Honing operations, e.g. microfinishing, are resulting in high quality surfaces with a roughness values, e.g., average roughness Ra, of only a few micro- to nanometer [1]. The simulation of honing processes can be beneficial to reduce experimental effort in terms of determining suitable process parameters for such processes. Various aspects of the finishing process can be investigated with the aid of process models, such as tool wear, tool life, the resulting surface quality or shape deviation. In addition, process simulations can be used to assist in the design of components with regard to desired functional properties. In order to model processes with such high accuracy, it is necessary to be aware of process influences on a microscropic scale. Such influences can be analyzed separately, for instance, by means of analogy experiments to reduce the complexity and dependencies of the occurring effects. In this work, a process force model was developed based on single-grain scratch tests, which takes into account the process-inherent kinematic variations. The occurring single grain forces in dependence of the orientation of the grains and in relation to the cutting direction were analyzed and modeled. This is important for a further analysis of the influences on tool wear to increase the accuracy of corresponding models.
Hinweise
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1 Introduction
In the manufacturing process of highly loaded components, e.g. crankshaft bearings, honing operations are often conducted as a final manufacturing step in order to adjust the functional properties of contact surfaces, eliminate shape deviations and increase the surface quality [2‐6] by reducing, e.g., the 2D roughness parameter Ra and 3D roughness parameter Sq [1]. After rough honing processes, a profile height up to 16 \(\upmu\)m can still be expected on the workpiece surface [7, 8]. A subsequent plateau-honing process can further improve the surface quality so that the profile height of the workpiece surface is less than 3 \(\upmu\)m [8]. Honing operations can be applied as long-stroke honing [9‐11], gear honing [12], broach honing [13] or short-stroke honing [3, 14], also called superfinishing or microfinishing. In microfinishing operations, the tool can be a flexible finishing belt [4, 15, 16] or tools with a rigid body, called honing stone. During microfinishing, the microfinishing tool is oscillated while the workpiece rotates [3, 14]. Thus, a tangential movement is superimposed with oscillation, which results in a continous changing cutting direction within the limits of the honing angle [17, 18] and recurring engagement conditions which leads to a multitude of achievable surface qualities.
The resulting surfaces are also influenced by the run-in behavior of the tool, grain wear and bond contact. Additionally, complex interrelations between process parameter values, tool specifications and the process result require a deep understanding of the process in order to determine suitable process parameter values. Hence, for the determination of process parameters of microfinishing processes a large number of experiments needs to be conducted. In order to reduce this experimental effort, the use of process simulations can be beneficial. In the past, simulation systems for different types of honing processes were successfully applied in order to gain further process understanding or adapting process strategies resulting in, e.g., a shortened run-in phase of the tool [4, 9‐13, 15, 16]. Such simulation systems are often characterized by the use of physical and empirical models, which can describe the systematic relationships of the process in a target-oriented manner. This allows various characteristics of processes to be predicted, e.g., process forces, process dynamics or the resulting surface quality of workpieces. In [15], the process force was calculated on the basis of the undeformed chip thickness. It should be noted that the undeformed chip thickness is determined segment by segment as a result of the kinematic depth of cut, which is the geometric intersection of the two involved components (grain and workpiece). In the honing simulation system, the tool and the workpiece surface were modelled as heightfields. The material removal was determined by defining the height of tool and workpiece and derive the intersection between the two heightfields as removed material. For each row of height values the uncut chip thickness was determined. Subsequently, local force values were derived from the chip thicknesses and summed up to a resulting normal force. Furthermore it was shown by Tsagkir Dereli et al. that the process force of a grinding process can also be influenced by the rake angle [19]. Thus, in the developed force model, effective normal vectors for each grain were calculated and the effective rake angle was determined in order to be taken into account for force calculation in the simulation system [19]. In contrary to grinding processes, the process kinematics of microfinishing operations leads to periodically changing cutting directions which also results in constantly varying effective rake angles. In the literature, suitable honing angles are specified in dependence of the workpiece and its application in a range between 40\(^{\circ }\) and 140\(^{\circ }\) [5, 6, 20‐22]. However, for microfinishing operations the honing angle can be even lower [3]. The constant change of the cutting direction leads to complex engagement situations in terms of single grain engagements. Hence, the prediction of individual process forces of single grains in the microfinishing process is a challenging task. Furthermore, such processes are force-controlled, which leads to a dependency of the engagement depth on the contact pressure of each grain and the resulting surface properties. In addition, different engagement depths result in effects, such as burr formation [23] or wear of the grains involved within the microfinishing tool. This leads to a time-variant material removal behavior. The knowledge about the process forces for single grains is important, since the force-dependent depth of cut and the orientation of the individual grain in correlation with the actual cutting direction is relevant for the determination of the resulting surface topography and tool wear. In this contribution, the influence of the changing cutting direction on the occurring process force is analyzed and used to parameterize a specified force model.
