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Cutting resistance of soft materials: Effects of blade inclination and friction
Abstract
In cutting soft elastic materials, friction is often the most relevant term of the total applied force, and techniques to minimise the required effort involve the restraint of frictional dissipation. It is well known from practical experience that cutting is made much easier if performed with a combination of slicing and pushing. A slice-push effect, known to reduce the cutting force, can be introduced by skewing the blade with respect to the travelling direction of the blade itself. The observed drop of the required force is connected to the competing dissipative contributions, with frictional dissipation being reduced at larger inclination angles. This study reports the results of several cutting tests on soft elastomeric plates, in which we have recorded the experimental force-displacement curves during the insertion of sharp stainless-steel blades. An energy-based model is employed to discern the different contributions to the measured force in the various stages of the cutting process, with particular focus on the steady state initiated after full penetration of the blade. The effects of the inclination angle of the blade are discussed with respect to the steady state force obtained from the experiments.
... Van Vliet (2014) experimentally investigated the deformation and fracture processes observed during the cutting of viscous products [9]. Spagnoli et al. (2019) compared the effects of blade inclination and friction on hard and soft polymeric materials [10]. Scientists, too, also performed a comparative study to evaluate the influence of biochemical composition and functional and rheological properties of fresh meat obtained from fish, squid, and shrimp on cutting techniques [11]. ...
... Van Vliet (2014) experimentally investigated the deformation and fracture processes observed during the cutting of viscous products [9]. Spagnoli et al. (2019) compared the effects of blade inclination and friction on hard and soft polymeric materials [10]. Scientists, too, also performed a comparative study to evaluate the influence of biochemical composition and functional and rheological properties of fresh meat obtained from fish, squid, and shrimp on cutting techniques [11]. ...
... Friction is indicated by force profiles and shear behavior. In addition, the effect of deformation of the portion should be taken into account, which is confirmed by the results of experiments performed by Spagnoli et al. (2019) [10]. For the accurate calculation of shear stress friction according to Atkins et al. (2006) [3] and Spagnoli et al. (2019) [10], it is necessary to quantify the contact surface between the blade and the food and determine how it is influenced by the geometric parameters of the knife inclination, and to determine the sliding speed of the cutting. ...
Mathematical models for predicting the resistance forces that are developed during the inclined and sliding cutting of food materials have been developed. The dependence of the actual cutting angle on the angle of inclination and sliding speed of the cutting edge at various sharpening angles have been investigated. For the inclined cutting mode, the dependence of the useful resistance force on the cutting speed has been determined at various angles of inclination of the cutting edge and designed sharpening angles. For the sliding cutting mode, the dependence of the useful resistance force on the feeding speed has been demonstrated at various sliding speed values and designed knife sharpening angles. The dependence of the transformed dimensionless sharp-ness of the knife on the angle of inclination of the cutting edge and the sliding speed has been established for different constructional sharpness values of the knife. The results of the study indicate that the useful resistance force is significantly reduced during the inclined and sliding cutting processes when compared with the normal cutting process, and a change in the pattern of fiber destruction , which significantly increases the cutting efficiency of cutting tools, is obtained.
... In an experimental study with inclined straight-edge blades, Spagnoli et al. (2019) showed that an increased slice-push angle leads to reduced cutting forces during steady-state cutting of soft solids. They present a model applying adhesive friction. ...
... The friction is indicated by the force profiles and slice behavior as discussed earlier. Furthermore, influences of the deformation of the slice as well as the food specimen should be included, which also results from the experiments performed by Spagnoli et al. (2019). Additionally, previous research suggests that a shear stress model of friction applies better to soft solids than Coulomb friction (Atkins et al., 2004;Spagnoli et al., 2019). ...
... Furthermore, influences of the deformation of the slice as well as the food specimen should be included, which also results from the experiments performed by Spagnoli et al. (2019). Additionally, previous research suggests that a shear stress model of friction applies better to soft solids than Coulomb friction (Atkins et al., 2004;Spagnoli et al., 2019). Therefore, further research might quantify the contact surface between blade and food and determine how it is influenced by the geometric parameters of the blade, as well as cutting speeds. ...
Industrial slicing is a common high-speed food cutting process to produce consumer-ready slices. High productivity is achieved by using curved blades that allow a continuous process. However, experimental research to validate theoretical models on the complex interactions of food and blade, which determine the cutting forces, are missing. An industrial slicing machine has been equipped with load cells to measure force profiles during slicing. The profiles of two types of processed meat at rotational blade speeds of 600 rpm and 1200 rpm are analyzed. Although both foods show a large variance in the force profiles, a velocity dependence of the forces can be shown. The otherwise irregular curvatures point to strong contributions of friction and deformation. We compare the measurement data with a fracture energy model of cutting forces for industrial slicing applications. The results show, that the model is inadequate. We conclude that the model would improve by including deformation and friction in the model.
... Specific research includes fish feature recognition, fillet defect detection, cutting parameters determination, and cutting process control. During the cutting process of fish flesh, the flesh will undergo changes of state from elastic deformation to plastic deformation and then to fracture (Spagnoli et al., 2019). The shorter the elastic and plastic deformation phase, the higher the quality of the cut. ...
... The slice-to-push ratio is the ratio of the tangential velocity to the normal velocity, in which increasing values reduce the cutting force. This finding is consistent with the study of Bremer and Matthiesen (2021) and Spagnoli et al. (2019). Moreover, the influence of the food properties on the cutting performance should also be considered. ...
Fish processing is an indispensable part of fish food production. It mainly involves de-heading, gutting, filleting, skinning, trimming, and slicing, with the cutting operations holding a critical role. Unfortunately, inefficiency, low quality, and poor safety are the primary problems facing the fish processing industry today, dramatically hindering the automation and intelligence of fish processing. Consequently, it is vital to develop intelligent cutting in current fish processing in an efficient, high-quality, and safe manner. This review summarizes the main cutting techniques for fish processing. The critical techniques to achieve intelligent cutting in fish processing from imaging, image processing, and modeling dimensions are outlined, with their applications in practical fish processing. Fish characteristics, cutting mechanisms, and cutting process control are emphasized. In addition, Industry 4.0 technologies, especially the Internet of Things (IoT), big data analytics, and digital twins (DT), are emphasized. Finally, challenges and future work are highlighted, which will serve as references for subsequent researchers and enterprises engaged in this field to promote the automation and intelligence of fish processing production, ultimately realizing the high-efficiency, high-quality, and safe production of fish food products.
... For stiff foods, the cutting force is large, and the deformation and fracture stages will occur within a short time. In summary, the consumed energy of an entire cutting can be expressed by strain energy, fracture energy, and frictional dissipation (King, 1999a;Spagnoli et al., 2019). ...
... Through the cutting experiments of the rotational blade in processing boiled sausage and cooked ham, Bremer and Matthiesen (2021) indicated that the higher ξ could reduce cutting force effectively. However, a large ξ is not encouraged due to the additional friction and compression phenomenon that will deteriorate the cutting performance (Spagnoli et al., 2019). ...
