Analysis of Lumped Mass Systems

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Chapter 13

• ????????
• Analysis of Lumped Mass Systems

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Contents

• 13.1 ????????????
• Elements for Mass-Spring-Damper Systems
• 13.2 ?? ????????????
• Design of Spring/Damper in a Recoil Landing
  System
• 13.3 ?? ???????
• Example Design of Damper in a Spring Scale
• 13.4 ?? ??????
• Example Quenching of a Shaft
• 13.5 ??????????
• Elements Related to Lumped-Mass Systems

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?13.1?

• ????????????
• Elements for Mass-Spring-Damper Systems

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13.1.1 MASS21 Structural Mass
Element Name MASS21
Nodes I
Degrees of Freedom UX, UY, UZ, ROTX, ROTY, ROTZ if KEYOPT(3) 0UX, UY, UZ if KEYOPT(3) 2UX, UY, ROTZ if KEYOPT(3) 3UX, UY if KEYOPT(3) 4
Real Constants MASSX, MASSY, MASSZ, IXX, IYY, IZZ if KEYOPT(3) 0MASS if KEYOPT(3) 2MASS, IZZ if KEYOPT(3) 3MASS if KEYOPT(3) 4
Material Properties None
Surface Loads None
Body Loads None
Special Features Large deflection
KEYOPT(2) Key for element coordinate system
KEYOPT(3) 0 - 3-D mass with rotary inertia2 - 3-D mass without rotary inertia3 - 2-D mass with rotary inertia4 - 2-D mass without rotary inertia
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13.1.2 COMBIN14 Spring/Damper
Element Name COMBIN14
Nodes I, J
Degrees of Freedom UX, UY, UZ if KEYOPT(3) 0ROTX, ROTY, ROTZ if KEYOPT(3) 1UX, UY if KEYOPT(3) 2etc.
Real Constants K, CV1, CV2
Material Properties None
Surface Loads None
Body Loads None
Special Features Nonlinear (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-damper1 - 3-D torsional spring-damper2 - 2-D longitudinal spring-damper (2-D elements must lie in an X-Y plane)
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13.1.3 Equivalent Mass/Spring/Damper
Translational Systems Rotational Systems
Kinetic Energy
Potential Energy
Dissipated Energy
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?13.2?

• ?? ????????????
• Design of Spring/Damper in a Recoil Landing System

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13.2.1 Problem Description
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13.2.2 Modeling Considerations
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13.2.3 Equivalent Spring/Damper
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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
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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
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?13.3?

• ?? ???????
• Design of Damper in a Spring Scale

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13.3.1 Problem Description
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13.3.2 Modeling Considerations
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13.3.3 Lumped Masses (1/4)Lumped Mass for a
Spring
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13.3.3 Lumped Masses (2/4)Lumped Mass for a
Gear-and-Rack Set
Vo
Mr
R
JG
Rolls without slipping
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13.3.3 Lumped Masses (3/4)Lumped Mass for a
Geared Shafts Set
J1
J2
N1
Jeq
N2
Shafts
Gears
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13.3.3 Lumped Masses (4/4)Lumped Mass for the
Spring Scale System
Gear set
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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, mMeq   N, 1, 0   N, 2, 1   TYPE, 1 REAL, 1 E, 1, 2   TYPE, 2 REAL, 2 E, 2   FINISH
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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, -m981   OUTRES, NSOL, ALL   SOLVE   FINISH /POST26   NSOL, 2, 2, U, X, DISP   /GRID, 1   PLVAR, 2
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?13.4?

• ?? ??????
• Quenching of a Shaft

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13.4.1 Problem Description
T(0)
Shaft
ms 0.069 lb
Bath
T(t)
mb 1 lb
Tb(0)
Tb(t)
Before quenching
After quenching
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13.4.2 Modeling Considerations
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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 4ATAN(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
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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
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?13.5?

• ??????????
• Elements Related to Lumped-Mass Systems

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13.5.1 Masses
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13.5.2 Springs/Dampers
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13.5.3 Thermal Links
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13.5.4 Circuit Element