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2 Experimental setup
In order to investigate the influence of the prevalent grain orientation on the occurring process forces, single grain scratch tests were conducted on the 5-axis machining center HSC 75 linear by DMG Mori. This machining center is equipped with a linear drive, which allows speeds of up to 1.5 m/s. Thus, process-related cutting speeds, that are often within the range of 1 – 3 m/s, could be reproduced [3]. For the scratch tests, a feed rate of \(v_{f}\) = 1 m/s is performed based on the cutting speed of \(v_{c}\) = 60 m/min, which is common in microfinishing. In the experiments, metallic bonded diamond tools with a grain size of D126 from Elgan-Diamantwerkzeuge GmbH & Co. KG were applied. To identify the systematic behavior of grains within the microfinishing process, single grains of a microfinishing tool were extracted. For this purpose, segments of the stones were separated, so that exactly one single grain remains within the metallic bond with sufficient grain protrusions of at least 30 \(\upmu\)m. A total of eight analogy tools, each containing one grain with different topographic characteristics, were manufactured, so that a variation of the grain shapes of a microfinishing tool can be represented. For each considered engagement depth and for each tool one repition was conducted.
The workpiece consisted of 16MnCr5 (1.7131) which was case hardened to approx. 58 HRC. In order to measure process forces during the cutting process, the triaxial piezoelectric force transducer 9327C from Kistler was used (see Fig. 1a)). For the analysis of the scratch marks of the analogy test with a depth of only a few micrometers, a high quality surface was essential. Initially, a face milling process was conducted to achieve plane-parallelism. The surface was then subjected to post-treatment with a polishing pencil, resulting in surfaces with roughness values \(Rz < 0.5\,\mu m\). However, the milling pre-processing of the workpiece resulted in a surface with a waviness of up to \(W_{t}\) = 10 \(\upmu\)m (ln = 20 mm) (Fig. 3). In order to achieve comparability of the single grain forces in the single grain scratch test with the industrial application, the engagement depths of the grains must be comparable. For the representation of a wide scope of applications and to avoid a large number of investigations, the waviness of the surface resulting from the milling process was used to obtain a variability of engagement depths with a defined infeed. For this purpose, infeeds of 1 \(\upmu\)m - 4 \(\upmu\)m per grain were applied, resulting in local engagement depths of up to 10 \(\upmu\)m. To reduce the occurrence of instantaneous stress during engagement, a chamfer with a 5\(^{\circ }\) inclination was applied at the edge of the workpiece.
Fig. 1
Overview of experimental setup. a Workpiece in experimental setup with single grain scratch tests. b Tool holder with imprint holder
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2.1 Digitization of experimental results
In order to be able to parameterize a force model according to the grain orientation in alternating cutting directions, both, tool and workpiece, must be digitized. To determine the qualitative differences of the grains utilized, they were digitized before and after each single grain scratch test. Thus, the condition of each grain was captured before and after each cut in order to differentiate whether major changes of the topography of the grain took place along the scratch path. A substantial change of the topography lead to uncertain force measurement results. In this case, the force measurement was not taken into account for the parameterization of the force model. For the digitization, the 3D surface measuring system Alicona Infinite Focus G5 was utilized, which uses focus variation for imaging surfaces. The resolution when capturing the data for the grains was 1 nm on the Z-axis (height) and 0.176 \(\upmu\)m on the X- and Y-axes (width). Subsequent to the initial digitization of the single-grain tools, the tool segments were inserted into a holding module in which they were fixed inside a slot with a grub screw for the single grain scratch tests (Fig. 1b)).
