Soil Reaction Forces Research Articles

Modeling soil-bulldozer blade interaction using the discrete element method (DEM)

Limited studies have been conducted to establish scaling relationships of soil reaction forces and length scales of bulldozer blades using the Discrete Element Method (DEM) technique. With a DEM-based similitude scaling law, performance of industry-scale blades can be predicted at reduced simulation efforts provided a calibrated and validated DEM soil model is developed. DEM material properties were developed to match soil cone penetration testing. The objectives of the study were to develop a DEM soil model for Norfolk sandy loam soil, establish a scaled relationship of soil reaction forces to bulldozer blade length scales (n = 0.24, n = 0.14, n = 0.10, and n = 0.05), and validate the DEM-predicted soil reaction forces on the scaled bulldozer blades to the Norfolk sandy loam soil bin data. Using 3D-scanned and reconstructed DEM soil aggregate shapes, Design of Experiment (DOE) of soil cone penetration testing was used to develop a soil model and a soil-bulldozer blade simulation. A power fit best approximated the relationship between the DEM-predicted soil horizontal forces and the bulldozer blade length scale (n) (R2 = 0.9976). DEM prediction of soil horizontal forces on the bulldozer blades explained the Norfolk sandy loam soil data with a linear regression fit (R2 = 0.9965 and slope = 0.9634).

Strength-based design analysis of a Para-Plow tillage tool

In this research, experimental field tests and an advanced computer aided design and engineering (CAD and CAE) based application algorithm was developed and tested. The algorithm was put into practice through a case study on the strength-based structural design analysis of a Para-Plow tillage tool. Para-Plow is an effective tractor attached tillage tool utilised as an alternative to the conventional deep tillage tools used in agricultural tillage operations. During heavy tillage operations, the Para-Plow experiences highly dynamic soil reaction forces which may cause undesired deformations and functional failures on its structural elements. Here, prediction of the deformation behaviour of the tool structure during tillage operation in order to describe optimum structural design parameters for the tool elements and produce a functionally durable tool become an important issue. In the field experiments, draft force and strain-gauge based measurements on the tool were carried out simultaneously. Subsequently, Finite Element Method based stress analysis (FEA) were employed in order to simulate deformation behaviour of the tool under consideration of the maximum loading (worst-case scenario) conditions tested in the field. In the field experiments, average and maximum resultant draft forces were measured as 33,514 N and 51,716 N respectively. The FEA revealed that the maximum deformation value of the tool was 9.768 mm and the maximum stress values impart a change on the most critical structural elements of between 50 and 150 MPa under a worst-case loading scenario. Additionally, a validation study revealed that minimum and maximum relative differences for the equivalent stress values between experimental and simulation results were 5.17% and 30.19% respectively. This indicated that the results obtained from both the experimental and simulation are reasonably in union and there were no signs of plastic deformation on the Para-Plow elements (according to the material yield point) under pre-defined loading conditions and a structural optimisation on some of the structural elements may also be possible.This research provides a useful strategy for informing further research on complicated stress and deformation analyses of related agricultural equipment and machinery through experimental and advanced CAE techniques.

Analysis of Penetration Depth of Pipeline on Cohesive Soil Seabed

This paper conducts laboratory tests to investigate detailedly the soil deformation law around the pipeline and its penetration depth under self-gravity. The seabed model is prepared by consolidating saturated soil using vacuum pressure technology, and the pipeline models are specifically designed to possess different radii. Based on the experimental results and digital images, the soil deformation process is analyzed and summarized, a kinematic admissible velocity field is given and an upper bound solution of pipeline penetration depth and soil reaction force is derived and proposed in this paper. In order to verify the accuracy of the upper bound solution deduced in this paper, a comparison is made among some published results and the solution suggested in this paper, the comparison results confirm that the upper bound solution and the soil failure mode are reasonable. Finally two empirical formulas are given in this paper to estimate the soil reaction force of seabed and the penetration depth of pipeline. The empirical formulas are in agreement with the upper bound solution derived in this paper, and the conclusion of this paper could provide some theoretical reference for the further study of the interaction between the pipeline and the soil.

