Benchmarking Generating Gear Grinding
Introduction
The following is a reworked version of the author's "Gear Grinding Handbook," first published in 2004 and edited across various versions until 2014 while working for the Winterthur Technology Group and later 3M, who still can supply this handbook. Many customers the author visited over that time still use the methods elaborated here, particularly in Japan, where seminars and handouts have widely communicated this method. Now working at Reishauer gear grinding machines, the author would like to clarify that these methods are not official company policy as Reishauer has more sophisticated software on its RSP platform for suggesting machining parameters. However, the formulas for Qw max and Q'w are still very useful for those who run previous generation machine. These formulas were originally given to the author by two Reishauer employees some 20 years ago: Dr. Peter Sch?cke and Dr. Wolfgang Thyssen. Once more, I wish to thank them for their support. As soon as I could use Qw max and Q'w, I could calculate the theoretical average chip thickness hm. In my view, the chip thickness is the most relevant factor in exploring the limits of any grinding process. Furthermore, knowing these limits allows the users to work efficiently within safe parameters. ?
Modern CNC machines offer the users a high degree of freedom but little help in setting the grinding and dressing parameters. In all fairness, and as mentioned, the latest Reishauer gear grinders do offer process parameter proposals. Nevertheless, the new machines represent only a small fraction of all the machines in the market. If the users know the limits of the most important parameters, they can set up their processes in the knowledge of being within industry benchmarks. For example, suppose users know that a grinding wheel can support a chip thickness of 0.6 microns (μm) and sets the process at a chip thickness of 0.4 microns. In that case, they can feel confident that their processes work well and still have a good safety margin and room for subsequent improvements. This chapter covers four parameters, as shown in the above title image, and are also listed in Illustration 1, "Performance Benchmarking." For this chapter, the "Aggressiveness Factor Fa" has been excluded. However, for those interested in this factor, the chapter "Creepfeed Grinding" fully explains its scope, usefulness, and relevance to gear grinding.?
Illustration 1: Performance benchmarking
1. Grinding wheel surface speed vc
Changing parameters of a grinding process always carries consequences to be considered. These consequences relate to the work spindle power requirements and the risk of grinding burns. This phenomenon is true of the surface speed vc, the feedrate fz, the depth of cut fx, or the amount of shifting Y shift, as shown in Illustration 2.?
Illustration 2: Influence of grinding parameters on burning risks and power requirements (1)
?Grinding technology tends to aim for as high a surface speed as possible. Processes such as cam grinding start a 100 m/s and may go as high as 160 m/s. The reason for increasing the surface speed is linked to the chip thickness and the load on the grinding wheel. The faster the grinding wheel works, the finer the chip thickness becomes. Hence, knowing the max chip thickness a grinding can support, one can proportionally increase the infeeds as one increases the wheel speed. Another reason to increase the wheel speed is the reduced contact time of the abrasive grains as they travel through the arc of contact between the grinding wheel and the workpiece. Reduced contact time translates into less heat entering the workpiece, reducing the risk of grinding burns. Hence for continuous generating grinding, one could surmise the dictum: "The higher the surface speed, the better the process works." This statement, however, is only partly correct. When selecting the cutting speeds, all conditions, such as the machine tool, the workpiece's rigidity, the clamping situation, the threaded grinding wheel specification, and the final gear quality, should be considered. ?
Continuous generating grinding differs in one major aspect: the threaded grinding wheel meshes with the workpiece. Hence, the workpiece RPM is interdependent to threaded grinding wheel's RPM. In all forms of cylindrical, surface grinding, and profile gear grinding, the wheel speeds and the workpiece speeds can be adjusted individually. For continuous generating grinding at high speed, the meshing of the threaded grinding wheel and the workpiece places high demands on the CNC's vector drive to synchronize the grinding wheel and the workpiece RPM to maintain a high gear quality. Presently, the surface speed limits of continuous generating grinding are at 100 m/s. In Europe, 100 m/s fully complies with the safety requirements. However, in Japan, for example, 100 m/s cannot be applied as the safety rules stipulate a safety factor of a twofold operating speed. Therefore, the wheels would have to be tested at 200 m/s. Today, vitrified threaded grinding wheels would burst before reaching 200 m/s.?
Furthermore, test beds for 200 m/s do not exist in the open market. Illustration 3 shows the influence of higher surface speed on the risk of burning and the work spindle power requirement. In continuous generating grinding, contrary to other grinding processes, the burning risk increases slightly. This increase may be due to the meshing movements of the threaded grinding wheel with the workpiece.
Illustration 3: Influence of surface speed (1)
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Illustration 4: Grinding wheel surface speed
2. Qw max material removal rate ?
Illustration 5: Qw max material removal rate
The maximum material removal rate is a useful indicator to ascertain whether the performance potential of a given machine has been fully reached. This parameter refers to the volume of material a grinding wheel can remove in one (1) second. The formula for calculating Qw max and all the relevant factors is given in Illustration 6.?
