Influence of Kinematics on the Face Grinding Process on Lapping Machines

influence of Kinematics on t h e Face Grinding Process on Lapping Machines E. Uhlmann, T. Ardelt Institute for Machine Tools and Factory Management, Berlin, Germany Submitted by G. Spur (11, Technische Universitat Berlin. Berlin, Germany Received on January 10, 1999

Abstract The substitution of many lapping processes by face grinding on lapping machines offers a new field of application for the kinematic model of relative motions in lapping. The selection of path types and velocities between parts and grinding wheels does not, as in lapping, primarily serve to avoid the profile wear of the wheels. Rather, the process development and thus, the part quality are directly influenced. Ceramic parts are used as an example to illustrate the improvement in performance made possible by the analysis of machining kinematics.

Keywords: Grinding, Lapping Machine, Ceramics

INTRODUCTION Lapping is increasingly substituted by face grinding on lapping machines in the production of plane-parallel mass components. This transposition permits higher material removal rates at highly reduced grain use. The preparation of the cooling lubricant, moreover, is comparatively easy. The reduced pollution decreases the cleaning effort for workpieces and machines and allows for an automate loading and unloading of the machine. Typical components for grinding on lapping machines are ceramic sealing discs, indexable inserts made of hard metals, motor parts, and hydraulic or pneumatic control parts [l-31. During face grinding on lapping machines, several workpieces are moved simultaneously between two horizontally positioned grinding wheels (Figure 1). The parts are fixed in holders that are led between two pin circles. This way, the characteristic cycloidal, path curves are generated between parts and grinding wheels. 1

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of size is much more difficult. On the one hand, the stiffnesses of the wheel dressers are often not sufficient. On the other hand, the material costs of the used diamond coatings are so high that multiple removal of greater profile deviations may endanger the economic viability of the process. Profiling causes special problems because of the interrupted cut at pellet grinding wheel surfaces. While searching for suitable parameters to minimize the wear profiles during grinding on lapping machines it was found that a variation of the types of movement directly influences the process development and particularly the quality of the produced parts. The influence of the kinematics on the part quality plays only a subordinate role during lapping. Due to the process development from lapping to grinding on lapping machines, the immense significance of the path types for the face grinding process has not been recognized earlier. This article discusses the effects of the path type on the process course and the parts quality. As a basis, kinematic possibilities of lapping and grinding machines are analyzed. The following experimental investigations demonstrate the influence of the path type on the driving moment and the removed workpiece height, as well as on the roughness and the flatness of the parts, KINEMATICAL FUNDAMENTALS The Institute for Machine Tools and Factory Management of the Technical University Berlin worked during the mideighties on an analytical description of the relative motions in cycloidal restricted guidance on lapping machines. A model was developed that calculates the profile wear of the lapping wheel as a function of the path curves of the workpieces on the wheels [4, 51. To depict the relative motions, the lapping coefficient KL is usually given. It describes generally the ratio of the revolutions of a workpiece holder around its own center to its revolutions around the grinding wheel center. For all machines with fixed external pin circle, the selectable kinematic parameters are reduced to the rotational speeds of the lower grinding wheel nl, the upper grinding wheel n, 2

Design of a double wheel lapping or grinding machine. Corresponding to these path curves, characteristic wear profiles emerge in the process which require that grinding wheels be conditioned in regular intervals. In contrast to lapping wheels, profiling of grinding wheels in this range Figure 1:

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and the internal pin circle n,. In the here presented investigations all path types and velocities are related to the lower grinding wheel. Thus, a simplified description with the rotational speed ratio

