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- Title
Vacuum-caps membranes' equilibrium state forms based on the energy criterion.
- Authors
Vatrenko, Oleksandr; Kyrylov, Volodymyr; Gavva, Oleksandr
- Abstract
Introduction. In order to describe the energy transformation that conditions the membranes' stable operation under a given mode of product processing, the studies of glass containers' vacuum caps membranes equilibrium state forms have been carried out. Materials and methods. The glassware containers represent the study object hereunder, the research subject being their caps' flexible membranes. Instrumental methods have been used to assess the membrane thickness and deflection. The forms of equilibrium state and membrane equilibrium energy levels were investigated through mathematical simulation by energy modeling. Results obtained and discussion. After loss of stability, the membrane shifts into a different position of stable equilibrium. The measurement results showed that at stability loss state, the membrane center additional deflection is f = 0,07 mm, that is significantly less than the membrane center initial deflection value, finit = 0,25 mm. Therefore, as a result of the stability loss the membrane working cone is not subjected to the mirror deformation. These deflection parameters ensure that the membranes are operable over a wide range of drop between the system backpressure (at an autoclave) and the container internal pressure throughout the product thermal processing. The circular plate total energy is represented as the sum of the zerotorque stress state energy, bending energy and the external pressure work values. Calculated is the derived membrane total energy equation, obtained are the membrane energy levels for different stable equilibrium states. Substituting the experimentally obtained value f in the calculated equation of stability loss state membrane total energy we get the cap membranes stability loss pressure value calculated for the considered case, P1 = 0,0326·106 Pa. The calculated value P1 is close to the cap membranes stability loss pressure value P1=0,03 MPa, specified by the caps manufacturer. The P1 pressure calculated value deviation from the real one can be influenced by the hardness of tin used to produce the cap bearing such membrane. The obtained energy levels of membrane's different equilibrium states at two different loads do correspond to the critical pressures of stability loss P1* and load releasing P2*. Both pressures energy levels diagrams built using the calculated equation, include the potential energy minimums. This form of the energy criterion curves for critical pressures is completely consistent with the Lagrange-Dirichlet theorem, since the pressure P1min* corresponds to the energy level minimum relative to other adjacent states. Conclusions The membrane total energy score equation and the energy levels for the equilibrium states corresponding to the critical pressures have been obtained.
- Subjects
GLASS containers; WORK values; GLASSWARE; POTENTIAL energy; ENERGY policy; VACUUM
- Publication
Ukrainian Food Journal, 2020, Vol 9, Issue 1, p185
- ISSN
2304-974X
- Publication type
Article
- DOI
10.24263/2304-974X-2020-9-1-16