* Corresponding author: j.hol@m2i.nl
EXPERIMENTAL AND NUMERICAL FRICTION
CHARACTERIZATION FOR LARGE-SCALE FORMING
SIMULATIONS
J. Hol
1*, V.T. Meinders
2, A.H. van den Boogaard
2 1Materials innovation institute (M2i) - P.O. box 5008 - 2600 GA Delft - The Netherlands
2
University of Twente, Faculty of Engineering Technology, chair of Nonlinear solid
me-chanics - P.O. box 217 - 7500 AE Enschede - The Netherlands
ABSTRACT:
A new trend in forming simulation technology is the development of friction models ap-plicable to large scale forming simulations. In this respect, the optimization of forming processes and the success of newly developed friction models requires a complete understanding of the tribological behavior involved. In this paper a frequently used metal-lubricant combination is characterized at one hand, and inter-correlated friction mechanisms acting on the micro-scale are discussed at the other hand. For this purpose, cold-rolled high formable mild steel is used in combination with the deep-drawing oil Quaker N6130. Re-sults have been used to calibrate a recently developed multi-scale friction model applicable for large-scale forming simulations. The objective of this paper is to gain a thorough understanding of the tribological be-havior involved supporting further optimization of enhanced friction models in forming processes.KEYWORDS:
Multi-scale, friction modeling, real contact area, ploughing, friction characterization1
INTRODUCTION
Regardless the forming process used to produce metal formed parts, the tool-workpiece interfacial friction characteristics are complicated functions of several inter-related variables. In the majority of forming simulations still a simple Coulomb friction model is used. The Coulomb friction model takes a constant coefficient of friction into account and does not include the influence of important pa-rameters such as pressure, punch speed or the type of lubricant used. Therefore, a new trend in form-ing technology is the development of friction mod-els applicable to large scale forming simulations [1-3].
As described in literature, friction is caused on a micro-scopic level by the adhesion and ploughing effect between contacting asperities [4-6]. The real area of contact, defined as the area summation of contacting asperities, plays an important role in characterizing friction. The real area of contact depends on the roughness of both tool and workpiece, where the roughness of the workpiece is liable to changes due to flattening and roughen-ing mechanisms. The main flattenroughen-ing mechanisms during sheet metal forming, which tends to in-crease the real area of contact, are flattening due to normal loading [7-9] and flattening due to com-bined normal loading and deforming the
underly-ing bulk material [7,10,11]. Roughenunderly-ing of asperi-ties, observed during deforming the bulk material without applying a normal load to the surface, tends to decrease the real area of contact [12,13]. The optimization of forming processes and the success of newly developed friction models re-quires a better understanding of the tribological behavior involved. For that purpose, an experi-mental and numerical study has been conducted and presented in the paper at hand. The first part of this paper presents a comprehensive study on the friction characterization of colled rolled high-formable steel in combination with the deep draw-ing oil Quaker N6130, a metal-lubricant combina-tion often used in the automotive industry. The development of the friction coefficient and amount of asperity deformation has been studied under different loading and sliding conditions. The ac-companying effect of straining the underlying bulk material on the frictional behavior has not been studied in this paper. Experiments have been exe-cuted with a high degree of similarity to the actual forming process, making the validation and/or calibration of recently developed friction models possible.
The second part of this paper discusses the newly developed friction model [3,14], applicable for simulations of large-scale forming processes. This friction model includes the effect of surface
chang-es due to normal loading and straining the underly-ing bulk material, as well as the effect of ploughunderly-ing and adhesion actions on the friction coefficient. Results obtained by the friction experiments will be used to calibrate the incorporated micro-friction models within this friction framework.
2
Loading and sliding experiments
The friction coefficient and the corresponding real contact area are depending on contact pressure. To investigate this dependency, the Rotational Friction Tester (RFT) [15], developed at Tata Steel Nether-lands, has been used. Specific locations on the sample have been scanned by 3D confocal micros-copy before and after the friction tests to track the development of real contact area. Measurements are performed on the same location (with an accu-racy of 1µm) to make a direct comparison of sur-faces before and after loading/sliding experiments possible.2.1 EXPERIMENTAL SETUP
The RFT consists a stationary punch and a rotating sample holder, see Figure 1. The sample holder is driven by a computer controlled brushless servo drive with a low inertia reduction gear. The punch consists of 3 small notches having a flat polished contact area, aligned in one plane and positioned at the same radius from the center of the punch. To ensure the notches are perfectly aligned the traces left on the sample (noticeable by the flattening of asperities) must be completely even. The tool is pressed on the sample by a hydraulic actuator. The applied load to the sample and induced torque due to sliding are measured by a load/torque transduc-er. The feasible pressure range applied to the notches can be increased or decreased by respec-tively decreasing or increasing the contact area of the notches. After applying the load, the tool is rotated over a user defined rotation angle. The conditions of the tests are listed in Table 1.