A novel rigid wheel for agricultural machinery applicable to paddy field with muddy soil

The working performance of agricultural machinery is largely determined by the walking performance of the wheel when driving in complex unstructured soil. However, the driving performance of existing wheels is not satisfactory for paddy field with muddy soil. The purpose of the current study is therefore to propose a novel rigid wheel for agricultural machinery which is applicable to paddy field with muddy soil. Firstly, a novel arc edge shaped wheel was designed based on the principles of mechanics on the ground. Then the driving performance of this arc edge shaped wheel was evaluated using FE modeling of interaction between rigid wheel and soil. Finally, the structure originally designed arc edge shaped wheel was improved according to FE modeling results, and this improved design was further evaluated by both FE simulation and prototype experiments. Both FE modeling and experimental results indicate that the improved arc edge shaped wheel proposed in this study has a good driving performance with regarding to wheel sinkage and soil reaction force. The proposed arc edge shaped wheel could be used as an effective component of rice harvester for paddy field with muddy soil.

Evaluación de un transductor integral para determinar la magnitud del error de medición.

The use of soil reaction force transducers coupled between the tractor and integral tillage implements are in their experimental phase in different parts of the world; however, these developments present measurement errors. The objective of this research was to corroborate the magnitude of error between an Integral Force Sensor (SIF) connected to the tractor three-point hitch and two individual sensors coupled to the work tools to monitor soil reaction forces at the integral implements. SIF was tested under laboratory conditions with calibrated equipment to register force measurements at different lever distances and at different weights, using a data acquisition system DaqBook 2000 (Measurement Computing) and a signal conditioner DBK43A (Iotech Inc.). Obtained results indicated that SIF is sensitive to the load position, equivalent to the tillage depth, in a 2 to 10% range of error. Field evaluations were performed with a chisel plow at different depths for validation, finding errors between 13.07 and 41.72%, where chisel arrangement of 0.30 m depth for front chisels and 0.30 m for the rear chisel, showed the smallest error. Applying the 10% calibration correction obtained in the laboratory for a chisel length of 0.70 to 0.90 m, the obtained error was 3.1%. Comparison of the methods spectral analysis and area under the curve, equivalent to the energy used to obtain the error, showed that there is no significant difference between the two methods.

SOCCER CLEATS WITH BLADE-SHAPED STUDS AND MECHANICAL OVERLOAD IN SOCCER: A SYSTEMATIC REVIEW

ABSTRACT Soccer cleats with blade-shaped studs promote greater traction on the pitch and can be beneficial for soccer performance. On the other hand, movements with rapid changes of direction, associated with the high traction of soccer cleats, can increase overload and risk of injuries. Given the lack of consensus on the effects of these cleats on mechanical overload during specific soccer movements, the aim of this systematic review was to determine the effects of wearing cleats with bladed studs on mechanical overload in soccer. A search was conducted in the PubMed, Scopus, and Web of Science electronic databases between October and November 2017. Non-original articles were excluded, as were those not related to soccer or cleats, and those not written in English. Eight articles were included that tested the effects of bladed studs on overload and that used biomechanical tests. The tasks evaluated were: running in a straight line or with changes of direction, and landing of jumps. The resulting joint torque, soil reaction force, electromyography, and plantar pressure were measured. There was no influence of bladed shaped studs on joint torque or on ground reaction force. There was an increase in plantar pressure on the lateral part of the foot in bladed studs compared to Society cleats and running shoes. When compared with round studs, the results were inconclusive for plantar pressure. Round studs, caused greater electromyographic activity in the quadriceps muscles than bladed studs. It was concluded that wearing bladed-stud cleats does not result in greater mechanical overload during running or landing of jumps. Evidence Level I, Systematic Review.

A Poroelastic Solution for Dynamics of Laterally Loaded Offshore Monopiles

In this study, a rigorous poroelastodynamic solution is proposed for monopiles which accounts for 3D (three dimensional) dynamic interaction of the soil and pile. The dynamic Biot's theory is used to model the soil, while Timoshenko beam is used to model the monopile. The perfect contact conditions between the soil and monopile are realized by decomposing the pile's horizontal translation to radial, hoop and vertical displacements. Correspondingly, 3D radial, hoop and vertical stresses on the pile surface are used to formulate the governing equations of the interaction problem. Using the integral equation methods, the governing differential equations are reduced to coupled integral equations, which are solved numerically. Selected numerical results for coupled lateral and rocking dynamic impedances together with the 3D dynamic contact stresses at the soil-pile interface are studied for different pile and poroelastic material parameters and frequencies of excitation. The distributed soil reaction force and moment along the pile are also obtained by integrating the 3D radial, hoop and vertical stresses along the circumference of the pile at the soil-pile interface. Finally, bending moment, shear force, horizontal translation and rocking rotation of the monopile are obtained based on the classical dynamic Timoshenko beam theory.