An important influence on the force calculation not yet considered in the force model was the grain orientation in relation to the cutting direction, as it directly influenced the undeformed chip thickness. In order to obtain the orientation of the grain along the scratch marks during the experiment, imprints of the grains were made before and after the experiment. Therefore, a two-part silicon rubber compound was used, which could be digitized afterwards, without the need to remove the tool (Fig. 1b)). The described approach effectively resulted in four suitable scratch tests conducted. Due to the rapidly occurring topographical changes in the grains used as a result of the static, inelastic engagement situations, the repeated experiments could not be considered for modeling the process force. For the reduction of occurring artefacts, e.g. caused by reflections on steep flanks of the grain, averaging filters were applied and the resolution of the grain was resampled to a point spacing of 3 \(\upmu\)m (see Fig. 2). In order to evaluate the resulting scratch depth in correlation with the measured process forces, the workpiece also needed to be digitized. The digitization of the workpiece was conducted using the 3D surface measuring system Confovis Duo Vario. The resolution was 0.1 nm on the Z-axis (height) and 0.237 \(\upmu\)m on the X- and Y-axes (width). The relative engagement depths of the grains must be analyzed on the basis of the surface measurements. Due to the waviness of the surface, the engagement depth was determined locally for each point in relation to the surrounding surface (see Fig. 3b)).
Fig. 2
Display of the digitization of the four considered grains
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3 Simulation of single grain scratch tests
Especially in the context of the small dimensions of microfinishing processes, influences on the process can have a huge impact on the resulting workpiece. In order to develope suitable process models, a sufficient model resolution and a holistic consideration of the measurement data was necessary. In this section, both, the model preparation and the inference of the developed simulation model, are described.
3.1 Evaluation of the experiments for simulations modelling
Due to the waviness of the surface and, thus, the local engagement depth, several force values for several engagement depths could be taken into account for the paramtererization and calibration of the force parameters. The local engagement depth was correlated with the measured forces at multiple positions on the scratch mark in order to depict suitable values for the force model parameters. The approach used to determine the parameter values from the scratch marks is visualized in Fig. 3.
Fig. 3
a Digitized surface of a scratch mark with b extracted profiles of the waviness of the surface (orange) and the derived engagement depth (blue). Note that engagement length is about 40 mm while engagement width for a single grain is below 50 \(\upmu\)m (color figure online)
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In the past, the linear force model, shown in Eq. 1, was parameterized for a grinding simulation based on the uncut chip thickness of single grains included in the grinding tool topography [24].
This model is applicable for the calculation of the process forces of microfinishing processes. However, due to the kinematics of microfinishing processes, the grinding model needed to be extended taking into account the constant change of the cutting direction of each individual grain. While in grinding the cutting direction of the single grains is constant, the constantly changing cutting direction in microfinishing results in varying uncut chip thicknesses for the same grain due to a varing active part of the grain topography in relation to the current cutting direction. Thus, the grain orientation needed to be taken into account for the calculation of the process forces. Hence, a parameter study to analyze the influence of the grain orientation on the derived process force has been conducted to achieve a high accuracy of the correspondence of the grain specific process forces. By synchronizing the active forces \(F_{a}\) and passive forces \(F_{p}\) over time, taking the corresponding engagement depths into account, a data basis was created to allow the determination of coefficients of a force model (see Fig. 4). The force data showed variations in amplitudes at different infeeds (see Fig. 4, orange dashed lines). This is particularly evident when comparing the force amplitudes of grain I and II, since with grain I a strongly increased infeed of up to 8 \(\upmu\)m leads to a passive force of only 18 N, while with grain II an infeed of 4 \(\upmu\)m already results in an actice force of higher than 40 N. These correlations show a decisive influence of the particular grain topography on the occurring process forces.