N, = -ni ”/

is possible. NL describes unequivocally for a single machine the path type on which the workpieces move relative to the lower grinding wheel. All path types can be covered with different velocities within the scope of the possible rotational speeds of a machine. 2.1 Analysis of path types and velocities In the following the connection between rotational speeds and emerging path curves is explained [6].This kinematic analysis is done for the example of a double-side fine grinding machine, type Duomat ZL 700, Hahn & Kolb GmbH, Schorndorf (now Stahli Lapp-Technik GmbH, Schonaich). The outer pin circle of this machine is fixed, whereas the two grinding wheels and the inner pin circle can be driven individually. Figure 2 shows the characteristic path types that a workpiece center point covers as a function of the rotational speed ratio NL. The occurring relative velocities vary more or less strongly depending on the shape of the curves. The related path velocity v’(t) given in the diagram is defined as the ratio of the path velocity v(t) to the mean path velocity Vm. For every kind of path types an example is printed in the top line of the figure.

the interlaced hypocycloids turn into stretched hypocycloids (e). Also here the variations of velocity are extreme. Figure 2 demonstrates that the kinematic conditions at equal mean path velocity depend heavily on the rotational speed ratio and thus, on the shape of the path curve. 2.2 Kinematic possibilities of machines Due to the technological progress in driving technology on the one hand and knowledge of lapping kinematics on the other, kinematic possibilities of machine systems are constantly expanded and improved. To illustrate this development, Figure 3 compares the kinematic possibilities of various generations of the machine family ZL by Hahn & Kolb GmbH.

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Comparison of kinematic possibilities of double wheel machines. For the ZL 800 (built in 1980), the rotational speed ratio between inner pin circle and lower lapping wheel is set firmly by a gearing. Changing the poles at the driving motor serves to realize four different velocities. Freely selectable rotational speeds permit any rotational speed ratios for the design ZL 700 CNC (1989). For the path velocities needed for grinding the range of possible path types is strictly limited. Possible rotational speeds are considerably higher for the ZL 700 built in 1998. Here, both grind,ing wheels can be driven with up to n l, = 2 435 min’ , the inner pin circle with up to n, = k 268 min”. These rotational speeds allow for mean path velocities vm of more than 600 m/min or 10 m/s. Figure 3:

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Path types and velocities of the Duomat ZL 700. All workpiece points cover stretched hypocycloids (a) on the grinding wheel at high negative rotational speed ratios NL.These path curves turn into stretched epicycloids (b) with increasing NL.At the transition between the two path types (NL= -2,38) the parts move on circular paths that run eccentrically around the grinding wheel center. The intersection of the curves for a maximum, mean, and minimum path velocity illustrates that these paths are covered with constant relative velocity. At NL= 2,15 the stretched epicycloids become interlaced epicycloids (c). Here, maximum velocity variations occur: the workpieces are slowed down to a momentary standstill and afterwards accelerated to more than 150 % of the mean velocity. Velocity variations reach their minimum again at the transition to interlaced hypocycloids (d). At NL= 1 1,09 Figure 2:

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3 EXPERIMENTAL SETUP AND PLANNING To illustrate the relation between process parameters and path types, machining operations were carried out with equal mean path velocity on two different path types. Circular paths running eccentrically around the grinding wheel center (NL= -2,38) were selected as a path type with constant curvature and without variation of the path velocity between the workpiece center point and the grinding wheel. Stretched epicycloids with NL= 0.6 were used for comparison, which show a path velocity variation at approximately f 40 % around their mean value. The driving moment of the lower grinding wheel motor MI and the workpiece height reduction Ahw were analyzed and evaluated as characteristic quantities of the process development. The workpiece height reduction rate A&, served to evaluate the process power. The arithmetical mean deviation Re and the workpiece bottom flatness F were used to assess the quality. A double wheel grinding machine, type Hahn & Kolb Duomat ZL 700 CNC, built in 1989, was available for the

experimental investigations. The rotational speed settings that correspond to the possibilities of the machine are presented in Table 1. The upper grinding wheel was driven with similar rotational speed, but with opposite direction of rotation to the lower grinding wheel.

process conditions to a blunting of the grinding wheels and a filling-in of pores.

