Hybrid manufacturing of topology optimized machine tool parts through a layer laminated manufacturing method

Even using the aforementioned penalization and density filtering methods, very complex part structures result from TO [7]. These may be hard or even impossible to produce using conventional subtractive manufacturing processes. For this reason, additive manufacturing (AM) is widely used to produce such optimized part structures [7, 8].

Metal parts are of particular interest for machine tools and are vital for various applications such as joints, guides and bearings [1]. Structural optimization of metal machine tool parts helps to improve machine performance [9], energy demands [10] as well as sustainability [11], e.g. by biologically inspired stiffness designs [12, 13]. Functionally graded lattice structures may be used to adapt TO results and provide significant stiffness enhancement compared to regular grid structures [14]. These omit the aforementioned penalization and instead mimic the numerically optimal intermediate densities by using lattices with variable thicknesses.

However, some challenges remain, such as part size limitations and cost. Especially for machine tool parts with high volumes and low per-part-cost, conventional manufacturing methods are still the preferred choice [15].

The layer laminated manufacturing (LLM) is referred to as a hybrid manufacturing process as it combines additive joining of coherent layers with their subtractive structuring before or after joining. Numerous process variants in terms of the layer materials and the joining process have been subject to research within the last decades [16‐20]. LLM has received limited industrial attention so far, even though it allows unique design freedoms such as enclosed inner cavities and virtually any material combination. However, the freedom of design must also be able to be used specifically, for which LLM-specific engineering tools are required. A novel slicing method that utilizes inner cavities in order to mimic intermediate densities from TO has been proposed by the authors in [21]. This allows the use of TO without penalization and permits intermediate densities to approximate the numerically optimal part structure in terms of manufacturing.

In this paper, a comprehensive approach towards the production of low-cost, structurally optimized metal parts is proposed in Sect. 2. This approach is based on previous work from [21], where a novel method for automatic modelling of optimized LLM parts was proposed and analyzed by simulation. However, practical challenges of LLM manufacturing using adhesive bonding as a joining technique are outlined in this paper and extensive tests are conducted on the resulting part properties. As a practical example to validate the proposed LLM method, the bearing block of a ball screw feed drive is topologically optimized and manufactured by bonding steel sheets. This optimized bearing block is experimentally investigated in its real assembly situation, as described in Sect. 3. Serving as reference, identical experiments are carried out using a solid bearing block as well as a bearing block, that has an almost identical geometry compared to the LLM bearing block but is manufactured using Laser Powder Bed Fusion (PBF-LB/M). The results of this comparison are shown and discussed in Sect. 4.

The basic steps along with details on implementation of the novel method for modeling topology optimized LLM components are described in [21] and illustrated schematically in Fig. 1.

First, the part to be optimized is sliced according to the build-up direction and the sheet metal thickness . The resulting 2D layers are then equipped with a virtual discretizaion called uniform manufacturing grid (UMG) , enabling the downstream modeling of individual cavities for each grid cell. Taking up the TO results, normalized grid cell densities are determined using piecewise linear interpolation. For each grid cell, a cavity is modeled to ensure that the remaining volume is approximately equal to the normalized grid cell density. Ultimately, all individually structured layers are extruded according to the metal sheet thickness and joined together to form an assembly CAD model .

A bunch of manufacturing parameters is used for cavity modeling along with the size of the grid cells - for instance, the minimum producible radius or the residual bridge width between two cavities. The simulative parameter study in [21] provided the best suitable combination of manufacturing parameters for the bearing block studied. The bearing block modeled with these parameters is selected for manufacturing, which is described below.

The LLM manufacturing process is based on layer-by-layer cutting and lamination of sheets of materials. A variety of possible materials and joining methods may be combined for LLM manufacturing. Each combination provides individual chances and challenges. In this work, the adhesive bonding of metallic sheets using high-strength epoxy-based structural adhesives is examined.

First, the part sheets are manufactured subtractively, for which laser cutting is used due to the individual structuring of each sheet. Special attention needs to be paid to ensure low thermal warpage and clean deburring of all edges of the contact surfaces. Mechanical surface preparation is also advisable in order to set a proper surface roughness and thus improve adhesion [22]. Due to the lack of automation, the application and distribution of the adhesive is done manually. Joining the individual layers and curing them without mutual slipping or rotating is also a practical challenge at this stage. The low shear strength of the adhesive just after dispensing leads to distortion of the bonding partners even under small transverse forces. For this, depending on the part contour, mechanical frame constructions or other clamping mechanisms are to be used to secure the position. Locked against twisting, the layers are finally applied with a pressure between \(0.1-12\) tons using a hydraulic press because thinner epoxy adhesive bond lines were found to provide larger bonding strengths and higher maximum shear strains [22]. Under pressure, the part is then cured in line with the curing time of the adhesive used. Once fully cured, subtractive finishing is necessary on functional surfaces and additional holes and threads are drilled.

