Chapter 73: Cylinder Upsetting with Plastic and Friction Heat Generation

73 Cylinder Upsetting with Plastic and Friction Heat Generation

Summary 1302

Introduction 1303

Modeling Details 1303

Results 1307

Modeling Tips 1309

Input File(s) 1310

Video 1310

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SummaryTitle Chapter 73: Cylinder Upsetting with Plastic and Friction Heat Generation

Features Plastic and friction heat generation, coupled analysis and user subroutine 'motion'

Geometry & Boundary Conditions

Material properties

Linear elastic material for the cylinder

E = 2.0e5 N/mm2; = 0.3; with yield stress σ y = 275 N/mm2, = 7220.262 N/mm2

k = 36 N/s/K, Cp = 3.77 N/mm2/K

Analysis characteristics Punch is modeled as a rigid body at fixed room temperature.

Contact Properties Touching contact with shear friction is defined between cylinder and punch.

Element type 3 node axi-symmetric triangle

FE results

Cylinder: Diameter 20mm x height 30mm Punch : Diameter 32mm x height 10mmInitial Temp 293KSymmetry Boundary Conditions - AxisymmetricPunch velocity V = 12*sqrt(H-20) mm/s

Temperature (305 to 364 K)

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IntroductionThis example demonstrates the thermal-mechanical coupling capability and the use of 'user subroutine' feature in MD-Nastran. It simulates a cylinder upsetting process considering the heat generation due to plastic heating and frictional effects. The mechanical and heat transfer analysis are handled in a staggered manner. While the mechanical analysis computes the deformation behavior considering the frictional effects and the plastic heating, the thermal behavior of the problem is analyzed in the heat transfer analysis. The model is created based on the literature (please see reference [1.]) and the results are compared with the experiments.

Modeling DetailsThe model is set up as an axi-symmetric, thermal-mechanical coupled problem. The cylinder is modeled using axi-symmetric elements and half symmetry is considered in modeling (shown in Figure 73-2). Punch is assumed to be a rigid body. The model will be analyzed with friction to show the combined effect of heat generation due to plastic deformation and the friction between punch and workpiece. The conversion factor from plastic work and friction work to the heat source is 0.9. Some heat loss due to the release of dislocations and due to the lubrication is considered.

Element ModelingThe cylinder is modeled using nonlinear axi-symmetric element. Axi-symmetric elements are selected using CTRAIX entry pointing to a PLPLANE entry which in turn, points to an auxiliary PSHLN2 entry as shown below. PSHLN2 entry specifies additional nonlinear properties for axi-symmetric elements. By choosing ISH option, implicit structural and heat elements are referred. Second line of PSHLN2 entry specifies element behavior and integration scheme for structural and heat pass. By selecting element structural behavior as IAX, an incompressible axi-symmetric element formulation is used.

...CTRIAX 1 1 91 1 92CTRIAX 2 1 91 92 93CTRIAX 3 1 94 2 1......PLPLANE 1 1 PSHLN2 1 1 1 + C3 IAX L AXSOLID L

Punch is modeled using four 2D NURBS.

BCBODY 101 2D RIGID 0.65 1 0 HEAT 4. 293. 1 RIGID 4 punch NURBS2D -2 2 50 0.0 15. 16. 15. 1. 1. 0.0 0.0 1. 1....

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Modeling ContactThe contact bodies are defined as follows: Cylinder as the deformable body and Punch as the rigid body

The contact boundary conditions are as follows:

1. Friction coefficient between the cylinder and the punch with bilinear shear friction law: 0.65

2. Heat transfer coefficient between cylinder and punch: 4 N/s/mm/K

3. Film coefficient to environment: 0.00295 N/s/mm/K

The BCPARA entry used in the model is given below. With ID zero, the parameters defined here belongs to all the subcases. FTYPE indicates the type of friction model to be used. In this example Bilinear Shear friction is used.

