides a basic reference for the further industrial application of wood friction welding technology.
Bu çalışmada 2018 Fen Bilimleri Dersi Öğretim Programı’nda (MEB, 2018) tüm sınıf seviyelerindeki öğrenme alanları altında yer alan kazanımlar ile bilim tarihinde yer alan önemli bilimsel deneyleri ilişkilendirerek sunmak amaçlanmıştır. Araştırmada nitel araştırma yöntemlerinden doküman analizi yöntemi kullanılmıştır. 2018 Fen Bilimleri Dersi Öğretim Programı ve bilim tarihi alanında yayınlanan kitaplar, fen disiplinleri alanındaki kitaplar, makaleler, tezler, bilimsel dergiler veri kaynağı olarak kullanılmıştır. Çalışmada kaynaklar taranarak elde edilen deneyler listesi 2018 Fen Bilimleri Dersi Öğretim Programı (MEB, 2018) kazanımları ile ilişkilendirilirken ana tema öğrenme alanı olarak belirlenmiştir. Ünite adı, sınıf seviyesi, kazanımlar ve ilişkili deneyler ise alt kategoriler olarak belirlenerek veriler anlamlı yapılar haline getirilmiş ve bulgular öğrenme alanları ve ünite-sınıf seviyesi-kazanım-deneyler ilişki tabloları halinde sunulmuştur. Tarihteki bilimsel deneylerin ortaokul öğrenci seviyesine uygun biçimde ilgili kavram ve kazanımla ilişkilendirilerek verilmesi yönünde önerilerde bulunulmuştur.
Wood–wood friction is an ancient subject, and its related mechanisms have been elucidated. However, the tribological mechanism of wood–wood friction at a high speed is still unclear. In this paper, an experimental equipment of wood friction welding was designed and fabricated. The influences of welding equipment and wood parameters on friction force, normal force, and welding interface temperature were studied. Results show that the speed of welding into wood has a significant effect on interfacial force and normal forces. Increase in wood moisture content reduces friction and normal forces, and increase in fiber angle increases friction force, normal force, and welding interface temperature. This study provides theoretical and technical basis for the study of wood friction welding.
Volume 18 addresses friction and wear from a systems perspective, while providing a detailed understanding of why it occurs and how to control it. It explains the basic theory of friction and wear, and offers valuable insight on the forces, mechanisms, and interactions that are involved. It examines common wear scenarios, including wear by particles or fluids, rolling-contact wear, sliding wear, impact wear, and both chemical and environmentally assisted wear. It also covers operational wear, addressing several cases, including tool and die wear, bearing wear, engine wear, turbine wear, pump wear, and seal wear. In addition, the volume provides information on lubricants and lubrication, coatings, surface treatments and modifications, and the tribology of irons and steels, cobalt-base alloys, titanium, aluminum alloys and composites, cemented carbides, ceramics, polymers, and polymer composites. It also introduces the topic of condition monitoring, addressing wear particle analysis, vibroacoustic monitoring, and motor current signature analysis. For information on the print version of Volume 18, ISBN 978-1-62708-141-2, follow this link.
Experiments, modeling, and simulation were used to study the nonlinear dynamics of a jointed structure in a shock tube. The structure was a full-span square cylinder with internal bolted connections excited by fluid loading. The Reynolds number based on width was ≈105. The cylinder was exposed to an impulsive force associated with the incident shock followed by transverse loading imposed by vortex shedding. Experimentally, aerodynamic loading was characterized with high-speed pressure sensitive paint (PSP). Digital image correlation concurrently measured the structural response. Maximum displacement occurred when the vortex shedding frequency most closely matched the structural mode of the beam associated with a rocking motion at the joint. A finite element model was developed using Abaqus, where Coulomb friction modeled the nonlinear contact in the joint. The PSP data supplied the input load to the model as a one-way-coupled interaction. The simulations matched well the trends observed in the experiment. Overall, the root-mean-square values of the transverse displacement agreed to within 24% of the experiment. The modeling showed rocking about the joint during vortex shedding was critical to the nonlinear damping and energy dissipation observed in the structure. This highlights the importance of jointed connections to energy dissipation in structures under aerodynamic loading.
