Extrusion Simulation of Tire Components Using HyperXtrude

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1 Extrusion Simulation of Tire Components Using HyperXtrude Vidit Bansal Dr. Jyoti Prakash Rath G. Unnikrishnan Tom Thomas Assistant Manager Head Vice President Executive Director Advanced Engineering(R&D) Advanced Engineering(R&D) R&D Technology and Projects CEAT Limited, Halol CEAT Limited, Halol CEAT Limited, Halol, CEAT Limited, Halol Pin ,INDIA Pin ,INDIA Pin: ,INDIA Pin: ,INDIA Keywords: Extrusion, Coextrusion, die swelling, Viscosity models, Numerical Simulation Abstract A tire is an assembly of different components that are made in a batch process. These components are either extruded or calendered. Of these, extruded components contribute more than 60% of total number of components of a tire and it is one of the most important processes in tire manufacturing. In an extrusion process, unvulcanized rubber compounds are pushed through a shaping die under specified operating conditions to create a profile of desired shape and acceptable tolerance. The shape and properties of extrudate have a great impact on tire performance. Further, viscoelastic nature of rubber by its memory and normal stress effects makes its flow behaviour challenging in producing the desired shape due to extrudate swell. Changes in the cross-section of the profile due to extrudate swell and mass flow imbalances depend on different parameters such as die design, flow rate, inlet pressure, temperature, and other operating conditions. This paper presents a numerical simulation of tire tread extrusion using Altair HyperXtrude to study the effect of above mentioned parameters on the shape and quality of the extruded profile. Introduction A modern day tire consists of many components, assembled together in a building machine to form a green tire followed by curing to produce a dimensionally stable product. Most of the important components of a tire, such as tread and sidewall, are extruded. Extrusion is a continuous process in which the soft rubber compounds are conveyed by a ram or screw and forced to the shaping die to take the required component shape. The dimensional integrity of the extruded components is essential to ensure the quality and needs to be controlled during manufacturing. In the final stage of the process, rubber compounds pass through a die that governs its shape and size. However, the dimensions of the extrudate depends not only on the die design but also on the properties of the rubber compound and process parameters [1]. Conventionally, trial and error methods are used for designing the die [2]. This method relies on heuristic knowledge and it is inefficient. In addition, this approach may not work for new materials and challenging new shapes that have not been extruded before. Hence, an accurate numerical simulation of the extrusion process is required [3] to overcome these challenges faced by modern day tire industry and in producing profiles of required shape and dimensional integrity. Unlike experimental techniques, where data is obtained at few points in the Simulate to Innovate 1

2 domain; numerical simulation provides velocity, pressure, temperature, strain rate, and other derived results at nodes in the domain. This detailed understanding of the process facilitates efficient correction and performance improvement of the die. Die Swelling The common observation during extrusion is the dimension of the extrudate is bigger than that of the die. This is because, when a polymer is forced by a screw into a die, it follows a partial recovery or swells back to the former shape and volume on exiting the die [4]. This phenomenon is known as die swelling or extrudate swell and is shown in Figure 1. It can be directly related to entropy and relaxation of the polymer molecules. Before entering into the die, the polymer molecules have mostly spherical conformation which is a state of maximum entropy. When the polymer starts flowing into the die its flow rate increases and the molecules lose its spherical conformation and become longer which is a state of lower entropy [5]. During travel through the die, only some of the entanglements get relaxed. When the polymer comes out of the die the constraints are removed and the un-relaxed molecules try to regain their former shape that is spherical conformation in order to maximize the entropy [5]. While designing the die it is important to keep the die land length at least 10 times longer than the thickness of extrudate profile to let the viscoelastic stresses relaxed before leaving the die. Extrusion of tread profile Figure1: Die swelling In the present work, a tread profile of the tire size 145/80R12 has been selected. A typical PCR tread profile is made of different types of components as shown in Figure 2. Figure 2: Typical tread profile Simulate to Innovate 2

3 Typically these three components are made of different rubber compounds. For extrusion of such a profile, co-extrusion technique is used, where more than one material entering into different barrels, are combined together to form a single profile. Before entering into the die, rubber components pass through preformer. Preformer has different inlets depending on number of components in an extrudate profile. The design of a performer and die has been shown in Figure 3. Figure 3: Preformer and die A PCR tread preformer has three inlets known as cap inlet, base inlet, and wingtip inlet, where the three materials are put together and forced to enter into the die. While flowing through these channels, behavior of rubber is very crucial. Its viscosity and viscoelastic nature change drastically at different shear rates, temperatures and other process parameters. To capture this complex nature of rubber in simulation, viscosity and viscoelastic material models are necessary. Extrusion Simulation In the present work, HyperXtrude is used for extrusion simulation of a tread profile. Typically two or three kinds of material are used to make a tread profile, In order to simplify the problem, in this work, only single material extrusion is considered. Data required for the analysis is prepared by meshing the flow volume in HyperXtrude interface in HyperMesh. Then material properties, process and control parameters are defined. The resulting data deck is solved using HyperXtrude solver and post processing has been done in Hyperview. The solving approach used by the solver is shown in Figure 4. Simulate to Innovate 3

4 Figure 4: Solving approach Velocity distribution in extruded profile: Results and Discussion The velocity contour of the extrudate is shown in Figure 5. It is observed that the velocity is very low near the edges of the die due to high shearing action of the die walls. The predicted velocity distribution is proportional to the die gauge. Maximum velocity is observed at the highest gauge region where as minimum or nearly zero velocity is observed at low gauge area. Figure 5: Velocity contour of extrudate Simulate to Innovate 4