Illustration 6: Qw max formula for calculating the material removal rate
Qw max performance values
The different machine tool generations have, of course, different performance levels. The following values given in Illustration 7 are a good guideline for setting up a new process. The basis for the guideline was a workpiece with the following characteristics: Module mn 2, No. of teeth z 35, face width b 17 mm. ?
Illustration 7: Qw max material removal rate for diverse machines
3. Specific material removal rate Q'w (Q-prime)
Illustration 8: Specific material removal rate Q'w of the Reishauer process?
The specific material removal rate, also known as Q'w or Q-prime, indicates how many mm3 one (1) mm wheel width removes per second (mm3/mm/sec). This value allows for a direct comparison between different grinding processes and/or grinding wheels as it always refers to only one (1) mm width of the grinding wheel. For grinding processes such as surface reciprocating and creep-feed grinding, the calculation of Q'w is very simple. The formula for continuous generation gear grinding is slightly more complex as the generating movements must first be converted into linear movements.
The formula for surface and creepfeed grinding processes:
ae = Infeed (depth of cut) per stroke in mm
vw = Feed rate in mm/min
?
Q'w for continuous generating gear grinding?
Illustration 9: Comparison of generating gear grinding with creepfeed grinding
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Illustration 10: Comparison of gear and creepfeed grinding
First, the generating feed must be converted into a "linear feed rate" as if it were a surface grinding process, here called vf. Additionally, one must operate with the equivalent wheel diameter (ds equi), which theoretically derives from the geometrical contact conditions between the threaded grinding wheel (using its pressure angle αn) and the workpiece.?
Illustration 11: Equivalent grinding wheel diameter ds equi?
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?Illustration 12: Equivalent diameter ds equi
?As the threaded grinding wheel does not grind on its periphery in continuous generation grinding but on its side, one must establish the resulting equivalent diameter ds equi to simulate the realistic contact conditions.
?Calculation of the linear feedrate vf
Illustration 13: Converting the generating feedrate into a linear feedrate
The linear infeed ax (depth of cut) must be calculated based on the contact conditions to arrive at the actual infeed (depth of cut) ae effective of the theoretical equivalent grinding wheel diameter ds equi:
?Illustration 14: Radial infeed and effective depth of cut ax
?The formula for the calculation of the specific material rate Q'w
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Illustration 15: Range of Q'w (Q-Prime) for the Reishauer process?
Guidelines of specific material rates Q'w
?Target value standard grinding:???????????????????????????????15 mm3/mm/sec
Performance grinding with ceramic abrasives: 25 to 35 mm3/mm/sec
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4. Theoretical Average Chip Thickness hm
Illustration 16: Theoretical average chip thickness hm
The theoretical average chip thickness hm is an important parameter for setting up and evaluating all grinding processes. It is easy to calculate this parameter if one disregards the changing wheel surface speed vc due to the constantly changing point of contact on the grinding worm during generating by taking a constant average diameter to calculate the wheel speed vc:?
It must be emphasized that when looking at the parameter, the keyword is "theoretical," as nobody knows the true thickness of a chip and how it is formed. During the grinding process, chips are compressed, pulled and/or welded together in a manner that cannot be established mathematically. This chip-forming process, however, is not relevant for a reasonable approximation as we always use the same formula to get constant comparative values. Based on the machining kinematics and parameters, the chip thickness can be calculated theoretically, and a model can be constructed. For other grinding processes, such as surface and cylindrical grinding, limits on the range of chip thicknesses have been established. For continuous generation gear grinding, these limits are very similar. Target values of chip thickness for continuous generation gear grinding:
?The target value for the roughing pass: 0.25 to 40 micrometer
Upper limit using ceramic abrasives:?????0.50 to 0.60 micrometer?
Illustration 17: The range of chip thickness hm
The theoretical average chip thickness hm, together with the given parameters such as depth of cut ae, feed rate vw, and surface speed vc, corresponds to the resulting depth of penetration of the individual grain halfway through the arc of contact lk. Experience has shown that at average chip thicknesses above 0.6 micrometer (0.0006 mm), the grinding wheel structures start breaking up. Inversely, at chip thicknesses below 0.1 micrometer (0.0001 mm), "rubbing" replaces chip formation and increases the danger of grinding abuse. The values given above for the average chip thickness hm are valid for all grinding processes and thus also for continuous generation gear grinding.
Setting up an Excel Worksheet
The formulas given in this chapter are best put into an Excel worksheet. In this way, all factors can be visualized and interpreted at one glance. The blue pentagon represents the limits of all the performance factors, while the red pentagon represents the values of the actual parameters against their maximum limits.
Illustration 18: Author's Excel worksheet "Process Parameters"
Conclusion
The method outlined here, particularly if converted into an Excel worksheet, allows for a quick and practical assessment of the process parameters. The users can feel confident that these parameters work economically, efficiently, and well within accepted ranges.
References
(1)???F. Klocke & C. Brecher, Zahnrad und Getriebetechnik, page 252, Carl Hanser Verlag, 2016
Walter Graf, The Philosopher's Grindstone, Copyright? 2004, first edition, and 2022