Vertical Force Components Research Articles

Effect of Sensorimotor Rehabilitation Protocol on Vertical Ground Reaction Force and Loading Rate in Men with Patellofemoral Pain: A Randomized Controlled Trial

ntroduction: The change of vertical ground reaction force and loading rate rate is a important factor in causing patellofemoral pain (PFP). The aim of this study was the effect of sensory-motor exercises on the vertical ground reaction force and loading rate in patients with PFP when stair descent. Methods: A total of 30 patients with PFP participated and were randomly divided into two experimental and control groups (15 subject in each group). Over a period of twelve weeks, the experimental group engaged in sensorimotor exercises, while the control group did not receive any therapeutic intervention. Pain intensity, fear of movement, quadriceps muscle strength, knee flexion angle, components of vertical ground reaction force and loading rate were evaluated in two stages pre-test and post-test. For data analysis SPSS 16 software and the covariance statistical method were used to compare the results between groups, and the significance level was considered 0.05. Results: The analysis of covariance analysis indicated that sensorimotor exercises in the experimental group compared to the control group had a significant difference in reduced pain (P <0.001), reduced fear of movement (P <0.001), incresed quadriceps muscle strength (P <0.001), incresed knee flexion angle (P <0.001), components of vertical ground reaction force (P <0.001), and reduced loading rate (P <0.001). Conclusion: The finding suggest that the experimental group experienced a boost in in quadriceps muscle strength, leading to diminished pain and fear of movement, an increase in knee flexion angle, and enhanced active shock absorption. Consequently, there was an increase in both peak forces while the loading rate and valley force decreased.

Precise instruction and consideration of the vertical and horizontal force component increases validity and reliability of the 90:20 Isometric Posterior Chain Test.

Hamstring injuries are associated with decreased hamstring strength. Matinlauri et al.'s 90:20 Isometric Posterior Chain Test (90:20 IPCT) efficiently assesses hamstring strength, but has not been validated so far. Furthermore, their rather unprecise original instruction allows high variability in test execution. We added a new instruction and variables and examined, whether this measure leads to increased reliability and validity. We assessed hamstring strength of 23 sport students via the 90:20 IPCT under the original instruction, to exert vertical force, and our new instruction, to exert vertical and horizontal force. Instead of only using bare vertical force as variable under the original (Fz_V) and our new instruction (Fz_VH), we also calculated the resultant force (Fres_VH) and the applied torque onto the force place (M_F_ortho_VH). To test for validity, we correlated the outcome variables with peak torque of gold standard dynamometry. Furthermore, we measured muscle activities of the mm. rectus femoris, biceps femoris, semitendinosus, and gluteus maximus under our new instruction and compared them to those under the original variable (Fz_V) via one sample t-tests. To evaluate reliability, tests were repeated on two separate days, for which we calculated intra class correlation coefficients (ICCs) and coefficients of variation (CVs). Our new instruction and variables (Fz_VH, Fres_VH, M_F_ortho_VH) showed better validity (mean r = 0.77, r = 0.81, and r = 0.85) and equally good or better reliability (ICCs: 0.87, 0.89, and 0.94; CVs: 4.7%, 4.1%, and 4.7%) than the original instruction and variable (Fz_V) (mean r = 0.70; ICC: 0.91; CV: 5.6%). There were no differences in muscle activities between the variables and instructions of the 90:20 IPCT. We recommend our new instruction and the applied torque onto the force plate as it makes the 90:20 IPCT a more reliable and valid tool to assess hamstring strength.

Behavioral biometric optical tactile sensor for instantaneous decoupling of dynamic touch signals in real time

Decoupling dynamic touch signals in the optical tactile sensors is highly desired for behavioral tactile applications yet challenging because typical optical sensors mostly measure only static normal force and use imprecise multi-image averaging for dynamic force sensing. Here, we report a highly sensitive upconversion nanocrystals-based behavioral biometric optical tactile sensor that instantaneously and quantitatively decomposes dynamic touch signals into individual components of vertical normal and lateral shear force from a single image in real-time. By mimicking the sensory architecture of human skin, the unique luminescence signal obtained is axisymmetric for static normal forces and non-axisymmetric for dynamic shear forces. Our sensor demonstrates high spatio-temporal screening of small objects and recognizes fingerprints for authentication with high spatial-temporal resolution. Using a dynamic force discrimination machine learning framework, we realized a Braille-to-Speech translation system and a next-generation dynamic biometric recognition system for handwriting.

