The optimal design of standard gearsets

A design procedure for sizing standard involute spur gearsets is presented. The procedure is applied to find the optimal design for two examples - an external gear mesh with a ratio of 5:1 and an internal gear mesh with a ratio of 5:1. In the procedure, the gear mesh is designed to minimize the center distance for a given gear ratio, pressure angle, pinion torque, and allowable tooth strengths. From the methodology presented, a design space may be formulated for either external gear contact or for internal contact. The design space includes kinematics considerations of involute interference, tip fouling, and contact ratio. Also included are design constraints based on bending fatigue in the pinion fillet and Hertzian contact pressure in the full load region and at the gear tip where scoring is possible. This design space is two dimensional, giving the gear mesh center distance as a function of diametral pitch and the number of pinion teeth. The constraint equations were identified for kinematic interference, fillet bending fatigue, pitting fatigue, and scoring pressure, which define the optimal design space for a given gear design. The locus of equal size optimum designs was identified as the straight line through the origin which has the least slope in the design region

An update on the life analysis of spur gears

An analytical method for predicting surface fatigue life of gears was presented. General statistical methods were outlined, showing the application of the general methods to a simple gear mesh. Experimentally determined values for constants in the life equation were given. Comparison of the life theory with test results and AGMA standards was made. Gear geometry pertinent to life calculations was reviewed

Exploiting correlogram structure for robust speech recognition with multiple speech sources

This paper addresses the problem of separating and recognising speech in a monaural acoustic mixture with the presence of competing speech sources. The proposed system treats sound source separation and speech recognition as tightly coupled processes. In the first stage sound source separation is performed in the correlogram domain. For periodic sounds, the correlogram exhibits symmetric tree-like structures whose stems are located on the delay that corresponds to multiple pitch periods. These pitch-related structures are exploited in the study to group spectral components at each time frame. Local pitch estimates are then computed for each spectral group and are used to form simultaneous pitch tracks for temporal integration. These processes segregate a spectral representation of the acoustic mixture into several time-frequency regions such that the energy in each region is likely to have originated from a single periodic sound source. The identified time-frequency regions, together with the spectral representation, are employed by a `speech fragment decoder' which employs `missing data' techniques with clean speech models to simultaneously search for the acoustic evidence that best matches model sequences. The paper presents evaluations based on artificially mixed simultaneous speech utterances. A coherence-measuring experiment is first reported which quantifies the consistency of the identified fragments with a single source. The system is then evaluated in a speech recognition task and compared to a conventional fragment generation approach. Results show that the proposed system produces more coherent fragments over different conditions, which results in significantly better recognition accuracy

The optimal design of involute gear teeth with unequal addenda

The design of a gear mesh is treated with the objective of minimizing the gear size for a given gear ratio, pinion torque, pressure angle, and allowable tooth lengths. Tooth strengths considered include scoring, pitting fatigue, and bending fatigue. Kinematic involute interference is avoided. The design variation on standard spur gear teeth called the long and short addendum system, is considered. In this system the mesh center distance and pressure angle are maintained as is the ability to manufacture the teeth with standard tooling. However, the pinion and gear tooth proportions are altered in order to obtain fewer teeth numbers for the same ratio as standard gears without kinematic involute interference. The effect of this nonstandard gearing geometry with on tooth strengths and gear mesh size are studied. For a 2:1 gearing ratio, the optimal nonstandard gear design is compared with the optimal standard gear design

Dynamic Capacity and Surface Fatigue Life for Spur and Helical Gears

A mathematical model for surface fatigue life of gear, pinion, or entire meshing gear train is given. The theory is based on a previous statistical approach for rolling-element bearings. Equations are presented which give the dynamic capacity of the gear set. The dynamic capacity is the transmitted tangential load which gives a 90 percent probability of survival of the gear set for one million pinion revolutions. The analytical results are compared with test data for a set of AISI 9310 spur gears operating at a maximum Hertz stress of 1.71 billion N/sq m and 10,000 rpm. The theoretical life predictions are shown to be good when material constants obtained from rolling-element bearing tests were used in the gear life model

Experimental and Analytical Load-Life Relation for AISI 9310 Steel Spur Gears

Life tests were conducted at three different loads with three groups of 8.9 cm pitch diameter spur gears made of vacuum arc remelted VAR AISI 9310 steel. Life was found to vary inversely with load to the 4.3 and 5.1 power at the L10 sub and L50 sub life levels, respectively. The Weibull slope varied linearly with maximum Hertz contact stress, having an average value of 2.5. The test data when compared to AGMA standards showed a steeper slope for the load-life diagram

NASA transmission research and its probable effects on helicopter transmission design

Transmissions studied for application to helicopters in addition to the more conventional geared transmissions include hybrid (traction/gear), bearingless planetary, and split torque transmissions. Research is being performed to establish the validity of analysis and computer codes developed to predict the performance, efficiency, life, and reliability of these transmissions. Results of this research should provide the transmission designer with analytical tools to design for minimum weight and noise with maximum life and efficiency. In addition, the advantages and limitations of drive systems as well as the more conventional systems will be defined

OH-58 helicopter transmission failure analysis

The OH-58 main transmission gearbox was run at varying output torques, speeds, and oil cooling rates. The gearbox was subsequently run to destruction by draining the oil from the gearbox while operating at a speed of 6200 revs per minute and 36,000 inch-pounds output torque. Primary cause of gearbox failure was overheating and melting of the planet bearing aluminum cages. Complete failure of the gearbox occurred in 28 1/2 minutes after the oil pressure dropped to zero. The alternating and maximum stresses in the gearbox top case were approximately 10 percent of the endurance limit for the material. Deflection of the bevel gear at 67000 inch-pounds output torque indicate a marginal stiffness for the bevel gear supporting system

Gearing

Gearing technology in its modern form has a history of only 100 years. However, the earliest form of gearing can probably be traced back to fourth century B.C. Greece. Current gear practice and recent advances in the technology are drawn together. The history of gearing is reviewed briefly in the Introduction. Subsequent sections describe types of gearing and their geometry, processing, and manufacture. Both conventional and more recent methods of determining gear stress and deflections are considered. The subjects of life prediction and lubrication are additions to the literature. New and more complete methods of power loss predictions as well as an optimum design of spur gear meshes are described. Conventional and new types of power transmission systems are presented

Minimization of the vibration energy of thin-plate structure

An optimization method is proposed to reduce the vibration of thin plate structures. The method is based on a finite element shell analysis, a modal analysis, and a structural optimization method. In the finite element analysis, a triangular shell element with 18 dof is used. In the optimization, the overall vibration energy of the structure is adopted as the objective function, and it is minimized at the given exciting frequency by varying the thickness of the elements. The technique of modal analysis is used to derive the sensitivity of the vibration energy with respect to the design variables. The sensitivity is represented by the sensitivities of both eigenvalues and eigenvectors. The optimum value is computed by the gradient projection method and a unidimensional search procedure under the constraint condition of constant weight. A computer code, based on the proposed method, is developed and is applied to design problems using a beam and a plate as test cases. It is confirmed that the vibration energy is reduced at the given exciting frequency. For the beam excited by a frequency slightly less than the fundamental natural frequency, the optimized shape is close to the beam of uniform strength