Since the bearing block acts as a fixed bearing in the axial force transmission, its effect on the axial stiffness of the feed axis is examined. For this, the axial stiffness behavior is considered as a series connection of springs (cf. Fig. 3). The screw stiffnesswith the cross section \(A_\mathrm {screw}\) and the Youngs’s modulus E decreases hyperbolically with the distance \(x_\mathrm {T}\) of the machine table from the fixed bearing. Due to this, the axial stiffness of the overall mechanical system also changes when moving the machine table. To account for this influence, the experiments are performed both at the minimum (\(x_\mathrm {T}=0 ~\mathrm {mm}\)) and maximum (\(x_\mathrm {T}=700 ~\mathrm {mm}\)) position of the travel distance. Since these represent the maximum and minimum stiffness of the mechanical system respectively, no additional measurements are performed in between.

A direct drive is installed on the test rig to apply defined disturbance forces \(F_\mathrm {D}\) to the machine table. Different constant disturbance forces are applied via this drive and the resulting displacement is determined at two locations of the mechanical system. On the one hand, the deflection of the machine table \(\Delta x_\mathrm {T}\) is determined via the direct measuring system. On the other hand, the deflection of the bearing system \(\Delta x_\mathrm {B}\) is determined using a laser vibrometer (resolution \(0.32~\upmu \mathrm{m}\)) as shown in Fig. 3.

Figure 4 shows the measured deflections resulting from gradually increased forces between \(0-800 ~\mathrm {N}\). The forces are held for \(10 ~\mathrm {s}\) at each step to achieve steady state. The force-deflection curves in Fig. 4 show an approximate linear relationship within the investigated force range as well as a superimposed hysteresis behavior, both for the bearing subsystem and for the overall mechanical system. This is in line with the expectations, as the forces are in the range of typical axial operating loads of a ball screw feed drive. The hysteresis may be explained by mechanical settling effects due to relative motion in the bearings and bolted connections. Linear regression is used to calculate the balancing lines shown, whose gradients in each case corresponds to the static stiffness.

Changing the static and dynamic properties of the bearing block not only affects the static stiffness, but also the frequency-dependent transmission behavior of the feed drive axis. A common method for assessing this behavior is the mechanical frequency response \(G_\mathrm {Mech}=\nicefrac {{\dot{x}}_\mathrm {T}}{{\dot{x}}_\mathrm {M}}\), which relates the motion of the machine table \({\dot{x}}_\mathrm {T}\) to the motor velocity \({\dot{x}}_\mathrm {M}={\dot{\Theta }}_\mathrm {M} i_\mathrm {bs}\) with the ball screw transmission ratio \(i_\mathrm {bs}\). A logarithmic sine sweep, whose parameters are shown in Table 3, is used as excitation signal for the machine table velocity \({\dot{x}}_\mathrm {T}\). A speed control is used here instead of a position control, see Table 2.

As the axial screw stiffness decreases with increasing travel distance, the measurements are performed at the minimum and maximum possible start position \(x_\mathrm {T,Start}\), which is determined by the offset velocity \({\dot{x}}_\mathrm {T,Offset}\) and the resulting travel distance.

Another measure for evaluation of the dynamic behavior is the compliance frequency response. It describes the elastic, frequency-dependent deflection resistance under a dynamic disturbance force acting on the machine table, such as during a milling process. Machining limits depend to a large extent on the dynamic behavior, which in turn results from the stiffness, structural mass as well as damping [23]. The stiffness is expected to be compromised by the adhesive layers of the LLM bearing block, as well as the material removed. Using the direct drive, a dynamic disturbance force \(F_\mathrm {D}\) is applied to the machine table as a sweep with the values shown in Table 4. The relation of the resulting machine table deflection \(\Delta x_\mathrm {T}\) to the disturbance force \(F_\mathrm {D}\) results in the transfer function \(G_\mathrm {Comp}=\nicefrac {\Delta x_\mathrm {T}}{F_\mathrm {D}}\).

Experiment variations result from the position \(x_\mathrm {T}\) of the machine table as well as the cascaded P-PI control being active or inactive respectively. Inactive control means that the motor is not powered, but is blocked by a mechanical brake. With active control, the motor reacts to the disturbance forces and compensates for the positioning errors measured on the position measuring system, which results in a different transmission behavior.

Damping is a key factor for improving machine performance, as the induced energy losses result in less sensitivity to vibration [23]. While the adhesive layers presumably reduce the stiffness of LLM parts, the damping can be expected to increase. It has already been found that hybrid machine elements lead to considerable increases in part damping by combining steel and composites [24‐26]. However, the damping of machines is mainly dominated by the motor and friction effects in connection interfaces [1, 23].

The extent to which increased part damping has a positive effect on the damping of the overall system and thus on the dynamic properties of the ball screw test rig is investigated. The decay behavior in the time domain is investigated for this purpose. A step excitation force of \(F_\mathrm {D}=800\) N is applied using the direct drive.

