Incremental Step Size Research Articles

Dimensional Accuracy of Single Point Incremental Forming

Dimensional Accuracy of Single Point Incremental Forming (SPIF) is studied with the use of a Box-Behnken design analysis. The dimensional accuracy of this process is determined by comparing parts manufactured using SPIF with the part drawings used to create the manufacturing toolpaths. Five factors are varied in the manufacturing of the SPIF process, and they are: material type, material thickness, formed shape, tool size, and incremental step size. The Box-Behnken design analysis allows for determination of how these factors affect the dimensional accuracy.

Influence of the incremental step size in work rate on exercise response and gas exchange in patients with pulmonary hypertension

BackgroundCardiopulmonary exercise testing (CPET) has become increasingly important as a routine procedure in daily clinical work. So far, it is generally accepted that an individualized exercise protocol with exercise duration of 6 to 12 minutes is preferable to assess maximal exercise performance. The aim of this study was to compare an individualized NYHA adapted exercise protocol with a fixed standard protocol in patients with severe pulmonary arterial hypertension.MethodsTwenty-two patients (17 female, 5 male; mean age 49 ± 14 yrs) underwent symptom limited CPET on a bicycle. On two consecutive days each subject performed a stepwise CPET according to a modified Jones protocol (16 Watt per minute stages) as well as an individualized NYHA adapted protocol with 5 or 10 Watt/min stages in a randomized order. Oxygen uptake at peak exercise (peakVO2) and anaerobic threshold (VO2AT), maximal ventilation (VE), breathing reserve (VE/MVV), ventilatory efficiency (VE vs. VCO2 slope), exercise time, maximal power and work rate were assessed and compared between both protocols.ResultsComparing both, adapted NYHA protocol and standardized Jones protocol, we found significant differences in maximal power (56.7 ± 19 W vs. 74 ± 18 W; p < 0.001) and exercise time (332 ± 107 sec. vs. 248 ± 72 sec.; p < 0.001). In contrast, no significant differences were obvious comparing both protocols concerning work rate, VE, VE/MVV, peakVO2, VO2AT and VE vs. VCO2 slope.ConclusionVariations of incremental step size during CPET significantly affect exercise time and maximal power, whereas relevant parameters for clinical judgement and prognosis such as oxygen uptake, ventilation and ventilatory efficiency remain unchanged. These findings have practical implications for the exercise evaluation of patients with pulmonary hypertension. To reach maximal results for ventilation, oxygen uptake and gas exchange an individualization of incremental step size appears not to be mandatory.

A normally latched, large-stroke, inchworm microactuator**This paper was presented at the 19th IEEE MEMS Conference, held in Istanbul, Turkey, 22–26 January 2006, and is an expansion of the abstract as printed in the Technical Digest of the meeting.

This paper presents the successful demonstration of a large-stroke, high-precision inchworm microactuator. The actuator is capable of zero-power latching, or forcibly maintaining its position by using pre-stressed spring load. The actuator is driven by a combination of a PZT-stack actuator unit for slider thrust and electrostatic comb-drive units for slider grip. Incremental step size is precisely adjustable to the tens of nanometers level by controlling the PZT-stack actuator voltage. The observed minimum step size was 59 nm/cycle. Large stroke is obtained by repeating the operation sequence numerous times. A large-stroke actuation exceeding 600 µm has been demonstrated. There is no conceivable limit to the stroke except for the length of the slider and external load.

Single Point Incremental Forming Limits Using a Boxbehnken Design of Experiment

Single Point Incremental Forming (SPIF) is a new method of forming sheet metal for which not all forming limits and forming parameters are yet completely understood. In this paper, a Box-Behnken design of experiment (DOE) is used to execute an experimental study used to determine the forming limits in Single Point Incremental Forming (SPIF). The Box-Behnken allows for good accuracy in defining a surface response for a relatively low number of experimental runs – hence its usefulness in experimental work. The Box-Behnken used in this paper solved five factors at three levels in forty six runs. The five factors analyzed are based on the most critical factors effecting SPIF; they are material type, material thickness, formed shape, tool size and incremental step size (depth of each step in form). The data resulting from the Box-Behnken progressed into graphical response surfaces; the response surfaces allow designers to determine what factors they need to select in order to successfully form a part using SPIF.