BCPARA 0 FTYPE 7

The definition of the contact bodies consists of the BCBODY bulk data entry which defines the deformable bodyincluding the body ID, dimensionality, type of body, mechanical and thermal properties for the contact body. Whilethe BSURF identifies the elements forming a part of the deformable body. The following BCBODY entries are used.

BCBODY 1 2D DEFORM 4 0.65 0 ++ HEAT 0.00295 293. 4. 2+...BSURF 4 1 THRU 220

To specify the characteristics of interaction between the contact bodies, the BCTABLE bulk data option is used. The BCTABLE with ID 1 is used to define the touching conditions between punch and workpiece. It is flagged using BCONTACT = 1 in the case control section to activate for both the SUBSTEPs in SUBCASE 1. The following BCTABLE entry is used in the analysis.

BCTABLE 1 1 + $ Pair: workpiece / punch+ SLAVE 1 0.65 + + MASTERS 101

Material ModelingAll the elements of the structure are modeled with isotropic, elasto-plastic material using the MAT1 and MATEP options. The yield stress is taken as 275 N/mm2. Thermal material properties are specified using MAT4 entry.

MAT1 1 200000. 0.3 MAT4 1 36. 3.77 1. MATEP 1 Table 1 Vmises Isotrop Addmean ...

The Young's modulus is 200000 N/mm2 and the Poisson's ratio is 0.30. According to the literature (please see reference [1]), the flow stress is assumed to be plastic strain dependent only. The flow stress function takes the following form:

and . This is entered in a piece wise linear manner and referred in MATEP entry

using the 'Table' option. The TABLES1 bulk data entry is used to enter this data. Third field in the TABLES1 entry

y 275 N/mm2

= y 7220.262 N/mm

2=

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defines the type of stress-strain curve. Option 2 indicates stress verses equivalent plastic strain data. This is shown in Figure 73-1.

TABLES1 1 2 + + 0.0 275. 0.1 394.946 0.2 473.595 0.3 526.675+ + 0.4 567.907 0.5 602.098 0.6 631.557 0.7 657.586+ + 0.8 680.999 0.9 702.342 1. 722. 1.4 788.538+ + ENDT

The heat transfer properties for cylinder are the thermal conductivity and the heat capacity k = 36 N/s/K, Cp = 3.77

N/mm2/K.

Figure 73-1 Stress Versus Equivalent Plastic Strain

Loading and Boundary ConditionsThe motion of the punch represents a type of mechanical press and is defined as

, where H is the current height of the cylinder. This motion is simulated through the use of the

user subroutine motion.f. Constant time increment of 0.01 is used with maximum 50 increments. This reaches 1/3 oftotal reduction in height.

V 12 H 20– mm/s=

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Boundary conditions are applied using SPC1 and SPCADD entries. Horizontal displacement along axis of symmetry (global Y axis) and vertical displacements on XZ plane are constrained. SPC set combination ID is referred in the SPC case control command.

SPC1 1 2 122 THRU 132SPC1 2 1 102 103 105 107 109 111+ + 113 115 117 119 121 132.SPCADD 10 1 2.SPC = 10

Figure 73-2 Boundary Conditions

Solution ProcedureSimulation is set up as a coupled job in which transient heat transfer analysis is done in the SUBSTEP 1. The temperature output is passed on to nonlinear structural run in SUBSTEP 2.

SUBCASE 1 TITLE=Coupled Cylinder Upsetting Simulation BCONTACT = 1STEP 1 NLSTEP = 3SUBSTEP 1 IC = 29 ANALYSIS = HTRAN THERMAL(SORT1,PRINT)=ALL FLUX(PRINT)=ALLSUBSTEP 2 SPC = 10 ANALYSIS = NLSTAT DISPLACEMENT(SORT1,PRINT,REAL)=ALL

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NLSTEP entry is used to describe the control parameters for mechanical, thermal and coupled analysis.

