Title of Invention

A VARIABLE STIFFNESS REGULATING WHEEL FOR A CENTRELESS GRINDING MACHINE

Abstract

. A variable stiffness regulating wheel for a centreless grinding machine, the body of the wheel being rotatably mountable on a spindle driven by a prime mover; an annular air chamber provided within the wheel, the said chamber having an inlet for the entry of pressurised air into the chamber; a pressure gauge provided for the wheel, and means for closing the air inlet, for enabling the air pressure within the chamber to be maintained at a predetermined value.

Full Text

This invention relates to a variable stiffness regulating wheel for a centreless grinding machine. Centuries grinding is a high volume high precision process for a variety of products, in centreiess grinding the workpiece is constrained by a regulating wheel, a grinding wheel and a work plate. The grinding wheel and the regulating wheel rotate in the same direction. The regulating wheel provides the means of rotation of the workplece. This wheel is often of the rubber-bonded type giving sufficient friction between it and the workplace. Often these wheels are available only in two or three different hardness and depending on the part being ground, the selection is made. The schematics of centreiess grinding is given in Fig.1 Workplece rounding mechanism is regenerative in centreiess grinding. This is due to the absence of centers for the workplece. When a workplece with a high spot is introduced in a centreiess grinder. Its position gets altered as it rotates In the machine. If the centers of the wheels and the workplece are all in one line, a high spot produces a concavity at diametrically opposite point. Since the distance between the two centers remain a constant, a of a constant "diameter" is produced. However, the resulting workplace need not be circular (cylindrical). This is called loping en-or. Usually, the workplece center is raised above those of the two wheels and as the high spot contacts the regulating wheel, it is pushed towards the grinding wheel. However, since the three centers are not in a straight line, the extent of feed is obtained by multiplying the height of the irregularity by the nonexpanding transmission ratio. Expressions for the transmission ratios can be derived from the geometry of the set-up. When the high spot comes in contact with the work plate, the work plate being at an angle to the horizontal tends to push the workpiece away from the grinding wheel. The extent to which it does is again determined by the corresponding transmission ratio. The gradual removal of the high spots together with a very limited development of low spots tends to improve the roundness of the work progressively, i-lowever, this achievement of roundness is modified considerably by any change in the geometrical configuration. Further all the preceding discussions have been from a geometrical point of view, considering the role of constraints In modifying the position of the workpiece center and consequently the cut. The cutting forces and the machine compliance have not been considered. These play a decisive role in the rounding mechanism. It was found that high machine stiffness was desirable when grinding awe performed at small angles of D (less than 60 ) in order to obtain a more effective rounding action. However, when grinding with larger values of the angle 0, a very stiff system could be worse than a compliant system. In centerless grinding, the workpiece is simultaneously in contact with (he work plate, regulating wheel and grinding wheel. Hence the instantaneous grinding conditions are determined by the instantaneous encores in workpiece shape at these three contact points. Workpiece errors in the contact point A with grinding wheel have a direct effect on the magnitude of instantaneous pre¬loading and enters at points B and C affect these values indirectly by displacing the work center. This has been discussed in detail by Rowe and Brash . A generalized geometry of the process is given in Fig.2. D The errors at B and C are not directly effective. The degree of their effect is determined by the transmission ratios. These ratios can be determined from the figure as: Transmission ratio K1 =8lnp/8in(a+p) Transmission ratio K2 * sin a / sin (a + p) if any reduction in radius from an initial reference circle Is considered as an error, the apparent reduction in radius R(() at the grinding wheel contact point A may be calculated In terms of the Indeed movement X(() considered In a direction OA (or 001) and the 8DDand 82 ( or 82 + 53 ) en-ors on the plate and the regulating wheel contact points respectively. R 0sX^0-K1.8D+K2.52 REPRESENTATION OF THE CENTERLESS Grinding MACHINE USING A DYNAMIC EQUIVALENT The centerless grinding process with flexible regulating wheels may be