Hole flanging with ironing process of two-ply thick sheet metal

An incremental updated Lagrangian elasto-plastic finite element method(FEM) was employed to analyze the hole-flanging with the ironing of circulate plates using a pre-determined smaller hole at the center of the two-ply sheet metals. An extended r min technique was employed such that each incremental step size can be determined not only by the yielding of an element Gaussian point, but also by the change under the boundary conditions of penetration, separation, and the alternation of the sliding-sticking state of friction along the tool-sheet interface. Two-ply sheet metals are generally composed of metals that have different mechanical properties. Thus, the forming process of these materials is complicated. A number of experiments and simulations were performed using a conical punch with a cone angle of 45°. The experimental results were compared with FEM-simulated results. It is found that using the elasto-plastic FEM can effectively predict the generation process of the deformed shape until unloading. The calculated sheet geometries and the relationship between punch load and punch travel are in good agreement with the experimental data.

An elasto-plastic finite element analysis of the sheet metal stretch flanging process

The incremental updated Lagrangian elasto-plastic finite element method (FEM) was employed in this study to analyse the stretch flanging of circular plates with a pre-determined smaller hole at the centre of the sheet metal. An extended r min technique was employed such that each incremental step size is determined not only by the yielding of an element Gaussian point, but also by the change in the boundary condition along the tool-sheet interface. The experimental results, using a low-carbon (BA-CQ2) sheet plate with a thickness of 1.0 mm, have been obtained and compared with the corresponding theoretical results. It was found that the flange thickness does not always decrease monotonically from the die shoulder to the flange edge. Reducing the punch diameter and increasing the flange height significantly reduced the flange thickness. Web width does not influence the thickness distribution of the flange. The tendency of flange thickness to thin decreases as punch diameter increases. The reduction of thickness at the die shoulder depends on the die shoulder radius. Simulation results of punch load of stretch flanging, the deformed geometry, and the distribution of thickness are compared with experimental data and found to satisfactorily agree.

Forming Limit Curves in Single Point Incremental Forming

New experimental data is presented on Forming Limits in Single Point Incremental Forming (SPIF), which is a sheet metal forming process which does not require dies. A Box-Behnken Design of Experiment is used to develop the experimental plan and analyze data. In former work, the most critical factors affecting Single Point Incremental Forming were found to be material type, material thickness, formed shape, tool size, and incremental step size. In this experimental work, new results are presented as graphical response surfaces which show the forming limit for all the critical factors listed previously. In addition, forming limits are presented in terms of Forming Limit Diagrams.

Finite element analysis of axisymmetric sheet stretching process

The incremental updated Lagrangian elasto-plastic finite-element method (FEM) was employed in this study to analyse sheet stretching under the axisymmetric condition. The extended rmin technique is utilized such that each incremental step size is determined not only by the yielding of an element Gaussian point, but also the change of the boundary condition along the tool-metal interface. The frictional force in the contact region between the sheet and the tools is computed by the application of Coulomb’s friction law. Low-carbon (BA-DDQ) sheet plates were used throughout the experiments, which were later performed using a hemispherical punch head. Experimental tests were performed to demonstrate formulation of the theory and development of the computer code. The experimental load shows good agreement with the value of the punch load predicted by the finite-element method. When performing numerical calculation, the entire loading process history, the deformed geometry, the nodal velocity, and the distributions of strain and stress are also obtained by considering carefully the moving boundary condition. From the results of the experiment and the FEM, it may be concluded that the method proposed here provides a good model for simulating the axisymmetric sheet stretching process.

The formability limitation of the hole-flanging process

The incremental updated Lagrangian elasto-plastic finite-element method (FEM) was employed in this study to analyze the hole flanging of circular plates with a pre-determined smaller hole at the center of the sheet metal. An extended r min technique was employed such that each incremental step size is determined not only by the yielding of an element Gaussian point, but also by the change in the boundary conditions along the tool–sheet interface. The frictional force in the contact region between the sheet and the tools is computed by the application of Coulomb’s friction law. Low-carbon (BA–CQ 2) sheet plates were used throughout the experiments, which later were performed using a flat punch head. The experimental results were compared with FEM simulated results. It was found that using the elasto-plastic FEM can effectively predict the limitation of formability and the finished shape of the flanged holes.

