IDMME 2002
Clermont-Ferrand, France, May 14-16 2002
ADVANCED NUMERICAL SIMULATION OF THE CRIMPING PROCESS OF ELECTRIC CONNECTORS Mickaël Abbas FCI France Corporate Research Center, rue Robert Surmont, 72402 La Ferté-Bernard,
[email protected]
Jean-Louis Batoz Institut Supérieur d’Ingénierie de la Conception, 27 rue d’Hellieule, 88100 Saint Dié des Vosges,
[email protected]
Thierry Courtin FCI France Corporate Research Center, rue Robert Surmont, 72402 La Ferté-Bernard,
[email protected]
Gouri. Dhatt Laboratoire ROBERVAL, Dept. GSM, Université de Technologie de Compiègne, BP20529, 60205 Compiègne CEDEX,
[email protected]
Abstract : The crimping is a classical technology process to ensure the electrical and the mechanical link between a wire and a connector. The numerical modelling of the process is helpful to choose and to optimize the dimensions of the crimping part of the connector. In this paper, we discuss a 2D simulation of the crimping, using implicit and explicit finite element method (ABAQUS/Standard and ABAQUS/Explicit) and we compare the results with experimental data from industrial process of crimping (geometry, shape, surfaces and punch force). This non-linear problem involves large elasto-plastic strains and multiple contact conditions, with friction between the strands and the grip. One of the major difficulties of the simulation is due to the definition of all possible contact couples between strands. The explicit method is preferred for the modelling of multi-contact, in spite of the quasi-static process of crimping. Thus, some simulations with the implicit method have been performed to compare the results and tune the simulation parameters of the explicit approach (space and time discretization). After that, some parametric studies show the effect of friction ratio or the position of the strands in the wire.
Keywords: Electrical connectors, crimping process, finite element method, large elastoplastic strains, contact with friction. 1
Introduction
The crimping is the operation to link a wire with the contact by the folding of two wings on the wire (see Fig. 2 and 3). The development of the electronic systems in cars increases the number of connections and requires more reliability of wiring harnesses. Moreover, to reduce the weight of the cars, the section of the wire decreases. The mechanical simulation of the crimping process is important to define the good reliability of the connector: the knowledge of the electrical contact resistance depends on the geometry and on the stress state of the connector after crimping. A limited number of papers has been published on the subject of numerical simulation of the crimping process. Villeneuve & al. [4] and Berry [2] used a dynamic explicit formulation, mainly because of the multi-contact problems. Their results present the advantage of the numerical simulation and show a good agreement of the final geometry obtained by the experimental method and by numerical simulations. Morita & al. [3] try to explain the problems of springback by using a visco-plastic model. This paper presents some results obtained by 2D finite element method of the crimping process. We use an explicit formulation in spite of the quasi-static aspect of the crimping process mainly because of the numerous and severe contact conditions. Meanwhile some
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IDMME 2002
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implicit simulations have been carried out to allow the tuning of the computational parameters of the dynamic simulation, especially for the springback evaluation. 2 2.1
Problem description Geometry and terminology
A 3D view of the crimping part of the connector with a seven strands wire is shown on Figure 2 (before complete crimping).
Fig. 1 : A simple electrical connector
wing Fig. 2: 3D view of the crimped part of an electric connector The “U”-form of the connector is called the wing or grip. For the B-shaped crimp, we use a double-curved punch and a curved die (Fig. 3). The die is fixed and the punch moves downward to fold the wing around the wire. Punch roof Punch wall
Wing Wire Die
Fig. 3: Baseline geometry for the2D simulation
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Tab. 1 presents the geometry of the wires considered in the present study Section - Commercial Number of strands Diameter of strands (mm) (mm²) 0.35 7 0.25 0.50 7 0.30 0.60 12 0.25 0.75 19 0.22
Section area (mm²) 0.34 0.49 0.59 0.72
Tab. 1 : Description of the wires 2.2
Material The grip and the wire are made with copper materials. An elasto-plastic constitutive law with isotropic hardening is considered for the simulation (Fig. 4). Material properties 600
500
True stress (MPa)
400
300
200
100
Grip Wire 0 0
0.05
0.1
0.15
0.2
0.25
Log strain
Fig. 4: Uniaxial stress-strain curves These curves are obtained by tensile tests but the crimping involves large compression strains and we need to extend the hardening curve to large strain values by slope extrapolation. 3
Simulation model
3.1
Analysis techniques Crimping is a very non-linear forming process involving • Large elastoplastic strains. • Multiple deformable body contact conditions with friction. In the present study, the simulations have been performed using the commercial package ABAQUS (Standard and Explicit). Explicit solvers are very efficient for forming problems, especially when they involve complex contact conditions. However, the problem is quasi static and some simulations have been performed with the implicit solver to check and to validate the results obtained by the explicit approach. The influence of the punch speed is particularly studied. A classical Von Mises plasticity model with isotropic hardening law is considered for the material behaviour.
