Improving minimum strain energy curve calculations for flexible blade cutting

2006 ◽  
Author(s):  
Adrie Kooijman ◽  
Johan Broek
Keyword(s):  
Strain Energy ◽  
Energy Curve ◽  
Minimum Strain Energy ◽  
Blade Cutting

Exploration of Local Blade Motions During Blade Shaping for Thick Layered Foam Cutting

2004 ◽  
Author(s):  
J. J. Broek ◽  
A. Kooijman
Keyword(s):  
Strain Energy ◽  
Cutting Tool ◽  
Cutting Speed ◽  
General Rule ◽  
Free Form ◽  
Linear Change ◽  
Minimum Strain Energy ◽  
Blade Cutting ◽  
Tool Position ◽  
Cutting Direction

The FF-TLOM (Free Form Thick Layered Object Manufacturing) technology is a Rapid Prototyping process based on flexible blade cutting of polystyrene foam. The heated blade is shaped by three parameters, which allows an infinite amount of minimum strain energy blade shapes with none, one or two inflexions. In the shaping domain stable and unstable blade shapes can exist. Stable shapes are defined as curves with none and one-inflexion and are applied for operational cutting of foam layers with the FF-TLOM technology. The tool motions are generated from the static tool poses and are calculated for a linear change of the flexible blade, when the cutting tool moves from one tool position to the next. The cutting blade is positioned to the foam slab with help of a point relative positioned on the flexible blade. The tool frame is positioned with a point fixed relatively to the tool frame. During the tool motions the blade curvature is changed and will introduce a shift of the half way point fixed on the blade (especially in the case of asymmetrical support inclinations and high curvature). Next the local displacement of the blade points in the bending plane of the blade due to blade shaping and tool pitching are quantified during the tool motions. These displacements induce an angle of attack of the blade in cutting direction, and will influence cutting speed and cutting accuracy. The quantification software is developed and will be used in the future for an overall prediction of the total tool curve displacements due to blade shaping, such as roll, pitch, yaw and linear positioning motions of the tool. A general rule for FF-TLOM cutting is minimization of all tool motions, which are not related to the forward cutting motion.

Shaping Minimum Strain Energy Curves for FF-TLOM

2003 ◽  
Author(s):  
J. J. Broek ◽  
A. Kooijman ◽  
A. de Smit ◽  
I. Horva´th
Keyword(s):  
Strain Energy ◽  
Tool Path ◽  
Computing Time ◽  
Free Form ◽  
Energy Curve ◽  
Calculation Algorithm ◽  
Path Creation ◽  
Blade Shape ◽  
Minimum Strain Energy ◽  
A Chain

Free Form Thick Layered Object Manufacturing (FF-TLOM) technology is based on foam cutting with a curved heated flexible cutting blade. Three single parameters shape the flexible blade. An infinite amount of blade shapes can be selected. However, many of these shapes are not suitable for cutting. Blade shapes with less than two inflexions can be applied successfully. When two inflexions are involved the blade; more than one different stable blade shape can be realized. For tool path creation and cutting procedures the blade shape must be known. A 2-D calculation algorithm based on (Kallay, 1987) is used. The calculation result is a minimum strain energy curve of a prescribed length, which is represented by a chain of segments. The shape is unfolded by rotating each segment under conditions of total energy decrease until no improvements are achieved. In this paper the process parameters are analyzed for sensitivity and influence on the accuracy and conditions of the blade shaping process. An overview of these parameters is given and the accuracy, computing time and trustworthiness of the implemented algorithm is checked. Typical FF-TLOM process characteristics are considered for its influence on the blade shape The elastic energy of curves is presented for a complete range of blade shapes. Regions of bi-stable blade shapes are perceived based on more than one blade inflexion. Finally a selection is presented for those minimum strain curves, which are applicable for the FF-TLOM technology.

Speed Control for Flexible Blade Cutting of Thick Foam Layers

2002 ◽  
Author(s):  
J. J. Broek ◽  
I. Horva´th ◽  
A. Kooijman
Keyword(s):  
Manufacturing Process ◽  
Strain Energy ◽  
Tool Path ◽  
Estimation Method ◽  
Cutting Speed ◽  
Free Form ◽  
Energy Curve ◽  
Optimal Orientation ◽  
Blade Cutting ◽  
Manufacturing Time

The FF-TLOM (Free Form Thick Layered Object Manufacturing) process is based on heated flexible blade cutting of thick foam layers in a free form manner. Both blade ends are supported in a U-shaped tool frame. During cutting the blade is shaped in a minimal strain energy curve. Positioning the tool in an optimal orientation is provided by pitch, roll, yaw and positioning of the tool frame. A restriction of the FF-TLOM cutting is the cutting speed. The cutting speed depends on melting of the foam at the blade location and does not allow outside forces on the blade. Nevertheless the manufacturing time must be as rapid as possible. In this paper an estimation method is proposed for the overall speed setting along a tool path. Hereto the blade is subdivided in blade segments and each segment is analyzed for the encountered speed and in the same time to prevent that the maximum allowable cutting speed is exceeded.