Cutting is an imperative operation in the food‐manufacturing factory, separating food into a predefined geometry. A broad range of solid foods, with various components, textures, and structures, pose enormous challenges to conventional cutting strategies. Additionally, the cutting performance is significantly impacted by the processing parameters, wherein trial‐and‐error or empirical methods are often used to select the parameters in source‐wasting and time‐consuming ways. Hence, there is a need to accelerate the development of advanced cutting techniques and novel modeling approaches in the food‐manufacturing industry. Recently, advanced cutting techniques (ultrasonic vibration‐assisted [UVA], laser, and waterjet cutting) are seen to be superior in processing foods of various textures, with the advantages of high cutting quality, low contamination, and easy operation. Compared with conventional cutting, advanced cutting techniques can dramatically reduce cutting force and energy consumption, resulting in high efficiency, energy‐and‐source saving, and low carbon footprint. Additionally, the finite element (FE) model does simulate the cutting process well, and artificial intelligence (AI) technology is competent to optimize the cutting parameters. This review is perhaps the first one focusing on the advanced cutting techniques applied in the food industry, serving as a summary of the cutting mechanisms, critical influence factors, and applications of conventional and advanced cutting techniques including UVA, laser, and waterjet cutting. In addition, the modeling approaches with respect to FE and AI models are emphasized. Finally, the challenges and future perspectives of advanced cutting techniques combined with modeling approaches are highlighted, and those approaches are promising in the future intelligent food‐manufacturing industry.
Practical Application
The review clearly demonstrates that advanced cutting techniques as having advantages such as high efficiency, energy‐and‐source saving, and low damages, thus exhibiting great potential in processing food of various textures with high cutting quality, low contamination, and easy operation. Additionally, the FE model does simulate the cutting process well and AI is competent in optimizing the cutting parameters, which possesses great potential in providing comprehensive cutting information and selecting the optimal combination of cutting parameters.
... 35 For instance, it was observed that the fracture is altered by friction and result in higher cutting forces. 10,36 Furthermore, rate-dependent effects have been analysed in terms of the insertion velocity 17,37,38 and correlated to tissue damage in biological tissues. 39 Overall, puncturing soft solids involves crack propagation at large strains, interaction with the geometry and mechanical properties of the penetrating tool, effects of the insertion technique and of friction exerted against the target material. ...
The integrity of soft materials against puncturing is of great relevance for their performance because of the high sensitivity to local rupture caused by rigid sharp objects. In this work, the mechanics of puncturing is studied with respect to a sharp-tipped rigid needle with a circular cross section, penetrating a soft target solid. The failure mode associated with puncturing is identified as a mode-I crack propagation, which is analytically described by a two-dimensional model of the target solid, taking place in a plane normal to the penetration axis. It is shown that the force required for the onset of needle penetration is dependent on two energy contributions, that are, the strain energy stored in the target solid and the energy consumed in crack propagation. More specifically, the force is found to be dependent on the fracture toughness of the material, its stiffness and the sharpness of the penetrating tool. The reference case within the framework of small strain elasticity is first investigated, leading to closed-form toughness parameters related to classical linear elastic fracture mechanics. Then, nonlinear finite element analyses for an Ogden hyperelastic material are presented. Supporting the proposed theoretical framework, a series of puncturing experiments on two commercial silicones is presented. The combined experimental-theoretical findings suggest a simple, yet reliable tool to easily handle and assess safety against puncturing of soft materials.
... In the other group tests, the c was taken as 1 mm. The β value determines the strength of the blade, and when the β is small, chipping is very likely to occur (Spagnoli et al. 2019;Kuhn et al. 2020). Therefore, the β value was set to 20° to 35°, and the level was set at 5° intervals. ...
Caragana korshinskii (C.K.) flat stubble residue is an abundant biomass energy source in China. Because branch cutting is closely related to the harvesting of forest biomass, it is practical for forestry production and ecological development to investigate the effects of cutting parameters on the peak cutting force and cutting energy consumption of C.K. branches. In this study, the effect of cutting parameters on the peak cutting force and cutting power consumption of branches was investigated by single-factor and multi-factor tests using an independently developed reciprocating cutting test bench, and an optimization model was established. The interaction term of average cutting speed and tool cutting edge inclination angle significantly affected the peak cutting force, while the interaction term of cutting clearance and wedge angle had a significant effect on the cutting energy consumption. The optimal combination of cutting parameters was an average cutting speed of 0.5 m/s, cutting clearance of 1.4 mm, wedge angle of 25°, and tool cutting edge inclination angle of 20°. With this combination of parameters, the corresponding peak cutting force was 644.38 N, and the cutting energy consumption was 5.90 J, which was less than 5% relative error between each performance index and the theoretical optimized value.
... [40,41]. The extent of deformation and the initial failure force depend on the material's elastic modulus and the knife's sharpness [42]. Since a blunt knife requires a higher force than a sharp one [43], the slope of the contact force at the initial stage of puncture is low due to the sharp tip of the knife. ...
In this paper, the puncture resistance of carbon fiber reinforced polymer (CFRP) with different thicknesses under various puncture energy was studied by in-situ observation. The puncture failure process of CFRP was analyzed using a high-speed camera and thin-film pressure sensor in terms of damage image and local pressure change. The experimental results show that the puncture threshold load (PTL) representing material penetration is usually located at the initial loss position of material stiffness. The penetration load can be divided into linear growth and delamination failure zones. Image localization was used to mark the puncture feature points on the puncture force-displacement curve to help characterize the puncture failure process. The theoretical equations of puncture force and displacement before material penetration are proposed and verified by introducing yield stress and friction force, and the correlation between the material thickness and the puncture resistance was proved. In addition, the failure modes and fracture morphology of CFRP after puncture are analyzed and summarized. After puncture impact, fiber fracture, pull out and slip deformation under the action of tensile force and cutting force, and matrix fracture and peel damage. The increase of impact energy leads to a broader range of impact damage but does not change the failure modes.
... The shape and size of the wound directly affected the healing effect of the tissue. Figure 8(e) showed the shape and size of the soft tissue Bevel angle (+) Positive [53] (+) Positive [93] Inclination angle (−) Negative [11,59,[93][94][95] (+) Positive [96][97][98] Normal rake angle (−) Negative [58,59] Edge number (+) Positive [58] Tissue characteristics Material (Y) Relevant [99] (X) Irrelevant [96,100] (Y) Relevant [101] Experimental pretreatment (Y) Relevant [102] (X) Irrelevant [103] Holding force (−) Negative [11] (−) Negative [11] Cutting method Velocity (−) Negative [11,98] after puncture [44]. Generally, the smaller the size of the crack, the faster the healing. ...
Biological soft tissues manipulation, including conventional (mechanical) and nonconventional (laser, waterjet and ultrasonic) processes, is critically required in most surgical innervations. However, the soft tissues, with their nature of anisotropic and viscoelastic mechanical properties, and high biological and heat sensitivities, are difficult to manipulated. Moreover, the mechanical and thermal induced damage on the surface and surrounding tissue during the surgery can impair the proliferative phase of healing. Thus, understanding the manipulation mechanism and the resulted surface damage is of importance to the community. In recent years, more and more scholars carried out researches on soft biological tissue cutting in order to improve the cutting performance of surgical instruments and reduce the surgery induced tissue damage. However, there is a lack of compressive review that focused on the recent advances in soft biological tissue manipulating technologies. Hence, this review paper attempts to provide an informative literature survey of the state-of-the-art of soft tissue manipulation processes in surgery. This is achieved by exploring and recollecting the different soft tissue manipulation techniques currently used, including mechanical, laser, waterjet and ultrasonic cutting and advanced anastomosis and reconstruction processes, with highlighting their governing removal mechanisms as well as the surface and subsurface damages.
... В основополагающих работах [5,6] раскрыты основные особенности механической обработки твердых материалов в пищевой отрасли. Публикации [7,8] освещают результаты, достигнутые при исследовании реактивных сил и сил трения, возникающих при взаимодействии вязкоупругих сред и режущего органа. Влияние режимов резания и разрушения материалов на качество готовой продукции прослеживается в работах [9,10]. ...