described by the equivalent system proposed below (Flg.3). D The equations of motion governing the response of the system described are given below. It may be noted that the work piece grmdmg wheel interface is assumed to be a line contact allowing only movement normal to the surface. The true depth of cut S(t) at any instant t is the difference between the apparent depth of cut A(t). and the machine deflection x(t) (on the grmdmg wheel side) S(t) = A(t)-X(t) (1) The above idea can be clarified by the following schematic (Fig.4) G, W, R are the grinding wheel the workpiece and the regulating wheel respectively, a, b, o represent the movement of the center due to errors at the regulating wheel, en-or at the work plate and the compliance of the regulating wheel. The relationship between this schematic and the model in Fig. 3 is evident The depth of cut S(t)=r(t>-r(t-T) (2) Where T is the time required for one full revolution of the workpiece. These equations are valid for a steady state condition or for small variations from the steady state. The apparent depth of cut is defined by: A(t) = Ki .r(t-T1) - K2.[r(t-T2) - Xz] - r(t-T) (3) Where X2 Is the deflection at the - regulating wheel contact point. Eliminating 8(t) and A(t) between 1,2 and 3, we get r(t) - K1 .r(t-T1) + K2.[r(t-T2) - x(t) (4) The normal grinding force, which is assumed to be proportional to the actual depth of cut is given by (5) Further, a component of this normal grinding force is transmitted on to the regulating wheel and hence x2 can be described in terms of the contact stiffness of the regulating wheel. x2 = - (6) Now, the grinding wheel has been described as a spring damper system where Km and C represent the machine stiffness and the damping constants respectively. Clearly, x2 being dependent on r(t) and r(t-T) according to equation 6, the above system is a single degree of freedom system. The equation of motion is then: = Ks.[r(t) - r(t-T)l (7) Substituting for x from equation 4 we get: M.{r"(t)- [K1.r"(t-T1)- K2.(r"(t-T2) - x2")l} + C.{r"(t) - IK1 .r"(t-T1) - K2.(r"(t-T2) -x2")]} + Km.{r(t) -■ [K1.r(t-T1) - K2.(r(t-T2) - x2)]} =« - Sir(t)-r(t-T)J (8) It may be noted that this equation ignores the steady state terms related to the average depth of cut and average deflections since these are generally inconsequential to the stability and the onset of chatter. With the above equation as the governing equation, the final forms obtainable were simulated. The results of simulation clearly bring out the fact that higher regulating wheel stiffness, under geometrically stable conditions, produces a better-rounded workpiece than its flexible counterparts (Flg.5). However, beyond certain stiffness, it may be noted that the improvement In the roundness is not very significant. This saturation occurs because of the compliance of the regulating wheel and the inherent work regenerative effect. As stiffness increases, the contribution of the compliance decreases but the work re generalize^ SL. No. erred slays uncurl Regulating anyed. Roundness Wheel stiffness encore ]vim 1 6.0 X10® 12.5D 2 1.2x10^ 8.53 3 6.0x10^ 6.95 4 6.0x10^ 6.13 Table 1. Summary of simulation results IMPROVEMENT OF SURFACE FINISH Any compliant control wheel is bound to reduce the In-feed in centreless grinding and give a fine feed rate during grinding. This results In Improved finish of the workpiece though the roundness encore does not get reduced. Thus a control wheel with low stiffness could impart an improved finish for the product. Hence It could be seen that a staffer control wheel could Improve the roundness, a compliant wheel of low stiffness could only Improve the finish. This was obscene/ed in earlier studies using rubber coated abrasive wheels of different thickness. Thicker coating of the rubber gave lower contact stiffness and resulted In better finish while the roundness showed no improvement [2]. A metal control wheel gave good roundness but poor finish [3]. CONTROL WHEEL OF VARIABLE STIFFNESS In centreless grinding both the roundness and finish are of importance to the woricpieoe being ground, it will be Ideal to grind the part with a relatively stiff control wheel to get better roundness and then switch on to a less stiff wheel to improve upon the finish. Changing the control wheel for this is practically impossible in production runs. Hence a variable stiffness control wheel, which could be used with ease in centreless grinding machines, was developed. For obtaining a variable stiffness control wheel it is proposed to have a pressurization chamber in the control mounting unit. The control wheel is mounted on this and by varying the pressure Inside the chamber the stiffness of the control wheel could be changed. This can also be made using perhaps an electo-reheologicai fluid In the chamber and changing its