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

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

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

4/ 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 D mass without rotary inertia D mass with rotary inertia D mass without rotary inertia

5/ 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 D torsional spring-damper D longitudinal spring-damper (2-D elements must lie in an X-Y plane)

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

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/ Problem Description Vehicle mass M Piston Cylinder Damper D Spring K Rod Foot

9/ Modeling Considerations y D K M

10/ Equivalent Spring/Damper y LL K 

11/ ANSYS Procedure (1/2) FINISH /CLEAR /TITLE, Recoil Landing System (SI) /PREP7 K = M = 2000 D = ! 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/ ANSYS Procedure (2/2) /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

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

14/ 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/ Modeling Considerations Item m Scale M Spring K Damper D y

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

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

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

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

20/ ANSYS Procedure (1/2) 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/ ANSYS Procedure (2/2) /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

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

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

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

25/ ANSYS Procedure (1/2) 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, MP, HF, 2, 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/ ANSYS Procedure (2/2) /SOLU ANTYPE, TRANS TRNOPT, FULL DELTIM, 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

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

28/ Masses

29/ Springs/Dampers

30/ Thermal Links

31/ Circuit Element