The relevance of mathematical modeling for the processes of food materials cutting by a circular knife has been shown. The muscle tissue of the raw material has been described by the Maxwell-Thomson viscoelastic rheological model. The process of product cutting by a circular knife has been investigated. The formulation and solution of the problem of mathematical modeling for the resistance forces during the movement of the circular knife in the material have been carried out. A differential equation for the line of immersion of an elementary knife into the material in polar coordinates has been proposed and solved. An expression for the actual cutting angle of the circular knife has been obtained. The scalar fields of variation of the actual cutting angle, as well as the sliding coefficient of an elementary knife, depending on its angular coordinate has been investigated. On the basis of expressions for determining the lines of immersion for
n
elementary knife into the material, mathematical models have been developed for calculating the harmful resistance forces
on the circular knife, as well as their moments relative to the axis of rotation of the knife. Diagrams of the vertical and
horizontal components of the dimensionless resistance force of the elementary circular knife form, as well as diagram of the
resulting resistance force for the elementary circular knife form its moment have been constructed. The ranges of the most
energetically favorable cutting angles, which are essential for resource saving in the design of cutting devices for processing
machines, have been determined. With the values of the measure of elasticity of the material 3; 10; 20; 30, the values of the maxima of the specified dimensionless force are 9.55; 10.28; 11.37; 12.45, and the values of the maxima of the dimensionless moment are 5.66; 5.97; 6.42; 6.88, respectively. With the values of the ratio of the tangent of the angle of the knife sharpening to its thickness 0.01; 0.3; 0.7; 1.0, the values of the maxima of the resulting dimensionless force of the circular knife resistance are 9.28; 10.54; 12.27; 13.55, and the values of the maxima of the dimensionless moment are 5.55; 6.07; 6.81; 7.37, respectively.
... Some studies introduced friction as the major force component in needle-tissue interaction [71][72][73]. Spagnoli et al. studied the fracture mechanics in cutting polymeric materials using a sharp thin blade. Their analysis of their experimental data indicated the strain energy contribution in floppy materials is one order of magnitude lower than frictional dissipation [73]. ...
Medical needles have shown an appreciable contribution to the development of novel medical devices and surgical technologies. A better understanding of needle-skin interactions can advance the design of medical needles, modern surgical robots, and haptic devices. This study employed finite element (FE) modelling to explore the effect of different mechanical and geometrical parameters on the needle's force-displacement relationship, the required force for the skin puncture, and generated mechanical stress around the cutting zone. To this end, we established a cohesive FE model, and identified its parameters by a three-stage parameter identification algorithm to closely replicate the experimental data of needle insertion into the human skin available in the literature. We showed that a bilinear cohesive model with initial stiffness of 5000 MPa/mm, failure traction of 2 MPa, and separation length of 1.6 mm can lead to a model that can closely replicate experimental results. The FE results indicated that while the coefficient of friction between the needle and skin substantially changes the needle reaction force, the insertion velocity does not have a noticeable effect on the reaction force. Regarding the geometrical parameters, needle cutting angle is the prominent factor in terms of stress fields generated in the skin tissue. However, the needle diameter is more influential on the needle reaction force. We also presented an energy study on the frictional dissipation, damage dissipation, and strain energy throughout the insertion process.
... This model was used to predict the force and torque generated from slicing thin flexible materials with negligible deformations [16]. Reduction in frictional force during soft material cutting was found to be related to a large inclination angle of the blade [17]. In paper industry, fracture mechanics is applied to model crack propagation during the slicing of a paper stack and the effect of friction on facilitating the process [18], [19]. ...
... Atkins (2006Atkins ( , 2015 performed a detailed theoretical and experimental study on the cutting processes of various food materials, investigated the optimal sharpening angles of cutting tools, and summarized the results of the study in the largest foreign monograph on the topic of cutting food products. Spagnoli et al. (2016Spagnoli et al. ( , 2019 studied the regularities of the cutting process in viscoelastic materials, conducted a comparative analysis of the cutting forces based on the operating parameters, and analyzed the friction forces. Voloski et al. (2016) researched the influence of cutting and deboning operations on the microbiological quality and shelf life of buffalo meat. ...
This study analyzed the relevance of the fish cutting process and modeled the forces of useful and harmful resistances. The muscle tissue of fish was described by the Maxwell–Thomson rheological model. The process of cutting of tuna muscle tissue with a wire knife and a flat-back single-edged knife was experimentally researched. The
obtained test results were compared with the results of theoretical calculations based on mathematical models. The quantitative dependence of the useful resistance force on the cutting speed was established, and the dependence of this force on the sharpness of the cutting tool was determined. The influence of temperature and
measure of elasticity of the fish muscle tissue on the value of the useful resistance force was studied, while the dependence of the harmful resistance force on the movement speed of a flat-back knife was established. In addition, the influence of the thickness of a flat-back knife on the value of the harmful resistance force was investigated, and the effect of temperature and rheological characteristics of the fish muscle tissue on the value of the harmful resistance force was determined. Furthermore, the empirical dependences of the useful and harmful resistance forces on
the process parameters were analyzed, and the values of the coefficients of the empirical equations and those of the coefficients of determination were calculated. The tests carried out confirmed the validity of the mathematical models and the assumptions made within the accuracy of the experimental data and the range of changes in the rheological characteristics of tuna.
... The analyses of fracture described in this work applies to wire cutting only when the first condition is met. With this assumption, we have neglected the role of friction, which is known to affect the fracture toughness of a material (Spagnoli et al., 2019). Furthermore, we have also considered that the criterion derived in an elastic situation is extended to the poro-hyperelastic material. ...
Brain tissue is a heterogeneous material, constituted by a soft matrix filled with cerebrospinal fluid. The interactions between, and the complexity of each of these components are responsible for the non-linear rate-dependent behaviour that characterizes what is one of the most complex tissue in nature. Here, we investigate the influence of the cutting rate on the fracture properties of brain, through wire cutting experiments. We also present a model for the rate-dependent behaviour of fracture propagation in soft materials, which comprises the effects of fluid interaction through a poro-hyperelastic formulation. The method is developed in the framework of finite strain continuum mechanics, implemented in a commercial finite element code, and applied to the case of an edge-crack remotely loaded by a controlled displacement. Experimental and numerical results both show a toughening effect with increasing rates, which is linked to the energy dissipated by the fluid-solid interactions in the process zone ahead of the crack.
... Mathematical modeling and experimental study of the friction process of food materials on a rough surface is a current scientific direction in engineering. Spagnoli et al. (2019) have investigated the effect of friction and the blade immersion depth on the resistance force when cutting viscoelastic materials. Also Spagnoli et al. (2018) have analyzed the laws of the process of destruction of a viscoelastic material with friction, have analyzed the effect of sharpness of the cutting unit on the distribution of stresses in the material. ...
The process of friction when cutting food materials has been investigated theoretically. The muscle tissue of the raw material has been described by the Maxwell-Thomson rheological model. When choosing an analytical description of a regular microrelief of food processing equipment knives, taking into account technological formative factors, a physical-technological theory of surface roughness has been used. A mathematical description of the profile of the knife rough surface in the form of a dimensionless periodic one-parameter function has been obtained. By solving the differential equation of viscoelastic material state in a dimensionless form, the law of distribution of dimensionless normal contact pressures over the microprotrusions of the edge rough surface has been obtained. An expression for the dimensionless deformation friction force has been obtained. It is established that at speeds tending to zero or infinity, this force tends to zero. The magnitude of the force increases monotonically with the increase in the measure of the material elasticity and the increase in the dimensionless length of the knife edge. The dimensionless width of the contact area of microprotrusion is monotonously depends on the measure of material elasticity and non-monotonously depends on the dimensionless sliding speed with a pronounced minimum.
... It is difficult to describe the cutting process analytically because of the time-varying nonlinear dynamics [6]. Some attempts have been made [7][8][9], but the effect is not very satisfactory. Gemici et al. [10] propose a method to model and learn physical properties (e.g., hardness, elasticity, adhesiveness) of the deformable objects based on haptic sensory, which can be used to cut and separate different kinds of food (e.g., tomatoes, bread, tofu). ...