viscosity to get different stiffness. DESIGN FEATURES OF A VARIABLE STIFFNESS REGULATING WHEEL To study the role played by the regulating wheel stiffness in the process of centreless grinding, It is essential to develop a variable stiffness-regulating wheel. Hence a new wheel was developed which could be changed for Its stiffness by air pressure. The sectional view of such a wheel is given in Fig.6. Specially made rubber bonded control wheel was used for the purpose. This wheel was glued on to a supporting metal ring. An air pressure chamber was designed as shown in the figure. Two rubber rings which are pressed along the internal taper of the outer supporting metal ring, using two retainer rings, allowed the chamber to be pressurized up to 12 bar. There was the provision for monitoring the pressure using a pressure gauge and for closing the air inlet. This modified wheel was designed to be fixed on an existing centreless grinding machine without any modifications to the machine. Contact stiffness of this wheel was tested using a simple set-up. Loading was done using a proving -ring and the deflection was monitored using a precision dial Indicator. Stiffness was measured for different pressures and the results are given in Fig.7. For the same load the deflection at low pressures are very much higher than at high pressures. EXPERIMENTAL STUDIES Using this variable stiffness wheel a set of preliminary experiments were conducted to confirm the simulation results. The regulating wheel was dressed after pressurizing it to the required pressure. For studying the form variations, a cylindrical work piece with a small flat ground on it was used. Roundness profiles were traced and the roundness error was noted from the instrument. Finish measurements were done after every grinding and the Ra values were obtained. Grinding was done in steps of 20 Dm in-feed (depth of out) with coolant. When the pressure was changed, the regulating wheel was dressed to avoid any error In compliance, This was essential as the two rubber gasket rings had some variations in their stiffness along their periphery. Actual grinding machine set-up is shown in Fig.8 with the pressurized regulating wheel. RESULTS All roundness and roughness readings were normalized for comparing the results. Normalized roundness error as well as roughness values are plotted in Fig.9 and Fig.10. The results clearly show that a stiffer regulating wheel achieves better roundness in a shorter duration. This is in line with the simulation results. As for the finish, lower stiffness gave better finish. This is understandable as the regulating wheel deflection allowed the feed to be made finer though the time for grinding increased slightly. In brief the twin objective of form and finish improvement can be achieved by using the right stiffness for the regulating wheel. Initial grinding is to be done with high stiffness to Improve the form accuracy and after achieving this the finish can be improved by using a lower stiffness for the wheel. As changing the air pressure could change the wheel stiffness, the regulating wheel becomes flexible In Its stiffness. Hence this changeover can be effected without any change in the regulating wheel. By suitably tuning the air pressure it is possible to achieve excellent form and finish in centerless grinding. We Claim A variable stiffness regulating wheel for a centreless grinding machine, the body of the wheel being rotatably mountable on a spindle driven by a prime mover; an annular air chamber provided within the wheel, the said chamber having an inlet for the entry of pressurised air into the chamber; a pressure gauge provided for the wheel, and means for closing the air inlet, for enabling the air pressure within the chamber to be maintained at a predetermined value. 1. A variable stiffness regulating wheel for a centreless grinding machine wherein the periphery of the said wheel has a known bonded surface of a flexible material, such as, rubber. 3. A variable stiffness regulating wheel for a centreless grinding machine wherein spaced inner and outer support metal rings are provided for the said wheel 1 . 4. A variable stiffness regulating wheel for a centreless grinding machine, wherein gasket rings are provided for acting as a seal for the air chamber. 5. A variable stiffness regulating wheel for a centreless grinding machine, substantially as herein described and illustrated with reference to the accompanying drawings.

Documents:

0206-mas-2001 claims duplicate.pdf

0206-mas-2001 claims.pdf

0206-mas-2001 correspondence others.pdf

0206-mas-2001 correspondence po.pdf

0206-mas-2001 description (complete) duplicate.pdf

0206-mas-2001 description (complete).pdf

0206-mas-2001 drawings.pdf

0206-mas-2001 form-1.pdf

0206-mas-2001 form-19.pdf

0206-mas-2001 form-26.pdf