1. Chapter 13 質點系統結構分析 Analysis of Lumped Mass Systems

2. 2/31 Contents 13.1 與質點結構系統有關的元素 Elements for Mass-Spring-Damper Systems 13.2 實例 : 登陸系統的彈簧及組尼設計 Design of Spring/Damper in a Recoil Landing System 13.3 實例 : 磅秤的組尼設計 Example: Design of Damper in a Spring Scale 13.4 實例 : 淬火溫度分析 Example: Quenching of a Shaft 13.5 與質點系統相關的元素 Elements Related to Lumped-Mass Systems

3. 3/31 第 13.1 節 與質點結構系統有關的元素 Elements for Mass-Spring-Damper Systems

4. 4/31 13.1.1 MASS21: Structural Mass Element NameMASS21 NodesI Degrees of FreedomUX, UY, UZ, ROTX, ROTY, ROTZ if KEYOPT(3) = 0 UX, UY, UZ if KEYOPT(3) = 2 UX, UY, ROTZ if KEYOPT(3) = 3 UX, UY if KEYOPT(3) = 4 Real ConstantsMASSX, MASSY, MASSZ, IXX, IYY, IZZ if KEYOPT(3) = 0 MASS if KEYOPT(3) = 2 MASS, IZZ if KEYOPT(3) = 3 MASS if KEYOPT(3) = 4 Material PropertiesNone Surface LoadsNone Body LoadsNone Special FeaturesLarge deflection KEYOPT(2)Key for element coordinate system KEYOPT(3)0 - 3-D mass with rotary inertia 2 - 3-D mass without rotary inertia 3 - 2-D mass with rotary inertia 4 - 2-D mass without rotary inertia

5. 5/31 13.1.2 COMBIN14: Spring/Damper Element NameCOMBIN14 NodesI, J Degrees of Freedom UX, UY, UZ if KEYOPT(3) = 0 ROTX, ROTY, ROTZ if KEYOPT(3) = 1 UX, UY if KEYOPT(3) = 2 etc. Real ConstantsK, CV1, CV2 Material PropertiesNone Surface LoadsNone Body LoadsNone Special FeaturesNonlinear (if CV2 is not zero), Stress stiffening, Large deflection, etc. KEYOPT(1)0 - Linear Solution (default) 1 - Nonlinear solution (required if CV2 is non-zero) KEYOPT(3)0 - 3-D longitudinal spring-damper 1 - 3-D torsional spring-damper 2 - 2-D longitudinal spring-damper (2-D elements must lie in an X-Y plane)

6. 6/31 13.1.3 Equivalent Mass/Spring/Damper Translational SystemsRotational Systems Kinetic Energy Potential Energy Dissipated Energy

7. 7/31 第 13.2 節 實例 : 登陸系統的彈簧及阻尼設計 Design of Spring/Damper in a Recoil Landing System

8. 8/31 13.2.1 Problem Description Vehicle mass M Piston Cylinder Damper D Spring K Rod Foot

9. 9/31 13.2.2 Modeling Considerations y D K M

10. 10/31 13.2.3 Equivalent Spring/Damper y LL K 

11. 11/31 13.2.4 ANSYS Procedure (1/2) 01 02 03 04 05 06 07 08 09 10 11 12 13 14 15 16 17 18 19 20 FINISH /CLEAR /TITLE, Recoil Landing System (SI) /PREP7 K = 72000 M = 2000 D = 24000 ! Critically damped V0 = 5 ! 18 km/Hr ET, 1, COMBIN14,,, 2 ET, 2, MASS21,,, 4 R, 1, K, D R, 2, M N, 1, 0 ! Ground N, 2, 1 ! Vehicle TYPE, 1 $ REAL, 1 $ E, 1, 2 TYPE, 2 $ REAL, 2 $ E, 2 FINISH

12. 12/31 13.2.4 ANSYS Procedure (2/2) 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 /SOLU ANTYPE, TRANS TRNOPT, FULL D, ALL, UY, 0 D, 1, UX, 0 IC, 2, UX, 0, -V0 DELTIM, 0.01 TIME, 2 OUTRES, NSOL, ALL SOLVE FINISH /POST26 NSOL, 2, 2, U, X, DISP /GRID, 1 /AXLAB, Y, DISPLACEMENT PLVAR, 2

