Variations in Reaction Force of the Center of a Sleeve depending on Coiling Conditions in a Coiling Process
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Coiling is a process to wind a steel strip around a mandrel or sleeve. To wind a coil safely and efficiently, coiling tension σ and coiling speed v are important, but their relationships with the outcome have not been established clearly. Especially, too non-linear behavior among contact layers has been treated as a big task.
To be possible to operate the coiling flexibly, this paper establishes a finite element model of the coiling process, and suggests that reaction force FR on the sleeve is a key variable in the dynamic characteristics of the coiling process to know slip and stick (S&S) phenomenon among contact layers according σ and v.
Based on the finite element model, FR is investigated by frequency analysis and parametric analysis. Even though FR signal is too non-linear to be described clearly, this paper suggests the coiling status criterion by checking the direction cosine θload of the FR vector in the time–frequency domain according to σ and v, and by separating frequencies of the FR signal into the natural frequencies of the strip, and the slip phenomenon between the sleeve and the strip. Epecially, critical σ that changes the general frequency distribution of FR was selected by using mean squared coherence and used to calculate minimum required σ at each the outer radius ro of a wound steel coil.
When σ is sufficient, θload of the FR vector is applied at ~ 0° horizontally to the center of the sleeve by simulating the finite element models and by comparing dynamic responses to a 1-DOF mass–spring system with the S&S phenomenon. As σ increases, unsteady vibrations of FR also decrease. However, when σ decreases, the natural frequencies of the strip predominate. This trend is reversed in case of v. Based on these facts, a novel σ profile according to ro is derived in case of the real operating condition.
The results of this paper suggest that a sensor for measuring displacement, velocity, or acceleration should be installed on the housing of the bearing to detect the unusual coiling vibrations by checking the translational vibrations of the housing and by analyzing vibrations with this method in real time. Moreover, the suggested σ profile reduces radial stress on the sleeve, so maintenance costs and fraction defective can be minimized by preventing the sleeve and the coil from dents.
KeywordsCoiling Coiling tension Coiling speed Planar motions of the center Natural mode frequency of the strip Slip and stick phenomenon
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