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Simulation Technologies

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Micro Metal Forming

Part of the book series: Lecture Notes in Production Engineering ((LNPE))

Abstract

Based on the physical principle of the conservation of momentum, the linear elastic deformation of a solid body is described by the time dependent or stationary elasticity equation.

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Abbreviations

apc :

Depth of cut (µm)

a 1pc , a 2pc :

Given depth of cut (µm)

a actpc (t):

Real depth of cut (µm)

a varpc :

Variation of the depth of cut (µm)

apcα :

Optimal depth of cut (µm)

a 1pcα :

Optimal depth of cut for a 1pc (µm)

a 2pcα :

Optimal depth of cut for a 2pc (μm)

Δapc :

Difference between the given a 1pc und a 2pc , the height of the ramp (µm)

a, b:

Parameters that describe the stochastic spread of the grain orientations around a basic orientation

B:

Force coefficient

C :

Stiffness matrix (MPa)

C :

Stiffness matrix of polycristal (GPa)

c :

Stiffness matrix of monocrystal (GPa)

F:

Force (N)

Fo :

Surface force (N)

Ft, Fr, Fax,:

Force in tangential, radial and axial direction (N)

Fx, Fy, Fz :

Resulting force in three orthogonal directions x, y and z (N)

F*:

Vector of three force components (N)

f:

Body forces (N/m3)

g, g0, \( \tilde{g} \) :

Rotation

hc :

Chip thickness (mm)

i:

Refraction index

j:

Number of cutting edges

k:

Number of small independent rotations

lh :

Height of the holder (mm)

Lq :

Lebesgue saces

m:

Function

n:

Rotational speed of the tool [Hz (1/s)]

q:

Parameters

t:

Time (s)

v:

Velocity (mm/s)

vf :

Feed velocity (mm/min)

v actf :

Current feed velocity (mm/s)

w:

Acement/deformation vector (m)

x:

Coordinate in x-direction (mm)

y:

Coordinate in y-direction (mm)

z:

Coordinate in z-direction (mm)

A :

Operator

α :

Regularisation parameter

γ :

run out angle [° (deg)]

δ :

Deflection (µm)

δt, δr, δax:

Deflection in radial, tangential and axial direction (µm)

δ v :

Virtual displacement (m)

Δ:

Difference (µm)

Δx:

Length of the ramp (mm)

ε :

strain tensor

ε, εel, εin:

Strain tensors

εxx,εyy,εzz,εxy,εxz,εyz:

strain tensor components

ζ :

orthogonal basis

θ1, θ2, θ3 :

Euler angle (rad)

η:

run out vector (µm)

ηx :

Run out vector in x direction (µm)

ηy :

Run out vector in y direction (µm)

υ :

variable

ξ :

Integration variable

ρ :

Density (kg/m3)

σ :

Stress tensor (MPa)

σ ij :

components of stress tensor (MPa)

\( \bar{\sigma } \) :

Averaged Stress tensor in RVE (MPa)

Φ :

Penalty functional

\( \phi \) :

accumulated plastic strain

φ :

Rotational angle [° (Deg)]

Ω :

Rotation matrix

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Authors and Affiliations

  1. Zentrum für Technomathematik, Universität Bremen, Bremen, Germany

    Peter Maaß

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  1. Peter Maaß
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Correspondence to Peter Maaß , Jonathan Montalvo-Urquizo , Jonathan Montalvo-Urquizo or Peter Maaß .

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Editors and Affiliations

  1. Klagenfurter Str. 2, Bremen, 28359, Bremen, Germany

    Frank Vollertsen

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Maaß, P. (2013). Simulation Technologies. In: Vollertsen, F. (eds) Micro Metal Forming. Lecture Notes in Production Engineering. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-30916-8_9

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  • DOI: https://doi.org/10.1007/978-3-642-30916-8_9

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  • Print ISBN: 978-3-642-30915-1

  • Online ISBN: 978-3-642-30916-8

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