Grinding Wheel Profile Research Articles

Design and manufacture of gear cutting tools and gears with an arbitrary profile. (A method for calculating grinding wheel-profile for hob finishing).

The theory for calculating the profile of a tool to be used for finishing gears with an arbitrarily given tooth-profile, which was shown in the previous report of this investigation, is expanded and new equations are derived to calculate the profile of a grinding wheel to be used for finishing a gear hob. In order to demonstrate the usefulness of the equations, profiles of a grinding wheel for finishing a hob to cut Novikov gears with concave teeth are calculated numerically. It is clearly shown that the profile of the gear cut by this hob is almost the same as the given tooth profile in the design state. The errors of tooth profiles of the gear cut by the reground hob are numerically calculated through the changes in the profiles of the basic rack expressed by the reground hob.

A study of the crowning method for the type 3 worm gear. (3rd Report, An analysis of calculation method for the profile of the relief grinding wheel).

A precise analysis has been made on the profile of the relief grinding wheel of the type 3 worm hob. Firstly, the type 3 worm thread surface, which is normal to the basic thread surface of the hob, is chosen as the helical cutting face of the type 3 worm hob. Secondly, the axis of the relief grinding wheel for this worm hob is tilted in a three-dimensional direction to the axis of the worm hob. Thirdly, the calculation method for the profile of the relief grinding wheel is obtained. Then, the experimental manufacture of a relief grinding wheel is made by applying this calculation method to a numerical example of the type 3 worm hob. The theories in this analysis are verified by practical relief grinding of the type 3 worm hob with this relief grinding wheel and by the measuring of the profile of the cutting edge of the worm hob. The necessity and the effectiveness of this calculation method are confirmed.

On the CAD of Profiles for Cutters and Helical Flutes - Geometrical Aspects

The paper deals with geometrical analysis and with software development for the designing of cutter and grinding wheel profiles. Two methods, the “direct” and the “indirect” allow for the prediction of the helical flute profiles and cutter profiles respectively. Programming was carried out on an IBM PC, and can easily be operated on any other similar system. Results are obtained either as printed data or in the form of plotted profile curves. Both methods can each be run with the results obtained by the other, allowing for the rechecking of the design. Applications are discussed and preliminary examples of program output presented.

Design and manufacture of gear cutting tools and gears with an arbitrary profile. 3rd report. A method for calculating grinding-wheel profile for hob finishing.

The theory for calculating the profile of a tool to be used for finishing gears with an arbitrary given tooth-profile, which was shown in the first and second reports of this investigation, is expanded and new equations are derived to calculate the profile of a grinding wheel to be used for finishing a gear hob. In order to demonstrate the usefulness of the equations, profiles of a grinding wheel for finishing a hob of Novikov gears with concave teeth are calculated numerically. It is clearly shown that the profile of the gear finished by this hob is almost the same as the given tooth profile in the design stage. The errors of tooth profiles of the gear finished by the reground hob are numerically calculated through the changes in the profiles of the basic rack expressed by the reground hob.

A study of the crowning method for the type 3 worm gear. 2nd report An analysis of calculation method for the profile of the relieving tool.

A precise analysis has been made on the profile of the relief grinding wheel of the type 3 worm hob. Firstly, the type 3 worm thread surface, which is normal to the basic thread surface of the hob, is chosen as the helical cutting face of the type 3 worm hob. Secondly, the axis of the relief grinding wheel for this worm hob is tilted in a three-dimensional direction to the axis of the worm hob. Thirdly, the calculation method for the profile of the relief grinding wheel is obtained. Then, the experimental manufacture of a relief grinding wheel is made by applying this calculation method to a numerical example of the type 3 worm hob. The theories in this analysis are verified by practical relief grinding of the type 3 worm hob with this relief grinding wheel and by the measuring of the profile of the cutting edge of the worm hob. The necessity and the effectiveness of this calculation method are confirmed.

Design and manufacture of gear cutting tools and gears with an arbitrary profile. (2nd report Trueing of wheel with NC dresser and form grinding of helical gears)

By applying the theory in the 1st report, the authors proposed a method to calculate the exact profile of a form grinding wheel for finishing a helical gear with an arbitrary tooth profile. Using this method, they calculated the exact wheel profile which can produce an involute tooth profile with a tip relief at a transverse section of the involute helical gears. The wheel profile was generated by a single point diamond dresser using a universal NC milling machine with an attachment made by the authors. The tooth flank and root of test gears were ground at the same time to prevent occurrence of a notch which is apt to be produced at the boundary of ground and unground surfaces. The accuracy of the form-ground test gears was in the 0 class of JIS and their surface roughness was in the range of 0.5 to 1.0 μm Rmax.