The deflections at the machine table \(\Delta x_\mathrm {T}\) are measured for minimum and maximum machine table position, as shown in Fig. 5. A clear oscillation with obvious damping is present in all cases. The level of deflection is slightly higher for LLM compared to the other bearing blocks, which indicates a reduction in stiffness. Also for the maximum table position \(x_{\mathrm {T}}=700 ~\mathrm {mm}\), there is a higher deflection of the machine table because of lower screw stiffness.

An exemplary decay curve is shown in Fig. 6 to demonstrate the damping identification. The position signal of the machine table is numerically differentiated to compensate for drift effects due to sensor drift and hysteresis behavior of the feed drive. Starting at the second peak of the decay curve, intervals of equal size are analyzed for each run. The damping of the observed vibration results from the ratio of subsequent peaks expressed as the decay rate of an exponential function, which is fitted to the upper envelope of the decay curve and is called e-Fit in the following [27].

The stiffness values derived in this way for the examined bearing blocks are visualized in Fig. 7, in each case using the mean value and the variation range. A significant reduction in the stiffness of the bearing subsystem by 20–22\(\%\) using the LLM bearing block is obtained, while the PBF-LB/M and the solid bearing block show almost identical mean values and overlapping variation widths. For the overall system, the influence is less clear and also less significant with 6–9\(\%\) stiffnes reduction using the LLM bearing block. This is explained by the fact that the axial stiffness \(k_\mathrm {screw}\) of the screw has the lowest value in the overall system and is therefore dominant as the weakest spring (cf. Fig. 3).

The mechanical frequency responses for table start position \(x_\mathrm {T,Start}=0 ~\mathrm {mm}\), as shown in Fig. 8 top, indicate a qualitatively similar behavior for all bearing blocks investigated. The first mechanical eigenfrequency is reduced by about \(6.2\%\) to \(57.40 ~\mathrm {Hz}\) using the LLM bearing block compared to the PBF-LB/M and the solid bearing block, which are almost identical at \(60.69 ~\mathrm {Hz}\) and \(61.18 ~\mathrm {Hz}\) respectively. This decrease in eigenfrequency is explained by the reduced axial stiffness of the system with LLM bearing block as described in Sect. 4.1. For the maximum possible start position \(x_\mathrm {T,Start}=389.7 ~\mathrm {mm}\), the eigenfrequencies are slightly lower. The solid bearing block and the PBF-LB/M again indicate almost identical values with 58.85  and \(59.10 ~\mathrm {Hz}\), while the LLM is about \(3.6\%\) lower at \(56.66 ~\mathrm {Hz}\).

The comparison between PBF-LB/M and LLM leads to the conclusion that it is not the topology but the adhesive layers that are mainly responsible for the reduced stiffness and the reduced eigenfrequency. This supports the functionality of the slicing method described in Sect. 2, but also shows that LLM fabrication is so far only viable for applications with sufficient stiffness margins.

The measured compliance frequency responses are shown in Fig. 9 for minimum and maximum table position as well as active and inactive P-PI control as described in Sect. 3.3.

The maximum dynamic compliance is considered, which is indicated by the peaks of the curves. For all studied variants, the highest peak compliance is observed when using the LLM bearing block, which is consistent with the results from Sects. 4.1 and 4.2. For inactive control, this peak compliance is \(7.1-7.7\%\) higher than for the solid bearing block, and for active control it is between 9.9 and 20.6\(\%\) higher depending on the table position \(x_\mathrm {T}\). For the PBF-LB/M bearing block, the difference is about \(6.2-6.3\%\) for inactive control and \(2.6-10.1\%\) for active control.

However, no consistent distance between the peak compliance of the bearing blocks is observed. Especially for the maximum table position, there is an increased measurement scatter and, with active control, significantly larger differences between LLM and PBF-LB/M than for inactive control. Reasons for this could be the friction behavior in the rear area due to surface rust on the screw as well as not ideally aligned guide carriages, since the software limit switch is located shortly behind this position.

Furthermore, the peak frequencies for LLM and PBF-LB/M are about 1.7–4.0\(\%\) lower than those of the solid bearing block. This decrease is on the one hand due to the reduced stiffness in axial direction and on the other hand due to static friction as no offset velocity is used.

The damping rates are determined via an e-Fit according to Sect. 3.4 and are shown with mean value and scatter width in Fig. 10.

The damping with LLM is the highest at both table positions and is \(3.9\%\) (\(x_{\mathrm {T}}=0 ~\mathrm {mm}\)) and \(14.0\%\) (\(x_{\mathrm {T}}=700 ~\mathrm {mm}\)) higher than with the solid bearing block. There is also an increase in damping of 0.6 and \(10.7\%\) using the PBF-LB/M bearing block.

Particularly noticeable are the differences in damping for both table positions with the PBF-LB/M bearing block, which cannot be readily explained physically. Moreover, other components, such as friction or the motor control, essentially contribute to the damping of the overall system. Nevertheless, it can be stated that the damping is increased using the bonded LLM bearing block, despite the higher scatter of the measurements with the LLM bearing block. The increased damping could be used specifically, for example, to passively damp machine elements or axes that are very sensitive to vibration.