Process design of a novel combination of peel grinding and deep rolling

The process forces in grinding are essential to the design of the deep rolling tool. With known force values, it is possible to position the deep rolling contact point in relation to the shaft in order to minimise the resulting forces on the shaft. Subsequently, the bearing forces of the shaft are reduced, which is essential as the shafts are clamped between centres. Moreover, the resulting deflection is reduced.

The results on the grinding forces show an incline with increasing feed rate as expected from the literature (Fig. 3) [15]. This behaviour was consistent for all grinding wheels and can be explained by the higher material removal rate with higher feed rate. The increase in grain size leads to relatively higher normal forces but smaller tangential forces when machining with low feed rate. As this equals a higher grinding force ratio, the high grain size B601 shows relatively more friction, which is explained by a reduced cutting angle for constant grain sizes in combination with low chip thicknesses. However, if the feed rate increases, the higher grain size caused a lower increase in normal forces and thus a lower grinding force ratio, as Fig. 3 illustrates on an example. The vitrified bonded CBN grinding wheels show lower grinding force ratios compared to galvanic plated CBN. However, the change in bond causes a change in grain distribution which limits the direct comparison of these tools. I.e. the galvanic plated CBN tools features a single grinding layer with higher grain protrusion. The process forces of the SC grinding wheels are remarkably low in relation to the CBN grinding tools. However, this is due to the workpiece material and its hardening state. The soft 16MnCr5 causes lower forces compared to the hardened 100Cr6. With regard to the novel process combination, the results on the grinding forces show that the grinding forces are mainly dependent on the feed rate. In order to achieve a force equilibrium between grinding and deep rolling forces, the deep rolling forces need to be adapted to the expected grinding forces.

The normal process force in deep rolling is calculated analytically, as the process force depends on the hydraulic conditions. Thus, the deep rolling force results of the pressure p_w and the intersection area of the roller ball with the diameter d_k. Additionally, a factor η describes the efficiency coefficient of the compressor system. The efficiency coefficient was determined by Denkena et al. to η = 0.79 for the tools of this study [13]. An increase in both, the ball diameter and rolling pressure leads to an increase of the deep rolling normal force as shown in Eq. (1).

With known grinding force values F_n and the calculated deep rolling normal forces F_n,w it is possible to calculated an inclination angle θ, for which a force equilibrium results Eq. (2). Tangential forces are neglected in this approach, as they are comparably little and as they equal a momentum that is absorbed by the workpiece spindle.

Equation (3) expresses F_n,w in direction and orthogonal to F_n. In addition, the algebraic signs are adapted to the direction as shown in Fig. 4 below.

As both deep rolling forces are equal (F_n,w1 = F_n,w2 = F_n,w), Eq. (3) can be reduced and rearranged to Eq. (4). With a further repositioning the inclination angle is calculated Eq. (5).

Figure 4 shows the resulting inclination angle for a variation in grinding force F_n and in deep rolling pressure p_w. The expressed charts are used to set an inclination angle for a chosen grinding wheel and process feed rate within the following simultaneous machining process. The relatively small values of θ are due to the small values of F_n, which are caused by the small infeed of a_e = 0.1 mm for peel grinding processes. The designed tool is capable of a maximal inclination angle of θ_max = 35.7° for ideal positioning with d_k = 13 mm and θ_max = 31.6° for d_k = 6 mm. As the actual inclination angle is beneath 8° (Fig. 4) the tool design is capable to use both deep rolling ball diameters as well as all grinding wheel specifications and feed rates. In a further study at the IFW under similar conditions but an infeed of a_e = 0.5 mm, grinding normal forces were determined up to > 600 N [3]. With the deep rolling pressure range of this study, inclination angles of θ = 3.7°–6.6° (for d_k = 13 mm) and θ = 17.4°–32.5° (for d_k = 6 mm) result, which is still capable for the deep rolling tool. An increase in infeed equals a further potential to increase the overall process productivity. Furthermore, it is possible by these results to adjust the inclination angle in order to minimise the resulting processing force on the shaft.