Dar kanat geometrisinin ayrık eleman metodu kullanılarak toprak arızası ve çekme kuvveti üzerindeki etkilerinin modellenmesi

In most earth moving machinery, such as bulldozers or tillage tools, the working tool is a tine. Thus, for tillage systems, accurate predicting of the forces acting on the tine is of prime importance to enhance their productivity. The initial conditions (i.e., blade geometry or soil type) and operating conditions (i.e., cutting speed and cutting depth) have been shown experimentally a great effect on machinery efficiency. Although experimental studies provide valuable information, they are expensive, time-consuming, and limited to certain cutting speeds and depths. Results obtained from experimental studies are also highly dependent on the accuracy of the measuring devices. However, with the increasing computational power and the development of more sophisticated mathematical models, numerical methods and in particular discrete element method (DEM) have shown great potential in analyzing the factors affecting soil-blade interaction. In this study, the effects of different rake angles, forward speed, working depth, and depth/width (d/w) ratio were investigated on a tine draught and vertical force using DEM modeling. Simulation results were also compared with the test results. It was found from the results that increasing travel velocity, tine rake angle, d/w ratio, and working depth increased draught and vertical force. Overall, based on the results of this study, DEM is able to predict soil reaction forces with an accuracy of more than 90%.

Nonlinear Response of Piled Gravity Base Foundations Subjected to Combined Loading

This study investigates the soil-structure interaction of a piled Gravity Base Foundation (piled GBF) supporting an offshore wind turbine tower. The piled GBF is a gravity base foundation supported by five piles with one center and four outer piles. A series of three-dimensional finite element analyses were performed to investigate p-y characteristics in the piled GBF. The results were validated against centrifuge test data prior to undertaking a detailed parametric study, exploring the relevant range of parameters in terms of foundation type, vertical load due to the gravity base self-weight, loading height, undrained shear strength, and the pile bearing condition. Overall, the center pile of the piled GBF showed the highest ultimate soil reaction force, while the leading pile indicated the lowest value. Due to the rotation of mat and self-weight of GBF, significant shear failure was mobilized near the leading pile, which reduced the ultimate soil reaction force. This was also confirmed through the comparison studies with group pile (no mat), piled raft (low self-weight of mat) and rock-socketed piled GBF (no rotation of mat).

Análise cinética e cinemática da marcha durante o transporte da mochila com rodas em escolares de 7 a 10 anos de idade

Introdução: A sobrecarga em mochilas escolares pode resultar em aumento de carga mecânica sobre o aparelho locomotuvo de estudantes durante a marcha. Objetivo: Analisar e comparar as variáveis temporais/espaciais cinéticas e cinemáticas durante a marcha e o transporte de mochilas com rodas (10% peso corporal (PC)) em escolares de 7 a 10 anos. Métodos: Dez crianças, saudáveis (7.8 ± 1.6 anos) participaram de duas condições experimentais, sendo a primeira envolvendo a marcha, enquanto a segunda ocorreu o transporte de mochila provida de rodas, 10% PC. Resultados: As forças de reação do solo não apresentaram diferenças entre as duas condições. Porém, mostrou-se que mochilas com rodas não alteram aplicação de forças para execução da tarefa quando comparadas a marcha sem carga na locomoção. A cinemática do tornozelo, do joelho e da pelve permaneceram inalteradas. Conclusão: O uso de rodas na mochila para o transporte de carga de 10% PC não influenciou no padrão de marcha aplicado durante a marcha no plano.

Development of The Method on The Prediction of Soil Plat Penetration Resistance

Abstract During operation, the lug wheels penetrate the soil and form certain angle to the soil surface at varying penetration depths. In order to determine the soil reaction force against plate penetration given to the soil, penetrometer was mounted on the plate. Plate sizes used in this experiment were 5×5 cm2, 5×10 cm2, 5×15 cm2 and 5×20 cm2. The measurement was carried out at varying angles and depths i.e. 90°, 75°, 60°, 45°, 30° and 4 cm, 8 cm, 12 cm and 16 cm, respectively. The objective of this research was to develop the method on the prediction of soil plat penetration resistance at varying depths and angles. Prediction method was developed using linear or polynomial regression method which compared with Artificial Neural Network (ANN). The research showed that ANN generated better prediction value which indicated by lower error magnitude compared with regression method i.e. 9.9% and 19.7%, respectively.