A method for calculating vector forces at human-mattress interface during sleeping positions utilizing image registration

The vector forces at the human-mattress interface are not only crucial for understanding the distribution of vertical and shear forces exerted on the human body during sleep but also serves as a significant input for biomechanical models of sleeping positions, whose accuracy determines the credibility of predicting musculoskeletal system loads. In this study, we introduce a novel method for calculating the interface vector forces. By recording indentations after supine and lateral positions using a vacuum mattress and 3D scanner, we utilize image registration techniques to align body pressure distribution with the mattress deformation scanning images, thereby calculating the vector force values for each unit area (36.25 mm × 36.25 mm). This method was validated through five participants attendance from two perspectives, revealing that (1) the mean summation of the vertical force components is 98.67% ± 7.21% body weight, exhibiting good consistency, and mean ratio of horizontal component force to body weight is 2.18% ± 1.77%. (2) the predicted muscle activity using the vector forces as input to the sleep position model aligns with the measured muscle activity (%MVC), with correlation coefficient over 0.7. The proposed method contributes to the vector force distribution understanding and the analysis of musculoskeletal loads during sleep, providing valuable insights for mattress design and evaluation.

Unrestrained Versus Vertically Restrained Loaded Countermovement Jumps: Are There Any Differences in the Components of Force Application?

The objective of this study was to compare a number of variables derived from the vertical and horizontal force components between loaded countermovement jumps performed in a Smith machine (SM modality; vertically restrained jumps) and with free weights (FW modality; unrestrained jumps). Twenty-three recreationally trained individuals, 6 women and 17 men, performed on a 3D force platform 5 maximal countermovement jump trials against 3 external loads (30%, 50%, and 70% of the SM 1-repetition maximum) using the SM and FW jumping modalities on separate sessions. The SM modality promoted greater values for virtually all the variables derived from the vertical force component (maximal force, maximal and minimum velocity, and impulse) and also shorter durations of the braking and propulsive phases. Regardless of the countermovement jump phase (braking or propulsive), the impulse directed toward the backward direction was always considerably greater for the SM compared with the FW modality. These results evidence that for recreationally trained individuals, the SM modality could be more effective to increase the general force capacity of the leg muscles due to increased external stability, while the FW modality is preferable when the orientation of force application is a crucial consideration, as it reduces the horizontal force component.

Effect of sensor number and location on accelerometry-based vertical ground reaction force estimation during walking.

Knee osteoarthritis is a major cause of global disability and is a major cost for the healthcare system. Lower extremity loading is a determinant of knee osteoarthritis onset and progression; however, technology that assists rehabilitative clinicians in optimizing key metrics of lower extremity loading is significantly limited. The peak vertical component of the ground reaction force (vGRF) in the first 50% of stance is highly associated with biological and patient-reported outcomes linked to knee osteoarthritis symptoms. Monitoring and maintaining typical vGRF profiles may support healthy gait biomechanics and joint tissue loading to prevent the onset and progression of knee osteoarthritis. Yet, the optimal number of sensors and sensor placements for predicting accurate vGRF from accelerometry remains unknown. Our goals were to: 1) determine how many sensors and what sensor locations yielded the most accurate vGRF loading peak estimates during walking; and 2) characterize how prescribing different loading conditions affected vGRF loading peak estimates. We asked 20 young adult participants to wear 5 accelerometers on their waist, shanks, and feet and walk on a force-instrumented treadmill during control and targeted biofeedback conditions prompting 5% underloading and overloading vGRFs. We trained and tested machine learning models to estimate vGRF from the various sensor accelerometer inputs and identified which combinations were most accurate. We found that a neural network using one accelerometer at the waist yielded the most accurate loading peak vGRF estimates during walking, with average errors of 4.4% body weight. The waist-only configuration was able to distinguish between control and overloading conditions prescribed using biofeedback, matching measured vGRF outcomes. Including foot or shank acceleration signals in the model reduced accuracy, particularly for the overloading condition. Our results suggest that a system designed to monitor changes in walking vGRF or to deploy targeted biofeedback may only need a single accelerometer located at the waist for healthy participants.