NLSTEP 3 0.5 GENERAL 20 2 FIXED 50 1 MECH PV 0.01 PFNT HEAT P 0.01 PFNT COUP 0.9 0.9

The NLSTEP keyword is followed by the identification number entry and by the total time of the analysis which is 0.5 in this case.

The second line gives the general stepping parameters associated with the analysis. The maximum number of iteration (=20), minimum number of iteration needed for each increment (=2) and the maximum number of bisections allowed in current step (=10).

The keyword FIXED defines the uniform time stepping procedure which is followed by the parameters like number of increments and output interval.

The keyword MECH stands for a mechanical analysis appended with the parameters such as flags for convergence criteria selection followed by the error tolerance for displacement, load and work respectively. PV stands for convergence criteria checking with respect to load vectors. The PFNT character parameter stands for “Pure Full Newton Raphson” which is the method for controlling stiffness updates.

The keyword HEAT stands for heat transfer analysis appended with the parameters such as flags for convergence criteria selection followed by the error tolerance for temperature, heat flux and work respectively. The PFNT character parameter stands for “Pure Full Newton Raphson” which is the method for controlling stiffness updates.

The keyword COUP defines conversion factor for heat generated due to plasticity and conversion factor for heat generated due to friction.

ResultsThe plots for x and y displacements are shown in the Figure 73-3, and Figure 73-4. Temperature distribution in the cylinder is shown in Figure 73-5. Results of this simulation are compared with the experimental results in Figure 73-6.

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Figure 73-3 Plot of X (Radial) Displacement

Figure 73-4 Plot of Y (Axial) Displacement

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Cylinder Upsetting with Plastic and Friction Heat Generation

Figure 73-5 Plot of Temperatures

Figure 73-6 Temperature History

Modeling TipsThe key aspect in this analysis is the usage of user subroutine feature available in MD Nastran. Following are the inputs through argument for subroutine motion.

nsurf - rigid body IDtime - the current timedtime - the current time incrementx(3) - current die defining coordinates:f(3) - the current surface load:inc - the increment number

Temperature (305 to 364 K)

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Along with these variables input argument contains INTEGER, REAL, and CHARACTER data specified through BCONUDS entry. Using above mentioned argument data, at the beginning of each increment, current surface velocity components are to be computed and returned for rigid bodies referred in BCONUDS entry.

BCONUDS 101 BCBODY CONTACT motion REAL 5.…

The above BCONUDS entry points to master body ID 101 which refers to the punch. This entry invokes the flag for usage of user subroutine ‘motion’ which controls the motion of the punch.

To execute the subroutine, user needs to build Dynamic Link Library (shared objects on Linux) which is loaded by MD Nastran executable. To simplify this task, MSC_SDK provides ready-made templates for all available user subroutines along with build utility SCA Scons. With one command it updates all dynamic link libraries.

To invoke User Defined Service, the following File Management Statement is required.

$CONNECT SERVICE contact 'SCA.MDSolver.Obj.Uds.Contact'$

References1. N.Rebelo and S.Kobayashi: “A Coupled Analysis of Viscoplastic Deformation and Heat Transfer – II”,

Int.J.Mech.,Sci. Vol.22, pp.707-718

2. Simulation Component Architecture (SCA) Guide.

3. User Defined Service Guide.

Input File(s)

VideoClick on the image or caption below to view a streaming video of this problem; it lasts approximately 39 minutes and explains how the steps are performed.

Figure 73-7 Video of the Above Steps

Files Description

nug_73.dat MD Nastran input for “Cylinder Upsetting with Plastic and Friction Heat Generation”

nug_73.f MD Nastran user subroutine motion

Cylinder: Diameter 20mm x height 30mm Punch : Diameter 32mm x height 10mmInitial Temp 293KSymmetry Boundary Conditions - AxisymmetricPunch velocity V = 12*sqrt(H-20) mm/s