Ji Wang - Milpitas CA Jiun-Der Yu - Mountain View CA Tsutomu Imai - Nagano-ken, JP
Assignee:
Seiko Epson Corporation - Tokyo
International Classification:
G06F 1750
US Classification:
703 13, 703 2, 703 4, 703 6, 703 7, 703 14
Abstract:
An apparatus and method for determining certain correction factors in analyzing the vibration frequency characteristics of an electroded crystal plate. The developed correction factors are introduced to correct the inaccuracies of third-order thickness-shear cut-off frequencies. The analysis is preferably carried out during the design of a piezoelectric device incorporating the electroded crystal plate before production of the device.
Slipping Contact Line Model And The Mass-Conservative Level Set Implementation For Ink-Jet Simulation
Jiun-Der Yu - Sunnyvale CA, US Shinri Sakai - Suwa, JP
Assignee:
Seiko Epson Corporation - Tokyo
International Classification:
G06G 7/48 G06G 7/50
US Classification:
703 9, 703 6, 703 13
Abstract:
A macroscopic physical model simulates and analyzes ink ejection from a piezoelectric print head. The model handles the slipping contact line problem and introduces a mass-conservative finite difference implementation using the level set method. First, the critical angle approach is adopted. The triple point is allowed to move if the critical angle is exceeded. Second, the no-slip boundary condition in the neighborhood of the triple point is relaxed and substituted by the free-slip boundary condition. Third, to allow the triple point to quickly accelerate when the critical angle is exceeded, an extra surface tension is added as a body force term in the governing equation. Fourth, the level set method is adopted to implement the slipping contact line model. Finally the above idea is incorporated in a fluid solver based on the higher-order projection method.
Coupled Quadrilateral Grid Level Set Scheme For Piezoelectric Ink-Jet Simulation
Jiun-Der Yu - Sunnyvale CA, US Shinri Sakai - Suwa, JP
Assignee:
Seiko Epson Corporation - Tokyo
International Classification:
G06G 7/50
US Classification:
703 9, 73861, 73488, 702 12, 702100
Abstract:
Methods for finite-difference-based inkjet simulation enable more precise control of ink droplet size and shape. A discrete transformation (mapping) is constructed so that a quadrilateral grid in physical space is transferred to the uniform square grid in a computational space. Since the grid in the computational space is square, numerical finite difference differentiation can be easily done. Governing partial differential equations, including a viscosity term, a surface tension term, and a level set convection equation for two-phase flows, are derived on the quadrilateral grid and then transformed to the computational space for application on the uniform square grid. A stable and powerful numerical algorithm is developed to solve the derived and transformed equations to enable finite-difference-based ink-jet simulation.
Consistent Back Pressure For Piezoelectric Ink-Jet Simulation
A consistent back pressure formulation is introduced into ink-jet simulation models and algorithms to solve an instability problem that occurs as the head of an ink droplet reaches the end of the solution domain during simulation. The consistent back pressure formulation is obtained in a way that is consistent with the idea of interface smearing. Formulas for calculating the pressure boundary condition on quadrilateral grids are disclosed. An ink-jet simulation example is given to demonstrate the improved models and algorithms.
Selectively Reduced Bi-Cubic Interpolation For Ink-Jet Simulations On Quadrilateral Grids
A selectively reduced bi-cubic interpolation on quadrilateral grids for level set re-distancing improves finite-difference-based ink-jet simulation. The “bi-cubic” nature of the interpolation helps the scheme conserve droplet mass. The “selectively reduced” logic prevents the higher-order simulation algorithm from introducing new instability factors.
2D Central Difference Level Set Projection Method For Ink-Jet Simulations
A coupled level set projection method is incorporated into a finite-difference-based ink-jet simulation method to make the simulation easier and faster to run and to decrease the memory requirements. The coupled level set projection method is based on a central difference discretization on uniform rectangular grids. A constructed numerical projection operator, in the form of either a finite difference projection operator or a finite element projection operator, can be used in the central difference scheme, in which case the resulting linear systems can be solved by a multi-grid method. The finite difference projection operator is used when the fluid velocity is located at grid points and the pressure at cell centers, whereas the finite element projection operator is used when the fluid velocity is located at cell centers and the pressure at grid points.
Coupled Algorithms For Viscoelastic Ink-Jet Simulations
Two finite difference algorithms on rectangular grids are provided for viscoelastic ink ejection simulations. The first algorithm is first-order accurate in time, while the second algorithm is second-order accurate in time. Each of these two algorithms seamlessly couples or incorporates several features: (1) a coupled level set-projection method for incompressible immiscible two-phase fluid flows; (2) a higher-order Godunov type algorithm for the convection terms in the momentum equations and level set convection equation; (3) the central difference for viscosity, surface tension, and upper-convected derivative terms; (4) an equivalent circuit for inflow pressure (or inflow rate). In the first algorithm, a simple first-order upwind algorithm is designed for the convection term in the viscoelastic stress equations. But in the second algorithm, a second-order Godunov type upwind scheme is employed for the convection term in the viscoelastic stress equations.
Odd Times Refined Quadrilateral Mesh For Level Set
A process for simulating the motion of a first fluid, a second fluid and an interface between the first fluid and the second fluid. The fluid velocities and pressures of the first and second fluids are calculated at a first set of nodes on a first mesh at a first time step, representative of movement of the first and second fluids at the first time step. The level set, which is representative of a position of the interface, is calculated at the first time step, at a second set of nodes on a second mesh. The second mesh is odd times finer than the first mesh. The new fluid velocities and pressures of the first and second fluids are calculated at the first set of nodes at a second time step, representative of new movement of the first and second fluids at a second time step. The new level set is calculated at the second set of nodes, representative of a new position of the interface at the second time step.