An approximating mathematical model of interaction between a freely rotating disk and soil

A generalized mathematical model of disk interaction with soil was built under general assumptions regarding the mode of the disk knife motion in soil, namely, in a mode of slippage, skidding or rolling without slippage and skidding. Previously constructed models follow from it as particular cases at certain values of parameters. However, because of computational complexity of this model for the case of a freely rotating disk knife consisting in the need for a preliminary numerical solution of a transcendental equation to determine the mode of disk motion, the generalized mathematical model has not found wide application. Therefore, an analytical two-dimensional approximation of a generalized model of disk interaction with soil which is a new model of approximation type was constructed on the basis of a computer experiment using the least squares method. An explicit expression was obtained for the kinematic parameter of a freely rotating disk knife which determines its mode of motion. It was established that this parameter is a rational function of relative depth of the disk penetration and the dimensionless dynamic coefficient characterizing soil properties. Also, explicit expressions were obtained for the projections of the resultant soil reaction forces acting on the blade of the disk knife and its side faces depending on the data of dimensionless parameters. It has been established that the horizontal component of the reaction which determines tractive resistance of the disk is also a rational function of the relative penetration depth and the dimensionless dynamic coefficient. It was established that the magnitude of the kinematic parameter significantly affects the magnitude and direction of the resultant soil reactions to the disk. The expressions obtained make it possible to significantly simplify experiments to determine the resultant soil reaction forces to a freely rotating disk knife and reduce their required number. These expressions make it possible to carry out strength calculations of soil-cultivating working tools with disks and determine their optimal parameters according to the strength criteria and the minimum specific energy consumption with accuracy sufficient for engineering practice. Adequacy of the obtained expressions was confirmed by comparison with experimental data of the disk knife dynamometry

PARTICLE MOTION ON THE SURFACE OF A CONCAVE SOIL-TILLING DISK

Relative particle motion on the internal rough surface of a concave soil-tilling disk, which rotates around horizontal axis under a soil reaction force, has been considered. A disk blade is positioned in a vertical plane, which makes an incidence angle with the direction of the machine movement. This angle has its acceptable limit and when it exceeds the limit, it causes disk dragging. In the paper, it has been assumed that dragging was non-existent, the rotational rate of a disk is stable and it depends on stabilized velocity of the machine movement and on an incidence angle. When a machine is operated, soil particles get onto an internal disk surface and perform a relative motion, which determines the slipping trajectory of a particle on a disk surface. The trajectory of the absolute particle motion relative to a fixed coordinate system allows tracing the rise height of a particle after its gets onto a disk surface. Differential equations of particle motion have been developed and solved using numerical methods. A particle gets onto a disk with specified initial criteria, namely the direction of its entering on a disk and its initial velocity. Two models of particle motion on a disk have been considered. According to the first model, we assume that further particle motion after its getting onto a disk surface is performed due to the kinetic energy of a particle at the moment of its getting onto a disk surface. According to the second model, the backup force of other particles, which breaks the force of particle friction on a surface, is taken into account. Differential equations of particle motion have been developed in projections onto a fixed solid system of axes. Thus, the system includes three differential equations in three unknown functions. One of the unknown functions is the surface reaction force and the dependences, which describe relative particle motion on a disk surface. For the purpose of the quality of soil loosening, we conducted multivariate experiment to determine the area of the soil dissipation. On the basis of field experiments, it has been determined that the production process quality of tillage machine meets agrotechnical requirements.

