1. Physics-guided machine learning for milling stability:
A numerical study of model training and updating
Jiang Jiang and Tony L. Schmitz
Mechanical Engineering and Engineering Science, University of North Carolina at Charlotte, Charlotte, NC, USA
Introduction
Physics-based model descriptions
receptance coupling substructure analysis (RCSA) used to predict the tool point receptance
mechanistic force model used to relate the cutting force to the commanded chip area
mean force frequency domain analysis used to predict stability limit using the first two models as inputs
Physics-based model uncertainty
deterministic models include uncertainty
for example, the actual extension length of the endmill from the holder
results in uncertainty in the tool point receptance which, in turn, leads to uncertainty in the stability limit
if a test is performed to determine the actual stability behavior of a spindle speed-axial depth combination, there is no straightforward mapping between this result and the model input parameters
New approach
use the (uncertain) physics-based stability model to train a machine learning (ML) algorithm
ML model is defined in the desired test domain of spindle speed-axial depth
updating can then proceed directly by collecting stability results and modifying the dataset used to re-train the ML stability model.
leverage Industry 4.0, where data collected during and after machining is used to achieve process improvement
each part becomes an experiment and the uncertainty in operating parameters can be reduced over time
Numerical case study
Physics-based models with intentionally inserted error
Updating Strategy 2 – grid
‘lazy update’ that selects a grid of equally spaced points over the full domain
number of points varied from 50 to 410
if the cut is unstable, then all the points with the same spindle speed but higher depth of cut are updated as unstable
if the cut is stable, then all the points with the same spindle speed but lower depth of cut are updated as stable
Define force model using best information available (includes errors).
Modeled force data
700 N/mm2 specific cutting force
68 deg force angle
True force data
800 N/mm2 specific cutting force
60 deg force angle
Define tool-holder-spindle-machine using best information available (includes errors).
Modeled tool
12 mm diameter
50 mm extension length from holder
4 teeth
True tool
53 mm extension length from holder
Tool point frequency response function for incorrect extension length
Chatter
Stable
Chatter
Stable
GOAL
By updating the training dataset, transform the stability limit from left (with errors) to right (true model)
Updating Strategy 3 – climbing
‘efficient update’ that uses fewer tests, 101 to 183
check stability for all points at 5 mm depth
for stable points, test at 7 mm depth (same spindle speeds)
for stable points, test at 10 mm depth (same spindle speeds)
requires less points and yields a better result
captures stability limit over full spindle range
Generate original dataset
from incorrect stability model, generate dataset with the shape of 20 (depth of cut/m) * 101 (spindle speed/rpm)
provides base for updating and online learning, features were normalized
dataset was divided into training set and test set with 70:30 ratio
Stage 1: Replicate the stability boundary
use three machine learning algorithms to replicate the stability boundary
determine accuracy from the test set (compared to the stability limit with input error)
Stage 2: Update the stability boundary with test cuts
Updating Strategy 1 – frequency analysis
‘smart update’ leverages physical knowledge to generate updating data points
select largest stable depth-spindle speed as the first cut, use MATLAB simulation to determine the process signals
determine if cut is stable or unstable, as well as the chatter frequency if it is unstable
use equation to find the spindle speed of the next cut
repeat
Physics-based model, y = f(x)
Input, x, related to output
Simulated output, ys
Physics-guided machine learning model, Y = f(x, ys, ym)
Output, Y
Measured data, ym, for input, x
AdaBoost
KNN
SVM
97.03%
96.20%
91.09%
Conclusion
study provides feasibility of physics-guided machine learning for milling stability
machine learning models to predict cutting stability for test dataset (with errors)
updated stability limit with error-free data
results were compared to the observed/true stability limit
accuracy of two updating strategies with three ML algorithms evaluated
climbing method for updating had highest accuracy
AdaBoost provided accuracy of 92.24% (model is correct for 92.24% of the test dataset compare to the true stability limit)
future research will consider other machine learning algorithms, such as neural network
combination of both synthetic and measured data will be used in future study
Machine learning
defined by Tom Mitchell as machine learns with respect to a particular task T, performance metric P, and type of experience E, if the system reliably improves its performance P at task T, following experience E
closely related to computer science, statistics, psychology and neuroscience
data mining, knowledge discovery, algorithm development, and problem solving
K-nearest neighbors (KNN)
makes decisions by referring to the K data points closest to selected data point
does not make assumptions over the distribution of the dataset
does not produce a generalized rule over the dataset
Support vector machine (SVM)
creates a hyperplane to separate the data points into two classes
chosen by maximizing distance between the hyperplane and the closest data points
maps the data points to a higher dimension, if required, so that a hyperplane can still divide them
AdaBoost
ensemble algorithm that groups weak classifiers into a combined classifier
with each round of training, the examples that were misclassified by the previous round get more weight when calculating the accuracy of the current classifier
forces the algorithm to focus on mistakes
base classifiers have weighted votes to generate the final results
Example
Test cut 1 with  = rpm, b = 20 mm
use MATLAB simulation to determine process signals
cut is unstable
choose spindle speed for Test cut 2
 = (60)/((j + 1)4) = rpm for j = 2, keep b = 20 mm
No.
Spindle Speed (rpm)
Depth of Cut (mm)
Status 1
15600 20 2
15233 3 15 4 5
15000 6
Test
AdaBoost
KNN
SVM
Original
dataset
81.19%
80.03%
84.82%
Grid
n=50
81.85%
80.20%
85.48%
n=110
82.01%
80.86%
86.14%
n=210
82.84%
82.18%
87.13%
n=410
Climbing
n=101
86.96%
87.79%
n=154
90.92%
89.60%
89.27%
n=183
92.24%
91.25%