Formation mechanism and modeling of surface waviness in incremental sheet forming

doi:10.1007/s11465-022-0679-1

Frontiers of Mechanical Engineering

2022, Vol. 17

Issue (2): 23 https://doi.org/10.1007/s11465-022-0679-1

本期目录

Formation mechanism and modeling of surface waviness in incremental sheet forming

Kai HAN^1,², Xiaoqiang LI¹, Yanle LI^3,⁴(

), Peng XU¹, Yong LI¹, Qing LI⁵, Dongsheng LI¹

¹. School of Mechanical Engineering and Automation, Beihang University, Beijing 100083, China
². Beijing Institute of Aeronautical Materials, Beijing 100095, China
³. School of Mechanical Engineering, Shandong University, Jinan 250061, China
⁴. Key Laboratory of High Efficiency and Clean Mechanical Manufacture, Ministry of Education, Jinan 250061, China
⁵. Materials Science Branch of Chinalco Research Institute, Chinalco Materials Application Research Institute Co., Ltd., Beijing 102209, China

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Abstract：

Improving and controlling surface quality has always been a challenge for incremental sheet forming (ISF), whereas the generation mechanism of waviness surface is still unknown, which impedes the widely application of ISF in the industrial field. In this paper, the formation mechanism and the prediction of waviness are both investigated through experiments, numerical simulation, and theoretical analysis. Based on a verified finite element model, the waviness topography is predicted numerically for the first time, and its generation is attributed to the residual bending deformation through deformation history analysis. For more efficient engineering application, a theoretical model for waviness height is proposed based on the generation mechanism, using a modified strain function considering deformation modes. This work is favorable for the perfection of formation mechanism and control of surface quality in ISF.

Key words： surface waviness incremental sheet forming numerical simulation formation mechanism deformation history

收稿日期: 2021-09-16 出版日期: 2022-07-20

Corresponding Author(s): Yanle LI

引用本文:

. [J]. Frontiers of Mechanical Engineering, 2022, 17(2): 23.
Kai HAN, Xiaoqiang LI, Yanle LI, Peng XU, Yong LI, Qing LI, Dongsheng LI. Formation mechanism and modeling of surface waviness in incremental sheet forming. Front. Mech. Eng., 2022, 17(2): 23.

链接本文:

https://academic.hep.com.cn/fme/CN/10.1007/s11465-022-0679-1
https://academic.hep.com.cn/fme/CN/Y2022/V17/I2/23

Fig.1

Fig.2

Fig.3

Tab.1

$σ 0$	K	n	F	G	H	N
61.83 MPa	192.67 MPa	0.28	0.56	0.58	0.42	2.99

Tab.2

No.	V/( $mm ? s − 1$ )	$F n$ /N	$F dcf$ /N	$μ$
1	10	499.99	125.88	0.13
2	10	999.81	307.34	0.15
3	10	1499.05	395.10	0.13
4	20	1001.26	241.12	0.12
5	30	999.48	240.20	0.12

Tab.3

Fig.4

Fig.5

Fig.6

Fig.7

Fig.8

Fig.9

Fig.10

$α$ /rad	$α f$ /rad	$α c$ /rad
π/6	0.51	0.64
π/4	0.74	0.83
π/3	0.98	1.09

Tab.4

Fig.11

Fig.12

Fig.13

Fig.14

Abbreviations
BS	Bending and stretching strain model
FE	Finite element
FM	Full model
ISF	Incremental sheet forming
MBS	Modified bending and stretching strain model
PM	Partial model
TPISF	Two-point incremental sheet forming
Variables
F, G, H, Q,M, and N	Material coefficients of Hill48 yield function
$F A$ , $F B$ , $F C$	Tangential forces per unit width in Regions A, B, and C, respectively
$F d c f$	Tension force in friction experiment
$F f$	Frictional force in friction experiment
$F n$	Compressive force in friction experiment
$H w$	Waviness height
$K$	Material coefficient of Ludwik constitutive function
$l$	Forming depth
L	Width size of partial FE model
n	Material hardening index of Ludwik constitutive function
r	Distance to the spherical centre
R	Tool radius
$R z$	Surface roughness of maximum peak to valley height
sz	Step size
$t 0$	Initial sheet thickness
V	Feed rate in friction experiment
$α$	Forming angle
$α f$	Actual contacting angle
$α t$	Actual forming angle after incremental forming
$β$	Residual forming angle
$σ 0$	Yield stress
$σ t a n$ , $σ c i r$ , $σ t h i$	Normal stresses in tangential, circumferential, and thickness directions, respectively
$σ tan A$ , $σ t h i A$	Tangential stress and thickness stress at Region A, respectively
$σ tan B$ , $σ t h i B$	Tangential stress and thickness stress at Region B, respectively
$σ t h i, r = R B$	Contact stress along the thickness direction at Region B
$σ x x$ , $σ y y$ , $σ z z$	Normal stresses along the X (rolling direction), Y (transverse direction), and Z (thickness direction) directions, respectively
$σ ¯$	Equivalent stress
$φ$	Current forming angle
$d ϕ$	Increment of tangential length
$d θ$	Increment of circumference width
$ε B, B S$ , $ε S, B S$	Bending strain and stretching strain in a bending and stretching strain model, respectively
$ε B, M B S$ , $ε S, M B S$ ,	Bending strain and stretching strain in MBS, respectively
$ε m a x P M$ , $ε m a x F M$	Max principal strain of partial and full model at specific forming depth of $l$ , respectively
$ε p$	Predeformation strain
$ε t a n$ , $ε c i r$ , $ε t h i$	Normal strains in the tangential, circumference, and thickness directions, respectively
$ε tan, B S$	Tangential strain evolution in BS
$ε tan, M B S$	Tangential strain evolution in MBS
$ε x x$ , $ε y y$ , $ε z z$	Normal strain along rolling direction, transverse direction and thickness direction, respectively
$ε ¯$	Equivalent strain
$μ$	Friction coefficient
$δ i$	Strain error

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