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tool: Dl26 C47 material: A1,0,

mean path vel.: 75 m/min grinding press.: 6 N/cm2 path curve: N, = 0,6 N, = -2,4

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Table 1: Survey of kinematic test parameters Gas pump caps made of alumina (A1203 content 96 %) were machined. These are cylindrical fillets with a diameter of 41 mm and an unmachined height of about 5 mm. Two pairs of synthetic resin bond diamond grinding wheels were used: one pair of the specification 046 C50 with radial and concentnc grooves and one pair of the specification D126 C47 without grooves. Mineral oil was used as cooling lubricant. The roughness characteristics were measured with a device of the type Form Taiysurf 120L. Rank Taylor Hobson. The tracer radius was 2 prn at an angle of 60". The workpiece height reduction rates were measured with a micrometer screw by Mitutoyo. A linear tracer integrated into the machine, situated in the rotation center of the grinding wheels and facilitating the process control, served to insitu record the workpiece height reduction. The decrease of rotational speed at the driving motor was measured and converted by means of the rotational speedltorque characteristic curve into the respective moment. Just as the rotational speeds, the measured values of the linear tracer were recorded, analyzed and evaluated using a personal computer. RESULTS The experiments proved that the selection of the path type is clearly reflected in both, the process development and the workpiece qualities. 4

4.1 Process course The upper part of Figure 4 presents the driving moments MI of the lower grinding wheel as a function of the grinding time tc for the two chosen path curves. The bottom graph lists the in-situ measured workpiece height reductions Ahw for the same phase of operation. The driving moments of the lower grinding wheel motor exhibit a regular course after a brief starting phase irrespective of the path type. On the average, the moments are by about 1,6 Nm higher on stretched epicycloids (NL= 0,6)than on eccentric circular paths. This corresponds to an increase of more than 30 %. The workpiece height reductions increase linearly with the grinding time. The workpiece height removed per time during machining on eccentric circular paths is about half as low as that for stretched epicycloids. The linear courses of these qua'ntities during the grinding time indicate constant cutting conditions at the individual grain in the self-sharpening range of the grinding wheels. Contrasting with this are observations by Funck [7],who reported strong decreases in workpiece height reduction rates with increasing process time during the machining of cold-worked steel wifh silicon carbide grinding wheels on the same machine. He attributes these instationary

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Figure 4: Driving moment MI and workpiece height reduction Ahw for the two path types. Figure 5 shows for both path curves the workpiece height reduction rate A t i as ~ a function of the mean path velocity Vm for different grinding pressures p. The removed workpiece heights on eccentric circular paths lie altogether considerably lower than on stretched epicycloids. &W increases initially with increasing path velocity irrespective of the path type, but decrease again at higher velocities. Weigmann [B] explains this effect, which also occurs during honing of ceramic materials, with the formation of a hydrodynamic lubricating film between workpieces and grinding wheel, leading to a reduction of the grinding pressure. The decrease of Ahw occurs at NL = -2.4 already at velocities above Vm = 50 m/min. The formation of this lubricating film can be opposed by an increase in grinding pressure. On stretched epicycloids, a lubricating film is formed only at much higher mean path velocities over vm> 100 m/min. The formation of lubricating films is hindered or existing films are interrupted by the velocity variations to which the workpieces are exposed during the process (see Figure 2). 300

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tool: D126 C47 material: AI,O, cooling lubricant: mineral oil grinding press.: -10 N/cm2 -=- 6 N/c@ -04N/cm2

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mean path velocity v, Figure 5: Workpiece height reduction rate Atiw as a function of mean path velocity vm.