Crack Driving Force in Anisotropic Media due to Non-Elastic Deformation

2004 ◽  
Vol 261-263 ◽  
pp. 75-80
Author(s):  
G.H. Nie ◽  
H. Xu
Keyword(s):  
Elastic Deformation ◽  
Driving Force ◽  
Strain Energy ◽  
Elastic Stress ◽  
Complex Function ◽  
Crack Driving Force ◽  
Special Cases ◽  
Degree Of Anisotropy ◽  
Minimum Strain Energy ◽  
Orthotropic Media

In this paper elastic stress field in an elliptic inhomogeneity embedded in orthotropic media due to non-elastic deformation is determined by the complex function method and the principle of minimum strain energy. Two complex parameters are expressed in a general form, which covers all characterizations of the degree of anisotropy for any ideal orthotropic elastic body. The stress acting on the long side of ellipse can be considered as a crack driving force and applied in failure and fatigue analysis of composites. For some special cases, the resulting solutions will reduce to the known results.

Prediction of Cylinder Flow Pressures in Mass-Flow Bins Using Minimum Strain Energy

1976 ◽  
Vol 98 (4) ◽  
pp. 1370-1374 ◽  
Author(s):  
A. G. McLean ◽  
P. C. Arnold
Keyword(s):  
Mass Flow ◽  
Strain Energy ◽  
Plane Flow ◽  
Geometry Design ◽  
Numerical Effort ◽  
Minimum Strain Energy ◽  
Flow Pressure ◽  
Energy Theory ◽  
Cylinder Flow ◽  
Complete Variation

Jenike, et al. [1] have presented a minimum strain energy theory to predict cylinder flow pressures in mass-flow bins. The complete variation of strain energy pressures is depicted by bounds requiring considerable numerical effort to develop for a specific cylinder geometry. Design charts are presented, but these are available for only two circular cylinder geometries. This paper summarizes and clarifies the minimum strain energy theory for predicting cylinder flow pressures. A single bound approximation which allows the magnitude of the peak flow pressure to be determined for both axisymmetric and plane flow cylinders is presented. This peak pressure may also be estimated by a single calculation of strain energy pressure. The usefulness and accuracy of these procedures are illustrated by reworking the example presented by Jenike, et al. [1].

Recent Results on the Elasticity Theory of Inclusions

1994 ◽  
Vol 47 (1S) ◽  
pp. S10-S17 ◽  
Author(s):  
Jin H. Huang ◽  
T. Mura
Keyword(s):  
Composite Materials ◽  
Work Hardening ◽  
Strain Energy ◽  
Volume Fraction ◽  
Exact Formula ◽  
Stress And Strain ◽  
Inclusion Problems ◽  
Elastic Fields ◽  
Work Hardening Rate ◽  
Minimum Strain Energy

A method drawing from variational method is presented for the purpose of investigating the behavior of inclusions and inhomogeneities embedded in composite materials. The extended Hamilton’s principle is applied to solve many problems pertaining to composite materials such as constitutive equations, fracture mechanics, dislocation theory, overall elastic moduli, work hardening and sliding inclusions. Especially, elastic fields of sliding inclusions and workhardening rate of composite materials are presented in closed forms. For sliding inclusion problems, the sliding is modeled by adding the Somigliana dislocations along a matrix-inclusion interface. Exact formula are exploited for both Burgers vector and the disturbances in stress and strain due to sliding. The resulting expressions are obtained by utilizing the principle of minimum strain energy. Finally, explicit expressions are obtained for work-hardening rate of composite materials. It is verified that the work-hardening rate and yielding stress are independent on the size of inclusions but are dependent on the shape and the volume fraction of inclusions.

Fracture of aluminum-epoxy layered composites containing cracks

1982 ◽  
Vol 17 (2) ◽  
pp. 75-78 ◽  
Author(s):  
E E Gdoutos
Keyword(s):  
Composite Plate ◽  
Strain Energy ◽  
Crack Extension ◽  
Critical Value ◽  
Layered Composites ◽  
Parallel Cracks ◽  
Two Parallel Cracks ◽  
Minimum Strain Energy ◽  
Uniaxial Compressive Stress ◽  
Strain Energy Density Theory

The plane problem of a composite plate consisting of two aluminum half-planes bonded together through an epoxy layer and containing two parallel cracks, one in the layer and the other in one of the half-planes was considered. The composite plate was loaded by a uniform uniaxial compressive stress distribution applied along the surfaces of the crack of either the layer or the half-plane. The critical value of the applied stress as well as the corresponding angle for crack extension were determined by using the minimum strain energy density theory. Valuable results governing the dependence of the critical failure stress of the composite plate as well as the angle of crack extension from the more vulnerable crack on the geometry of the plate were derived.

Optimization Research on Geometric Parameters of Scallop-Shaped Lattice Shells

2015 ◽  
Vol 724 ◽  
pp. 192-196
Author(s):  
Na Li ◽  
Ren An Chang ◽  
Wei Zong ◽  
Qi Hang Yu
Keyword(s):  
Mechanical Properties ◽  
Strain Energy ◽  
Geometric Parameters ◽  
Free Form ◽  
Spatial Structures ◽  
Shaped Surface ◽  
Minimum Strain Energy ◽  
Optimal Values ◽  
Lattice Shells

<p>Free-form and bionic spatial shells are popular in the area of spatial structures. Scallop-shaped surface is the product of evolution and a kind of spatial shells that can satisfy the mechanical requirements. Based on the scallop-shaped lattice shells, this paper focused on the optimization of geometric parameters. The principle of minimum strain energy was applied to conclude the influence law of the geometric parameters on mechanical properties. Finally the optimal values of geometric parameters were obtained. The results show that the optimization of geometric parameters presents the integrated significance to improve scallop-shaped lattice shells.</p>

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