The results on the surface roughness after the grinding process show an increase with increasing feed rate that can be explained by a reduced overlap of finishing zone paths of the grinding wheel. This is shown as a representative result in Fig. 5. According to the state of the art, it is expected that a decreasing grain size leads to a decreased surface roughness [15]. This effect was observed within one category of grinding wheel type only to a minor extend, with the exception of the relatively low roughness of grain size B426. The low level of roughness as well as the variation is explained by the dressing procedure, by which single protruding grains are levelled. In pre-test before dressing, surface roughness of Rz > 40 µm were examined. In case of the conventional grinding wheels, an untypical increase is observed. The higher roughness in case of SC100 was caused by clogging on the grinding wheel topography. Therefore, the roughness is mainly depended on the used axial feed rate. This incline in roughness reveals the potential for the process combination, by which the surface roughness is maintained at higher feed rates.

The results on the surface roughness after the deep rolling process show a decreasing roughness with increasing ball diameter and increasing rolling pressure up to 71%. Figure 6 illustrates these results on the example of the highest roughness after grinding, which resulted from the grinding wheel B601. The resulting roughness can be explained by the Hertzian contact conditions. According to Hertz, the contact width a_pw can be calculated by Eq. (6) [16].

Herein, ν is the combined Poisson’s ratio and E the combined Young’s modulus. They can be calculated by means of Eqs. (7) and (8) with the individual Young’s moduli E_1/2 and Poisson ratios ν_1/2 [17].

Therefore, an increase in deep rolling force as well as in ball diameter lead to an increase in contact width a_pw. A higher contact width however leads to a higher overlap of deep rolling paths, when maintaining the axial feed rate. With the process parameters of this study, the contact width is calculated for d_k = 6 mm in a range of a_pw = 0.215 mm (p_w = 25 MPa) to a_pw = 0.261 mm (p_w = 45 MPa). The range in contact width for d_k = 13 mm is a_pw = 0.473 mm (p_w = 25 MPa) to a_pw = 0.575 mm (p_w = 45 MPa). For this calculation the Young’s modulus was set to E = 210 GPa for 100Cr6 and to E = 600 GPa for cemented tungsten carbide. The Poisson ratio was ν = 0.3 (100Cr6) and ν = 0.21 (cemented tungsten carbide).

The experimental results show that in case of an axial feed rate of f_a = 0.3 mm the increase in a_pw of + 120% by means of an increase in d_k does not correspond to an equally high effect on the surface roughness reduction. This can be explained by the overlap of deep rolling paths, which is negative for all d_k = 6 mm cases, however just slightly in case of f_a = 0.3 mm. The axial distance between two paths is with a_pw = 0.261 mm only 39 µm. The overlap is only in case of d_k = 13 mm and a feed rate of f_a = 0.3 mm positive. Accordingly, this negative overlap explains the decreasing effect of the deep rolling process on the roughness reduction with increasing axial feed rate. The decline in influence of the deep rolling process with increasing feed rate limits the achievable raise in productivity.

The surface roughness after deep rolling shows a strong dependence on the surface after grinding. In case of all CBN grinding wheels, a reduction in roughness of more than 70% was achieved for f_a = 0.3 mm (Fig. 7). The lower effect in case of the conventional grinding wheels is caused by the change in material. Due to the lower hardness, the shape of the roller ball was projected on the surface. This prompted in combination with a highly negative overlap an intense rise in roughness up to Rz = 65.8 µm (f_a = 1.7 mm; d_k = 13 mm; p_w = 40 MPa).

In order to generate a comprehensive understanding about the influence of the deep rolling process on the resulting surface of ground shafts, the resulting topography was investigated in more detail. Therefore, material contact area curves, SEM measurements and intersections of the shafts were evaluated for the grinding tool B601, as this tool shows the highest surface roughness. As Fig. 8 shows, deep rolling caused a compression of the entire profile but mainly on the heights, as illustrated on the maximum peak height. The related average reduced peak height Rpk was reduced from 0.9 to 0.3 µm.