Fig. 1 Rotational Friction Tester
Table 1: Test conditions Rotational Friction Tester Material
Lubricant Notch size
Mean radius notches Sample size Speed Pressure Sliding angle DC06 N6130, 0.6g/m2 8x8mm 46mm 120x120mm 10mm/s 10,20,30,45,60 MPa 80°/120°
2.2 DEVELOPMENT REAL CONTACT
AREA
Confocal measurements have been performed before and after RFT friction tests to track the deformation of asperities due to loading and
slid-ing. For loading only the tool was pressed on the specimen till a specific pressure was reached. In case of sliding, the tool was loaded and subse-quently slided over a sliding angle of 80˚.
Figure 2a and 2b gives a 3D surface impression of sliding-induced asperity deformation. The surface experienced sliding under a load of 60MPa. The sliding direction equals the negative y-direction. The same asperities before and after sliding can be easily traced back from the figures. Shallow ploughing tracks of the tool asperities are clearly visible in Figure 2b. Cross-sections of both the deformed and undeformed surface at different locations are compared in Figure 2c and 2d. The undeformed surface is indicated by grey lines, the deformed surface is indicated by black lines. Fig-ure 2c shows that asperities are smeared out over a larger area in sliding direction. Perpendicular to the sliding direction asperities are distributed over a larger area due to the sliding action, as shown in Figure 2d.
The relation between contact pressure and real contact area (α) is shown in Figure 3 for both load-ing and loadload-ing + slidload-ing cases. Experimental re-sults are expressed by dots, the overall trend is predicted by the solid lines. It can be seen that the influence of sliding on the real contact area is sig-nificant. The ratio αslide/αload is around 3 over the
complete range of pressures. Most conceivable, the large increase in real contact area can be lead back to 2 sliding mechanisms, as further discussed in Section 3.3.1. In addition, non-linear behavior of the real contact area as function of the load-ing/sliding pressure is observed for both cases. The non-linearity is induced by work-hardening effects of the deformed asperities, resulting an increase in real contact area less then proportional with pres-sure [15].
2.3 DEVELOPMENT FRICTION COEFFICIENT
Equivalent to the experimental procedure discussed in Section 2.1, the RFT has been used to obtain a relation between the friction coefficient and the applied nominal contact pressure. Experiments have been performed using a pressure range of 5-60MPa over a sliding angle of 120°. Conditions of the sliding tests can be found in Table 1. The fric-tion coefficient is derived from the measured load and measured torque, obtained from the load/torque transducer (see Figure 1).
The static friction coefficient and the dynamic friction coefficient as function of contact pressure are shown in Figure 3b. Both the static and dynam-ic frdynam-iction coeffdynam-icient decreases with increasing contact pressure. The decrease in friction coeffi-cient can be explained by the theoretical approach described by Hol et al. [3]. They adopted a dis-crete ploughing model which accounts for the formation of tool contact patches ploughing through a softer workpiece material. For low pres-sures the formed contact patches are small having a relatively large attack angle. For increasing contact pressures, contact patches are joining together
(a) 3D surface texture before sliding (b) 3D surface texture after sliding with 60MPa
0 0.1 0.2 0.3 0.4 0.5 -6 -3 0 3 6 Lineprofile at X = 0.23 y [mm] z [ µ m ] 0 0.1 0.2 0.3 0.4 0.5 -6 -3 0 3 6 Lineprofile at X = 0.43 y [mm] z [ µ m ]
(c) Cross-section undeformed and deformed surface in y-direction 0 0.1 0.2 0.3 0.4 0.5 -6 -3 0 3 6 Lineprofile at Y = 0.18 x [mm] z [ µ m ] 0 0.1 0.2 0.3 0.4 0.5 -6 -3 0 3 6 Lineprofile at Y = 0.38 x [mm] z [ µ m ]
(d) Cross-section undeformed and deformed surface in y-direction
Fig. 2 Impression undeformed and deformed surface after sliding with 60MPa
0 13 26 39 52 65 0 0.07 0.14 0.21 0.28 0.35 Pressure [MPa] R e a l c o n ta c t a re a α [ -] Trend α loading Trend α sliding (a) 0 13 26 39 52 65 0.12 0.134 0.148 0.162 0.176 0.19 Pressure [MPa] µ [ -] Static COF Dynamic COF (b)
resulting in a decrease of the effective attack angle. Smaller attack angles yield less resistance against sliding, resulting lower friction values.