Automatic cutting is an essential task in the field of robot-assisted surgery (RAS). In this paper, a novel vision-based cutting control algorithm is proposed to cut a deformable object along the pre-designed path with specified cutting depth. The method to model soft tissue considering viscoelasticity is developed, and unknown parameters of the deformation model are estimated online by introducing the visual feedback of feature points. According to the position of trajectory points after deformation, we illustrate how to generate the desired pose of the knife in real-time to minimize the object's deformation. In this way, the cutting task has recast into a visual tracking problem, that is, controlling the knife's projection to track a target surface in the image plane. To cope with this problem, we choose two parallel linear segments (including the direction and the length) extracted from the edge of the knife's projection as image features, which has a one-to-one mapping with the pose of the knife, and design a dynamic-based controller based on the combined feature. The asymptotic stability of the closed-loop system is proved by Lyapunov analysis. A series of experiments using different materials are conducted to validate the effectiveness of the proposed cutting control algorithm.
... В статье [2] исследовано резание пищевых сред при больших скоростях и проанализированы реактивные силы сопротивления материала сжатию и изгибу. В работе [3] найдены зависимости затрат энергии и качества поверхности среза от угла заточки лезвия. В исследовании [4] разработан конечно-элементный подход к анализу процесса резания вязкоупругого пищевого материала и рассмотрены режущие органы с различной геометрией. ...
The relevance of the knife profile optimization to ensure resource saving during fish cutting has been shown. The mechanical behavior of the muscle tissue of the raw material corresponds to the Maxwell-Thomson rheological model and by the Kelvin differential equation is described. When modeling the shape of a knife curved facet, a third degree polynomial has been used. The rough surface of the facets has been approximately represented as a periodic function with one harmonic. Based on the expression for the dimensionless contact pressure, the dimensionless deformation friction force has been determined. As a result of a numerical solution of the optimization problem, the values of the optimal half angle of knife sharpening have been obtained, at which the minimum energy consumption for the deformation component of friction when the knife moves in the muscle tissue of the fish is provided. The dependences of the indicated optimum angle on the dimensionless cutting speed, the angle of mating of the edges, the dimensionless half thickness of the knife, and the measure of elasticity of the fish have been established. The optimal angle substantially depends on the dimensionless half thickness of the knife and the angle of conjugation of the edges, and also monotonously depends on the dimensionless speed with a pronounced minimum. It was determined that when cutting fish with a knife with a minimum mating angle of the edges, the optimal half sharpening angle is in the range of 25-28 degrees, which is about 3-5 degrees more than the half sharpening angle, optimal according to the criterion of the minimum shape resistance force.
Recycling end-of-life tires (ELTs) poses an enormous challenge in waste management, as tires are not biodegradable and, if not correctly disposed of, can cause problems for human health and the environment. The transportation of ELTs from waste collection points to recycling facilities is one of the biggest problems in the recycling process, as a whole piece of ELT takes a large volume, resulting in high costs and transport delays. Therefore, a possible solution is a pre-cutting process at collection points to reduce volume and facilitate transport. Cutting processes play an essential role; hence, the devices used in this operation must be efficient to keep a minimum energy consumption. This study addresses the numerical evaluation of several blade profiles to find the most efficient regarding the force and work done for the cutting of tire tread. The numerical results regarding the performance of the profiles were validated experimentally confirming that the most efficient geometry between the evaluated correspond to a hollow profile.
Cutting of soft materials is a complex problem, which is still not well understood at the fundamental level, especially for soft materials. The cutting process we consider is slicing, which starts with indentation, followed by sliding of a knife on the material to be cut. Here, we describe cutting experiments on PDMS elastomers with three different moduli. Our experiments reveal typical stages of this cutting process, starting with indentation and ending at steady state cutting. The process starts with a pre-cutting phase in which the blade does not slip grossly relative to the solid to be cut, and deformation is mostly elastic. Slip of the blade initiates suddenly and is often accompanied by initiation of cutting. Cutting is relatively smooth in the next stage, which requires a continuous increase in shear force. For soft PDMS, this smooth cutting stage is followed by one in which folds or creases form on the cutting surface. The corresponding shear force response is no longer smooth as “steady” sliding occurs in a stick–slip fashion with oscillatory forces. The average shear force reaches a plateau and no longer increases with shear displacement. Experimental observations of the various cutting stages are interpreted quantitatively.
Показана актуальность разработки комплекса математических моделей, позволяющих рассчитать удельную работу при резании рыбы с целью определения коэффициента полезного действия элементарного ножа. Получено выражение для вычисления безразмерной удельной работы разрушения мышечных волокон. Сформулирована модель расчета указанной величины при упругом вырыве волокна с большой скоростью деформирования. Определена удельная работа вязкого разрыва при большой скорости резания. Получена математическая модель, позволяющая вычислить безразмерную удельную работу, необходимую на упругий вырыв волокна при не очень больших скоростях. Рассчитана безразмерная удельная работа вязкого разрыва волокна при не очень малых скоростях. Численным методом определены зависимости безразмерных удельных работ упругого вырыва и вязкого разрыва от безразмерной скорости деформирования. Установлено, что с ростом безразмерной скорости происходит нелинейное увеличение безразмерной удельной работы вязкого разрыва. При достижении максимального значения безразмерной удельной работы разрушения, соответствующего характерной безразмерной скорости, происходит смена вязкого разрыва на упругий вырыв волокна. При этом с дальнейшим ростом безразмерной скорости безразмерная удельная работа упругого разрушения изменяется немонотонно. При мере эластичности материала 3; 5; 8; 12 максимальные значения удельной работы разрушения составляют 0,0694; 0,0417; 0,0262; 0,0173 и достигаются при характерных безразмерных скоростях 0,0982; 0,0549; 0,0331; 0,0218, при этом минимальные значения безразмерной удельной работы упругого вырыва составляют 0,05761; 0,02714; 0,01279; 0,00641 и достигаются при безразмерной скорости 0,248; 0,217; 0,187; 0,161 соответственно. С увеличением меры эластичности материала максимальная безразмерная удельная работа разрушения и минимальная работа упругого вырыва существенно снижаются. Также с ростом меры эластичности уменьшается значение характерной безразмерной скорости, при которой вязкий разрыв сменяется упругим вырывом.
Based on the results of experimental studies of the experimental root crop grinder, the dependence of the cutting force during grinding of root crop on the constructive and regime factors of the grinder was determined: α c - chevron angle, deg., α i - angle of installation of knives in the knife wall, deg., v k.w. – speed of the knife wall, m/s, h w – height of the knife wave, mm in the form of a regression equation. According to this equation, the dependencies of the influence of factors on the value of the cutting force are constructed. As a result of the processing of graphic material, the studied factors are determined at the optimal level: α c = 48...49 deg., α i = 26...27 deg., v k.w. = 0,92...0.94 m/s and h w = 1...2.
The effectiveness of slicing in cutting soft solids (i.e., transverse motion along the blade) is natural to anyone with even the slightest kitchen experience, but the underlying mechanism remains intriguing. This study seeks to unveil the mystic role of slicing by looking into the effect of friction in cutting soft materials. With the increase of indentation depth, the nonlinearity of the large deformation in the superficial layer diverts the lateral stress from the compression of the classic linear elastic solution and introduces a tension that accounts for the ultimate fracture. However, when friction is present between the blade and material, there is always a finite no-slip region on the contact surface, under which stress remains compressive in all directions. The slicing motion of the blade, on the other hand, directs the friction toward the horizontal direction, thus minimizing its contribution in resisting the cutting process in the vertical plane, and enabling a clean cut. Through a numerical model of frictional contact between a cutting wire and a hyperelastic solid, we show that the slicing action diverts the friction force, enables sliding, and facilitates the development of local tension. Without a trustworthy stress-based fracture criterion for soft solids, we then study the energetics of the cutting process. By introducing a small pre-existing crack underneath the blade, we compute the energy landscape of the system and show that the friction reduction in the vertical plane greatly decreases the energy barrier of crack opening and thus promotes cutting.
