Position-varying surface roughness prediction method considering compensated acceleration in milling of thin-walled workpiece

doi:10.1007/s11465-021-0649-z

Front. Mech. Eng.

2021, Vol. 16

Issue (4) : 855-867 https://doi.org/10.1007/s11465-021-0649-z

RESEARCH ARTICLE

Position-varying surface roughness prediction method considering compensated acceleration in milling of thin-walled workpiece

Zequan YAO¹, Chang FAN¹, Zhao ZHANG²(

), Dinghua ZHANG^1,², Ming LUO^1,²(

)

¹. Key Laboratory of High Performance Manufacturing for Aero Engine (Ministry of Industry and Information Technology), Northwestern Polytechnical University, Xi’an 710072, China
². Engineering Research Center of Advanced Manufacturing Technology for Aero Engine (Ministry of Education), Northwestern Polytechnical University, Xi’an 710072, China

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Abstract

Machined surface roughness will affect parts’ service performance. Thus, predicting it in the machining is important to avoid rejects. Surface roughness will be affected by system position dependent vibration even under constant parameter with certain toolpath processing in the finishing. Aiming at surface roughness prediction in the machining process, this paper proposes a position-varying surface roughness prediction method based on compensated acceleration by using regression analysis. To reduce the stochastic error of measuring the machined surface profile height, the surface area is repeatedly measured three times, and Pauta criterion is adopted to eliminate abnormal points. The actual vibration state at any processing position is obtained through the single-point monitoring acceleration compensation model. Seven acceleration features are extracted, and valley, which has the highest R-square proving the effectiveness of the filtering features, is selected as the input of the prediction model by mutual information coefficients. Finally, by comparing the measured and predicted surface roughness curves, they have the same trends, with the average error of 16.28% and the minimum error of 0.16%. Moreover, the prediction curve matches and agrees well with the actual surface state, which verifies the accuracy and reliability of the model.

Keywords surface roughness prediction compensated acceleration milling thin-walled workpiece

Corresponding Author(s): Zhao ZHANG,Ming LUO

Online First Date: 10 September 2021 Issue Date: 28 January 2022

Cite this article:

Zequan YAO,Chang FAN,Zhao ZHANG, et al. Position-varying surface roughness prediction method considering compensated acceleration in milling of thin-walled workpiece[J]. Front. Mech. Eng., 2021, 16(4): 855-867.

URL:

https://academic.hep.com.cn/fme/EN/10.1007/s11465-021-0649-z
https://academic.hep.com.cn/fme/EN/Y2021/V16/I4/855

Fig.1 Milling dynamic model of thin-walled workpiece.

Fig.2 Flowchart of the proposed surface roughness prediction method based on compensated acceleration.

Fig.3 Thin-walled workpiece milling experimental setup.

Fig.4 Surface roughness measuring setup: Alicona InfiniteFocus G4.

Fig.5 Diagram of surface profile measurement.

Fig.6 Collected stable milling signal under the parameter of spindle speed 900 r/min, feed rate 180 mm/min, axial depth of cut 2 mm, and radial depth of cut 0.1 mm.

Fig.7 Scatter diagram of peak acceleration under sampling period of one rotation cycle.

Fig.8 Surface profile height of (a) initial signal and (b) eliminating outliers’ signal.

Tab.1 Recommended values for sampling length and evaluation length

Fig.9 Calculated surface roughness curve of the processed surface.

Fig.10 Mutual information coefficient and R-square of extracted features versus surface roughness. RMS: root mean square, STD: standard deviation, Var: variance, ARM: arithmetic mean.

Fig.11 Comparison between measured and predicted surface roughness.

ANN	Artificial neural network
ARM	Arithmetic mean
CNC	Computer numerical control
FA	Fuzzy algorithm
GA	Genetic algorithm
MIC	Mutual information coefficient
RMS	Root mean square
RA	Regression analysis
STD	Standard deviation
SVM	Support vector machine
TA	Taguchi analysis
Var	Variance
a _k	Elements of acceleration feature matrix
a _max	Maximum of the fitting function g( l)
a( l)	Monitored acceleration ( g)
$a ′ (l)$	Compensated acceleration at any position ( g)
A	Acceleration feature matrix
b	Undetermined constant
b ₀	$b 0 = lg ? ψ$
$b^0$ and $b^$	Regression coefficients
C( l)	Compensation coefficient
g( l)	Fitting function between vibration attenuation and distance (g)
H	Information entropy

J	Number of elements for surface roughness feature matrix
K	Number of elements for a certain acceleration feature matrix
l	Milling position
ln	Evaluation length (mm)
lr	Sampling length (mm)
m	Number sample data
n	Number of measuring points within the sampling length
P( a _k) and P( ra _j)	Probabilities of a _k and ra _j in features A _i and RA
P( a _k, ra _j)	Joint distribution probability of a _k and ra _j
ra _j	Elements of surface roughness feature matrix (μm)
Ra( l)	Surface roughness (μm)
RA	Surface roughness feature matrix
x	$x = lg ? a ′ (l)$
X	Coefficient matrix of x _i
y	$y = lg ? R a (l)$
$y^$	Statistical variable
Y	Coefficient matrix of y _i
z( x) and z _i	Ordinate value from each point on the assessed contour line to midline (μm)
α	Coefficient matrix of undetermined constant b
γ _i	Independent sample values
$γ ˉ$	Arithmetic mean of sample values
ε _i	Random error
ε	Random error matrix of ε _i
$ν i$	Residual error of sample values
σ	Standard deviation
ψ	Coefficient of cutting conditions and material

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