3
Numerical study
Results of the experimental study have been used to calibrate the micro-mechanical friction models incorporated in the recently developed multi-scale friction model by Hol et al. [3,14]. This model describes friction phenomena that play a role in the boundary lubrication regime, the most common condition during sheet metal forming. The model includes a fast and efficient translation from micro to macro frictional behavior, making the applica-tion to forming simulaapplica-tions feasible.
3.1 NUMERICAL FRICTION MODEL
The multi-scale friction model describes a 3 step methodology. In the first step, the input step, sur-face characteristics and material properties are defined. 3-Dimensional surface textures of both tool and workpiece are read-in to characterize surface properties and to determine stochastic vari-ables. Step 2, the flattening step, includes the effect of surface changes due to normal loading and straining the underlying bulk material. An asperity flattening model [3], including work hardening effects, has been adopted to describe the increase of real contact area due to normal loading. Asperi-ty flattening due to stretching has been described by the flattening model proposed by Westeneng [7]. The last step, the friction step, calculates the influence of ploughing and adhesion actions on the coefficient of friction. The model of Challen & Oxley [5,6] has been used to describe frictional behavior on the micro-scale. A deterministic ap-proach has been adopted to model ploughing con-ditions under high fractional contact areas [17]. This model accounts for the formation of contact patches ploughing through the contacting material. For a detailed description of the proposed solution the reader is referred to [3].
3.2 STEP 1: INPUT STEP
To run a friction analysis, material properties and 3 dimensional surface scans of both the tool and the workpiece material are required. Material proper-ties, such as hardening parameters and hardness values, are provided by the material supplier Tata Steel Netherlands. 3D surface scans are obtained by confocal microscopy. To execute a reliable friction analysis a representative surface scan is required. This means that the chosen pixel size should be fine enough, while the size of the meas-urement area should be large enough to capture the most important details of the surface. To satisfy these requirements, an area of 0.5x0.5mm using a pixel size of 0.36µ m was used to measure the tool surface (Sa=0.06µ m), while an area of 2x1mm, using a pixel size of 2.2µ m, was used to measure the workpiece surface (Sa=1.6µ m).
3.3 STEP 2: ASPERITY FLATTENING The flattening step covers models to describe both flattening due to normal loading and flattening due to bulk straining. Since the accompanying effect of straining the underlying bulk material has not been studied in this paper, the latter flattening model will not be discussed in this section.
The non-linear normal loading model incorporated in the multi-scale friction model describes the deformation of crushed asperities and the rise of non-contacting asperities stochastically. Two un-known parameters have been introduced in this model; 1) the persistence parameter η which de-scribes the amount of energy required to lift up non-contacting asperities and 2) the initial height of asperities λ required to calculate shear stresses and work-hardening effects of the deforming asperities. The values of these parameters have been deter-mined by calibrating the analytical results with the experimental results, i.e. minimizing the error between the results.
Regarding the persistence parameter, a value of
η=0 means that no energy is required to lift up
non-contacting asperities, a value of η=1 implies that the same energy is required to lift up asperities as to crush asperities. The amount of deformation of
0 13 26 39 52 65 0 0.03 0.06 0.09 0.12 0.15 λ=1S t λ=2S t λ=4St Pressure [MPa] R e a l c o n ta c t a re a [ -]
Exp: Loading only
Sim: Loading only (η = 0; λ = 1St,2St,4St)
(a) 0 13 26 39 52 65 0 0.07 0.14 0.21 0.28 0.35 k=6 k=9 k=6 k=9 k=14 Pressure [MPa] R e a l c o n ta c t a re a [ -]
Exp: Loading only Exp: Loading + sliding Sim: Sliding (k = 6,9,14)
(b)
rising asperities is difficult to quantify. From the confocal study, see Figure 2, the amount of rising asperities seems insignificant in comparison with the amount of deformation of the crushed asperi-ties. For this reason, the persistence value is set to
η=0, implying that it only costs energy to indent
asperities, while it does not requires energy to rise asperities.
To reduce the error between the analytical and experimental results the value of the initial height of asperities λ has been adapted. The amount of strain build up in the asperities, and therefore work-hardening effects, will be lower when using a higher value for λ. Consequently, the development of real contact area will be higher. Results using different values for λ are shown in Figure 4a. The value of λ has been expressed as function of the maximum peak to valley distance St between as-perities. From the results it can be seen that the trend in contact area development can be predicted accurately (mean error = 1.83%) when using a value of λ=2St.
