Download presentation

Presentation is loading. Please wait.

Published byCali Tillison Modified over 2 years ago

1
Simple Is Beautiful – Refreshing thinking in engineering modeling and beyond Liming Chang Professor Penn State University Guest Professor National Chung Cheng University

2
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…….

3
I. An Analytical Model for the Basic Design Calculations of Journal Bearings R. K. Naffin and L. Chang

4
A basic journal bearing

5
Long-bearing model (L/D > 3)

6
Short-bearing model (L/D < 1/4)

7
A finite-bearing model Define a dimensionless load: Then for short bearings for long bearings

8
Take log: Or, short bearings long bearings

9
Approximate finite bearings by:

10
II. A Theory for the Design of Centrally-Pivoted Thrust Bearings L. Chang

11
Centrally-pivoted plane-pad thrust bearing

12
Classical lubrication theory fails to predict

13
Potential mechanisms of lubrication Viscosity-temperature thermal effect

14
Load capacity by thermal effect

15
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

16
A simple thermal-lubrication model: equations Reynolds equation: Pad equilibrium: Temperature equation: Oil ~ T relation:

17
Temperature distribution Temperature rise Dimensionless variables:

18
Pressure distribution Pressure Pad equilibrium Given solve for and

19
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

20
One-to-one relation between C th and W th

21
Bearing film thickness, h o h max = outlet film thickness under isothermal maximum-load-capacity condition (X =.58 )

22
Verification with numerical results for square pad

23
Further development of the theory for finite pads Y. Yan and L. Chang – Tribology Transactions, in press Infinitely-wide padFinite-width pad

24
h o /h max results

25
III. Research on gear meshing efficiency L. Chang and Y. R. Jeng Manuscript in review

26
Meshing of a spur gear pair Meshing loss can be less than 0.5% of input power

27
Meshing of a spur gear pair

28
Governing equations Reynolds equation Load equation Film-thickness equation Temperature equation Friction calculated by

29
Experimental repeatability scatter Test number Pinion speed (rpm) Pinion toque (N- m) Repeatability amounts to 0.04% of input power

30
Well, simple is beautiful! Hertz pressure distribution Parallel film gap Numerical solution of temperature equation

31
Thermal shear localization Cross-film velocity No localization With localization Upper surface Lower surface w

32
Effects of shear localization on oil shear stress

33
Effect of load on gear meshing loss

34
Effect of speed on gear meshing loss

35
Effect of gear geometry – module

36
Theory vs. experiment Theory Experiment Test number Pinion speed (rpm) Pinion toque (N-m)

37
Effect of gear geometry – pressure angle

38
Effect of gear geometry – addendum length

39
Oil property – viscosity-pressure sensitivity

40
Oil property – viscosity-temperature sensitivity

41
Effect of gear thermal conductivity

42
w Shear stress reduction with one surface insulated

43
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.

Similar presentations

© 2016 SlidePlayer.com Inc.

All rights reserved.

Ads by Google