Keywords

1 Introduction

Hollow shafts are widely used in many technical fields due to lightweight design, resource efficiency and the necessity of the integration of functionalities. Their weight saving potential can be explained by comparing the section modulus of a solid and a hollow shaft. With an increasing internal diameter of the hollow shaft, the section modulus decreases only slightly compared to a solid shaft with an identical outer diameter. This means that the spared volume has only a minor impact on the resistance to bending and torsion of the shaft [1]. Therefore, hollow shafts are often used, e.g., for torque transmission in gearboxes, while the saved volume also offers additional assembly space [2]. Regarding the high torsional load in such cases, cold forging processes appear appropriate for manufacturing of such shafts due to the strain hardening of the material [3].

Rotary swaging and axial forming (for splined components) are often used cold forming processes for manufacturing tailored hollow shafts for lightweight applications [4]. Those processes offer a certain flexibility and therefore are recognized for manufacturing such tailored components. However, the flexibility of rotary swaging requires higher cycle times compared to non-incremental processes. There are also some investigations regarding drawing and axial forming processes using a movable mandrel for manufacturing hollow components with different cross sections along their length [5, 6]. Further approaches for manufacturing hollow profiles with varying wall thickness have been carried out in hot extrusion of round [7, 8] and rectangular [9] aluminum tubes.

At the Institute for Metal Forming Technology at the University of Stuttgart, a novel cold forging process has been developed which allows for manufacturing hollow shafts with varying cross sections in one single press stroke by use of an adjustable forming zone [10]. The process is based on a conventional hollow cold forging process while the mandrel comprises at least two different cross sections which can be moved relatively to the die. By means of this relative position adjustment, it is possible to adjust the forming zone during the process. Until now, numerical investigations have been carried out regarding this process [11, 12] and also a tool concept for the required tool kinematics has been developed [13]. The main objective of this present study is the experimental proof of the feasibility of the process in general. Furthermore, the numerically calculated and the experimentally determined part geometries were compared regarding the radial underfilling at the outer surface of the workpieces.

2 Material and Methods

At first, a material characterization and further numerical investigations for the material AA6082 were carried out. Afterward, experimental tests were conducted and the results were compared to the numerical results by means of optical measurement of the part geometry. The material characterization, developed numerical model and experimental setup are described below.

2.1 Flow Curves and Numerical Model

The flow curves of the test material AA6082 were determined by compression tests using a Gleeble 3800c thermomechanical simulator and are depicted in Fig. 1. Cylindrical specimens having a height of 15 mm and a diameter of 10 mm were used for the compression tests according to [14]. To consider the rate and temperature dependence of the deformation behavior of the material flow curves for three different strain rates (0.1 s−1, 1 s−1, 10 s−1) and four different temperatures (20 °C, 100 °C, 200 °C, 300 °C) were obtained. These temperatures were chosen since the material heats up during deformation which leads to a softening of the material. During the compression tests, copper paste and graphite foil were used as lubricants to keep friction low and reduce barreling of the specimens to a minimum. Nevertheless, very slight barreling of the specimens was observed.

Fig. 1
figure 1

Experimental determined flow curves of the test material AA6082

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For the numerical investigations, the FEM software DEFORM was used. Figure 2 shows the numerical model for the 2D and 3D simulations. Since the investigation of radial underfilling at the outer surface of the workpieces was one of the objectives of this study, the workpiece was modeled as an elastic–plastic object (flow curves depicted in Fig. 1, constant Young’s modulus of 70 GPa and constant Poisson’s ratio of 0.33).

Fig. 2
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Numerical model for the 2D and 3D simulations

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Regarding the tool components, only the die was modeled as an elastic object (constant Young’s modulus of 207 GPa and constant Poisson’s ratio of 0.3). Mandrel, hollow punch and ram-side ejector were modeled as rigid objects. The hollow punch is considered as stationary and the die is moved in the -z direction at a constant velocity of 30 mm/s. The ram-side ejector is pushed in the upward direction during the forming process. At the same time, a very low counterforce is applied on the workpiece. The respective load–displacement curve of the ram-side ejector was determined experimentally for this numerical investigation.