Показана актуальность математического моделирования режимов разру-шения волокон мышечной ткани при резании рыбы. Мышечная ткань сырья опи-сана вязкоупругой реологической моделью Максвелла-Томсона. Определены два режима разрушения волокна материала – вязкий разрыв и упругий вырыв. Вязкий разрыв обеспечивает высокое качество поверхности среза. Получен комплекс ма-тематических моделей, позволяющих рассчитать интервалы времени наступления вязкого разрыва и упругого вырыва в зависимости от структурно-реологических свойств мышечной ткани и скорости ее деформирования режущим органом рыбоперерабатывающего оборудования. Разработаны модели, описывающие режим разрушения волокон, который характеризуется внезапно возникшей постоянной деформацией материала. Результаты моделирования показывают, что при увеличении безразмерной скорости качество поверхности среза сначала повышается за счет сокращения времени вязкого разрыва, а затем, при достижении характерного значения и дальнейшем росте скорости, ухудшается вследствие наступления упругого вырыва волокон. Установлено, что к снижению качества поверхности среза приводят увеличение меры эластичности материала, рост безразмерной скорости резания, а также изменение безразмерного критерия прочности материала. Показано, что с ростом величины внезапно возникшей относительной деформации интервал времени вязкого разрыва немонотонно снижается и стремится к нулю. Определено, что с увеличением мгновенного и запаздывающего модулей упругости материала интервал времени наступления вязкого разрыва существенно сокращается. С повышением коэффициента динамической вязкости мышечной ткани вязкий разрыв наступает позже. При значениях критерия прочности, равного 3, длительного модуля упругости 63158 Н/м2, меры эластичности 3; 5; 8; 12 значения характерной безразмерной скорости составляют 0,095; 0,055; 0,032; 0,021, при этом показатели безразмерного интервала времени, соответствующего смене режима разрушения с вязкого разрыва на упругий вырыв, составляют 10; 20; 30; 45 соответственно.
Показана необходимость разработки математического описания профилей ножей для резания рыбы. Проанализированы методы интерполяции траекторий рабочих органов в современном оборудовании с ЧПУ. С учетом технологии изготовления ножей для аналитического моделирования их профилей предлагается использовать полином третьего порядка. Разработана математическая модель, задающая форму передней криволинейной грани. Геометрия ножа характеризуется половинным ножом заточки, углом сопряжения граней, высотой фаски и половинной толщиной лезвия. При изменении параметров модели получены формы ножей с вогнутыми, выпуклыми, вогнуто-выпуклыми и выпукло-вогнутыми фасками. Модельная функция является непрерывной до второй производной включительно, за счет чего обеспечивается отсутствие на профиле уступов, изломов и скачков в кривизне. На участке от режущей кромки до боковой грани ножа функция имеет не более одной точки перегиба, что обеспечивает отсутствие местной волнистости на фаске. Определены условия монотонности на участке от острия ножа до точки перехода в боковую грань. Получено выражение для расчета координат точки перегиба указанной функции. Разработанное математическое описание профиля ножа является основой для постановки оптимизационных задач с целью определения наилучшей геометрии ножа с точки зрения ресурсосбережения. Наличие математической модели фаски позволяет определить оптимальный половинный угол заточки по критерию минимальной силы сопротивления резанию. Создана возможность рассчитать оптимальный половинный угол заточки, а также оптимальную половинную толщину ножа по критерию минимальной деформационной силы трения. Предложенный подход используется при постановке и решении вариационных задач по определению вида аналитических функций, задающих оптимальные профили режущих органов с минимальными вредными сопротивлениями.
Обсуждается вариант минимизации функций и функционалов, дифференцируемых лишь в слабом смысле, методом градиентного спуска, способ вычисления направления спуска, ε-допустимого направления (попутно предлагается про-стой алгоритм решения однородных линейных неравенств). Приведены примеры конкретных вычислений для функций и функционалов. Показано, что разумная стратегия выбора последовательности ε → 0 позволяет получать приемлемые ре-зультаты.
The method of acquisition, analyzation and evaluation of cutting characteristics was developed on a hollow rectangular tube-like structure made of an electrical insulating paper (so called the slot liner in the motors of electric vehicles). The slot liner was cut by a steel disk blade. The cutting force was measured by the dynamometer, to evaluate the specific energy of the cutting: Cp, and the ratio of tangential and normal component of the force: μ, as the indicators of the cutting quality. Parameter estimations were applied using computer simulations of the slot liner in evaluating Cp and μ, with different cutting history (cutting length) of the blades. The difference of the cutting quality was found in variation of μ. Then filling up the hollows using the solid type jig and observations of by high-speed camera were helpful for eliminating the effect of the deformation.
The necessity of computation the minimum permissible knife sharpness during
food materials cutting has been shown. Based on the expression for the useful resistance force, models for determining the dimensional and dimensionless minimum permissible sharpness at which the cutting edge strength is preserved during the destruction of the product structural filaments have been proposed. The dependences of dimensionless sharpness on the structural and rheological properties of the material, the structural and strength characteristics of the knife, the angle of lateral feed and cutting speed have been established. The minimum permissible sharpness of the blade monotonically depends on the angle of knife sharpening at side feed angles of less than 15 deg, which demonstrates the existence of the best angle of sharpening at which the sharpness is minimal. It is shown that with an increase in the lateral feed angle and cutting speed, the dimensionless sharpness of the blade monotonously increases.
The paper shows the necessity of developing a mathematical description of the profiles of knives for cutting fish. The methods of interpolation of the working tools tra-jectories in modern equipment with CNC have been analyzed. Taking into account the technology of manufacturing knives for analytical modeling of their profiles, it is pro-posed to use a third-order polynomial. A mathematical model defining the shape of the front curvilinear edge has been developed. The knife geometry is characterized by a half angle, a mating angle of the edges, the height of the chamfer and half-thickness of the blade. By changing the model parameters, the shapes of knives with concave, convex, concave-convex and convex-concave chamfers have been obtained. The model function is continuous up to and including the second derivative, which ensures the absence of ledges, kinks, and jumps in the curvature on the profile. In the section from the cutting edge to the lateral edge of the knife, the function has no more than one inflection point, which ensures the absence of local waviness on the chamfer. The conditions of monoto-ny in the section from the knife edge to the transition point to the lateral edge have been determined.
An expression for calculating the coordinates of the inflection point of the speci-fied function has been obtained. The developed mathematical description of the knife profile is the basis for setting optimization problems in order to determine the best knife geometry from the point of view of resource conservation. The presence of a mathemat-ical model of the chamfer allows you to determine the optimal half angle of grinding according to the criterion of the minimum force of resistance to cutting. The opportunity to calculate the optimal half angle of sharpening, as well as the optimal half thickness of the knife, according to the criterion of the minimum deformation friction force, has been created. The proposed approach is used in the formulation and solution of variational problems to determine the type of analytical functions that determine the optimal pro-files of cutting tools with minimal harmful resistances.
