Influence of the tilt angle of an spherical diamond head for roughness parameters

The article presents the results of experimental research for grinding of corundum ceramic with the use of an spherical diamond head. Article shows the influence of tilt angle and feed on roughness parameters. Authors also described influence of tilt angle and thickness of the grinding layer on effective cutting speed.

In recent years, there has been a clear increase in the demand for elements made of corundum ceramics with complex geometry.This applies to parts used both in the tool industry and in medical engineeringfor elements of bone, joint or tooth implants [1][2][3].
Currently used machining technologies allow to perform these complex geometrical structures on five-axis milling centers made of metal materials andto a very limited extentfrom ceramic materials (in principle this applies only to the green state, after isostatic pressing) [2].The shaping of elements with complex geometry from sintered corundum and zirconium ceramics takes place only on multi-axis machining centers in the process of diamond grinding, spindle grinding wheels with small diameterson the order of a few millimeters [4,6].The use of such small tools requires high speeds of the tool spindle in order to achieve the right grinding speed.Achieved grinding speeds are usually around 5 m/s.
The kinematics of such a five-axis grinding process with spherical grinding wheels is shown in fig. 1.In this process, the grinding spindle axis orientation should be appropriately changed in order to obtain the grinding speed vc.This applies both to the angle of tilt of the grinding wheel axis β (in the ZY plane) as well as the angle of advance α (in the ZX plane).Depending on the change of the tilt angle of the grinding wheel axis β, the effective diameter of the grinding wheel changes (contact of the grinding wheel working surface with the machined surface) (fig.2).Fig. 1.Orientation of the grinding wheel position angles (apgrinding depth, aegrinding width, αlead angle, βtilt angle, nsgrinding wheel rotation speed) [1] Fig. 2. Influence of the tilt angle β of the grinding wheel axis on the change of the effective diameter of the grinding wheel [5] Values of the minimum and maximum effective cutting speed vc min and vc max at the angle of advance α = 0° and variable angle of tilt β assume values resulting from the following relationships: (1) where: nswheel rotation speed, ds minminimum effective wheel diameter, ds maxmaximum effective wheel diameter.
Due to the change in the effective contact diameter of the grinding wheel, the effective cutting speed vc also changes.
The following parameters were adopted for the analysis of the influence of the angle of tilt of the wiper shaft axis on the effective cutting speed value:  wheel diameter ds = 4.4 mm,  rotation speed of the grinding wheel ns = 25,000 rev/min,  cutting depth ap = 30 μm,  cutting width ae depending on the theoretical roughness, Rt = 0.5 μm, according to the following formula: Fig. 3.The values of the effective cutting speed obtained for the Dremel 7105 grinding wheel with a variable tilt angle β of the tool axis It was noted that for small values of the angle β the difference between the maximum and the minimum effective cutting speed is significant (fig.3).As the value of the β angle increases, the difference decreases.For the angle β = 5° the ratio vcmax/vcmin is equal to 3.79, and for β = 35° it is 1.26.

Research stand and test conditions
The study of the corundum ceramics grinding process was carried out on a five-axis Sauer machining center (fig.4) with the Sinumerik 840D control system.The treatment was carried out using a galvanized, diamond coated grinding wheel 7105 from Dremel.Nominal diameter of the grinding wheel ds = 4.4 mm.The grinding tests were carried out on a pre-baked corundum frame.The purpose of these tests was to determine the influence of the tilt angle β of the grinding wheel axis on the roughness parameters Ra and Rz at different values of feed speed vf.
Three identical pro-walled samples were prepared for the grinding tests, divided into seven equal parts (zones) on the end face (fig.5).The samples were ground at different feed rates and with a constant grinding depth ap.In each zone, different values of the angle of tilt of the axis of the grinding wheel β have been adopted (tab.I).The following parameters were used in the grinding process:  rotation speed of the grinding wheel ns = 25,000 rev/min,  cutting depth ap = 30 μm,  tilt angle of the grinding wheel axis β = 5°, 10°, 15°, 20°, 25°, 30°, 35°depending on the work zone (tab.I),  lead angle α = 0°for each machining zone,  feed vf = 200, 600 and 1000 mm/min,  cutting width aeprogrammed so that the value of the theoretical roughness Rt parameter does not exceed 0.5 μm.

TABLE I. Values of the tilt angles β between the zones machining
The division of samples into machining zones (fig.5) and the machining program containing the mentioned parameters were obtained in the NX 11.0 program.

Surface roughness measurement
The surface roughness measurement after grinding was carried out on the Mahr MarSurf GD profile.The measuring head MFW-250: 1 (#6851855) was used for the measurements.The presented results of roughness parameters Ra and Rz measurements indicate that the value of the tilt angle of the β axis has a significant influence on the obtained surface roughness.The smaller the value of this angle, the greater the surface roughness.With the increase of the β-angle, an improvement in the Ra and Rz parameters was observed.

The values of
Corresponding to the increase in the feed speed vf, the Ra and Rz roughness parameters also increased (fig.6 and fig.7).The slope angle β = 20° was characteristic.For this value there was a significant increase in the Ra and Rz roughness (fig.6 and fig.7).The smallest values of Ra and Rz parameters were obtained with the highest value of β angle and the smallest feed value vf.The setting of the high value of the angle β with the high velocity vf gave similar effects to the previously discussed parameter combination.
It was also observed that with the increase of the β angle, the influence of feed on the roughness of the surface being treated decreases.
Considering all the results obtained, it was found that in order to obtain the best in terms of Ra and Rz parameters, the surface roughness and to ensure adequate machining efficiency, the greatest possible values of the tilt angle β and the accompanying high feed rates should be used.

Conclusions
The tests show that the roughness of the surface to be machined largely depends on the effective cutting speed, which in turn is significantly conditioned by changes in the angle of tilt of the axis of the abrasive β.The value of the feedrate vf is also significant, which causes a clear change in the roughness parameters Ra and Rz, especially in the case of small values of the angle β.With the increase of the angle β, the influence of feed on the roughness of the surface being treated decreases.
The next step in the process of grinding the corundum complex with the mandrel spherical grinding wheel should be the analysis of the influence of angles controlling the position of the tool relative to the surface to be machined on selected parameters of the geometric structure of the surface for different material sintering stages.An important issue is also the verification of phenomena causing a sudden increase in the values of Ra and Rz parameters for the angle β = 20°.
Translation of scientific articles, their computer composition and publishing them on the website www.mechanik.media.plby original articles in Polish is a task financed from the funds of the Ministry of Science and Higher Education designated for dissemination of science.

Fig. 5 .
Fig. 5. Division of the sample into grinding zones Ra and Rz parameters of surface roughness in individual treatment zones, obtained for different angles β and feedrate vf, are shown in tab.II and tab.III as well as in fig.6 and fig.7.

Fig. 7 .
Fig. 7. Surface roughness parameters values obtained at variable values of angle β and different feed values vf

TABLE III . Rz roughness parameter values
Fig. 6.Ra surface roughness parameter values obtained with variable values of angle β and different feed values vf