Abstracts
In order to solve the problem of complicated calculation and large counter error of curve fitting method in industrial processing of noncircular glass ornaments, this paper proposes a grinding point searching algorithm. The successive approximation is used to find the grinding point of the workpiece contour and the grinding wheel. The proposed algorithm does not require complicated formula derivation and calculation and has good counter accuracy. According to the discrete characteristics of point-cloud data, a discrete cross-coupling iterative learning control algorithm is proposed to suppress the contour processing control error. Based on the norm theory, the convergence analysis and convergence conditions of the algorithm are presented. The effectiveness of the proposed algorithms is verified by experiments.
Similar content being viewed by others
Data availability
The datasets generated and analyzed during the current study are available from the corresponding author on reasonable request.
Code availability
Not applicable.
References
Bourhis EL (2007) Glass: mechanics and technology. Weinheim, WileyVCH
Zhong ZW, Venkatesh VC (2009) Recent developments in grinding of advanced materials. Int J Adv Manuf Technol 41(5–6):468–480
Lim SH, LEE CM (2006) A study on the development of CAD/CAM system for high precision cam profile CNC grinding machine. Transactions of the Korean Society of Machine Tool Engineers 15(5):44–50 (in Korean)
Kim HS, JEONG KS, LEE GD (1995) Structural design and evaluation of the three axis ultra-precision CNC grinding machine [J]. Trans of KSME 19(12):3392–3402
Suvorov VN (1970). Automatic machinery for processing the edges of round glass articles[J]. 27(6):372-374
Demirci I, Mezghani S, Mkaddem A, Mansori ME (2010) Effects of abrasive tools on surface finishing under brittle-ductile grinding regimes when manufacturing glass. J Mater Process Technol 210(3):466–473
Zhong ZW, Tian YB, Xie TG (2016) Investigation of subsurface damage of ground glass edges. Int J Adv Manuf Technol 87:3261–3269. https://doi.org/10.1007/s00170-016-8733-y
Sayuti M, Sarhan AAD, Fadzil M, Hamdi M (2012) Enhancement and verification of a machined surface quality for glass milling operation using CBN grinding tool-Taguchi approach. Int J Adv Manuf Technol 60(9-12):939–950
Ramesh R, Mannan MA, Poo AN (2005) Tracking and contour error control in CNC servo systems. Int J Mach Tools Manuf 45(3):301–326
Hu J, Shen H, Zeng S, Wang Y (2006) B-spline tool offset of a free-form curve in the shoe last high-speed machining CNC system. Int J Adv Manuf Technol 30(9-10):864–869
Yeh SS, Sun HC (2009) Implementation of online NURBS curve fitting process on CNC machines. Int J Adv Manuf Technol 40(5-6):531–540
Jiang H, Jiang BC, Xia L, Da-Zhu LI (2015) A B-Spline curve fitting algorithm based on contour key points. Appl Math Mech 36(4):423–431
Zhang M, Yao Z, Hu J (2010) Offset Algorithm for Non-circular Contour with Point Cloud Data. International Conference on Computer Application and System Modeling. Washington, D.C. USA: IEEE 2010(9):150–153
Huan J, Ma W (2010) Method for graphically evaluating the workpiece's contour error in non-circular grinding process. Int J Adv Manuf Technol 46(1-4):117–121
Zhang BL, Cao RM, Hou ZS (2019) The model-free adaptive cross-coupled control for two-dimensional linear motor. Trans Inst Meas Control 42(5):1059–1069
Wallam F, Tan CP (2019) Output feedback cross-coupled nonlinear PID based MIMO control scheme for pressurized heavy water reactor. Journal of the Franklin Institute 356(15):8012–8048
Tao S, Nelson CA, Justin B (2018) Design of a model-free cross-coupled controller with application to robotic NOTES. J Intell Robot Syst 95:473–489
Lu H, Fan W, Zhang Y, Ling H, Wang S, Alghannam E, Duan M (2018) Cross-coupled fuzzy logic sliding mode control of dual-driving feed system. Advances in Mechanical Engineering 10(2):168781401875551
Cao Y, Zhang Z (2018). Cross-coupled repetitive control of an XY compliant nanomanipulator[C]// Chinese Control Conference
Koren Y, Lo KC (1991) Variable-gain cross-coupling controller for contouring[J]. CIRP Annals- Manufacturing Technology 40(1):371–374
Funding
This study has been supported by the National Key Research and Development Project of China (Grants No. 2016YFC1400302), the National Science Foundation of China (61871163), the Zhejiang Provincial Natural Science Foundation of China (No. LQ19E070003), and Zhejiang Provincial Key Lab of Equipment Electronics.