Shear performance of tapered box girders with corrugated steel webs in extradosed cable-stayed bridges under cable forces

The integration of box girders with corrugated steel webs (CSWs) and an extradosed cable-stayed design gives rise to an innovative and distinctive bridge design, recognized as the extradosed cable-stayed bridge with CSWs. The synergistic integration of the technical benefits facilitates expanding the maximum span and enhancing the adaptability of this structural configuration. Subjected to cable forces, the main bridge superstructure featuring a box girder with CSWs experiences vertical shear, substantial axial force, and bending moments. Shear buckling on the CSWs emerges as a prominent issue influencing design considerations. In response to heightened internal forces near support, the main girder is typically configured with variable height. The Resal effect in the tapered girder leads to additional shear stresses from axial forces and bending moments, consequently modifying the effective shear stress on the CSWs. Therefore, traditional basic calculation assumptions that solely account for the vertical component of cable forces in shear stress calculations are frequently inaccurate. This study presents a modified theoretical method for calculating shear stress in tapered box girders with CSWs subjected to cable forces by considering the Resal effect. The proposed modified method incorporates not only the vertical shear but also considers bending moments and axial forces. The finite element simulation and experimental results showcase its remarkable accuracy, concurrently validating the presence of the Resal effect in tapered box girders with CSWs under cable forces. Additionally, this study quantitatively analyzes the shear force redistribution phenomenon induced by vertical shear, axial force, and bending moments considering the Resal effect. This reveals the shear performance of tapered box girders with CSWs under cable forces. The study is expected to provide a strategy and theoretical guideline for rapidly and efficiently obtaining the shear stresses of tapered box girders with CSWs in extradosed cable-stayed bridges under cable forces.

Footwear Modification in Patients with Peripheral Neuropathy by Use of Three-dimensional Force Plate

Abstract Background: Peripheral neuropathy is the most common chronic complication of both type 1 and type 2 diabetes, with an estimated lifetime prevalence exceeding 50%. Loss of cutaneous sensory information from the foot sole is reported to be a critical factor contributing to walking instability, poor balance and falls, in people with diabetic peripheral neuropathy (DPN). Although there is a very little evidence in the literature on the effectiveness of microcellular rubber insoles, they may offer a new rehabilitative approach, which promotes self-management by the user, to improve balance and walking, and reduce the risk of falling, in adults with diabetes and this study aims to find out the effectiveness of microcellular rubber insoles in peripheral neuropathy. Materials and Methods: This was a prospective observational study. A total of 30 patients with DPN, fulfilling the inclusion criteria, were selected for the study. All of the participants were clinically tested for the presence of neuropathy and evaluated by the force platform, after which they were advised to wear micro cellular rubber insole footwear (which was made in institutional set up as per patient’s foot size) for a period of 4 weeks. At the end of the stipulated period, the participants were again evaluated on the same parameters in the force platform. Results: After 4 weeks of intervention, there was a significant improvement in the postural stability as evidenced by a decrease in the mean of anterior–posterior sway (7.1225 ± 0.7102/5.7972 ± 0.6901) (P < 0.0001). Mean mediolateral sway also shows an improvement (4.9570 ± 0.5106/3.9639 ± 0.5749) (P < 0.0001). Similarly, improvements shown in mean sway area (368.4048 ± 58.9558/313.8788 ± 57.5957) (P = 0.0040) and sway velocity (23.2842 ± 2.1151/21.8840 ± 1.8419) (P < 0.0001). The step length, however, did not show any statistically significant improvement (0.6474 ± 0.0524/0.6333 ± 0.0597) (P = 0.2820). There was a significant reduction in the vertical component of the ground reaction force post-use of the insole (737.4333 ± 73.1577/659.3667 ± 82.7937) (P < 0.0001) with a reduction of 13% mean value. Conclusion: This study demonstrates that neuropathy deteriorates postural balance and gait; the present evidence provides insight indicating that footwear interventions do significantly alter static balance performance in the neuropathy population. Footwear interventions seem to have the capacity to alter underlying strategies controlling static and dynamic movement patterns through a combination of mechanical and sensorimotor mechanisms, for which in-depth investigation of neurophysiologic responses to footwear interventions is necessary to help confirm any sensorimotor adaptations.

