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

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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:

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.


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