Author information
Authors and Affiliations
Contributions
Xungen Li: conceptualization and methodology. Shuaishuai Lv: data curation, validation, and writing-original draft preparation. Mian Pan: visualization and investigation. Qi Ma: supervision. Wenyu Cai: writing-reviewing and editing. Haibin Yu: writing-reviewing and editing.
Corresponding author
Ethics declarations
Ethics approval
The research does not involve human participants or animals, and the authors warrant that the paper fulfills the ethical standards of the journal.
Consent to participate
It is confirmed that all the authors are aware and satisfied of the authorship order and correspondence of the paper.
Consent for publication
All the authors are satisfied that the last revised version of the paper is published without any change.
Conflict of interest
The authors declare no competing interests.
Additional information
Publisher’s note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Appendix
Appendix
Proof: substitute Eq (8) into Eq. (11) to get
Equation (15) can be rewritten as follows:
Reorganize Eq. (24) to get
For any given control input uk(j),j ∈ [0, N], the general solution xk(j) to the traffic system
can get
Take the norm on both ends of (28) to get
Define κ ≔ max {‖Aj − i − 2‖, j ∈ [0, N], i ∈ [0, j − 2]}, Eq. (29) can be sorted out.
By multiplying both sides of (30) by a−λj and making use of some trivial manipulations, we can obtain that for any j ∈ [0, N], what we can obtain after finishing is
where uk = max {‖ek − 1(i)‖λ| i ∈ [0, j − 2]},vk = max {‖τ(i)‖λ‖ek − 1(i)‖λ| i ∈ [0, j − 2]}.
By virtue of the contractive condition of (22),
\( {\displaystyle \begin{array}{l}\left\Vert \boldsymbol{I}-\boldsymbol{CB}{\varGamma}_d-\boldsymbol{CB}\omega {\tilde{\varGamma}}_{\varepsilon, d}{\omega}^T\right\Vert \\ {}+\left\Vert \boldsymbol{CB}\right\Vert \left(\frac{1}{2\rho}\left\Vert {\tilde{\varGamma}}_{\varepsilon, d}{\omega}^T\right\Vert +\frac{1}{2\rho}\left\Vert \omega {\tilde{\varGamma}}_{\varepsilon, d}\right\Vert +\frac{1}{4{\rho}^2}\left\Vert {\tilde{\varGamma}}_{\varepsilon, d}\right\Vert \right)<1\end{array}} \) with a sufficiently large λ, we can obtain
Taking limit as k → ∞, we have \( \underset{k\to \infty }{\lim }{\left\Vert {\boldsymbol{e}}_k(j)\right\Vert}_{\lambda }=0 \), and based on Eq. (18), we can obtain \( \underset{k\to \infty }{\lim }{\left\Vert {\varepsilon}_k(j)\right\Vert}_{\lambda }=0 \).
That is, as the number of iterations increases, the single-axis error and contour error both tend to 0.
Rights and permissions
About this article
Cite this article
Li, X., Lv, S., Pan, M. et al. Grinding method of noncircular glass ornaments based on successive approximation and discrete cross-coupling iterative learning control. Int J Adv Manuf Technol 114, 3823–3835 (2021). https://doi.org/10.1007/s00170-021-07076-5
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00170-021-07076-5