Mechanical Stability and Unfolding Pathways of Parallel Tetrameric G-Quadruplexes Probed by Pulling Simulations.

Guanine quadruplex (GQ) is a noncanonical nucleic acid structure formed by guanine-rich DNA and RNA sequences. Folding of GQs is a complex process, where several aspects remain elusive, despite being important for understanding structure formation and biological functions of GQs. Pulling experiments are a common tool for acquiring insights into the folding landscape of GQs. Herein, we applied a computational pulling strategy─steered molecular dynamics (SMD) simulations─in combination with standard molecular dynamics (MD) simulations to explore the unfolding landscapes of tetrameric parallel GQs. We identified anisotropic properties of elastic conformational changes, unfolding transitions, and GQ mechanical stabilities. Using a special set of structural parameters, we found that the vertical component of pulling force (perpendicular to the average G-quartet plane) plays a significant role in disrupting GQ structures and weakening their mechanical stabilities. We demonstrated that the magnitude of the vertical force component depends on the pulling anchor positions and the number of G-quartets. Typical unfolding transitions for tetrameric parallel GQs involve base unzipping, opening of the G-stem, strand slippage, and rotation to cross-like structures. The unzipping was detected as the first and dominant unfolding event, and it usually started at the 3'-end. Furthermore, results from both SMD and standard MD simulations indicate that partial spiral conformations serve as a transient ensemble during the (un)folding of GQs.

Step Displacement Improving Method of Inertial Actuated Piezoelectric Robot Based on Diagonal Deformation Trajectory

For the miniature piezoelectric robots operated by inertial driving method, the step displacements were limited by the deformations of the inertial units. Thus, a diagonal inertial driving method (DIDM) was proposed in this work to increase the step displacement. The prominent feature of DIDM was that the inertial force was in diagonal direction by using the designed piezo-leg with square cross-section. The vertical component of the inertial force reduced the friction force and even made the robot jump to achieve a larger step displacement. Experimental results indicated that the proposed DIDM increased the step displacement successfully. The increase effect was optimal when the vertical component of the inertial force was equal to the horizontal one, and the realized step displacement was as high as 156% to the deformation of the inertial unit in motion direction. Moreover, the force and displacement responses of the driving foot in vertical direction were measured, which indicated that the robot realized jumping action to increase the step displacement under DIDM, and the maximum speed realized by DIDM was 2.3 times of that achieved by TIDM. We believe that the proposed DIDM can broaden the solutions of improving the performances of the inertial miniature piezoelectric robots.

Biomechanical gait analysis and rehabilitation in a traumatic hallux deficit patient: a case report

BackgroundThe hallux plays a crucial role in maintaining standing balance and facilitating forward and backward movements during gait.Case presentationA 21-year-old Japanese patient, suffering from a traumatic hallux deficit with only a portion of the basal phalanx intact, underwent rehabilitation treatment. The thenar area exhibited instability, leading to impaired balance and walking difficulties. Biomechanical assessment revealed the need for a rehabilitation strategy for the foot, as well as the knee, hip, and trunk. A rehabilitation protocol was designed to enhance medial foot loading during walking and standing, including balance and trunk strength training. After a 12-week rehabilitation period, the patient’s gait showed significant improvement. Specifically, the load response and single-support phases of the gait cycle on the affected side increased from 46.9% to 49.3%, while the pre-swing phase decreased from 14.6% to 11.6%. The vertical component of the ground reaction force rose from 599.8 to 647.5 N. The enhanced stability from balance training and increased muscle strength contributed to the patient’s improved walking and balance.ConclusionA patient with a traumatic hallux deficit underwent conservative treatment through strategic rehabilitation according to biomechanical assessment. This case report underscores the value of biomechanical gait analysis in the conservative management of similar conditions.

