However, the surface structure from lapping superimposed to a precisely ground  flank surface presents a combination of accuracy and texture which could significantly  enhance the rolling performance of bevel gearsets. In generating grinding for bevel  pinions and generated bevel ring gears, the grinding wheel represents a tooth of the  generating gear to the work, while the work rolls on the generating gear to finish profile  and lead. The contact zones are lines that lie under an inclination angle αt (Fig. 1).


The regularities in the generating flats and in the roughness lines are the sources  of certain noise excitations. The frequencies induced can be high multiples of the tooth  mesh frequency, but are often also reflected in the first three mesh harmonics. Figure 2  shows in an exaggerated way the generating flats and the tracks of the tool roughness.  In grinding, the generating flats are very small, but the grinding grain tracks are  dominating with respect to surface roughness.


Generating flats in grinding, however, are theoretically non- existent because the  grinding wheel surface represents a microscopic cutting edges. But practical experience  teaches us differently. The explanations for those generating marks are the texture on  the grinding wheel surface, run out and imbalance in the grinding wheel, and  inaccuracies caused by the wheel dressing cycle. In addition to the wheel-based effects, the machine movements could also cause generating marks. The part program that  consists of basic settings is converted into a table of axis positions; i.e. — it can be  visualized as several hundred lines, where each line has a position value for each axis  of the free form machine (X, Y, Z, A, B and C). As the machine moves from one line of  axis positions to the next, the controller software tries to connect the discrete positions  with a smoothing function. However, the machine might pause for some milliseconds  in each position and generate a “microflat.” Figure 1 shows a tooth surface with a  number of microflats, which is in reality a factor of 10 higher then shown. Each flat has a  cone envelope function that can be modified in different ways.


Until today, no attention had been paid to the fact that not only are the microflats  consistent with the timing of each tooth.


image

Figure 1 Micro flats on a ground flank  surface under inclination angle at.


image

Figure 2 Generating flats and grinding wheel  roughness traces.


mesh, but also with each other imperfection as well as desired flank surface 

modifications such as UMC relief section and, for example, Flankrem are located along 

the path of meshing at the same roll position. The roll positions of each tooth around the 

circumference of a gear repeat with a phase shift from tooth to tooth which is equal to 

one pitch:

qi = q1 + i * 360°/z 

where: 

(1) qi particular roll position; e.g. start roll position on tooth i 

q1 particular roll position on tooth number 1 

i number of any chosen tooth on observed gear → {1 ≤ i ≥ z} 

z number of teeth of observed gear


All disturbances or dynamic events that repeat from tooth to tooth during the operation  of a gear set will repeat, depending on the manufacturing tolerances very precisely to  one pitch. The consequence of this is, for example, that flats or imperfections will  generate audible sound with a frequency equaling the number of their occurrence per  tooth mesh, multiplied with the fundamental tooth mesh frequency. It is worth  mentioning that such frequencies that are commonly between two and twelve times the  tooth mesh frequency will also increase the intensity of the amplitude of the tooth mesh  frequency.


Previous: Gearshaft : Analysis Of Secondary Machine Elements

Next: Length And Profile Crowning Of Usable Bevel Gearset Development

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