Consideration of geometric nonlinearity in rigid—plastic finite element formulation of continuum elements for large deformation

A rigid—plastic finite element formulation for the continuum elements employing the geometric nonlinearity during an incremental time step is presented. In sheet metal deformation, the displacement for each step is considerably large even though the effective strain increment is very small. For such large displacement problems, geometric nonlinearity must be considered. In the elastic—plastic finite element using continuum elements, general incremental formulations to include the geometric nonlinearity are available. However, in the conventional rigid—plastic finite element analysis using continuum, elements, the geometric nonlinearity has not been considered properly during an incremental time step. In this paper, in order to incorporate geometric nonlinearity to rigid—plastic continuum elements during a step, the convected coordinate system is introduced. To show the stability of strain distributions by the effect of geometric nonlinearity according to incremental step size, two sheet metal forming processes, stretching and deep drawing process, are analysed with various step sizes. Then the computed results using the derived equation are compared with those obtained without considering geometric nonlinearity.

Influence of the die arc on formability in cylindrical cup-drawing

The incremental updated Lagrangian elasto-plastic finite-element method was applied in this study towards analyzing cylindrical cup-drawing under axisymmetric conditions. The extended r-minimum technique was employed such that each incremental step size is determined by not only the yielding of an element gaussian point but also by the change of the boundary conditions along the tool-metal interface. The Coulomb friction law was also adopted in calculating the influence of friction coefficients on the drawing process. A low-carbon steel (BA-CQ 2) was used as the test material in the experiments. Also, five various die-arc radii were designed, of value four-times to twelve-times the blank thickness, each die being used to draw the blank in the experiments. Results obtained for the punch-load in drawing, the material thickness variation after drawing and the limit drawing ratio (LDR) were compared both with the results of experiment and with the results of FEM analysis: the experimental and FEM results both confirmed that a greater LDR and a generally greater thickness would be obtained as a larger die-arc radius is used in the die-arc portion. These results have not only verified the reliability and accuracy of the computer simulation, but also could be used as references in the designing and manufacturing of dies for industrial applications.

Numerical and experimental study of large deflection of symmetrically laminated composite plates in compression

The stability behaviour of symmetrically laminated rectangular composite plates with loaded ends clamped and unloaded edges simply-supported, and subjected to uniform in-plane compression is investigated. A numerical and experimental investigation is presented in this contribution. The stacking sequence of the laminated glass/epoxy composite plates is symmetric about the middle surface and consists of 8-ply [0, 90, +45, -45]s lamination. Numerical predictions were obtained through the use of the finite element method. The above plates were modelled with 8-noded isoparametric layered shell elements. The effect of the input parameters such as the degree and forms of prescribed initial imperfection and the incremental step size required for incremental loading, on the convergence of the solution is thoroughly examined. Experimental results are presented for 10 test panels. All test panels were made from glass/epoxy unidirectional prepregs and have aspect ratio of 5.088. The laminate thicknesses were found to vary from 1.054 mm to 1.066 mm. Comparison of experimental data with predicted results show good correlation and give confidence in the finite element model.

P-Version two-dimensional beam element for geometrically nonlinear analysis

This paper presents a p-version geometrically nonlinear formulation (GNL) based on the total Lagrangian approach for a three-node two-dimensional curved beam element. The hierarchical element approximation functions and the corresponding nodal variables are derived directly from the Lagrange family of interpolation functions. The resulting element displacement approximation is hierarchical and can be of arbitrary and different polynomial orders in the longitudinal and the transverse directions of the beam element and ensures C 0 continuity. The element geometry is described by the coordinates of the nodes located on the axis of the beam (middle surface) and the nodal vectors describing the top and bottom surfaces of the element. The element properties are established using the principle of virtual work and the hierarchical element displacement approximation. In formulating the properties of the element complete two-dimensional stresses and strains are considered hence the element is equally effective for very slender as well as extremely deep beams. Incremental equations of equilibrium are derived and solved using the standard Newton-Raphson method. The total load is divided into increments, and for each increment of load, equilibrium iterations are performed until each component of the residuals is within a preset tolerance. Numerical examples are presented to show the accuracy, efficiency and advantages of the present formulation. The results obtained from the present formulation are compared with those reported in the literature. The formulation presented here removes virtually all of the drawbacks present in existing GNL beam finite element formulations and has many additional benefits. First, the currently available GNL beam formulations are based on fixed order of approximation for the displacements and thus are not hierarchical and have no provision for changing the order of approximation for the displacements u and v. Secondly, the element displacement approximations in the existing formulations are either based on a linearized displacement field for which a true Lagrangian formulation is not possible and the incremental load step size is severely limited or are based on nonlinear nodal rotation function approach in which case even though the description of the displacement field for the element is exact but additional complications arise due to the noncummutative nature of the nonlinear nodal rotation functions. The p-version displacement approximation used here does not involve the traditional nodal rotations that have been used in the existing beam formulations, thus the difficulties associated with their use are not present in this formulation.