3.3.1 Adaptions to the normal loading model The normal loading model incorporated in the multi-scale friction model is adapted to account for sliding effects, which have a significant influence on the development of real contact area (Section 2.2). In this paper, it is assumed that the increase in real contact area during sliding is due to 2 mecha-nisms. First, the normal loading model assumes full contact between the tool asperities penetrating into the softer workpiece asperities. Based on this assumption, energy equations are solved to meet force equilibrium between the applied load and the calculated real contact area. If sliding occurs, only half of the tool asperities are in contact. Conse-quently, the real contact area must grow with a factor 2 (assuming ideal plastic material behavior) in order to satisfy force equilibrium. A further increase in real contact area can be initiated by the underlying mechanisms of junction growth [16], implying an increase in real contact area due to increasing tangential load. Tabor [16] postulated that an increase in real contact area occurs before sliding occurs, which follows from the requirement to maintain a constant Von Mises stress at yielded contact points. This means that asperities which were already plastically deformed by a given nor-mal load, must grow when subjected to an addi-tional tangential load in order to reduce the mean pressure at contact spots and be able to accommo-date the additional shear stresses. Based on the Von Mises yield criterion, Tabor proposed a relation to describe the effect of junction growth on the real contact area, see Equation 1.
2
1
µ
α
increase=
+
k
(1)Experiments by Tabor [16] showed that values in between 3 and 25 can be expected for the constant
k. Experimental results, as discussed in Section 2.2,
will be used to find a proper value for k. Since the proposed relation is a function of the friction coef-ficient µ an iterative scheme is required to find the increase in real contact area αincrease. Figure 4b
shows the development of real contact area for different values of k. The friction coefficient, used to solve αincrease, has been calculated as discussed in
Section 3.4. As can be seen in Figure 4b, an accu-rate prediction of the development of real contact area can be made if a k value of 9 is used (mean error = 2,2%). The non-smooth development of real contact area is introduced by the friction model used to account for sliding effects, which adopts a deterministic approach to model friction condi-tions.
3.4 STEP 3: FRICTION MODELING
Ma [17] proposed a multi-scale friction model that account for asperities forming contact patches under high fractional contact areas. The model of Ma is based on the projection of two rough surfac-es onto each other. The surface height matrix of the workpiece material is adapted for the amount of flattening and rise of asperities, which follows from the statistically based flattening models as discussed in the previous section. The plateaus of the flattened workpiece asperities are assumed to be perfectly flat, in which the harder tool asperities are indenting. The separation between the mean plane of the tool surface and the flattened peaks of the workpiece surface is calculated based on force equilibrium, obtained by the summation of the load carried by the formed contact patches.
The contact model of Ma has been coupled to Challen & Oxley’s friction model [5,6] to calculate friction forces acting on the individual contact patches. Since the model of Challen & Oxley is based on a plane strain assumption an effective attack angle should be determined in the direction of the sliding velocity. A relation of the effective attack angle has been proposed in [17], introducing a shape-factor χ to capture the 3D nature of contact patches in a 2D expression. A value of χ=0.8 has been proposed in [18], obtained for both carbon steel and stainless steel. The effect of χ on the obtained dynamic friction coefficient is visualized in Figure 5. Decreasing the shape factor χ increases the effective attack angle, resulting in higher fric-tion coefficients. The shape factor has a large in-fluence on the developed friction coefficient, as shown in Figure 5. Comparing analytical and ex-perimental results show that exex-perimental results can be predicted best by using a value of χ=0.8. Though the (negative) slope of the predicted fric-tion coefficient is overestimated, the trend is pre-dicted correctly and values found are within the same order of magnitude.
0 13 26 39 52 65 0.1 0.12 0.14 0.16 0.18 0.2 χ=0.6 χ=0.8 χ=1.0 Pressure [MPa] F ri c ti o n c o e ff ic ie n t [-]
Exp: Dynamic friction coefficient
Sim: Dynamic friction coefficient (χ=0.6,0.8,1.0)
Fig. 5 Effect of shape factor χ on friction
4
Conclusions
The frictional behavior of cold rolled high forma-ble mild steel in combination with Quaker N6130 oil has been characterized in this paper. Results have been used to calibrate the recently developed friction model, applicable to large-scale forming simulations.
Loading and sliding experiments have been con-ducted to track the development of real contact area and friction coefficients. It was found that sliding has a significant effect on the development of real contact area compared to loading only cas-es. Results have been used to calibrate the flatten-ing models incorporated in the numerical friction model. Both loading and loading + sliding experi-ments can be predicted accurately by the incorpo-rated flattening models. Friction tests showed that both the static and the dynamic friction coefficient decreases with increasing contact pressure. The numerical friction model predicts this trend cor-rectly, and values found are within the same order of magnitude.
5
Acknowledgment
This research was carried out under the project number MC1.07289 in the framework of the Re-search Program of the Materials innovation insti-tute M2i (www.m2i.nl).
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