Fig. 4
Measured process forces and engagement depth of single scratch tests synchronized for the determination of a process force model
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3.2 Tool model
In order to determine a suitable force model for the calculation of the process forces based on the experimental data, sufficient understanding of the prevalent grain shape was necessary. For this purpose, the specific orientation during the scratch test was identified for each grain and the grain model was rotationally aligned with it. The rotated digitized grain topography was then triangulated, so that the relevant surfaces in the cutting direction could be determined. This enabled an accurate identification of the contour of each grain (5c)), which defined the engagement profile for the local engagement depth. In addition, an analysis of the grain topography was conducted. Especially for the nonlinear progression of the process forces regarding the engagement depth, a consideration of the grain shape was necessary. The different engagement depths also lead to a change in the grain segments involved.
For this reason, each grain was divided into a number of vertical segments (see Fig. 5a), purple segments). Subsequently, each segment was examined for all occurring depths of cut (with \(a_e\in \mathclose [ 1;12 \mathopen ]\)) to determine an overall direction vector. This was done by sampling the grain using a regular grid to aggregate the portion of the relevant surface normals (Fig. 5b), black arrows) into an accumulated surface normal for each respective segment (Fig. 5b), green arrow). These accumulated surface normals were then projected onto the tangential planes to quantify the deviation in the lateral direction. For all considered engagement depths of a grain (Fig. 5c)), these local lateral normals were determined. As can be seen in Fig. 5d), the lateral normals varied with respect to the feed direction. Grain I showed a high roundness of -90\(^{\circ }\) to 90\(^{\circ }\) at a local engagement depth of 12 \(\upmu\)m (black dotted line), while a very low local engagement depth of 1 \(\upmu\)m exhibits a very inhomogeneous normal progression (gray dotted line).
Fig. 5
a Triangles of grain I visible in feed direction including the direction vectors present. b Sampling of triangles for the determination of direction vectors. c Representation of the occurring grain profile. d Direction vectors along the profile for different engagement depths in radial and axial direction
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With reference to the micromaterial removal mechanisms [25, 26], a round grain offers less resistance to micromachining than a segmented or inhomogeneous grain shape, which may even have negative chip angles. Hence, the roundness of the grain was an important indicator for the interpretation of the occurring cutting forces in relation to the contour information. Based on the results from [25, 26], the conception of the model is based on the assumption of a grain as an ideal hemisphere. Thus, the lateral normal progression was then quantified by determining the deviation from a fictitious optimal roundness \(\mathbb {O}^{+}\), which progresses linear from -90\(^{\circ }\) to 90\(^{\circ }\) over the width of the grain (Fig. 5d, orange line). To normalize this metric, the function values were related to the most divergent profile shape, namely a concave shape of the grain \(\mathbb {O}^{-}\) with invers lateral directions from 90\(^{\circ }\) to -90\(^{\circ }\). This was used to determine the characteristic value of roundness \(\breve{r}\) as
with each i corresponding to a measurement position along the width of the digitized grain. Thus, the roundness of the grains as well as inhomogeneities along the grain structure, e.g. due to chipping, were assessed. At higher infeeds, plateau-like or segmented areas of a grain topography could be involved in the cutting process, as well.
3.3 Derivation of a grain-specific process force model
The linear process force model described in [24] was extended by the use of the presented roundness metric. Depending on the engagement depth, an integral was formed for a grain over the cross-sectional area, i.e., for each occurring chip thickness t in a segment with width dx the occurring force \(F_{i}\) with \(i \in \{c, n\}\) (e.g.in cuting and normal direction) was summed up with
This equation is parametrized by the linear coefficients \(k_i\) and \(o_i\) with \(i~\in ~\{c, n\}\), which quantify the process force model regarding engagement depth (\(k_i\)) and roundness of the grain (\(o_i\)). To identify these coefficients, a regressive optimization was performed using the method L-BFGS-B [27] for all four suitable scratch tests and the associated grains. Here, an optimum was identified with \(k_c~=~828~968.16\), \(k_n~=~354~012.93\), \(o_c~=~2.60\) and \(o_n~=~7.16\). In Fig. 6 the results of the linear process force model and the extended process force model compared to the experimental data are shown. The comparison of the results of the extended process force model with the experiments showed a good correlation, depending on the roundness of the grains. Especially in comparison with a linear force model, the variations at, e.g., grain I and grain II were better approximated. In the case of the linear force model, these effects cannot be included, whereby overestimations of the process forces of a factor of four can occur. However, it is noticeable that an exact correspondence of the forces is not possible even with this model. A reason for this could be the complexity of the material removal mechanisms, e.g. the influence of micro-chipping or micro-ploughing, which have not yet been fully researched. Furthermore, it can be assumed that the effect of elasticity leads to an axial tool displacement and, thus, lead to a remaining deviation between the experimental and the simulation results.