4.2 Workpiece quality Figure 6 shows the arithmetical mean deviation Ra as a function of the mean path velocity Vm for both path types. The surfaces generated on eccentric circular paths exhibit considerably lower mean deviations. The arithmetical mean deviation values are more than 30 % below those of samples machined on stretched epicycloids. This effect

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mean path velocity v, Figure 6: Arithmetical mean deviation R a as a function of mean path velocity Vm. can be attributed to the altogether more homogeneous grinding conditions regarding path curvature and path velocity. The path type exerts thus a bigger influence on the roughness than the mean path velocity. The surface roughnesses decrease initially, irrespective of the shape of the path curve, with increasing path velocity. This effect also known from honing (81 can be put down to single plastic deformations and a filling of grinding traces with workpiece material. Figure 7 presents the arithmetical mean deviation R a as a function of the grinding pressure p for both path types.

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grinding pressure p Figure 7: Arithmetical mean deviation Ra as a function of grinding pressure p. Workpieces machined on eccentric circular paths reveal only a very small relation to the grinding pressure. The decrease in roughness that can be observed with increasing pressure, on the other hand, indicates a smoothing by plastic deformations of the surface. The experiments with Nc = 0,6 at p = 10 and 12 N/cm* had to

be stopped because moments were too high. The path type exerts also in this case a greater influence on the mean deviation than the grinding pressure. A second test series served to vary the rotational speed ratio NL at constant grinding pressure p and steady mean path velocity Vm. The flatnesses were measured on the bottom sides of 3 of 40 workpieces. Figure 8 represents the flatnesses F of the workpieces as a function of the rotational speed ratio NL. It becomes apparent that minimum deviations from the ideal geometry occur during the machining on eccentric circular paths, while the irregularity shows a local maximum at NL = 0,6. A direct correlation between irregularities and variations of relative velocities in the process, however, could not be proved. 5 CONCLUSION During face grinding on lapping machines, the types of relative motions between workpieces and grinding wheels do not only affect the formation of wear profiles in the tools. Rather, the path type directly influences the process course and the work result. Reductions of depth of roughness of more than 30 % and improvements of flatness of more than 40 %, caused by changing the path type, were observed for workpieces made of alumina during experimental investigations. At the same time, the driving moment of the lower grinding wheel dropped by about 30 % and the material removal rate fell by 50 %. The variation of the path type has here a more distinct impact on the process result than the change of grinding pressure or path velocity. Controlling the rotational speeds serves to realize rough- and finishmachining just by varying the path type in one manufacturing step. These results indicate that regular path curves lead more easily to low workpiece height reductions and good surfaces, while path curves with gradients regarding curvature and velocity produce higher removal rates at reduced part quality. The application of machines with higher rotational speeds and thus, greater kinematic flexibility is necessary to search for correlations between results and kinematic parameters.

REFERENCES Uhlmann, E., 1998, Developments in Grinding of Ceramic Materials, Abrasives Magazine, July/August:28-34. Tbnshoff, H. K., Egger, R., Mackensen, V. v., Preising. D., 1998, Fine Grinding of Engineering Ceramics as Substitution for Double-Side Lapping, ASPE Proceedings, 18:161-164. Wolters, P., 1998, Fine grinding can be the answer for machining difficult-to-grind materials, Tooling and production, 6:45-46. Simpfendorfer, D., 1988, Entwicklung und Verifizierung eines ProzeOmodells beim Planlappen, Dissertation,Technical University Berlin. Spur, G.,Eichhorn, H., 1997, Kinematisches Simulationsmodell des LappscheibenverschleiOes, Industrie Diamanten Rundschau, 31/2:169-178. Uhlmann, E., Ardelt, Th., Daus, N., 1998, Kinematische Analyse von Zweischeibenmaschinen, Werkstattstechnik, 88/6:273-276. Funck, A., 1994, Planschleifen mit Llppkinematik, Dissertation, Technical University Berlin. Weigmann, U.-P., 1997, Honen keramischer Werkstoffe, Dissertation, Technical University Berlin.

n tool: D46 C50 material: AI,O, cooling lubricant: mineral oil

grinding press.: 8 N/cm2 grinding time: 120 s mean path vel.: 50 m/min

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Figure 8: Workpiece flatness F as a function of rotational soeed ratio NI .

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