The paper shows the necessity of developing a mathematical description of the profiles of knives for cutting fish. The methods of interpolation of the working tools trajectories in modern equipment with CNC have been analyzed. Taking into account the technology of manufacturing knives for analytical modeling of their profiles, it is pro-posed to use a third-order polynomial. A mathematical model defining the shape of theThe paper shows the necessity of developing a mathematical description of the profiles of knives for cutting fish. The methods of interpolation of the working tools tra-jectories in modern equipment with CNC have been analyzed. Taking into account the technology of manufacturing knives for analytical modeling of their profiles, it is pro-posed to use a third-order polynomial. A mathematical model defining the shape of the
The relevance of the development of a calculation method for determining the deformation component of the friction coefficient when cutting fish has been shown. The muscle tissue of the raw material has been described by the Maxwell-Thomson viscoelastic rheological model. The shape of the rough surface of the knife has been described by a periodic one-parameter function containing one harmonic. Based on the models for the deformation friction force and the force of normal contact pressure on the front inclined edge, an expression for the deformation component of the friction coefficient, as well as its reduced value, has been obtained. The deformation component of this coefficient and its reduced value are non-monotonic functions of the dimensionless cutting speed. At cutting speeds that tend to zero or infinity, this coefficient tends to zero, which corresponds to the solution of the problem for an absolutely elastic material. For a given dimensionless velocity, the deformation component of the friction coefficient increases monotonically with an increase in the measure of elasticity and a dimensionless half thickness of the knife, and at certain values of the dimensionless velocity there are pronounced maxima. With the values of the elasticity measure 5; dimensionless half the knife thickness 50; 100; 150; 200, values of the maxima of the deformation component of the friction coefficient are 0.00426; 0.00851; 0.01277; 0.01703, respectively. At values of the dimensionless half thickness of the knife 100; elasticity measures 2; 5; 8; 12, values of the maxima of this component are 0.00485; 0.00851; 0.0107; 0.00125, respectively. The simulation results show that the dependence of the deformation component of the friction coefficient on the angle of sharpening the knife is not significant. The development of mathematical models for calculating the deformation component of the friction coefficient creates a practical basis for optimizing the knife geometry according to the criterion of minimum cutting resistance taking into account parameters of various scales: the macrogeometric shape of the cutting unit and the microgeometric roughness of its surface.
The relevance of researching the process of friction when cutting fish has been shown. The fish muscular tissue has been described by a Maxwell-Thomson rheological model. When choosing an analytical description of a regular microrelief of fish-processing equipment knives, taking into account technological formative factors, a physical-technological theory of surface roughness have been used. A mathematical description of the profile of the knife rough surface in the form of a dimensionless periodic one-parameter function has been obtained. By solving the differential equation of viscoelastic material state in a dimensionless form, law of distribution of dimensionless normal contact pressures over the microprotrusions of the edge rough surface has been obtained. On the basis of the energy approach, an expression for the dimensionless deformation friction force, which includes the shape parameter of the roughness, has been obtained. It is established that at speeds tending to zero or infinity, this force tends to zero. The force value increases monotonically with increasing measure of the material elasticity and increasing the dimensionless length of the knife face. At a low sliding speed, the dependence of the friction force on the shape parameter is non-monotonic. When a certain value of speed is reached, the indicated force decreases monotonically non-linearly with a decrease in the fill factor of the microprotrusion. The dimensionless width of the irregularities contact area monotonously depends on the measure of material elasticity and non-monotonously depends on the dimensionless sliding speed with a pronounced minimum. As the shape parameter increases and the fill factor decreases, the dimensionless coordinate of the extreme contact point decreases nonlinearly. When the muscle tissue elasticity measure is 5; value of the dimensionless edge length is 50; value of the dimensionless speed is 1, values of the form parameter are 1, 2, 8, 12; then values of the dimensionless deformation force of friction are 31.6670, 33.0792, 25.0945, 21.9402, respectively; at a value of dimensionless speed of 10 – 4.3652, 4.0174, 2.7255, 2.3433, respectively.
The process of friction when cutting food materials has been investigated theoretically. The muscle tissue of the raw material has been described by the Maxwell-Thomson rheological model. For choosing an analytical description of a regular microrelief of food processing equipment knives, taking into account technological formative factors, a physical-technological theory of surface roughness has been used. A mathematical description of the knife profile rough surface in the form of a periodic function with two harmonics has been considered. By solving the differential equation of viscoelastic material state, the law of distribution of contact pressure over the microprotrusions of the edge rough surface has been obtained. An expressions for dimension and dimensionless deformation friction forces has been obtained. It is established that at speeds tending to zero or infinity, this force tends to zero. The value of the dimensionless force increases monotonically with the increase in the measure of the material elasticity and the increase in the dimensionless length of the knife edge. The dimensionless width of the contact area of the irregularities monotonously depends on the measure of material elasticity and non-monotonously depends on the dimensionless sliding speed with a pronounced minimum. The approach to research of deformation friction forces during chilled fish cutting is proposed. The viscoelastic properties of chilled fish raw material are described by a three-element rheological model. The mathematical description of the knife rough surface profile in the form of a dimensionless periodic function with three harmonics has been used. The dimensionless contact pressures over the microprotrusions of the cutting body rough surface from the material has been analyzed. A mathematical model for computation the dimensional and dimensionless friction forces has been developed. It is shown that with an increase in the processing speed, the deformation component of the friction force tends to zero. Up to a certain sliding speed there is a full contact of the material with the regularities of the edge. With an increase in elasticity and lengthening of the edge of the knife the considerated force increases monotonously. The dependence of the dimensionless width of the micro protrusions contact area with the material on elasticity is monotonic, and the dependence of the indicated dimensionless width on the dimensionless speed is nonmonotonic. With values of elasticity measure 5, dimensionless speed of 0.001; 0.03; and 0.12, maximum amplitude of contact pressure is 1.250; 1.973; and 3.635, respectively. With values of the elasticity measure 3; 5; 8; and 12, the minimum values of the dimensionless width of the contact pad are 0.615; 0.593; 0.575; and 0.563, respectively, the limit value is 0.679. With values of the elasticity measure 5; dimensionless length of the edge 10; 20; 30; and 50, values of the maximum deformation friction force are 9.345; 18.693; 28.040; and 46.724,respectively. With values of the dimensionless length of the edge 20; elasticity measures 2; 5; 8; and 12, values of maximum strength are 7.471; 18.693; 29.914; and 44.876, respectively.
The approach to research of deformation friction forces during chilled fish cutting is proposed. The viscoelastic properties of chilled fish raw material are described by a three-element rheological model. The mathematical description of the knife rough surface profile in the form of a dimensionless periodic function with three harmonics has been used. The dimensionless contact pressures over the microprotrusions of the cutting body rough surface from the material has been analyzed. A mathematical model for computation the dimensional and dimensionless friction forces has been developed. It is shown that with an increase in the processing speed, the deformation component of the friction force tends to zero. Up to a certain sliding speed there is a full contact of the material with the regularities of the edge. With an increase in elasticity and lengthening of the edge of the knife the considerated force increases monotonously. The dependence of the dimensionless width of the micro protrusions contact area with the material on elasticity is monotonic, and the dependence of the indicated dimensionless width on the dimensionless speed is nonmonotonic. With values of elasticity measure 5, dimensionless speed of 0.001; 0.03; and 0.12, maximum amplitude of contact pressure is 1.250; 1.973; and 3.635, respectively. With values of the elasticity measure 3; 5; 8; and 12, the minimum values of the dimensionless width of the contact pad are 0.615; 0.593; 0.575; and 0.563, respectively, the limit value is 0.679. With values of the elasticity measure 5; dimensionless length of the edge 10; 20; 30; and 50, values of the maximum deformation friction force are 9.345; 18.693; 28.040; and 46.724,respectively. With values of the dimensionless length of the edge 20; elasticity measures 2; 5; 8; and 12, values of maximum strength are 7.471; 18.693; 29.914; and 44.876, respectively.
