Finite Element Model of Gear Induction Hardening

Transcription

1 Finite Element Model of Gear Induction Hardening J Hodek, M Zemko, P Shykula To cite this version: J Hodek, M Zemko, P Shykula. Finite Element Model of Gear Induction Hardening. 8th International Conference on Electromagnetic Processing of Materials, Oct 2015, Cannes, France. EPM2015. <hal > HAL Id: hal Submitted on 20 Jun 2016 HAL is a multi-disciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

2 Finite Element Model of Gear Induction Hardening J. Hodek 1, M. Zemko 1, P. Shykula 2 1 COMTES FHT, Prumyslova 995, Dobrany, Czech Republic 2 Miba, Nabrezie Oravy 2222, Dolny Kubin, Slovakia Corresponding author: josef.hodek@comtesfht.cz Abstract This paper presents a finite element model of a gear induction hardening process. The gear was surface-heated by an induction coil and quickly cooled by spraying water. The finite element model was developed as a three-dimensional model. The electromagnetic field, temperature field, stress distribution and microstructure distribution were examined. Temperature and microstructural characteristics were measured and used. The gear material data was obtained in part by measurement and in part by calculation. Keywords: gear hardening, finite element, induction heating Introduction Gears are machine parts that are widely used in industry. The end-use properties of selectively hardened parts of gears, in particular their hardness, wear resistance and contact fatigue resistance can be controlled to a great extent through the parameters of the heat treatment used. FEM simulations [1-4] and measurement of material properties, temperatures and martensite layer thickness are useful tools for describing the properties of gears upon heat treatment. Process Description The gear teeth are induction-heated (Fig. 1) to the required heat treatment temperature and then cooled rapidly. By varying the heat treatment temperature, the inductor power and the cooling method, one can obtain various mechanical properties upon heat treatment. The power and frequency of the inductor used in the present process was 100 kw and 200 khz, respectively. The heating time was 0.8 seconds. The diameter of the gear was 100 mm and the module was 1.64 mm. Ø100 Fig. 1 Induction heating of the gear Material Data Acquisition The L75PT dilatometer was used for the thermal expansion measurement. From the thermal expansion profile, the austenitizing temperature was determined. The LFA1000 laser flash instrument was used for the determination of heattransport properties: the specific heat and thermal diffusivity as a function of temperature. Thermal conductivity was calculated from thermal diffusivity and measured density values. The rest of the properties required were calculated using the JMatPro software. JMatPro is simulation software which calculates a wide range of material properties from the chemical composition. It focuses particularly on multicomponent alloys used in industrial practice. The following temperature-dependent data were computed: electrical conductance, Young s modulus, Poisson s ratio and the flow stress for all components of the material s mixture. Measurement of Temperature Temperature profiles during heating and cooling were measured for several combinations of power and time. Thermocouples were used for the measurement (see Fig. 2). At every instant, four temperatures were measured simultaneously: at two points at the top of the tooth and at two points at its bottom. Average values were then calculated from the temperatures of the tooth top and bottom. Those values should be understood to be approximations because it was not possible to weld the thermocouples onto exactly same locations. During the temperature measurement, the gear was not revolving.

3 Fig. 2 Temperature measurement Fig. 3 Martensitic layer after heat treatment Martensitic Layer Thickness The thickness of the martensitic layer was measured in the centre of the tooth. The shape of the martensitic layer is shown in Fig. 3. Mathematical Model The mathematical model is defined by the following equations: 1) The electromagnetic field is described by equations for the vector A and scalar V potentials [5]. For the sake of simplicity, the problem is considered to be a harmonic one, where μ stands for the magnetic permeability, ω is angular frequency and γ denotes electrical conductance: (1) (2) 2) The transient temperature field is expressed by the Fourier equation [6]: (3) Here, c denotes specific heat, ρ stands for density, λ is thermal conductivity and w represents the heat loss during induction heating. 3) Stress and transformation field In the DEFORM 3D software, strain, heat transfer and transformation are strongly related parameters. Any change in one of them has impact on the other two. In the model, a material is defined as a mixture of phases where rules for phase transformations apply [6]. The stress strain relation is defined as an elastic-plastic relation for all phases: (4) Here, σ denotes the flow stress, c represents a material constant, ε is the effective plastic strain, n stands for the strain exponent, m is the strain rate exponent and y represents the initial yield value. The initial phase is pearlite. The model contains two phase transformation rules: a. Pearlite austenite: diffusional transformation described by the Avrami equation. b. Austenite martensite: martensitic transformation characterised by the martensite start temperature and the 50%-martensite temperature. Owing to high cooling rates used in the process, other phase transformations only take place on a very limited scale. Hence, they are omitted from this analysis. FE Model of Heat Treatment Procedure The block diagram of the calculation is shown in Fig. 4. The entire calculation procedure consisted of two parts. In the first one, the electromagnetic and temperature fields were studied using the MSC Marc software. The data for the temperature field just after the end of heating was then fed into the DEFORM 3D software by means of the Python script. The cooling process, the stress distribution and transformation of microstructure constituents were then analysed using DEFORM 3D. Fig. 4 FEM model

