# Coupling Analytical and Numerical Models to Simulate Thermomechanical Interaction During the Milling Process of Thin-Walled Workpieces

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

## Abstract

Lightweight design is continually gaining in importance within the engineering sector, thus leading to a wide array of low rigidity components that are very demanding regarding the milling process in case manufactured by cutting. Within this chapter a new approach to model thermomechanical effects that occur during the milling process of thin-walled structures is introduced. For this purpose, an empirical process heat model was developed, which is calibrated by deformation measurements. In conjunction with well-established analytical cutting force models, the proposed process heat model was coupled with a numerical model of the workpiece to predict process induced deformations. This allows for the design of counter measures in order to either reduce occurring workpiece deflections or to compensate the resulting geometrical error. It was shown in experiments that both, an optimization of process parameters as well as a tool path adaption, can be successfully applied to avoid the violation of tolerance specifications without affecting the productivity of the milling operation.

## Nomenclature

a

Area of active surfaces associated to the heat flux in vector $$\uplambda_{\Delta }$$

$${\text{a}}_{\text{e}}$$

Cutting width

$${\text{a}}_{\text{p}}$$

Cutting depth

$${\text{b}}_{\text{w}}$$

Remaining wall thickness

c

Model constant

d

Tool diameter

$${\text{f}}_{\text{z}}$$

Feed per tooth

i, j

Counter of independent parameters

$${\text{J}}_{\text{T}}$$

Cost function of thermal regression models

k

Number of regression model

$${\text{k}}_{\text{c}}$$

Specific cutting energy

$${\text{m}}_{\text{k}}$$

Row size of vectors and matrices

$${\text{n}}_{\text{k}}$$

Column size of matrices

n

Rotational speed of the tool

p

Position

$${\text{P}}_{\text{c}}$$

Cutting power

$${\text{Q}}_{\text{w}}$$

Material removal rate

$${\dot{\text{q}}}$$

Heat flux

$${\text{R}}^{2}$$

Coefficient of determination

t

Time

$${\text{u}}_{\text{y}}$$

Total deformation of the workpiece (in y-direction)

$${\text{u}}_{\text{T}}$$

Thermally induced deformation of the workpiece

$${\text{u}}_{\text{dyn}}$$

Dynamic component of the deformation

$${\text{u}}_{\text{stat}}$$

Static component of the deformation

$${\text{u}}_{\text{plast}}$$

Plastic component of the deformation

$${\text{v}}_{\text{c}}$$

Cutting speed

$${\text{v}}_{\text{f}}$$

Feed

x

Independent parameter

z

Number of flutes

$${\text{z}}_{\text{MP}}$$

Z-position of the measuring point (MP)

$$\beta$$

Helix angle of the tool

$$\Delta$$

Difference of two regression models (k)

$$\upgamma$$

Angular position of the leading cutting edge

$${\varvec{\uplambda}}$$

Vector of independent parameters

$${\boldsymbol{\varphi }}$$

Vector of linear model constants

$${\varvec{\Omega}}$$

Matrix of quadratic and linear interacting model constants

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