The heat energy due to deformation was calculated as a product of the mechanical energy and a constant value of 0.9 according to the standard setting in DEFORM. Regarding friction, the shear friction model with a constant factor of m = 0.2 was used based on experience gained in various research projects at the institute. Mesh windows were used to refine the mesh in relevant sections, e.g., for the internal splined sections of the workpiece. In the 2D simulation, 4,000 quadrilateral elements were used for the mesh of the workpiece comprising a minimum edge length of 0.14 mm. In the 3D simulation, 300,000 tetrahedral elements were used for the mesh of the workpiece comprising a minimum edge length of 0.05 mm.

Besides the tip of the mandrel, the geometry of all other components was the same for the 2D and 3D simulations. The length of the workpiece was chosen to be 58 mm, its outer diameter was 31.9 mm and its internal diameter 19.05 mm. The internal diameter of the die was initially 32 mm and was reduced to 26 mm in the forming zone using a radius of 15 mm at the end of the forming zone. The outer diameter of the die was 160 mm with a height of 85 mm. In the 2D simulation, the diameter of the mandrel was chosen to be 19 mm in its lower section and 17 mm at the tip of the mandrel. In the 3D simulation, a splined mandrel with 15 teeth, a teeth height of 1 mm, a tooth tip diameter of 19 mm and a flank angle of 30° was used. Only half of a tooth was calculated in this case, so a 12° segment of the forming process was investigated. Due to the boundary conditions of machining process of the splined mandrel, all radii at the teeth were chosen to be 0.32 mm, while the tooth thickness corresponds to the tooth gap at medium tooth height.

The movement of the die was directly coupled with the movement of the ram. The mandrel kinematic was implemented as a position control in relation to the ram position. Figure 3 shows the position of the mandrel and die in relation to the absolute value of the ram position. At the beginning, the mandrel and die move synchronously with the same velocity (1). Then the mandrel stops, causing a reduction of the cross section in the forming zone (2). For a certain amount of time, the mandrel remains in this position. In order to return to the initial relative position with respect to the die and thus to increase the cross section in the forming zone again, the mandrel is moved at a higher velocity compared to the die (3). Finally, the movement of the mandrel and the die is synchronized when they reach the same position (4).

Fig. 3
figure 3

Position of the mandrel and die in relation to the absolute value of the ram position

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2.2 Experimental Setup

For the experimental investigations, a hydraulic press SMG HPZUI/300/300–1300/1000 with a maximum capacity of 6,000 kN was used. The used tool consists of an upper, a lower and a base frame (Fig. 4). The base frame includes a hydraulic cylinder with a maximum force of 563 kN during extension and a maximum force of 343 kN during retraction at 280 bar. The hydraulic cylinder is driven by a separate hydraulic unit. The mandrel is connected to the rod of the hydraulic cylinder. The lower frame holds the hollow punch and is connected to the press table via the base frame. Thus, the hollow punch does not move during the process. The upper frame contains the die and the ram-side ejector. Zinc stearate was used as a lubricant and was applied homogeneously on the surface of the billets.

Fig. 4
figure 4

Sliced CAD model and real tool with labeling of main tool components

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Load cells based on strain gauges were used to measure the tool load at mandrel, hollow punch and die. Furthermore, the displacements of ram (die) and hydraulic cylinder (mandrel) were measured. After the process, the outer surface of the pressed parts was measured by using the optical measurement system GOM ATOS Compact Scan 5 M and the radial deviation compared to a cylinder was determined.

3 Results and Discussion

First of all, it can be stated that the feasibility of the process could be successfully demonstrated with the developed tool. At first, the experiments with an increased wall thickness toward the ends of the hollow shaft were carried out. The underfilling at the outer surface of the pressed parts, which was already observed in the numerical investigations, also occurs on the real parts. Figure 5 depicts sliced pressed parts made of AA6082 and their main dimensions.

Fig. 5
figure 5

Sliced pressed parts made of AA6082 and main dimensions: a increased wall thickness toward the ends of the shaft, b increased wall thickness in the center of the shaft due to a varied mandrel kinematic and c local internal splined sections toward the ends of the shaft

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Figure 5a shows a sliced hollow shaft with an increased wall thickness toward the ends of the shaft by using the mandrel kinematic shown in Fig. 3. In a further experiment, the mandrel kinematic was varied in such a way that a hollow shaft with an increased wall thickness in the center of the shaft could be pressed (Fig. 5b). These results demonstrate the high flexibility of the presented process with regard to the variation of radial dimensions within the axial proportions of the pressed parts. Besides the experiments with the non-splined mandrel, tests with a splined mandrel were also carried out. By using the same mandrel kinematic as shown in Fig. 3, it was possible to manufacture a hollow shaft with local internal splined sections within one single press stroke. A respective pressed part with such a geometry is depicted in Fig. 5c.