Leonardo da Vinci (1452–1519) was a visionary engineer, scientist, and polymath of the Renaissance era who performed numerous experiments in tribology, including experiments on wear. As discussed by Prof. Dowson, due to the delayed discovery of several caches of his notebook pages (particularly the Codex Madrid I) recognition of Leonardo's immense contributions to the field of tribology was delayed and continues to unfold. Leonardo's illustrations and investigations clearly describe studies and patterns of wear, particularly for loaded shafts and bushings. In this work, we present an attempt to faithfully recreate Leonardo's observations of wear using bushing and shaft systems made from olive wood. Our experiments, performed roughly 500 years after Leonardo's, reproduced his findings and demonstrated shape evolutions during operation as a result of wear. Leonardo's elegant demonstration of a 2-dimensional bushing-and-shaft system in which the shaft is turning inside of the bushing, showed wear to both components and resulted in a tear-dropped shape as the shaft was consumed. Our experiment, which took over 260 days to complete generated a similar tear-drop shape with an acute angle within 5° of the angle in Leonardo's original drawing. This undertaking also revealed the extensive duration of time over which experiments, and mechanisms operated in Leonardo's laboratory and adds to our understanding of the laboratory environment: a dynamic, active, and busy laboratory in motion, with numerous ongoing experiments and moving mechanical assemblies at work. As Prof. Dowson recognized, Leonardo da Vinci was clearly curious and passionate about tribology, as the Codex Madrid I contains thousands of illustrations of tribological components and experiments in friction, wear, and lubrication.
This chapter highlights a number of friction models that are used to study the behavior within an interface, including Coulomb friction, viscous friction, stiction, Stribeck friction, the LuGre model, the Jenkins element, the Iwan element, and the Bouc–Wen hysteresis model amongst others. At present, there is no predictive model of friction; however, several models have demonstrated the ability to reproduce the hysteretic behavior of an interface accurately once calibrated. From an assessment of the current state of the art, three trends emerge. First, an improved physical understanding of the mechanisms of friction is needed. Second, new strategies for accounting for model form error could improve the applicability of existing friction models. Third, with improved physical understanding and better strategies for managing model form error, a potential path forward may result in a two-model process: a highly detailed model that is used to predict the friction parameters for a specific system and a less detailed model that uses those results convoluted with new model form error strategies to simulate the dynamics of the system of interest.
Because of the way interpenetrating sheets deform, the harder you pull, the greater the friction force resisting separation.
Based on a detailed study of Leonardo da Vinci׳s notebooks, this review examines the development of his understanding of the laws of friction and their application. His work on friction originated in studies of the rotational resistance of axles and the mechanics of screw threads. He pursued the topic for more than 20 years, incorporating his empirical knowledge of friction into models for several mechanical systems. Diagrams which have been assumed to represent his experimental apparatus are misleading, but his work was undoubtedly based on experimental measurements and probably largely involved lubricated contacts. Although his work had no influence on the development of the subject over the succeeding centuries, Leonardo da Vinci holds a unique position as a pioneer in tribology.
We show experimentally that the sliding friction on sand is greatly reduced by the addition of some-but not too much-water. The formation of capillary water bridges increases the shear modulus of the sand, which facilitates the sliding. Too much water, on the other hand, makes the capillary bridges coalesce, resulting in a decrease of the modulus; in this case, we observe that the friction coefficient increases again. Our results, therefore, show that the friction coefficient is directly related to the shear modulus; this has important repercussions for the transport of granular materials. In addition, the polydispersity of the sand is shown to also have a large effect on the friction coefficient.
The controlled use of fire was a breakthrough adaptation in human evolution. It first provided heat and light and later allowed
the physical properties of materials to be manipulated for the production of ceramics and metals. The analysis of tools at
multiple sites shows that the source stone materials were systematically manipulated with fire to improve their flaking properties.
Heat treatment predominates among silcrete tools at ~72 thousand years ago (ka) and appears as early as 164 ka at Pinnacle
Point, on the south coast of South Africa. Heat treatment demands a sophisticated knowledge of fire and an elevated cognitive
ability and appears at roughly the same time as widespread evidence for symbolic behavior.
Analytic results and experiments in ultrahigh vacuum indicate that the static friction between two clean crystalline surfaces
should almost always vanish, yet macroscopic objects always exhibit static friction. A simple and general explanation for
the prevalence of static friction is proposed. “Third bodies,” such as small hydrocarbon molecules, adsorb on any surface
exposed to air and can arrange to lock two contacting surfaces together. The resulting static friction is consistent with
experimental behavior, including Amontons' laws.
Scitation is the online home of leading journals and conference proceedings from AIP Publishing and AIP Member Societies
Early interest in tribology in the New World (c. 1500-1850 A. D. ) is reviewed, along with the early development of the petroleum industry. The contribution to tribology by Robert Henry Thurston and the formation of the American Society of Mechanical Engineers are discussed, including the foundation of ball and roller bearing companies. Professional societies and tribology in the U. S. A. are described. Future aspects are dealt with.
Significance
In the history of mechanical engineering, it is commonly believed that transporting huge stones with sliding sledges hauled by men did not occur in ancient China, because there were well-developed wheeled vehicles in China around 1500 B.C. However, some books contain brief remarks that the Large Stone Carving in the Forbidden City in Beijing was pulled to the site with a sledge sliding on an artificial ice path. Here we investigate the Chinese case based on historical documents and modern experimental results. We demonstrate that wood-on-ice sliding is more reliable and efficient than other lubrication methods, and pouring water on the contact surface is necessary to make this type of transport feasible.
