The use of face gears in helicopter transmissions was explored. A light-weight, split torque transmission design utilizing face gears was described. Face-gear design and geometry were investigated. Topics included tooth generation, limiting inner and outer radii, tooth contact analysis, contact ratio, gear eccentricity, and structural stiffness. Design charts were developed to determine minimum and maximum face-gear inner and outer radii. Analytical study of transmission error showed face-gear drives were relatively insensitive to gear misalignment, but tooth contact was affected by misalignment. A method of localizing bearing contact to compensate for misalignment was explored. The proper choice of shaft support stiffness enabled good load sharing in the split torque transmission design. Face-gear experimental studies were also included and the feasibility of face gears in high-speed, high-load applications such as helicopter transmissions was demonstrated.

With the advent of new routing methods, the distance to which a message is sent is becoming relatively less and less important. Thus, assuming no link contention, permutation seems to be an e cient collective communication primitive. In this paper we present several algorithms for decomposing all-to-many personalized communication into a set of disjoint partial permutations. We discuss several algorithms and study their e ectiveness from the view of static scheduling as well as runtime scheduling. An approximate analysis shows that with n processors and assuming that every processor sends and receives d messages to random destinations, our algorithm can perform the scheduling in O(dn ln d) time on an average, and use an expected number of d + log d partial permutations to carry out the communication. We present experimental results of our algorithms on the CM-5.

The deviations of a gear’s real tooth surface from the theoretical surface are determined by coordinate measurements at the grid of the surface. A method has been developed to transform the deviations from Cartesian coordinates to those along the normal at the measurement locations. Equations are derived that relate the first order deviations with the adjustment to the manufacturing machine-tool settings. The deviations of the entire surface are minimized. The minimization is achieved by application of the least-square method for an overdetermined system of linear equations. The proposed method is illustrated with a numerical example for hypoid gear and pinion.