研削砥石のクラッシングに関する研究(第2報)

For the purpose of clarifying the truing effect of crushing, crush roll wear rate during crushing and grinding wheel wear caused by grinding are measured for various crushing conditions by controlling the sliding speed between crush roll and grinding wheel. Results are as follows : (1) Crush roll wear rate increases with an increase in the sliding speed, and decreases with an increase in the crush roll infeed rate when the sliding speed is constant. (2) Rate of grinding wheel wear caused by grinding increases with an increase in the crush roll infeed rate per one revolution of grinding wheel, and becomes smaller when the sliding speed increases. (3) An averaged value of the sliding speed over the crush roll profile can be minimized by shifting the rolling pitch point between grinding wheel and crush roll to an optimum position with a forcible manner, and this results in the improvement in grinding wheel profile accuracy. Furthermore, it is revealed that an application of creep feed grinding onto the crush formed grinding wheel contributes to the improvements in grinding wheel wear rate, profile accuracy, and finished surface roughness as compared with conventional plunge grinding.

Probabilistic Analysis of the Surface Grinding Process

The surface grinding process is simulated by developing a special purpose computer package, where the grinding wheel surface is presented statistically by a Rayleigh distribution, and by using the Monte Carlo techniques. The effect of the grinding wheel profile and the kinematic input parameters on the internal parameters of the process and the workpiece surface roughness have been investigated. These are strongly related to the input parameters (νs,νw,a). The investigation shows that the active cutting edges represent only a small percentage of the total cutting edges (2% - 12%).

Dressing of Conventional and CBN Grinding Wheels with Diamond Form Rollers

Dressing with diamond form rollers has already been mentioned in 1965 and was developed parallel to the introduction of NC-technics into grinding machines. In comparison to diamond profile rollers which generate the required profile with only one radial feed motion, diamond form rollers have in any case a smaller width than the grinding wheel and generate the grinding wheel profile by a two axis control system in radial and axial direction. Form rollers are therefore more flexible as profile rollers. Wide wheels with steep profile flanks can be generated and shape deviations are small because of low dressing forces. Form rollers are - compared with fixed dressing tools like single point diamonds - extremely wear resistant. Dressing of CBN grinding wheels has - in most cases - to include a sharpening operation to prepare the wheel for the grinding process. Results have shown that jet sharpening is an easy operation with relatively short sharpening times.

Grinding Wheel Profile for Hob Relief Grinding

In this paper a method is described for the calculation of the dished and pencil grinding wheel profiles for relief grinding of hobs for manufacturing spur, helical, and worm gears. Archimedean, convolute, involute, and ground worm gear drives are dealt with. For the purposes of control of the calculated grinding wheel profiles and of the determination of the generation error in the case of the profile curve approximation to a straight-line or a circular arc, the method contains the calculation of the hob tooth profile, relief ground with a grinding wheel of the calculated or approximated axial profile.

A mathematical model of the grinding wheel profile required for a specific twist drill flute

Obtaining a straight cutting edge in the case of small twist drills warrants an accurate grinding of the “primary” flute. A transformed mathematical model which would yield the proper flute-grinding wheel profile for a straight cutting edge is developed from an existing orthogonal flute model. Also discussed in this paper is a mathematical model that describes the wheel profile for the “secondary” (non-cutting edge) flute as a function of parameters such as land width, web thickness and chip removal capacity of the drill. The model enables an analysis of the effects of improper wheel setting and point grinding on the straightness of the cutting edge. From this analysis, an optimum wheel profile that would grind a maximum number of acceptable flutes can be obtained.

Measurement and analysis of grinding wheel surfaces

Understanding of the mechanism of grinding is hampered by the difficulty of defining the effective cutting geometry This paper describes a simple technique for the analysis of grinding wheel profiles. This study includes the random process analysis of the section and effective profiles of the wheel

A new irregular surface measuring system

To measure and record highly irregular configurations, a new surface measuring system using an oscillating stylus is developed and coordinated with a data handling unit capable of direct interfacing with a computer. This on-line non-destructive measurement system is found to be accurate, capable of a comprehensive range of utilization and easily operated. Examples of measured grinding wheel profiles and tool craters are shown.

Selection of Sampling Parameters for Modeling Grinding Wheels

Autoregressive-moving average models are developed to represent grinding wheel profiles for different combinations of sampling parameters including the sample interval, the number of observations, and the length of record. Using 46 and 120 grit grinding wheels, the effects of the choice of sample interval and number of observations on the appropriate model form are investigated. Discrimination between models for different grit size grinding wheels is discussed. A new criterion is proposed for the selection of the sample interval, based on observations per grit (OPG), to achieve comparable discrete approximations of the wheels and to maximize discrimination between models of different wheels.

Characterization of grinding wheel profiles by autoregressive-moving average models

The cutting profiles of three common grinding wheels, 32A80-H8, 32A80-L8, and 32A60-J8, were analyzed by Box-Jenkins autoregressive-moving average models. The analysis involves three stages, i.e., identification, estimation, and diagnostic checking. It was found that second-order autoregressive models represent the profiles of the three wheels fairly well. An analysis of replicate profiles taken from each wheel indicated that the profiles were ergodic. The models and their parameters were related to the qualitative characteristics of the profiles. The analysis was achieved through the use of many charts developed for engineering applications.