4 As the problem is geometrically symmetrical, the computational model only comprised one quarter of a single tooth (see Fig. 5). The models of the electromagnetic and temperature fields in the MSC Marc software comprised the gear, the inductor and a sufficiently large portion of the environment. The calculation of stresses, temperatures and transformations in DEFORM 3D only involved the gear. Relevant boundary conditions were defined for individual mathematical expressions. The model was meshed to comprise at least three elements across the skin depth (see Fig. 6) Fig. 5 FE model one quarter of the gear tooth Fig. 6 The meshed model Model Calibration The model was calibrated using the measured data in order to obtain agreement with the real-world processes that take place during heat treatment. 1) Temperature calibration: the inductor current was varied until the measured and calculated temperatures were in agreement (see Fig. 7). During cooling by the water spray, heat was removed rapidly from the gear. The heat transfer coefficient value for this cooling sequence was determined by inverse analysis. 2) Calibration against the martensitic layer depth: the diffusional transformation model and the martensitic transformation model were varied until the measured and calculated martensitic layer data were in agreement (see Fig. 8). Fig. 7 Comparison between calculated and measured temperatures Fig. 8 Comparison between calculated and measured shape of martensitic layer Results and Discussion Several heating and cooling possibilities were computed. The following computation results were obtained for 0.8- second heating and 8-second water cooling. The temperature of the tooth upon heating (see Fig. 9) is between 1000 and 1200 C. The region where the temperature is sufficiently high becomes austenitized (see Fig. 10). Fig. 9 Temperature distribution after heating Fig. 10 Austenite distribution after heating

5 The progress of the martensitic transformation and the distribution of effective stress during cooling are shown in Fig. 11 and Fig. 12, respectively. Fig. 11 The progress of martensitic transformation at the start of the process and 2 s, 2.5 s, 3 s, 3.5 s and 8 seconds into the process Fig. 12 Effective stress at the start of the process and 2 s, 2.5 s, 3 s, 3.5 s and 8 seconds into the process Fig. 11 and Fig. 12 clearly show that the strongest effect on the stress distribution comes from transformation processes. The post-heat treatment residual stress reaches its highest values at the bottom of the tooth. Conclusion The above-described FE model characterises the behaviour of gears during surface hardening. The model integrates calculations of electromagnetic, temperature and strain parameters and accounts for phase transformations. It was calibrated against measured temperatures and the thickness of the martensitic layer. Temperature-dependent material properties were in part measured and in part calculated. Using the FE model, one can estimate the behaviour of the gear during heat treatment, namely the time profiles of temperature, phase and stress distribution. In their follow-up research, the authors will focus on the relationship between the residual stress distribution and the contact fatigue resistance of gears. Acknowledgment These results were created by project Development of West-Bohemian Centre of Materials and Metallurgy No.: LO1412, financed by the MEYS of the Czech Republic. References [1] J. Barglik3D, Journal of Computational and Applied Mathematics 270 (2014) [2] J. Montalvo-Urquizo, Computational Materials Science 79 (2013) [3] P. Šuchman, J. Hodek, Optimization of Induction Hardening Parameters through FEM Simulation, 20th IFHTSE Congress, October , Beijing [4] J. Hodek, 23 th International Conference on Metallurgy and Materials, Fem Simulation Induction Heating Process [5] Marc 2014, VolumeA: Theory and User Information, 331 [6] Deform v System Documentation