Flow and fracture of some soft solids may be described by the ‘solid’ mechanical properties of elastic modulus, yield stres and fracture toughness, all being dependent on rate, temperature and environment. Other soft solids behave more like ver viscous materials. When cutting soft solids, friction is often high between the blade and the material, and cutting is mad easier when performed with a thin wire. The wire may be held taut in a frame like a fretsaw, but cutting is often done usin an initially slack wire pulled into the solid by hand or machine. For both types of material behaviours, we investigate th curved shape taken by a loaded wire, elements along which cut into the material both radially and tangentially.
For soft materials displaying solid properties, the treatment is based on the analysis of bi-directional cutting by Atkin et al. (Atkins et al. 2004 J. Mater. Sci. 39, 2761–2766), in which it was shown that the ratio ξ of tangential to radial displacements strongly influences the cutting forces. The shapes of wires of various lengths arrange as bowstrings, and the loads in the wires, are assessed against experiments on cheddar cheese. The resultant force takes minimum value for a particular length of the wire, owing to the competition between lower cutting forces, but higher frictio at large ξ and vice versa.
Passage of a wire through very viscous materials is flow at very low Reynolds number. To determine the path swept out, w make use of the property of all slender bodies of revolution in highly viscous flow, namely, that the drag exerted acros the body is approximately twice as large as along. Comparison is made with the experiments on weighted threads falling unde gravity in glycerine.
Regelation is another example of passage of a wire through a solid. The mechanism is completely different but, in the contex of the present paper, we provide in appendix A the solution for the typical hours-long school demonstration where, unlike most reported studies, non-uniform temperatur fields develop in the block of ice. Comparison is made with experiment.
An experimental campaign has been carried out with the aim of providing an insight into the fracture processes occurring during the cutting of different types of polymers, with features ranging from typically brittle to soft hyperelastic behaviour. The steady state of cutting is investigated using a sharp thin blade, and tracking the insertion force versus the penetration displacement. For soft, highly-deformable polymers, the influence of large deformations at the crack tip is also taken into account, through full-field finite strain maps obtained by means of digital image correlation. In brittle polymers, the influence of the cutting tool sharpness is discussed with respect to the onset of crack propagation, through a comparison with a simplified analytical model, and numerical finite element analyses. The results suggest that the propagation of the cut clearly depends on the tool sharpness, and for a class of brittle polymers it appears that this may happen as a stable fracture process, with the distance between the blade and the crack tip remaining constant during propagation. On the contrary, soft polymers appear to be much less sensible to the tool profile, and it is the large deformation that ultimately determines the fracture behaviour when the crack tip is reached by the blade.
It is a well known phenomenon that cutting materials with a slicing motion is much easier than cutting by simply pushing the knife down into the material. Energy-based analyses proof that slice-push cutting reduces the overall cutting forces with an increasing slicing motion. In this investigation, a model describing the cutting of a thin and planar material with an asymmetrical knife is developed, using equilibrium of forces and basic concepts of fracture mechanics. Finite-element-simulations are performed to determine the relationship between cutting forces and the parameters describing crack propagation. Consequently, normal pressure on the crack surface caused by the flanks of the cutting edge of the blade is the main cause leading to a crack tip opening and thus propagation of the crack. Overall cutting forces are augmented by the friction forces caused by the relative motion between cutting knife and material. Thus, the slicing motion allows the advance force to be reduced. The presented model is experimentally verified by sideways cutting stacked paper sheets.
A review is given of the mechanics of cutting, ranging from the slicing of thin floppy offcuts (where there is negligible elasticity and no permanent deformation of the offcut) to the machining of ductile metals (where there is severe permanent distortion of the offcut/chip). Materials scientists employ the former conditions to determine the fracture toughness of ‘soft’ solids such as biological materials and foodstuffs. In contrast, traditional analyses of metalcutting are based on plasticity and friction only, and do not incorporate toughness. The machining theories are inadequate in a number of ways but a recent paper has shown that when ductile work of fracture is included many, if not all, of the shortcomings are removed. Support for the new analysis is given by examination of FEM simulations of metalcutting which reveal that a ‘separation criterion’ has to be employed at the tool tip. Some consideration shows that the separation criteria are versions of void-initiation-growth-and-coalescence models employed in ductile fracture mechanics. The new analysis shows that cutting forces for ductile materials depend upon the fracture toughness as well as plasticity and friction, and reveals a simple way of determining both toughness and flow stress from cutting experiments. Examples are given for a wide range of materials including metals, polymers and wood, and comparison is made with the same properties independently determined using conventional testpieces. Because cutting can be steady state, a new way is presented for simultaneously measuring toughness and flow stress at controlled speeds and strain rates.
Elastic contact between a shallow elastic wedge, whose apex is blunted by a finite radius, and an elastically similar half-plane is studied. A closed-form contact law is found, and the interior stress field is then deduced using a Muskhelishvili’s solution in series form, for frictionless and sliding conditions. This geometry removes one of the principal objections to classical solutions to the wedge indentation problem—the unrealistic infinite stress concentration implied by an atomically sharp apex—and in the latter part of the paper the strength of the contact is evaluated explicitly. Further, cases of partial slip associated with the application of tangential load less than needed to cause sliding are considered.
Application of the tearing energy criterion (Part I of this work) to the problem of the tearing of a rubber strip that contains a small cut or tear of length c in one edge and is stretched in simple extension is based on the relation Wi – W = K(λ)c2hE, where Wi and W are the total stored energies of the strip in the absence and presence of the cut, respectively, h is the thickness λ0 of the strip, E is the stored-energy density in the central region of simple extension, and K(λ) is a numerical factor that varies with the extension ratio λ in this region. An experimental method is described for measuring (Wi – W), which enables the factor K(λ) to be evaluated. The results indicate that K(λ) decreases from a value of about 3 at low extensions to a value somewhat below 2 at λ = 3. The experiments also provide a more stringent test of the accuracy of the above relation than has been possible hitherto.
Investigations into parameters affecting cutting forces in foods were undertaken to identify basic trends such as the relationship of cutting forces to cutting speeds and food temperatures. A simple plain blade was used to cut three typical foodstuffs (cheese, bacon and beef) at three feed speeds and three temperatures. After each cut the blade was passed through the product a second time to measure forces indicative of friction on the sides of the blade.Cutting forces for cheese decreased with increasing temperature and increased with cutting speed. The relatively homogeneous nature of the samples resulted in consistent and repeatable measurements. For bacon, variable salt content gave rise to different ice contents and thus hardnesses in samples at the same ‘frozen’ temperatures. Layers of fat and muscle boundaries also produced marked deviations from the average forces. Force results were therefore scattered but increased with decreasing temperature. The effect of cutting speed was not consistent for all forces, but higher speeds generally produced higher forces. For beef, there was a marked difference between frozen and unfrozen samples but little difference between samples at different unfrozen temperatures. In unfrozen samples, cutting speed had little effect on forces, whereas faster cutting speeds produced higher forces in frozen samples. The proportion of total cutting forces made up by friction was found to be consistent over all temperatures and speeds for cheese and bacon, but markedly higher in the frozen beef samples compared to the unfrozen samples.
The fracture properties of foods are relevant to texture but can be difficult to measure because of limitations of size or shape. Many established engineering tests for the measurement of crack growth and unstable propagation of cracks require specific test geometries, sizes and compliances of the specimen. With food materials this is rarely possible. The wedge penetration technique can usefully be adapted to foods to determine fracture parameters of brittle and semi-brittle foods such as moderately hard cheeses and raw and cooked fruits and vegetables.