The first part of this paper is occupied by a rapid review of the labours of mechanicians on the subject of friction, from the period of those of Amontons at the end of the 17th century, to those of Coulomb and of Vince in the years 1779 and 1784; from which the author draws the conclusion that the progress of knowledge in this department of science has been slow and unsatisfactory, and that a wide field is still left open to experimental investigation. With a view to elucidate several points not yet sufficiently ascertained by former writers, the author instituted several sets of experiments; some calculated to determine the forces required for dragging bodies of various kinds along a horizontal surface, and others for measuring the angle at which a plane was required to be inclined to the horizon in order to admit of the body sliding down it, attention being paid to the circumstances of pressure, extent of surface, time of previous contact, and velocity of motion. The following are the principal conclusions which the author deduces from his experiments. The friction of ice rubbing upon ice diminishes with an increase of weight; but without observing any regular law of increase. When dry leather is made to move along a plate of cast iron, the resistance is but little influenced by the extent of surface. With fibrous substances, such as cloth, the friction diminishes by an increase of pressure, but is greatly increased by the surfaces remaining for a certain time in contact; it is greater, cœteris paribus , with fine, than with coarse cloths; the resistance is also much increased by an increase of surface. With regard to the friction of different woods against each other, great diversity and irregularity prevail in the results obtained; in general the soft woods give more resistance than the hard woods: thus, yellow deal affords the greatest, and red teak the least friction. The friction of different metals also varies principally according to their respective hardness; the soft metals producing greater friction under similar circumstances than those which are hard. Within the limits of abrasion, however, the amount of friction is nearly the same in all the metals, and may in general be estimated at one sixth of the pressure. The power which unguents have in diminishing friction, varies according to the kind of the fluidity of the particular unguent employed, and to the pressure applied.
Analytic results and experiments in ultrahigh vacuum indicate that the static friction between two clean crystalline surfaces should almost always vanish, yet macroscopic objects always exhibit static friction. A simple and general explanation for the prevalence of static friction is proposed. "Third bodies," such as small hydrocarbon molecules, adsorb on any surface exposed to air and can arrange to lock two contacting surfaces together. The resulting static friction is consistent with experimental behavior, including Amontons' laws.
- M Kranzberg
- C W Pursell
Kranzberg, M., Pursell, C.W.: Technology in Western Civilization, vol. 2. Technology in the Twentieth Century (1967)
Archaeological ages as technological stages
- V G Childe
Childe, V.G.: Archaeological ages as technological stages.
J. Anthropol. Inst. G. B. Irel. 74, 7-24 (1944)
Fire-Making, Fuel and Lighting. A History of Technology
- H Harrison
Harrison, H.: Fire-Making, Fuel and Lighting. A History of
Technology, pp. 216-237. Oxford, Clarendon (1954)
The Life of Rekhmara: Vezîr of Upper Egypt Under Thothmes III and Amenhetep II (circa B.C. 1471-1448)
- P E Newberry
Newberry, P.E.: The Life of Rekhmara: Vezîr of Upper Egypt
Under Thothmes III and Amenhetep II (circa B.C. 1471-1448).
The Notebooks of Leonardo da Vinci
- E Mccurdy
McCurdy, E.: The Notebooks of Leonardo da Vinci, vol. 1.
Reynal & Hitchcock, New York (1938)
Experiments on the friction and abrasion of the surfaces of solidsArticleType: research-article/Full publication date: 1829)
- G Rennie
Rennie, G.: Experiments on the friction and abrasion of the
surfaces of solids. Philos. Trans. R. Soc. Lond. 119 (ArticleType:
research-article/Full publication date: 1829), 143–170 (1829).
doi:10.2307/107775
Friction and Lubrication: Determinations of the Laws and Coëfficients of Friction by New Methods and with New Apparatus
- R H Thurston
Thurston, R.H.: Friction and Lubrication: Determinations of the
Laws and Coëfficients of Friction by New Methods and with New
Apparatus. Railroad gazette (1879)
On the Motion of Bodies Affected by Friction. By the Rev. Samuel Vince, A. M. of Cambridge
- S Vince
- A Shepherd
Vince, S., Shepherd, A.: On the Motion of Bodies Affected by
Friction. By the Rev. Samuel Vince, A. M. of Cambridge;
Plumian Professor of Astronomy and Experimental Philosophy at Cambridge
Communicated by Anthony Shepherd, D. D. F. R. S. Plumian
Professor of Astronomy and Experimental Philosophy at Cambridge. Philos. Trans. R. Soc. Lond. 75 (ArticleType: researcharticle/Full publication date: 1785/), 165-189 (1785). doi:10.
2307/106753
Théorie Des Machines Simples
- C A Coulomb
Coulomb, C.A.: Théorie Des Machines Simples. Bachelier, Paris
(1821)
- A H Layard