Experimental study on the droplet size distribution of radial orifice gas–liquid pintle injector at ambient pressure

Pintle injector can achieve reliable and stable combustion of propellant, thereby greatly reducing the design difficulties of the combustion chamber. Droplet size, which has a great influence on the subsequent combustion process with high ambient pressure, is an important atomization characteristic. However, the influence of ambient pressure on the droplet size distribution of radial orifice gas–liquid pintle injector has not been extensively investigated. At the ambient pressures of 0.4–0.6 MPa, the tests were carried out in the ambient pressure chamber with the liquid mass flow rates of 10–15 g/s and the gas mass flow rates of 7.2–15 g/s. Droplet size was measured by Spraylink High-speed Spray Particle Size Analyzer. The results indicate that droplets Sauter mean diameter (SMD) increases with axial and radial distances. A dimensionless parameter N, which represents the ratio of the vertical component of droplet aerodynamic force to gravity, is defined to analyze the reasons for the change trend of axial droplet size in the central reflux zone of the spray field where droplet size increases with axial distance. Droplets SMD increases with ambient pressure and liquid mass flow rate, and decreases with increasing gas mass flow rate. Furthermore, droplets SMD is positively correlated with local momentum ratio (LMR), whereas negatively correlated with Weber number (We). The empirical formula for axial cross-sectional droplets SMD was fitted with a determination coefficient of 0.993. The results can help elucidate droplet spatial distribution and the influences of several working parameters on the spray characteristics, thereby facilitating the design of pintle injector.

A numerical study on the effect of asymmetry on underwater noise emission in offshore monopile installation

Offshore wind energy holds significant promise as a solution in the energy transition. However, installing offshore pile foundations can generate substantial levels of underwater noise, posing potential risks to marine life. This paper examines the influence of asymmetric impact forces and pile inclination on producing underwater noise and seabed vibrations based on cases of a small- and large-diameter monopile. The study focuses on scenarios involving inclined and eccentric forces and tilted piles. The analysis reveals that non-symmetrical conditions significantly impact the sound pressure levels around the ring frequency of the pile due to various noise generation mechanisms. However, it is observed that the vertical component of the impact force predominantly contributes to the generation of underwater noise, primarily due to its considerably higher amplitude.

Comparison of the Vertical and Horizontal Components of the Ground Reaction Force of Patients with Anterior Cruciate Ligament Reconstruction and Healthy Individuals during Walking

Introduction: The aim of this research was to compare the vertical, medial-lateral and anterior-posterior components of ground reaction force after anterior cruciate ligament reconstruction with the healthy individuals during walking.
 Methods: This was an analytic cross sectional research. The participants of this research included 46 football and volleyball athletes, who were divided into two groups of individuals with anterior cruciate ligament reconstruction (ACLR) and healthy individuals. A force plate was employed to evaluate the components of the ground reaction force while walking.The data were statistically analysed using independent t test and SPSS version 16 software.
 Results: The results related to the vertical component of ground reaction force showed that the participants with anterior cruciate ligament reconstruction applied more force to the ground during heel strike and toe-off compared to healthy individuals, although the difference between the two groups was not significant (p=0.09 and p=0.35), but this difference was greater during heel strike. Likewise, the results related to the horizontal components of the ground reaction force showed that participants with anterior cruciate ligament reconstruction applied more force to the ground in all horizontal components of the ground reaction force, but the biggest difference between the two groups was in the first 20% of the stance phase and in the posterior (p<0.007) and lateral (p<0.02) directions. This difference between the two groups was significant.
 Conclusion: The results of the research showed that the most important difference between the two groups occurred in the first 20% of the stance phase. Although among the 6 measured components, only the posterior (p < 0.007) and medial (p < 0.02) ground force components were significant.