An elasto-plastic finite-element analysis of the axisymmetric sheet stretching process

This paper applied the incremental updated Lagrangian elasto-plastic finite-element method to sheet stretching under the axisymmetric condition. The extended r-minimum technique is utilized such that each incremental step size is determined by not only the yielding of an element Gaussian point but also the change of the boundary condition along the tool-metal interface. Experimental tests were performed to demonstrate the formulation of the theory and the development of the computer code. The experimental load shows good agreement with the value of the punch load predicted in the finite-element method. In the solution of the numerical calculation, the entire loading process history, the deformed geometry, the nodal velocity and the distribution of strain are obtained also by carefully considering the moving boundary condition. From the results of the experiment and the FEM, it may be concluded that the method proposed here provides a good model to simulate the axisymmetric sheet stretching process.

Adaptive load incrementation algorithm during a process of local unloading in the elastic-plastic finite element analysis.

There are two approaches in the incremental finite element analysis of elastic-plastic problems; one takes an explicit scheme using forward Euler integration formula with adaptive load incrementation, the so-called rmin method, and another implicit scheme with iterative procedures such as the Newton method. This paper discusses an algorithm of determining incremental step size in the former approach. A new additional restriction is proposed for the determination of the loading factor rmin when unloading takes place. A concept of admissible error is introduced where errors in stress increments are defined as the difference between one computed by assuming the elastic-plastic constitutive relation and the other computed by assuming the elastic relation. The error norm should be restricted within specified value. Numerical examples are demonstrated to show that the algorithm is reasonable.

An Automated Profile Meter for Surface Roughness Measurements

ABSTRACT A profile meter for measuring linear profiles of stabil-ized sand surfaces was designed and constructed. A series of height measurements was obtained using a linear variable differential transformer (LVDT) as the sensing element. A stepper motor and gear train provid-ed the incremental step size between elevations. Data collection, recording and processing were performed using analog and digital computers in a fully automatic operation.

Sensorimotor discrimination during free jaw movements in man

Subjects carried out voluntary, unrestrained movements of the jaw to estimate position in space, a task involving coordinated sensory and motor functions. Incisal separation was derived from three-dimensional coordinates of movement by a magnetometer-based transducer system. Two experimental paradigms were used. One, based upon information theory, was designed to measure discrimination in terms of the number of reliably attained levels when 10 were attempted over two different ranges in both the opening and closing directions. The other method measured the variation of mean step size when subjects moved their jaws in small, equally-spaced incremental steps, opening and closing at different speeds. Using perceptual references at the intercuspal and maximum jaw opening positions, 6.5 separate levels were distinguished with accuracy, irrespective of the direction of movement. The group performance was significantly less (4.5 levels) over the smaller range between intercuspal and half-open positions. Discrimination was always best near the intercuspal position and at maximum jaw opening. No significant differences were evident in mean step size for the group in either direction of movement or speed of performance but there were marked individual differences in performance. In some, variations in incremental step size were smaller in closing than in opening phases. The presence of a zone of heightened sensorimotor acuity near the intercuspal position during free jaw movement indicates a specific adaptation of the nervous system.

CHARACTERISTICS OF AVERSIVE THRESHOLDS MEASURED BY A TITRATION SCHEDULE.

Three variables were studied for their single and joint effects on aversive thresholds obtained by a titration schedule with electric shock as the aversive stimulus. One variable was the interval between the periodic increments in shock amplitude. Another was the size of this increment. The third was the size of the decrement produced when the subject responded. Both monkeys and humans tolerated more shock at the shorter increment-to-increment intervals than at the longer ones, confirming rat data previously obtained. Reducing the decremental step size also led to an increase in the amount of shock tolerated by monkeys. In addition, simply reducing both incremental and decremental step size without changing the interval between increments led monkeys to tolerate more shock. The attempt to explain these data was based on the changes that such manipulations might produce in the amount of avoidance behavior elicited.