5 Analysis of Flow Behavior of Rubber By studying the streamlines and how material flow from inlet to exit regions, flow behavior of different rubber compounds that make the tread and its final shape is analyzed. Figures 6(a) and 6(b) show the streamlines of cap and base material flow respectively. The flow is found to be continuous and proper. Figure 6(a) Downstream particle traces of the cap material Figure 6(b). Downstream particle traces of base material Comparison of different viscosity models Selection of material models has large impact on the accuracy of simulation results. There are several viscosity models available which can be used to model the flow behaviour of polymers. Among all the available models Modified Cross and Carreau-Yasuda models are two of the most popular and widely used models to describe the constitutive behaviour of the material. In this work, these two models are compared on the basis of percentage die swell in the extruded profile. Modified Cross model: η = Aα T /(1 + (Aα T γ)/τ*) (1-n)..(1) Where, A Consistency (Pa-s) n Exponent (dimensionless) γ Effective shear rate (s -1 ) τ* Reference shear stress (Pa) α T Temperature dependence (Dimensionless) This model has three parameters: consistency-a, exponent-n, and reference shear stress-τ*. Consistency is modified using the temperature dependent function α T to introduce the effect of temperature on the computed viscosity. There is a very subtle difference between Cross and Modified Cross model, this difference enables (by appropriate choice of parameters) one to easily set up Carreau-Yasuda model to mimic the modified Cross model. This model describes the viscosity using a power-law relationship. Simulate to Innovate 5

6 Carreau-Yasuda Model: η = η α T + α T (η 0 - η ) (1 + (λ α T γ)a) (n-1)/a......(2) Where, η 0 Zero shear Viscosity (Pa-s) η Infinite shear Viscosity (Pa-s) n Exponent (dimensionless) γ Effective shear rate (s -1 ) λ Time Constant (s) a Transition parameter (dimensionless) α T Temperature dependence (Dimensionless) This model has a well defined upper (zero shear viscosity) and lower (infinite shear viscosity) limits for the polymer viscosity. Typically, the value of transition parameter is 2. Time constant λ, alters the nonlinear behavior of the fluid and its dependence on the shear rate. If the time constant is 0, then the fluid becomes Newtonian, with a high value for the time constant η, becomes a strong function of shear rate. By suitable choice of parameters, many other models can be mimicked by this model. Figure 7(a) & 7(b) shows the die swell of the extrudate using Modified Cross and Carreau-Yasuda model respectively. As shown in the figure below, as soon as the material comes out of the die, the material tries to get a shape of increased dimensions. It has been observed that while exiting from the die, there is greater change in the gauge (thickness direction) of the profile than that of the width. The percentage die swell data is presented in Table 1. Simulate to Innovate 6

7 Figure 7(a) Predicted swell using Modified Cross model Figure 7(b) Predicted swell using Carreau-Yasuda model Table I: Comparison of computed die swell with different viscosity models % Increment in Gauge(mm) Width(mm) Gauge Die % Increment in Width Modified Cross Model Carreau Model Experimental results show that the gauges swell around 60-70% and the width around 10 %. According to the computed results, Carreau-Yasuda model showed better die swell correlation with experimental results than Modified Cross model. Since die swell is a critical phenomenon in case of rubber extrusion, Carreau-Yasuda model is found to be a suitable one for extrusion simulation of tire tread profiles Simulate to Innovate 7

8 Summary and Benefits This work demonstrates the importance and complexities of extrusion process in tire manufacturing; and the need for numerical simulation. HyperXtrude is used for simulating extrusion process of tire components and it has proven successful in modeling tire extrusion. HyperXtrude has a user friendly interface and a robust solver. These enable its use for studying tire extrusion. Since the interface is built on HyperMesh, it has all the necessary meshing and CAD tools for easily preprocessing the data. Challenges and Future Plans In order to accurately study extrudate swell, one has to consider the viscoelastic effects (such as normal stress effects) in the material modeling. This will be studied in the next phase of the work. HyperXtrude can enhance the non-newtonian viscosity model (Modified Cross or Carreau-Yasuda) with viscoelastic Criminale-Ericksen-Filbey model. Latter includes the effect of first and second normal stress differences on the flow behavior. In addition, future studies will also focus on verifying the simulation of extrusion of different tread profiles and co-extrusion. Conclusions In this study, Carreau-Yasuda viscosity model predicted the extrudate swell better than Modified Cross model. This conclusion will be corroborated with additional studies. Flow behaviour of rubber inside the die is analyzed in detail by looking the contour plots of computed data and the streamlines. Latter helps to track and identify how the material flows from the inlet to different regions of the profile. Numerical simulation is useful in quantitatively predicting the die swell and visualizing the material flow. This will help and play a critical role in designing and correcting the dies. ACKNOWLEDGMENTS We would also like to thank Altair HyperWorks and ATC-2013 for providing us an opportunity to present this work. The authors would like to thank the CEAT management for allowing publishing this work. We would also like to thank Amit Patil and Mukesh Parmar, the process experts, from CEAT for their support in actual extrusion process. REFERENCES [1] T. Tran-Cong. and N. Pi-Ian-Thien, Die design by boundary element method, Journal of Non-Newtonian Fluid Mechanics, 30 (1988) [2] G. Zhao, Y. Mu, Finite-Element Simulation of Polymer Flow and Extrudate Swell through Hollow Profile Extrusion Die with the Multimode Differential Viscoelastic Model, Advances in Polymer Technology, Vol. 32, No. S1, E1 E19 (2013) [3] Carneiro, O. S., Nobrega, J. M., Pinho, F. T., Computer aided rheological design of extrusion dies for profiles, Journal of materials processing technology, 114, pp , [4] C.Sirisinha, A review of extrudate swell in polymers, J.Sci. Soc, Thailand, 23(1997), [5] Simulate to Innovate 8

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