The method for calculating the traction resistance of a flat disk

Scuffler with flat discs are widely used in areas, which are subject to wind erosion of soils, to cover moisture on the stubble fields. Flat discs do not wrap the layers they remove, but only loosen them, shifting them aside. It is preferable to use such scrapers during presowing tillage and on steam, since in this case there is less sputtering of the soil, and its lower (moist) layers are not carried to the surface. Therefore, many industrially manufactured scufflers are equipped with flat discs, and the task of constructing a mathematical model for the interaction of such discs with soil is topical. Many mathematical models of the disc-soil interaction, taking into account the distribution of soil reaction forces on the disk, have been proposed, but all these models were constructed assuming that the disk is moving in its plane. Therefore, they are not applicable to the disk of a lakeshield moving with a non-zero angle of attack in the soil. The purpose of this work is to construct a mathematical model that allows calculating the traction resistance of a disk moving with a given angle of attack. The basic assumptions made in the construction of this model: the speed of the translational movement of the disk and its depth are constant; friction in the disk bearing can be neglected; the soil pressure on the lateral surface of the disc and the force of the soil reactions per unit length of its blade can be replaced by their mean values. An explicit expression is obtained for the traction resistance of a disk of a scuffler moving with an angle of attack, depending on its relative depth, the angle of attack, and the empirical coefficients. The adequacy of the constructed mathematical model is confirmed by comparison with known experimental data. It makes it possible to significantly reduce the number of full-scale experiments on the study of the interaction of flat discs of a scuffler with the soil, replacing them with computational ones, and reasonably carry out power and strength calculations of such discs. In addition, it can be used to optimize the parameters of the flat discs of the scuffler.

Dynamic performance of a no-till seeding assembly

Precise seeding depth plays an important role in achieving reliable germination rate and even plant emergence. In no-till seeding, this aim is more challenging due to the inappropriate response of the machine dynamics to harsh soil conditions, such as compacted soil undulations and stubble. In this paper, a sensor-frame was mounted on a no-till seeder, to measure the field surface profiles during seeding operation. Its accuracy was validated by acquiring the profile of trapezoidal bumps with known dimensions resulting in a root mean squared (RMS) error of 7.3 and 8.7 mm for travelling speed of 2 km h−1 and 10 km h−1, respectively. Strain gauges were used to measure the soil reaction forces, on one of the seeding assemblies during seeding operation at travelling speed of 10 km h−1. After seeding wheat (Triticum aestivum L.), the geo-referenced position of each single seed was measured using a total station, to calculate the seeding depth. The correlation between the seeding depth variation and the developed forces showed that the frequencies of 11.8 Hz and 17.8 Hz of the vertical forces, which corresponded to a wavelength of 0.21 m and 0.14 m, respectively, were responsible for the high variation in seeding depth. For the profile impact forces, these values were equal to 10.7 Hz and 20.6 Hz. The corresponding wavelengths were equal to 0.23 m and 0.12 m. The peak value of seeding depth was detected at a frequency of 8.3 Hz with 0.3 m wavelength for both vertical and impact profile forces.

The effect of the disc setup angles and working depth on disc harrow working resistance

Horizontal, longitudinal and vertical components of working resistance of a compact disc harrow (CDH) were investigated in a field experiment. Three values of the attack angle (12°, 16°, 21°) and two of the tilt angle (7°, 15°) of the plane of the front discs were used. The third parameter was the working depth measured at the lowest point of discs circumference edge. The dependent variable was the horizontal and vertical resultant component of forces occurring in the three-point linkage system on a tractor. Statistically significant differences in the resistance components were found depending on the disc set-up. For evaluation of soil reaction forces on harrow discs the above resistance components were transformed into components of the unit resistance relating to the units of actual working width and depth. Their dependence on the CDH setting parameters was next examined using the empirical estimation of the regression equation. Horizontal and vertical components of the bearing and the pressure area of the discs were used as independent variables. Values of the bearing area were close to zero and only the components of pressure were used. This model describes the components of the horizontal and vertical resistance as a function of design parameters and disc settings expressed by means of pressure area. It reflects the empirical results with 99.7% accuracy for the horizontal component and in 99.9% for the vertical component of the resistance.

