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Figure 5. Roughness measurement given in a mean isotropic PSD: Spatial frequency ranges and calculated values of Sq W( green area) and Sq R( yellow area) having a slight overlap.( adapted from [ 29 ]).
8.4 10 �1 lm �1. Figure 5 gives an example of a mean isotropic power spectral density function( PSD) of a lapped and PJP surface( adapted from [ 29 ]). The spatial frequency ranges that can be measured using the two objectives have a slight overlap. Waviness and roughness Sq values( designated as Sq W and Sq R, respectively) were calculated from the areal measurements after removal of a 2nd polynomial surface, to subtract the curvature due to the sample surface geometry.
4 Results
The following section presents the primary findings of the investigations into freeform machining of FS. It is divided into three parts: the experimental grinding tests, the transfer point to PJP and the optimization of PJP.
4.1 Grinding investigations on fused silica
The grinding of freeform geometries is characterized by a number of special kinematic features. For example, the use of spherical grinding tools results in near point-shaped tool engagement or a very small contact surface with the component. A defined tool inclination is required for machining outside the center of the spherical tool( where cutting speed = 0 m / s), while a constant angular contact with the surface normal is maintained by simultaneous axis movements. Along the surface, there is usually a descending or meandering path movement in the x / y-direction. This can result in unwanted periodic or mid-spatial frequency form errors. Theoretically, the surface structure is formed by superimposing the individual tracks with the ball shaped grinding tool, as illustrated in Figure 6( A), whichleadstoa wavy surface depending on the path distance PD and infeed depth a p. This should be prevented as far as possible by optimizing the kinematic parameter settings, or minimizing the amplitude and wavelength of the structure, respectively, in order to provide sufficient conditions for the subsequent PJP process.
To investigate kinematic interactions and reduce such errors, as well as generate a homogenous surface quality with low roughness, several experiments were carried out on FS samples( HPFS 7980, Corning, Inc.). In addition, the shape deviations between the actual and target geometry should be as small as possible. For this purpose, a logical and yet novel investigation approach was pursued for grinding applications, which successively progresses from the tool impression in a single grinding path, comparable to the generation of a tool removal function during polishing, to the surface generation of several grinding paths and then to complex real free-form machining.
In the preliminary tests using flat components, it was first analyzed to what extent the shape of the grinding paths with spherical tools corresponds to the theory, i. e. whether the topography formed actually reflects an ideal spherical impression. For this, several single grinding paths were generated and measured regarding depth, shape and width, while varying parameters like ball tool diameter( between 5 and 30 mm in diameter), cutting depth and inclination angle. This was done for fine grinding with metal bond and for ultra-fine grinding with resin bond tools.
The generation of grinding tracks with a circular crosssection has been generally confirmed. However, the paths ground using resin-bonded tools were up to 50 % wider than the geometrically expected value, compared to a maximum of 20 % higher width for the metal-bonded tools. This indicates an expectedly greater tool deformation in the area of contact with the surface in the resin-bonded tool, which can be explained by the higher elasticity and lower strength of the bond. It means that the tools get slightly pressed wider by the contact forces acting during grinding, which can actually be beneficial since a wider tool shape reduces the height of the grinding structures for a constant PD. This effect is illustrated in Figure 6( B).
No significant influence regarding inclination angle, tool diameter or cutting depth on the relative width deviation to the geometrical value of the grooves was observed. However, regarding the generation of a constant grinding depth and efficient production best results were achieved with an inclination angle of a = 30 ° and cutting depth of a p = 60lm for metal bond fine grinding and a p = 10lm for resin bond ultra-fine grinding.