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IDMME 2002
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3.2
Finite element type The crimping process is a 3D problem. But to reduce the computing time, we simplify the model and study a 2D cross-section. The depth of the grip part is 3.4mm and we did the plane model hypothesis. As we can observe on Fig. 5, the plane stress assumption is better because it allows the out-of-plane extrusion and we can observe this extrusion on real crimped connectors. The plane strain model is too stiff and the simulation does not converge because of the incompressibility locking of the model. Between these two choices, we consider also the generalized plane strain assumption which allows a limited extrusion between two rigid planes.
Free extrusion
Plane stress
Limited extrusion Generalized plane strain
No extrusion
Plane strain
Fig. 5: Finite element formulation The influence of mesh density was studied in a number of tests. No mesh adaptivity was considered. Triangular (T3) and quadrilateral elements (Q4) with linear approximations have been used. 3.3
Friction Coulomb model of friction is considered with a friction coefficient between 0.10 and 0.30. Different coefficients have been used between the wing and the punch wall and between the wing and the die. 3.4
Punch velocity The velocity of the punch is about 0.5 m/s in the process: crimping can be considered as a quasi-static process. Using a dynamic explicit solver, we have to increase the punch velocity to find a compromise: • High velocity leads to low computing time. The explicit method is conditionally stable and the longer the time length observed by simulation is the higher the number of increments needed is. • Low velocity is physically better since the phenomena is quasi static. Rules to simulate a quasi-static process with dynamic solver can be extracted from a number of publications: • The tool velocity must be less than 1% of the sound velocity in the material. For copper, the sound speed is about 6,000 m/s. • The kinetic energy during the complete simulation must be less than 1% of the total energy of the system.
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IDMME 2002
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From these considerations and with information extracted from [1], [2] and [3], we tried several velocities using ABAQUS/Explicit and we compared the results with the ones obtained using implicit solver. 4 4.1
Results Definition The compression ratio t is defined by equation (1) and Fig. 6: t=
final initial S crimped − S wire
(1)
initial S wire
initial is the initial wire area (4th row of the Tab. 1) Swire final Scrimped is the final crimped area
We define two other geometrical parameters (see Fig. 6): • The crimping height Hc. • The crimping width Wc. final S crimped
Hc
Wc Fig. 6: Geometrical parameters at the final stage of crimping The crimping ratio is very important and is the most frequently used factor to determine the quality of crimping. That ratio is usually around 15%. 4.2
Implicit simulations The results of the two formulations (plane stress and generalized plane strain) are compared on Fig. 7.
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IDMME 2002
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Plane stress (PS)
Generalized plane strain (GPS)
Real section (from experiments) Fig. 7 : Deformed cross-section - Effect of formulation These deformed shapes (starting from the situation of Fig. 3) have been obtained with 1,566 quadrilateral elements to discretize the wing and 700 elements to represent the strands. The punch displacement is controlled (5 steps) and the CPU is about 6h30 for plane stress and 3h30 for generalized plane strain on a Unix workstation (alpha 866MHz bi-processor). 45% 40%
Compression ratio
35% 30% 25% 20% 15% 10% 5% 0% 0.93 -5%
Plane stress Generalized plane strain 0.98
1.03
1.08
1.13
1.18
Crimping Height (mm)
Fig. 8 : Compression ratio and crimping height for two elements formulation The generalized plane strain method is too stiff and the final compression ratio is found too high. The plane stress formulation which permits out-of-plane extrusion appears to be the best model to simulate 2D crimping. For the 0.35mm² wire, we see on the Fig. 9 the good agreement of the experimental values with the simulation.
