Numerical Analysis of Cold Rolling of Lubricated Thin Metallic Foils
Date Issued
2007
Date
2007
Author(s)
Ko, Chang
DOI
zh-TW
Abstract
In this thesis, the lubrication problem by numerical simulation of foil rolling process is presented. We analyze the corresponding relationships between roll, foil and film shape which uses the two-dimensional Reynolds equation and refers to the mechanism of cold rolling of Coulomb friction established by Fleck. Meanwhile, we compute the distributions of pressure, strip stress and shear stress, which is based on the full lubrication configuration combined with the slab model. The mutually sensitive influence between film thickness and pressure adds to the difficulty and uncertainty of full-lubrication analysis. In order to obtain more stable results, scholars have generally adopted a mixed-lubrication regime in the past to guarantee the mutually dependent profiles between roll and foil. Due to asperities suppressed by the roll in the bite, it maintains the complete profile match. Even though the lubricant is presented, it is confined only in the valley. The foil deformation is grasped and the computation has comparatively good stability in the numerical simulation process.
Under full lubrication, high non-linearity appears and the completely coupled governing equation cannot be constructed because the roll and the foil are still separated by the lubricant. In addition, the diverse equilibrium equations and yielding criteria in discrete regions add to the complexity of unceasingly revising the boundary position during the iterative process.
In the study, the numerical results show that the flat zone and pressure hill are not obvious when the load is low. In addition, there exists only one neutral point between roll and foil. The maximum pressure peak position moves toward the outlet but cannot surpass the center of roll while increasing the initial load. Simultaneously, the reduction was also unable to increase apparently. In order to enhance the reduction, the pressure distribution of neutral zone is approximated as Hertz pressure when high load is applied. Then we repeatedly correct and iterate the pressure and film thickness at the inlet and outlet to obtain the second plastic reduction at the outlet. In this way, the reduction is enhanced and the final pressure curve is similar to Fleck’s Coulomb friction solution. Because of the interaction between the viscosity and the pressure at high reduction, it produces a friction coefficient higher than the Coulomb friction. Therefore, the load and torque are higher.
In the example analysis, we first compare the results of the same cases by Fleck and Sutcliffe and confirm the correctness of theory and computer program adopted in this research. At the same time, in other example calculation results, we completely discuss the related effects on rolling quality with the rolling speed, the viscosity of lubricating oil, the roll radius, the material strength of foil and forth and back tension. Furthermore, through the results in this research, it shows that pressure distribution of low and high reductions are distinctly approximated to hydrodynamic and elastohydrodynamic(EHD) lubrications respectively, which also corresponds with physical phenomenon.
Apart from confirming the practicability of cold rolling of full lubricated foil, this research also shows that the viscosity is the primary factor of apparent enhancement of friction shear stress and normal pressure, which will seriously affects rolling efficiency. Therefore, selecting lubricant of suitable viscosity will be an important topic of cold rolling of lubricated foil.
Subjects
冷軋
軋輥
金屬箔片
完全潤滑
塑性縮減
黏滯區
赫茲接觸
Cold Rolling
Roll
Metallic Foil
Full Lubrication
Plastic Reduction
Stick Region
Hertz contact
Type
thesis