Effect of protective taping on knee eversion angle and jump height during single-leg vertical jumps in patients with anterior cruciate ligament reconstruction.

[Purpose] Taping is often performed to prevent injury and injury recurrence. However, it is unclear how taping affects landing and jumping kinematics in patients undergoing anterior cruciate ligament reconstruction. Therefore, this study aimed to determine the kinematic effects caused by taping during single-leg vertical jumps in patients with anterior cruciate ligament reconstruction. [Participants and Methods] Ten young patients who underwent anterior cruciate ligament reconstruction were included. The maximum knee joint flexion angle, peak value of the vertical component of the floor reaction force, maximum knee joint eversion angle, and jumping height during a single-leg vertical jump were measured using a three-dimensional motion analyzer and compared among the following three groups: without taping, with protective taping using elastic tape, and with protective taping using non-elastic tape. [Results] There were no significant differences in the peak value of the vertical component of the floor reaction force or the maximum knee joint flexion angle among the three groups. The maximum knee joint eversion angle and jumping height were significantly lower in the elastic tape and non-elastic tape groups than in the non-taping group. [Conclusion] Anterior cruciate ligament taping does not affect the magnitude of the impact on the body and can decrease knee joint eversion. However, jumping height was lower in the two taping groups than in the no-taping group. There were no significant differences in the items studied between the two taping groups.

Analytical theory of composite beams with CSWs using the state space method

Based on the zig-zag theoretical model of corrugated steel web beam (CSW), the governing equations in the form of state equations are derived and their analytical solutions are obtained for different loads, variable cross-sections and boundary conditions. Through numerical examples, it is verified that the bending moment, deflection and stresses predicted by the present analytical method have a good agreement with the results of the three-dimensional finite element model. The applicability of the present method for non-prismatic continuous beams with CSWs under different loads is also demonstrated. Meanwhile, it is found that the quasi-plane assumption is still valid in non-prismatic continuous beams with CSWs. Through quantitative analysis of the flexural stresses in the top and bottom slabs, it is confirmed that the zig-zag theory in this study can well reflect the accordion effect of CSWs. Because of the inclined bottom slabs in the non-prismatic beams with CSWs, the Resal effect on the shear stresses in the CSWs and bottom slabs, which is caused by the vertical component of the axial force in the bottom slab, is discussed. A refined shear formulation is developed for more accurate shear stresses in the CSWs and bottom slabs, which provides fundamental theoretical support for the strength prediction of the non-prismatic beam with CSWs.

Mixing of powders under periodic shear stress: effect of initial filling level

Powder Mixing continues being of great importance in the field of particle technology because of the challenge to get homogeneous mixtures at a large scale. However, it is still moderately understood because of the complexity of designing 3D experiments that consider all the factors affecting the powder flow and powder mixing, hindering the acquisition of enough data that would provide a basic conception of powder behavior. This study involves a simple granular material mixing system of low friction that has five walls, where two of them are high friction moving walls following a cyclic function, and the others are non-friction static walls. The purpose was to create a complete set of 3D experiments of powder distribution to have a better insight into the inside mixing behavior as a function of the initial powder filling level. Experiments at different filling heights were run, obtaining the best mixing at the highest filling level. It was obtained a non-mixing zone with a triangle shape highly affected by the column particle weight. The increase of the vertical component of the resultant force produced by the acrylic motion walls causes a high momentum transfer in the x, y and z directions resulting in a decrease in the no-mixing zone. It was found an asymptotic behavior of the triangle height as a function of the initial filling height of the powders which indicates that values above a limited initial filling level will not have a significant effect on the triangle. A filling height increment of 100 % from 3.81 to 7.62 cm causes an increase in the mixing of 4.44 %. DEM simulations for mixing in the low-shear equipment were run to compare the experimental work