Minimising soil disturbance and reaction forces for high speed sowing using bentleg furrow openers

Australian no-till farmers often use narrow point openers to create furrows for seed and fertilizer placement. However, operational speeds are limited due to excessive lateral soil throw reducing furrow backfill and causing interactions between adjacent furrows. This study measured the effects of speed (8, 12 and 16 km h−1) on soil disturbance and tillage forces for five different openers, aiming to evaluate suitable options for high speed seeding. Three straight shank openers, 90° (blunt and chamfered face) and 53° rake angles were compared to two bentleg geometries (45 and 95 mm offsets), in a dry silt-loam field soil. The 53° straight opener showed the largest response to speed, reducing furrow backfill and increasing lateral soil throw (from furrow center). The addition of a double sided chamfer reduced lateral soil throw and maintained 100% backfill at 8 km h−1 but soil disturbance increased at 12 and 16 km h−1. Both bentleg openers maintained 100% backfill and operated with a lateral soil throw less than half the straight openers at 8 km h−1. However, the 45 mm offset bentleg opener had more soil throw at speed. This resulted in reduced furrow backfill and increased lateral soil throw at 16 km h−1 (reaching similar to the straight shank openers). The 95 mm offset bentleg was able to maintain its low soil disturbance characteristics at speeds up to 16 km h−1. The findings show potential for new opener technology to increase operating speeds of no-till seeding operations by minimising soil disturbance and draft, therefore improving work-rate and timeliness of sowing.

Riser-soil interaction model effects on the dynamic behavior of a steel catenary riser

A mathematical model employed to analyze the global dynamics of a Steel Catenary Riser (SCR) taking into account the interaction with the seafloor and the effect of the soil reaction forces is established. The choice of soil model plays an important role for the dynamic behavior of SCRs. The riser has been modeled using flexible beam with large curvature and elastic foundation beam to describe the riser-soil interaction by means of realistic nonlinear load-deflection (P–y) curves. The study is made to improve an existing finite element numerical code for dynamic analysis of mooring lines and risers, known as CABLE 3D, which is based on a slender rod assumption. Effects of nonlinear seabed model on the dynamic behavior of SCRs under vessel cyclic perturbation have further been investigated and discussed using a realistic P–y curve to simulate soil deformation and resistance forces. The interaction model depends on several factors, such as soil strength, penetration depth and riser characteristics. The dynamic responses of the riser Touchdown Point (TDP) excited by vessel periodic heave motion are studied and the results are compared with those from the linear spring model. SCR has been perturbed by 10 regular sinusoidal cycles and the responses calculated by improved code show a number of features such as suction force mobilization, gradual increasing penetration depth, and gradual reduction of soil resistance at maximum penetration. The riser behavior at the touchdown zone (TDZ) depends on the riser top motion amplitude, nonlinear soil stiffness and suction force. The impact of the riser-soil interaction model on the dynamic behavior in the TDZ has been thoroughly studied in this paper.

Response of circular flexible foundations subjected to horizontal and rocking motions

A methodology using modal analysis is developed to evaluate dynamic vertical displacements of a circular flexible foundation resting on soil media subjected to horizontal and rocking motions. The influence of the soil reaction forces on the foundation is considered by introducing modal impedance functions, which can be determined by an efficient procedure with ring elements. The displacements of the foundation can then be easily solved by modal superposition. Parametric studies for modal responses of the flexible foundation indicate that the coupled response of the foundation is significantly influenced by relative stiffness among the foundation and the soil medium, vibration frequency range, foundation mass, and boundary contact conditions. The welded boundary condition should be considered to predict the coupling response while the relaxed boundary condition may be used to predict approximately the vertical displacements. As a foundation with a relative stiffness ratio more than three, it is found that the foundation can be considered as rigid to calculate coupling displacements. For a slightly flexible foundation, considerations of three modes are sufficient enough to obtain accurate foundation responses. Moreover, at low frequencies, the coupling effect due to higher mode can be neglected.

Comparative Finite Element Analysis of the Effects of Tillage Tool Geometry on Soil Disturbance and Reaction Forces

In this study a comparative finite element analysis was conducted to investigate the effects of tillage tool geometry on soil disturbance and reaction forces. A nonlinear three dimensional finite element model, using ANSYS software, was developed to study the soil cutting process by trapezoidal (T₁) and rectangular (T₂) flat tools that inclined to the horizontal at three rake angles (R₁ = 30°, R₂ = 60° and R₃ = 90°), therefore a total of six treatments were considered in this analysis. The soil media was assumed as elastic-perfectly plastic material with Drucker- Prager’s model. Results of this study revealed that the maximum vertical soil displaced by T₁ is greater than that of T₂; hence T₁ disturbed the soil better than T₂. Results also showed that a significant reduction in draft force was noticed when cutting the soil with T₁ in comparison to T₂. Designing the tool in the form of T₁ significantly reduces the surface area of the tool; thus conserving the engineering material.