The SEM measurements of the surface after the grinding process reveal burrs that can be explained by the material removal mechanism of ploughing (Fig. 9). These burrs were than clinched onto the surface by the following deep rolling process. In addition to the SEM measurements, microscopic pictures reveal that burrs and chips with remaining cohesion appear on all ground shafts. Therefore, this effect is not limited to a specific type of grinding wheel within this study. However, without specified application demands of the shaft, the generated surface does not represent a process limit to the process combination.

The residual stresses were measured on the shafts that have been ground with the coarsest grinding wheel B601. The measurement results on the surface after grinding show that the residual stress values are mostly compressive (Fig. 10). Only in case of f_a = 1.7 mm a tensile stress value is observed, which represents a thermal induced damage. As expected from the state of the art, the deep rolling process leads to a shift of the residual stress towards higher compressive stress values. The coherence that negative overlaps prompt a decrease of the effect of the deep rolling process did not occur in this case. This can be explained by measurement spot size within the X-Ray diffractometry. With 2–4 mm this is significantly higher than the applied feed rate f_a. Subsequently, macroscopic changes in residual stresses are measured. The further analysis show a higher effect with increasing deep rolling pressure. The increased deep rolling force and the subsequent increased Hertzian pressure in the shaft surface under processing cause this effect. Additionally, the stress value in axial direction σ_a is higher compared to the circumferential direction σ_ci at both stages after grinding and after deep rolling. This can be explained by the processing direction. In both cases the tools engage in the circumferential direction with a subsequent friction that leads to tensile stress shares [18]. On the other side, both processes show a high lateral contact pressure with subsequent lateral material flow, i.e. ploughing. From these results it can be seen that an increase in feed rate, i.e. productivity, causes a shift of the residual stresses towards tensile stresses, which are considered as a process limit. The deep rolling process can compensate this raise in residual stress value, so that the feed rate can be raised, while maintaining the residual stress level. This, however, is limited by the negative overlap, by which parts of the shaft are not processed by deep rolling. This causes inconsistencies within the surface of the shaft. Due to the small infeed value of a_e = 100 µm, primarily compressive residual stresses resulted after grinding, which is why the surface roughness is considered as the predominant process limit within this study.

Within the second experimental part of this study, the designed tool combination is implemented into the grinding machine. In order to determine the transferability of the established knowledge on surface generation to the process combination, the shaft topography is investigated after machining by means of the process combination. As shown in Fig. 11 the topography shows a macroscopic groove with a pitch equal to the feed. However, from a frequency analysis it can be seen that two engagement paths can be detected, as the spectrograph shows a secondary peak at a wavelength of 0.5·f_a. When filtering the surface profile with a high pass filter with a cut-off of λ_g < 0.5 ·f_a, the engagement paths can be examined regarding depth and lateral distance. From the results, the profile can be described by a major groove with increased depth and a secondary groove with reduced depth. As the deep rolling tools engage under constant force load, the variation in groove depth is due to a change in deformation behaviour. From the geometrical process procedure, one of both deep rolling balls is leading. The second deep rolling ball is following partially within the groove of the first ball. For the explanation of this change in indention height two contrary explanatory approaches are likely. The first approach is that the leading ball causes a lower deformation capability of the workpiece, as it can be seen from the results on the residual stresses (Fig. 10). Thus, the secondary engagement depth is lower. On contrary, the second explanatory approach is that the secondary engagement prompts a deeper groove, as the respective material is processed twice, i.e. with a positive overlap. Hence, the determination of the according mechanisms should be investigated in further studies.

Next to the height of the grooves, the lateral, axial distance between the grooves can be considered. This distance differs in the results from the half of the axial feed. The investigation of the cause is also objective to ongoing work. However, two main influencing factors affect the position of the groove. Firstly, the deep rolling balls feature a floating bearing. Thus, the following ball is forced to run within the leading groove. Secondly, the tolerance of the axial installation position causes a change in ideal engagement position.

These results demonstrate the transferability of the established technological basis for the process combination of peel grinding and deep rolling. The topography analysis also shows that the doubling of the deep rolling ball does not lead to two similar deep rolling paths. The existence of two similar grooves, however, is crucial for an additional increase in productivity by means of doubling the number of deep rolling balls.