Monitoring of structures with bearing elements in the form of long vertical rods

A building structure is considered, which in the design form consists of two vertical rectilinear interacting elements. One of them is loading, the other is carrying. The bearing element is presented in the form of a long thin rod loaded with an external axial vertical force. Due to the errors of geodetic verification and installation work, the bearing rod will be installed with some inclination and displacement relative to the coordinate axes. The external load on the bearing element is represented by the force vector, which is equivalent to the loading rod. Errors of geodetic verification and installation work will change the design direction of the force line and its design position on the supporting element. An inclined force vector will have a vertical and horizontal force component. Thus, the line of action of the loading force and the longitudinal axis of the supporting rod will be located at an angle to each other, which will cause bending momentsand transverse forces in the sections of the rod. A design "changed" in relation to the project is created. Bending moments and horizontal forces in this design will contribute to premature bending of the rod. An unevenly heated rod also acquires the ability to distort. The influence of the specified factors can be increased, and the stability of the rod significantly weakened due to uneven subsidence, horizontal displacement or tilting of the supporting structure due to dangerous exogenous geological processes. Therefore, errors in the position of elements, changes in temperature, geological processes disrupt the linear form of equilibrium of the bearing rod and its position in space. The change in shape and relative position contributes to the premature emergence of an unstable state under an increasing external load. In the changed design, the bearing rod may suddenly find itself in a critical stress-deformed state. The task of monitoring is to sense and properly record changes and dynamics of the stress-strain state. For this purpose, measuring complexes with a certain configuration are designed, which provide with the necessary specified accuracy the measurement of changes in the physical state of the elements of building structures.

Prediction Of The Coefficient Of Friction In The Single Point Incremental Forming Of Truncated Cones From A Grade 2 Titanium Sheet

The aim of this paper is to analyze the effect of the process parameters on the coefficient of friction (COF) in the single-point incremental forming process. This investigation may be useful for further FEM analyses where the tool-workpiece contact must be set appropriately to obtain adequate results. The friction was analyzed between a solid tungsten carbide ⌀8 hemispherical ended tool with a radius of 4 mm and a grade 2 pure titanium sheet. As a lubricant, 10W40 engine oil was used. The experiment was of a central composite design and 20 runs in random order were carried out. The influence of input factors, namely spindle speed, tool feed and incremental step depth, was analyzed for the COF response. Two type of equations founded in the literature have been acquired to calculate COF values. An investigation of COF analysis was done for initial tool contact, the first tool full depth contact and stabilized forming region. Additionally, single components of the horizontal force (X-axis and Y-axis) were taken into account. Analysis of variance shows that there is no correlation between the input factors and the COF responses. However, the mean model fitted to the results obtained allows for the prediction of the COF by using the vertical force component and only one horizontal force component. The resulting mean value of the COF between the tool and the workpiece equals 0.4 for Eq. (1) initial contact, stabilized forming: Eq. (1) 0.656 and Eq. (2) 0.469.

Deformation and breakup behaviors of a Giesekus viscoelastic droplet in Newtonian shear flow

The deformation and breakup of a Giesekus viscoelastic droplet suspended in a Newtonian matrix under simple shear flow is investigated through a lattice Boltzmann method, which uses the color-gradient model for immiscible two-phase flows while coupling a lattice advection-diffusion scheme for the Giesekus constitutive equation. The influence of the Deborah number (De) and shear-thinning mobility parameter (α) of the droplet is first explored for relatively low capillary numbers (Ca). The transient overshoot is observed before the deformation reaches the steady state, and the overshoot generally increases with De but decreases with α. With the increase of De, the steady-state deformation parameter first decreases and then increases, which is attributed to two opposite effects on the elastic force, namely the promoting effect from the increased polymer extension and the inhibiting effect caused by the deviation of the location where the maximum elastic force occurs from the droplet tips. The droplet inclination angle varies little with α but increases with De, where the latter can be explained as an increased vertical component of viscous and elastic forces in the tip regions. Upon increasing α, the steady-state deformation parameter becomes higher due to the reduced elastic force at the droplet tips. In addition, the phase diagrams of Ca-De and Ca-α are presented in which the critical capillary number Cacr characterizing the droplet breakup can be identified. It is found that Cacr varies non-monotonically with De, while Cacr is not very sensitive to α.