In this example, presents an analysis for finding the deformation of the gear due to induction hardening using a two way coupled Magnetic / thermal stress study in JMAG.
Eddy current Loss
Fig. 1 shows the eddy current loss density distribution of the cross-section of a tooth top.
The coil is feed with a high frequency (30 kHz) current that will generate an oscillating magnetic field that will create induced current in the gear. Because of the High frequency nature of the Magnetic field the currents will be located in a small portion of the gear because of the skin effect. The skin depth can be calculated using the equation shown in Fig. 2.
The Magnetic Field frequency Analysis will allow us to find the induced current in the work piece. The losses induced by those currents will be shared with the thermal stress study. The changes in temperatures and deformation of the work piece will be used as an input constraint of the FQ analysis.
Fig. 3 shows the temperature distribution of the gear, and Fig. 4 shows the temperature variation versus time of the tooth tops. Fig. 4 shows the temperature variation of the tooth top at the measuring points shown in Fig. 3.
The Losses created by the induced current will act as an heat source and increase the temperature of the work piece. In the Thermal stress study will set the losses found in the magnetic study as an input constraint. As the losses are mainly concentrated in the outer layer of the workpiece, this area will naturally have the highest temperature changes. The resulting temperatures will be shared with the Magnetic study where the magnetic properties of the material will be change according to it.
Thermal Stress (deformation)
Fig. 5 and Fig. 6 shows the deformation of the gear. Using a scaling factor of 100 we can observe the expansion of the work piece.
The changes in temperature in the work piece will create thermal stress that will lead to the thermal expansion of the heated geometry. We can observe that the parts subject to the most temperature have the highest expansion. After 4 sec the work piece deformed up to 0.18 mm. Furthermore we can also the impact the gravity has on the deformation of the work piece as it bending because of the force pulling it to the ground.