A criterion for tearing of test-pieces cut from thin sheets of a natural rubber vulcanizate, similar in form to the Griffith criterion for spreading of a crack, is formulated. This criterion involves a characteristic energy for tearing which is independent of the shape of the test-piece and of the disposition of the cut. It is shown how this characteristic energy can be found experimentally for a particular vulcanizate and used to predict the force required to tear test-pieces of the vulcanizate.
A method for assessing the resistance of rubbers to cutting by sharp objects is described. It involves the application of the cutting implement -a razor blade-to the tip of a crack in a stretched tear test piece. The method enables effects of friction on the cutting process to be substantially eliminated. Under these conditions two distinct forms of cutting are observed: one is a slow time-dependent process, while the other involves rapid, catastropic failure. Effects of test piece shape and deformation on the cutting behaviour can be taken into account by use of fracture mechanics. The relative cutting resistance of different rubbers is found to vary according to the test conditions. At low deformations the onset of catastrophic cutting can be defined by a simple relationship which is applicable to all rubbers examined.On dcrit une mthode pour tablir la rsistance des caoutchouc la coupure par des objets affts. Cette mthode comporte l'application d'un moyen de coupage (lame de rasoir) l'extrmit d'une fissure dans une pice d'essai soumise dchirement. La mthode permet d'liminer de manire substantielle les effets de la friction lors du processus de coupure. Sous ces conditions, deux formes distinctes de coupures sont observes: l'une est un processus lent dpendant du temps, tandis que l'autre comporte une rupture rapide et catastrophique. En utilisant la mcanique de la rupture, on peut tenir compte des effets de la forme des pices d'essai et de la dformation sur le comportement lors du coupage. La rsistance relative au coupage de diffrents caoutchoucs parait varier avec les conditions d'essai. Lors de faibles dformations, le dmarrage de la coupure dite catastrophique peut tre dfini par une relation simple qui est applicable dans tous les cas des caoutchoucs examins.
An analysis is given for determining G for removing a thin layer using a wedge. Corrections are described for both friction and the plastic bending of the layer. Experimental results are analysed for adhesive joints and for cutting tests on polymers and biological materials. In all of these the fracture toughness could be found. Some general observations on schemes for analysing these tests are given.
Why it is easier to cut with even the sharpest knife when pressing down and sliding than when merely pressing down alone is explained. A variety of cases of cutting where the blade and workpiece have different relative motions is analysed and it is shown that the greater the slice/push ratio given by (blade speed parallel to the cutting edge/blade speed perpendicular to the cutting edge), the lower the cutting forces. However, friction limits the reductions attainable at the highest . The analysis is applied to the geometry of a wheel cutting device (delicatessan slicer) and experiments with a cheddar cheese and a salami using such an instrumented device confirm the general predictions.
The sharpness of a blade is a key parameter in cutting soft solids, such as biological tissues, foodstuffs or elastomeric materials. It has a first order effect on the effort, and hence energy needed to cut, the quality of the cut surface and the life of the cutting instrument. To date, there is no standard definition, measurement or protocol to quantify blade sharpness. This paper derives a quantitative index of blade sharpness via indentation experiments in which elastomeric materials are cut using both sharp and blunt straight edge blades. It is found that the depth of blade indentation required to initiate a cut or crack in the target material is a function of the condition or sharpness of the blade’s cutting edge, and this property is used to formulate a so-called “blade sharpness index” (BSI). It is shown theoretically that this index is zero for an infinitely sharp blade and increases in a quadratic manner for increasing bluntness. For the blades tested herein, the sharpness index was found to vary between 0.2 for sharp blades and 0.5 for blunt blades, respectively. To examine the suitability of the index in other cutting configurations, experiments are performed using different blade types, target materials and cutting rates and it is found that the index is independent of the target material and cutting rate and thus pertains to the blade only. In the companion Part II to this paper a finite element model is developed to examine the effect of blade geometry on the sharpness index derived herein.
The assumption that negligible work is involved in the formation of new surfaces in the machining of ductile metals, is re-examined in the light of both current Finite Element Method (FEM) simulations of cutting and modern ductile fracture mechanics. The work associated with separation criteria in FEM models is shown to be in the kJ/m2 range rather than the few J/m2 of the surface energy (surface tension) employed by Shaw in his pioneering study of 1954 following which consideration of surface work has been omitted from analyses of metal cutting. The much greater values of surface specific work are not surprising in terms of ductile fracture mechanics where kJ/m2 values of fracture toughness are typical of the ductile metals involved in machining studies. This paper shows that when even the simple Ernst–Merchant analysis is generalised to include significant surface work, many of the experimental observations for which traditional ‘plasticity and friction only’ analyses seem to have no quantitative explanation, are now given meaning. In particular, the primary shear plane angle φ becomes material-dependent. The experimental increase of φ up to a saturated level, as the uncut chip thickness is increased, is predicted. The positive intercepts found in plots of cutting force vs. depth of cut, and in plots of force resolved along the primary shear plane vs. area of shear plane, are shown to be measures of the specific surface work. It is demonstrated that neglect of these intercepts in cutting analyses is the reason why anomalously high values of shear yield stress are derived at those very small uncut chip thicknesses at which the so-called size effect becomes evident. The material toughness/strength ratio, combined with the depth of cut to form a non-dimensional parameter, is shown to control ductile cutting mechanics. The toughness/strength ratio of a given material will change with rate, temperature, and thermomechanical treatment and the influence of such changes, together with changes in depth of cut, on the character of machining is discussed. Strength or hardness alone is insufficient to describe machining. The failure of the Ernst–Merchant theory seems less to do with problems of uniqueness and the validity of minimum work, and more to do with the problem not being properly posed. The new analysis compares favourably and consistently with the wide body of experimental results available in the literature. Why considerable progress in the understanding of metal cutting has been achieved without reference to significant surface work is also discussed.
The wire cutting process is used in the food industry during the manufacture and testing of products. The cutting process involves fracture as well as large strain deformation and surface friction. This paper investigates the mechanics of the wire cutting process of cheese through a combination of experiments, theory and finite element simulations. The experiments revealed that there was secondary damage on the cut surface, thus a higher fracture energy would be consumed than the common assumption of a single crack propagation. The numerical simulations showed that there was a six-fold change in the strain rate when wire diameters of 0.25 to 2 mm are used. This strain rate effect was modelled through a modification of a previous theoretical analysis of the wire cutting process. The numerical models were also used to predict the cutting forces using two failure criteria: critical strain, which was applied to the initiation of cracking, and a cohesive zone model to simulate crack propagation. Both criteria showed reasonable success in predicting the cutting forces, particularly for cuts made with small wire diameters.
Several aspects of the mechanics of indentation of a half-space by an elastic indenter which is either conical or wedge-shaped are addressed. These include elucidation of the contact law, the state of stress induced when the indenter is either pressed normally or sliding with Coulomb friction, the strength of the contact, and the influence of shearing forces less than those necessary to cause sliding, including those induced by elastic mismatch.
A simplified model to determine the contribution of strain energy in the failure process of thin biological membranes during cutting
- C F Doran
- B A O Mccormack
- A Macey
C.F. Doran, B.A.O. McCormack, A. Macey, A simplified model to determine the
contribution of strain energy in the failure process of thin biological membranes
during cutting, Strain 40 (4) (2004) 173-179, https://doi.org/10.1111/j.1475-1305.2004.00165.x.
The Science and Engineering of Cutting: The Mechanics and Processes of Separating, Scratching and Puncturing Biomaterials, Metals and Non-metals
- A G Atkins
A.G. Atkins, The Science and Engineering of Cutting: The Mechanics and Processes
of Separating, Scratching and Puncturing Biomaterials, Metals and Non-metals,
Butterworth-Heinemann/Elsevier, Oxford, 2009.
- A Spagnoli
A. Spagnoli, et al.
Theoretical and Applied Fracture Mechanics 101 (2019) 200-206