Simulation Technologies

• Peter Maaß
Chapter
Part of the Lecture Notes in Production Engineering book series (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.

Keywords

Tool Path Representative Volume Element Forward Model Current Time Step Feed Velocity
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Latin

apc

Depth of cut (µm)

apc1, apc2

Given depth of cut (µm)

apcact(t)

Real depth of cut (µm)

apcvar

Variation of the depth of cut (µm)

apcα

Optimal depth of cut (µm)

apcα1

Optimal depth of cut for a pc 1 (µm)

apcα2

Optimal depth of cut for a pc 2 (μm)

Δapc

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

ab

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)

vfact

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)

Greek

A

Operator

α

Regularisation parameter

γ

run out angle [° (deg)]

δ

Deflection (µm)

δt, δr, δax

Deflection in radial, tangential and axial direction (µm)

δv

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

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)

σij

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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