A Guide to Air Ventilation Holes in Draw Die
Bridging Current Practices and Model Simulation
Prepared for
Fang Loong Cheng, Ph.D.
Senior Manager Stamping Technology
Advance Stamping Manufacturing Engineering
DaimlerChrysler Corporation
by
Edmund E. Yuen, Ph.D., P.E.
Assoc. Professor of Civil Engineering
Lawrence Technological University
Current Trial & Error Activity to Determine Number and Size of Air Vent Holes
Significant Cost & Time Savings
Simplified Model for Number & Size of Air Holes
+
Current Experience for Locating Air Holes at Die Tryout
Considerable Model Simulation Time Reduction
3-D CFD Model for Number & Size of Air Holes
+
Simulation to Optimize Hole Location
CAD Draw Die Development & CAE Forming Process Overview
Design CAD
Draw Model
Perform
CAE/FEA Draw
Simulation
CATIA
Resolve
Manufacturing/
Formability
Issues
LSDYNA Incremental
Perform “Vent Hole“ Simulation
Using Simplified Hand
Calculation Models
Recommend
Number of Holes & Size
Implementation of Air Pressure Model
Note:
Note:
Decision on the locations for air vent holes
still remains as an activity at die tryout
phase
Release Draw
Development/
Simulation
Analytical Air Pressure Model for Air Cavity in Draw Die
Dd @ t = 0
Air Cavity
vd
Ad
h(t)
ve
Mass flow rate = ρ ve Ae
Ambient pressure = pb = patm
Ambient atmospheric conditions






vd Ad

p=
 

  ( k −1)  

  vd Ad
vd t   

 +


ln
C
(
C
n
A
)
ln
1
−
⋅
−


o
d
e
k −1
2  
Dd   


  2 k

  p atm
 

 Co (Cd ⋅ n Ae ) + e
2k
k −1
Calibration of Analytical Air Pressure Model
Air Vent Hole Discharge
Coefficient Calibration
Calibration using Experimental Air
Pressure Data for Cowl Plenum
3-D Computational Fluid Dynamics Model
Simulation with Moving Boundary
Moving Boundary at 12%
to Home Position
Air Vent Hole Velocity Vectors from 3-D CFD Model
• Proof of Converging Streamlines Phenomenon
• Estimated Discharge Coefficient of 0.7 to 0.8
3-D CFD Model Results at
12 % to Home Position
• Uniform Air Pressure Inside
Trapped Air Cavity
• Choked Air Flow at Air Vent –
Mach Number greater than One
Note:
Mach number is the speed of sound in air
Verification of Analytical Model with 3-D CFD Model
Rectangular Box Air Cavity with One Air Vent Hole
Comparison of Analytical Model and 3-D CFD Model
9
Pressure Ratio ( p / patm )
8
7
6
5
4
3
2
1
0
0.0
0.1
0.2
0.3
0.4
0.5
0.6
Time, t (secs)
Analytical Model
3-D CFD Model
0.7
0.8
0.9
1.0
Model Parameters Comparison at 12 % to Home Position
Cavity Air
Pressure
(N/m2 abs.)
Exit
Velocity
(m/s)
Air
Density
(kg/m3)
Temperat
ure
(°K)
Mass
Flux
(kg/s)
Analytical
Model
2.229 × 105
243.8
2.138
368.43
0.1876
3-D
CFD Model
2.272 × 105
242.5 to
377.3
2.188
370.4
0.20318
1.9
0.5 to 35.4
2.3
0.53
7.7
Percent Error
(%)
Application of Analytical Model Results
Sonic to Subsonic Flow at Ventilation Holes
Pressure Ratio, p / patm
5
4
3
2
1
0
0
10
20
30
40
50
60
70
80
90
Number of 0.25" Dia. Air Ventilation Holes
Sonic_8SPM
Sonic_10SPM
Sonic_12SPM
Sonic_14SPM
Sonic_16SPM
Sonic_18SPM
SPM8
SPM10
SPM12
SPM14
SMP16
SPM18
DR Fender – Draw Die Cavity with Too Many Drilled Holes
• Actual Number of Drilled
0.25” dia. Holes = 64
• Model Recommended Number of
Drilled 0.25” dia. Holes = 23
Conclusions
• An analytical air pressure model is now available to determine
number of air vent holes for trapped air cavities in draw die
• Analytical model has been calibrated and to some extent being
tested
• Analytical model correlates well with 3-D CFD model using
Star-CD for a test case trapped air cavity with one air vent hole
• Number of air holes predicted by analytical model seems
reasonably low compared to available drilled draw dies
Recommendations
• Determine the number of air vent holes for each trapped air cavity
based on a pressure ratio criterion of 2 and a press speed of 18 SPM
• Implement future verification program for the analytical air
pressure model using soft dies for outer panels
• Complete further experimental program to collect air pressure data
• Use 3-D CFD model when feasible only for the purpose of verification
of experimental data and checking the analytical air pressure model