By William D. Mark

A mathematically rigorous rationalization of ways production deviations and harm at the operating surfaces of drugs enamel reason transmission-error contributions to vibration excitations

Some gear-tooth working-surface production deviations of important amplitude reason negligible vibration excitation and noise, but others of minuscule amplitude are a resource of important vibration excitation and noise.   Presently on hand computer-numerically-controlled committed apparatus metrology apparatus can degree such blunders styles on a apparatus in a couple of hours in enough element to permit actual computation and analysis of the ensuing transmission-error vibration excitation.   How to successfully degree such working-surface deviations, compute from those measurements the consequent transmission-error vibration excitation, and diagnose the producing resource of the deviations, is the topic of this book. 

Use of the expertise during this publication will enable caliber spot assessments to be made on gears being synthetic in a construction run, to prevent bad vibration or noise excitation via the synthetic gears.  moreover, these operating in academia and wanting an entire mathematical knowing of the relationships among the teeth working-surface deviations and the vibration excitations brought on by those deviations will locate the ebook fundamental for functions touching on either gear-quality and gear-health monitoring.

Key features:

  • Provides a really effective approach for measuring parallel-axis helical or spur gears in adequate aspect to permit exact computation of transmission-error contributions from working-surface deviations, and algorithms required to hold out those computations, together with examples
  • Provides algorithms for computing the working-surface deviations inflicting any user-identified tone, reminiscent of ‘ghost tones,’ or ‘sidebands’ of the tooth-meshing harmonics, permitting analysis in their production motives, together with examples
  • Provides causes of all harmonics saw in gear-caused vibration and noise spectra.
  • Enables new release of three-d screens and specified numerical descriptions of all measured and computed working-surface deviations, together with examples
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Additional info for Performance-Based Gear Metrology: Kinematic - Transmission - Error Computation and Diagnosis

Sample text

17b), no single term characterized by the index pair k, can provide a contribution to any other term characterized by another index pair, even if one of the two indices of the two pairs of indices is the same. 18). 1 (Mark, 1979, 1982). 7. Note that our sign convention defines a positive value of tooth deviation ηCj (y, z) as ‘‘removal’’ of material from a perfect involute surface. Hence, the terms k = 2, = 0 and k = 0, = 2 showing negative values at the center of the spans therefore describe positive fullness because of the sign convention of ηCj (y, z).

5, construct a normal to the plane of contact that passes through the shaft center of the lower gear (2), shown dashed. This dashed normal intersects the plane of contact at the point of tangency between the plane of contact and the lower base cylinder. The length of the normal is the base-cylinder radius Rb , whereas the distance between the shaft center of the lower gear and the pitch point is the pitch-cylinder radius Rp . Moreover, the angle between the dashed normal and the line connecting shaft centers is φ, the pressure angle.

D. (2003) Gear Noise and Vibration, 2nd edn, Marcel Dekker, New York. 2 Parallel-Axis Involute Gears Virtually all present-day parallel-axis gears utilize the involute tooth form. Meshinggear-pairs with rigid equispaced perfect involute teeth would transmit exactly constant speed ratios resulting in zero transmission error. Because the subject of this book is computation of the kinematic transmission-error contributions arising from geometric deviations of the working surfaces of the teeth from equispaced perfect involute surfaces, it is appropriate to describe in this chapter the geometric properties of the equispaced perfect involute tooth-working-surfaces of parallel-axis helical gears that these geometric deviations can depart from.

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