August 2019 Volume 1

FORGING RESEARCH

Figure 2-15: Distribution of the Normalized Wall Thickness Deviation

applying heat flux to the workpiece surface. Technically, the current distribution of a workpiece inside an induction coil is not uniform. The maximum of current density is always located on the surface of the conductor and the current density decreases from the surface towards the center. This phenomenon is called the skin effect. The depth of the surface layer where 86% power concentrate is called the penetration depth, which depends on the frequency of the AC power and material properties [14]. However, the penetration depth is much small compared with magnitude of workpiece dimension. Second, heat transfer during transportation of the workpiece among stations is ignored. Third, the heat transfer coefficient between the workpiece and the die, convection coefficient between the workpiece and the environment, and relative emissivity of the workpiece are assumed to be constant for simplicity. Fourth, the shear friction law is assumed to prevail due to the large normal stress within the die-workpiece interface. Fifth, environment temperature is taken as room temperature all the time. Sixth, the initial temperature distribution in the die is assumed to be uniform. The initial tube simulated is 942mm long, has a 20 mm inner diameter and a 50mm outer diameter and is initially meshed with 6000 elements. In the modeling of induction heating, a hybrid thermal boundary condition which contains heat flux, radiation and convection is applied to a section of the surface which is marked by a red line in Figure 2-16.The amount of the heat flux can be estimated by the Equation 1, where c is the specific heat of the workpiece which is a function of temperature, ρ is the density of the workpiece, OD is the outer diameter, ID is the inner diameter, T f is the final temperate, T i is the initial temperature, η is the heating efficiency (around 85%), t is the heating period. In this case, heat flux is set at 315000 w / m ². Radiation is specified by setting the relative emissivity of 0.7. Convection is characterized by a 20 o C environment temperature and a 10 w /( m 2 K ) convection coefficient. A convection boundary

2.4. FEModeling In order to confirm the feasibility of the differential heating based process and investigate effects of process variables on product and process characteristics, FE models are created. FEM simulations are carried out with the commercial FEA software DEFORM2D. Steel AISI4140 (20-1200 o C) is loaded from the material library as the workpiece material. AISI4140 is a low-alloy steel containing chromium and molybdenum as strengthening agents. This alloys is widely used in the automotive industry for manufacturing of gears, shafts, and spindles. Ideally it should not be forged below 900 o C [12]. AISI H-13 is selected as the die material. H-13 is a chromium, molybdenum, vanadium hot work tool steel which is characterized by high hardenability, good hot strength and excellent toughness. The molybdenum and vanadium act as strengthening agents. The chromium content assists H-13 in resisting softening when used at high temperatures. H-13 offers excellent combination of shock and abrasion resistance. It is able to withstand rapid cooling and resist premature heat checking. Typical applications are hot press dies, hot work punches, brass forging and pressing dies, aluminum and zinc die casting dies, extrusion mandrels, etc [13]. The overall simulation is divided into three operations: i) heating, ii) upsetting and iii) flanging. Only heat transfer mode is activated in the first operation. Both heat transfer mode and deformation mode are activated for the last two operations. In order to consider thermal and deformation history, the mesh at the final step of an operation is identical to that at the initial step of the subsequent operation. That is, values of nodal variables are not changed or lost at the connection between two operations. Simulation mode and operation number are set in the SimulationControl dialoguewindowofDEFORM2D. The FEM modeling is based on the following assumptions: First, penetration depth of the induction heating is assumed to be so small that heat generation of induced current is equivalent to

FIA MAGAZINE | August 2019 59