Fig. 6
Representation of all considered experiments with the four grain shapes and the determined process forces with a linear process force model described in [24] (blue line), the experimental data (black line) and the extended process force model (red line, Eq. 3) on the basis of the regressive optimization (color figure online)
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3.4 Investigation of the direction-dependent process forces
Since the engagement conditions are periodically variable due to the superposition of a linear motion with an oscillation in a microfinishing process, the variability of the process forces during cutting was investigated for the analyzed grains. For an exemplary microfinishing process with a resulting honing angle of 64\(^{\circ }\), the grains were each rotated within a range of – 32\(^{\circ }\) to 32\(^{\circ }\) and the parameters \(\hat{r}\) for the roundness were identified accordingly for all occurring engagement depths occurring (see Fig. 7). As can be seen, the roundness can vary depending on the angle of rotation, so that widely different process forces can occur.
Fig. 7
Illustration of the variation of lateral directions and grain profiles for an unrotated and a 32\(^{\circ }\) rotated grain, indicating varying degrees of roundness
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For the given engagement depth, the process forces were calculated with the proposed force model. These process forces are shown for two different grains in Fig. 8. It is evident that there are grain shapes that lead to a strongly non-linear increase of the forces depending on the angle of the grain rotation. On the other hand, almost congruent forces can be observed at lower engagement depth independent of the angle, but significant variations can be observed at higher infeeds. This implies that for a more detailed consideration of the force-controlled microfinishing process on a microscopic scale, a detailed analysis of the occurring grain shapes related to the used grain size is required.
Fig. 8
Depiction of the calculated process forces under constant engagement conditions in relation to rotations of 32\(^{\circ }\) and – 32\(^{\circ }\). The influence of the resulting roundness on the process forces is visible
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4 Conclusion
Since microfinishing typically is a force-controlled process, accurate knowledge about the occurring load on the tool can increase the quality of the simulation result. In this paper, a process force model was developed, which takes the grain orientation into account in relation to the cutting direction. In order to determine the relation between occurring process forces, engagement depth and grain orientation, single grain scratch tests were conducted. The normal vectors of single segments of the grains were examined for all occurring engagement depths and, afterwards, used to determine an overall direction vector. Furthermore, the roundness of the grain was considered as an important indicator for the interpretation of the occurring process forces. Thus, a fictional optimal roundness was determined and the deviation of the grain was used to quantify a lateral normal progression. A nonlinear behaviour of the process forces in dependence of the local engagement depth and the grain topography could be observed. This becomes clear when comparing the active force \(F_{a}\) of the explicitly shown grains in relation to the respective local depth of engagement. A cut with grain I with a high engagement depth lead to low process forces. The scratch with grain II resulted in a high active force even though the engagement depth of grain II was considerably lower than the engagement depth of grain I. Consequently, it can be assumed that the grain topography, the cutting direction and the local engagement depth has a significant influence on the resulting process force.
A linear force model was extended by the use of a roundness metric. In order to identify the linear coefficients of the model, a regressive optimization was performed. The extended force model resulted in a better approximation of the simulated forces in terms of deviation from the measured force data. In a final step, process forces were calculated for a given engagement depth for different rotational angles. It could be shown that the extended force model was able to represent the nonlinear behaviour of the process forces. In further applications, the described approach can be used for different grain sizes in order to evaluate how significant the nonlinearity of the single grain force occurs for smaller grain sizes, like D54, and how relevant the presented relationships are for such tools. Furthermore, the presented model can also be used to parameterize tool models which explicitly represent the bonding behavior, since the grain and bond wear is related to the tool load.
Acknowledgements
We would like to thank Bruker Alicona, ELGAN Diamantwerkzeuge GmbH & Co. KG and NAGEL Maschinen- u. Werkzeugfabrik GmbH for their support.
Declarations
Conflict of interest
The authors have no relevant financial or non-financial interests to disclose.
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