Figure 6 shows the numerical and experimental determined tool load onto the hollow punch and the mandrel versus the absolute value of the ram displacement for the splined part geometry.

Fig. 6
figure 6

Numerical and experimental determined tool load onto the hollow punch and the mandrel versus the absolute value of the ram displacement for the splined part geometry

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The maximum tool load onto the hollow punch was measured to 174 kN in the experiment and calculated to 152 kN in the simulation. Regarding the mandrel, a minimum load of −42 kN was measured in the experiment and a minimum load of −22 kN was calculated in the simulation. These deviations can be explained by the friction modeling in the simulation on the one hand and the rigid modeling of the mandrel and the hollow punch on the other hand. However, the qualitative characteristic of the experimental and numerical load–displacement curves appear to be very similar.

Figure 7 shows a comparison of the optical measurements of the pressed part and the numerical results in terms of the radial deviation of the part geometry compared to an ideal cylindrical shape. Figure 7a shows the comparison for the non-splined part and Fig. 7b for the internally splined part. It can be obtained that the experimentally determined radial deviation matches the numerically determined radial deviation quite well with respect to the quantitative values. The underfilled section has a minimum radial deviation of −0.13 mm in the optical measurement and −0.12 mm in the simulation.

Fig. 7
figure 7

Comparison of optical measurements and numerical results in terms of radial deviation of the part geometry compared to an ideal cylindrical shape: a non-splined part and b splined part

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However, a slight axial misalignment regarding the axial position of the radial deviations was found which can be seen in Fig. 7a. This can be explained by three aspects, namely the modeling of the mandrel in the simulation as a rigid body, the characteristics of the displacement sensor of the hydraulic cylinder and the delay of the hydraulic control unit. An elastic modeling of the mandrel will have an impact on the ram-position-related change of the forming zone due to the elastic elongation of the mandrel. When comparing the sensor signal with gauge blocks and a dial indicator, a slight nonlinear sensor behavior of the sensor for measuring the axial position of the mandrel was detected. Since this sensor signal is the reference signal for the control unit of the mandrel, the kinematics require a correction before being transmitted to the control unit. For further experiments, this correction curve for compensation of the nonlinear sensor behavior has already been determined based on the current results. In addition, a delay in the hydraulic control unit has been identified. This results in a small deviation of the defined and the actual position of the mandrel during the process. It has been found that the delay depends on the load at the mandrel.

Figure 7b in particular proves that a continuous back pressure between the workpiece and the mandrel induced by the tooth tips of a splined mandrel leads to a significant reduction of the underfilling. This hypothesis has already been stated in the numerical investigation in [10].

In addition to the experimental investigations conducted with AA6082, also a few tests were carried out with the low-carbon steel DIN/EN-1.0303. The gained results showed that the developed tool can also be used for cold forging of steel parts with a variable wall thickness.

4 Conclusion and Outlook

In this contribution, the first experimental results regarding a special cold forging process characterized by a locally adjustable forming zone are presented. The locally adjustable forming zone of this process allows for the production of hollow shafts having a variable wall thickness within one single press stroke. At first, the material data and the numerical model are presented. A splined and a non-splined workpiece geometry were investigated and the respective used numerical models (3D and 2D) were described. Additionally, relevant geometric details and the developed tool and used hydraulic press are presented.

The experimental tests were carried out successfully with the developed tool presented in this paper. Thus, the feasibility of the proposed process for cold forging of hollow shafts having a variable wall thickness or local internal splined sections within one single press stroke has been proven. Although the main focus was on the material AA6082, the tool was also capable of forming low-carbon steel DIN/EN-1.0303. Regarding the radial underfilling at the outer surface of the workpieces, it was found that the deviation between the numerical and experimental results is quite low with a maximum radial deviation of −0.13 mm in the experiment and −0.12 mm in the numerical investigation. Furthermore, it could be proven that a continuous back pressure between the workpiece and the mandrel induced by the tooth tips of a splined mandrel leads to a significant reduction of the underfilling.

In order to further improve the numerical model and to reduce the kinematic and geometrical deviations between the experiment and the simulation, further adjustments to the numerical model will be carried out, such as the use of the actual mandrel kinematics from the experiment and the elastic modeling of the mandrel and the hollow punch. In the next step, an experimental investigation with the case-hardening steel AISI 5115 will be carried out.