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IDMME 2002
Clermont-Ferrand, France, May 14-16 2002 0.5
Crimped area (mm²)
0.45
Experimental Numeric
0.4 0.35 0.3 0.25 0.2 0.15 0.6
0.7
0.8
0.9
1
1.1
Crimping height (mm)
Fig. 9 : Compression ratio and crimping height for the 0.35mm² wire 4.2.1
Partial conclusion The implicit method is possible but the tuning of the model is difficult to achieve convergence. In order to minimize the rigid body movements of the strands, we have to add some springs and to focus attention on the geometry (no gap between parts) and on the friction coefficients. This method requires a lot of computing time but allows to simulate springback and to find adequate parameters for the explicit method (as the punch velocity for example). 4.3 4.3.1
Explicit simulations Punch speed
Using the dynamic explicit approach, we need to reduce the amount of kinetic energy. The value of the punch velocity is very important. Therefore, we perform different analyses at different velocities. It appears that inertial effects are not significant if the punch velocity is less than 15 m/s. The results presented in the following figures have been obtained without -9 PDVVVFDOLQJZLWK WDURXQG[ s and for a punch speed of 10m/s. 200
2000
160
Increments Simulation time
1500
120
1000
80
500
40
0
Simulation time (min)
Number of increments (x1000)
2500
0 0
10
20 30 Punch velocity (m/s)
40
50
Fig. 10 : Computing time and cost of the explicit approach.
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IDMME 2002
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Fig. 10 shows the cost of computing using the explicit approach. The computing time decreases hyperbolically with the punch speed. 7000
6000
5000
Explicit - Plane stress
Force (N)
Implicit - Plane stress 4000
3000
2000
1000
0 3
3.2
3.4
3.6
3.8
4
4.2
4.4
4.6
4.8
5
Tool displacement (mm)
Fig. 11: Explicit and implicit methods comparison On Fig. 11, we compare the punch load punch displacement curves using the explicit and implicit approaches. It is demonstrated that both approaches give quite similar results. The CPU is about 40min for explicit approach with a punch velocity of 10m/s. 4.3.2
Effect of the strand positions So far, we assumed that the initial position of the strands was always symmetrical. Several simulations with different strand positions have been performed in order to evaluate the influence of that assumption (see Fig. 12), for the same gauge (0.50mm²).
1
2
3
4
5
6
Fig. 12: Strands configuration
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IDMME 2002
Clermont-Ferrand, France, May 14-16 2002
We can see on Fig. 13, that the final compression ratio (for 0.93mm crimping height) is not too much affected (less than 5%) by the strand positions. Indeed, we run all the simulations with the configuration 1, the error on the final compression ratio is less than 5%. Shift from reference configuration
10%
Config. 2 Config. 3 Config. 4 Config. 5 Config. 6
5%
0%
-5% 0.93
0.95
0.97
0.99
1.01
1.03
Crimping height (mm)
Fig. 13: Effect of strands position on crimping ratio
4.3.3
Effect of global friction coefficient
We studied the effect of uniform friction coefficient on the final deformed shape. On Fig. 14, we observe that a too high friction coefficient excessively compresses the wings and does not allow them to properly surround the wire.
0.05
0.15
0.25
0.50
Fig. 14: Effect of global friction coefficient 5
Conclusions The numerical simulation of the crimping process of electric connectors using advanced FE packages such as ABAQUS is possible. Good results can be obtained using explicit
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IDMME 2002
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dynamic approaches as found in ABAQUS/Explicit. We have shown that a good representation of the out-of-plane extrusion is possible using 2D plane stress elements. The strands configuration shows less than 5% error on the final configuration. The friction coefficients are important to have a nice shape of the crimping. The study of the springback phenomena is also an objective as well as complete 3D simulations in order to achieve a full understanding of the process and before performing optimization of the process parameters. 6
References
[1] “ABAQUS Theory Manual”, Version 6.2, Hibbit, Karlsson & Sorensen Inc., 2001. [2] D.Berry. “Development of a crimp forming simulator”, ABAQUS Users’ conference, 1998. [3] T.Morita, Y.Saitoh, M.Takahashi & al. “Numerical model of crimping by finite element method”, IEEE Holm, 1995, pp. 154-164. [4] G.Villeneuve, D.Kulkarni, P.Bastnagel et D.Berry. “Dynamic finite element analysis simulation of the terminal crimping process”, IEEE Holm, 1996, pp. 156-171.
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