13. 13/31 第 13.3 節 實例 : 磅秤的阻尼設計 Design of Damper in a Spring Scale

14. 14/31 13.3.1 Problem Description Item placed on platform mass m Plateform mass M p Spring K mass M k Rack mass M r Damper D mass M d Calibrated dial J c Gear ratio n Geared magnifier J g R

15. 15/31 13.3.2 Modeling Considerations Item m Scale M Spring K Damper D y

16. 16/31 13.3.3 Lumped Masses (1/4) Lumped Mass for a Spring L VoVo V x dm Equivalent lumped mass M eq

17. 17/31 13.3.3 Lumped Masses (2/4) Lumped Mass for a Gear-and-Rack Set R MrMr JGJG VoVo Rolls without slipping

18. 18/31 13.3.3 Lumped Masses (3/4) Lumped Mass for a Geared Shafts Set J1J1 J2J2 N1N1 N2N2 J eq Gears Shafts

19. 19/31 13.3.3 Lumped Masses (4/4) Lumped Mass for the Spring Scale System Gear set

20. 20/31 13.3.4 ANSYS Procedure (1/2) 01 02 03 04 05 06 07 08 09 10 11 12 13 14 15 16 17 18 19 20 FINISH /CLEAR /TITLE, Spring Scale (cgs) /PREP7 m = 1500 ! G Meq = 500 ! G K = 3.2E6 ! dyn/cm D = 6.4E4 ! dyn-s/cm ET, 1, COMBIN14,,, 2 ET, 2, MASS21,,, 4 R, 1, K, D R, 2, m+Meq N, 1, 0 N, 2, 1 TYPE, 1 $ REAL, 1 $ E, 1, 2 TYPE, 2 $ REAL, 2 $ E, 2 FINISH

21. 21/31 13.3.4 ANSYS Procedure (2/2) 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 /SOLU ANTYPE, TRANS TRNOPT, FULL DELTIM, 0.02 TIME, 2 KBC, 1 D, ALL, UY, 0 D, 1, UX, 0 F, 2, FX, -m*981 OUTRES, NSOL, ALL SOLVE FINISH /POST26 NSOL, 2, 2, U, X, DISP /GRID, 1 PLVAR, 2

22. 22/31 第 13.4 節 實例 : 淬火溫度分析 Quenching of a Shaft

23. 23/31 13.4.1 Problem Description T(0) T b (0 ) T(t) T b (t) Shaft Bath m b = 1 lb Before quenching After quenching m s = 0.069 lb

24. 24/31 13.4.2 Modeling Considerations m s, C s, T s m b, C b, T b h, A

25. 25/31 13.4.3 ANSYS Procedure (1/2) 01 02 03 04 05 06 07 08 09 10 11 12 13 14 FINISH /CLEAR /TITLE, Unit: lb(mass)-ft-(Btu)-hr-F /PREP7 PI = 4*ATAN(1) ET, 1, MASS71 R, 1, PI*(1/4/12)**2/4*(5/12) MP, DENS, 1, 486 MP, C, 1, 0.11 ET, 2, LINK34 R, 2, 0.028 MP, HF, 2, 300 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 ET, 3, MASS71,,, 1 R, 3, 1/62 MP, DENS, 3, 62 MP, C, 3, 1.0 N, 1, 0 N, 2, 1 TYPE, 1 $ REAL, 1 $ MAT, 1 E, 1 TYPE, 2 $ REAL, 2 $ MAT, 2 E, 1, 2 TYPE, 3 $ REAL, 3 $ MAT, 3 E, 2 FINISH

26. 26/31 13.4.3 ANSYS Procedure (2/2) 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 /SOLU ANTYPE, TRANS TRNOPT, FULL DELTIM, 0.0001 KBC, 1 TIME, 0.01 IC, 1, TEMP, 1300 IC, 2, TEMP, 75 OUTRES, NSOL, ALL SOLVE FINISH /POST26 NSOL, 2, 1, TEMP,, SHAFT NSOL, 3, 2, TEMP,, WATER /GRID, 1 PLVAR, 2, 3

27. 27/31 第 13.5 節 與質點系統相關的元素 Elements Related to Lumped-Mass Systems

28. 28/31 13.5.1 Masses

29. 29/31 13.5.2 Springs/Dampers

30. 30/31 13.5.3 Thermal Links

31. 31/31 13.5.4 Circuit Element