Presentation on theme: "Simple Is Beautiful – Refreshing thinking in engineering modeling and beyond Liming Chang Professor Penn State University Guest Professor National Chung."— Presentation transcript:
Simple Is Beautiful – Refreshing thinking in engineering modeling and beyond Liming Chang Professor Penn State University Guest Professor National Chung Cheng University
Implications of Simplicity Deep understanding leads to simple approaches to problem solving Simple solutions often generate time-lasting significance Ability to solve a complex problem simply is the highest level of competency Three examples…….
I. An Analytical Model for the Basic Design Calculations of Journal Bearings R. K. Naffin and L. Chang http://www.mne.psu.edu/chang/me462/finite-journal.pdf
A simple thermal-lubrication model: assumptions Infinitely wide pad Conduction heat transfer negligible Convection heat transfer at cross-film average velocity Uniform shear-strain rate
A simple thermal-lubrication model: equations Reynolds equation: Pad equilibrium: Temperature equation: Oil ~ T relation:
Temperature distribution Temperature rise Dimensionless variables:
Pressure distribution Pressure Pad equilibrium Given solve for and
Bearing dimensionless load parameter, W th Load and dimensionless load Bearing load parameter = viscosity-temperature coefficient ~ 0.04 o C -1 = lubricant density ~ 900 kg/m 3 c = lubricant specific heat ~ 2000 J/kg- o C w/B = bearing working pressure ~ 5.0 MPa
Governing equations Reynolds equation Load equation Film-thickness equation Temperature equation Friction calculated by
Experimental repeatability scatter Test number Pinion speed (rpm) Pinion toque (N- m) 16000413 26000546 36000684 48000413 58000546 68000684 710000413 810000546 910000684 Repeatability amounts to 0.04% of input power
Well, simple is beautiful! Hertz pressure distribution Parallel film gap Numerical solution of temperature equation
Thermal shear localization Cross-film velocity No localization With localization Upper surface Lower surface w
Effects of shear localization on oil shear stress
w Shear stress reduction with one surface insulated
Summary Clever simple approaches to problem solving can help reveal fundamental insights and/or produce key order-of-magnitude results/trends. It is no small feat to develop a mathematic model that is simple and generally applicable. The significance of a simple model of general validity can be tremendous and long lasting.