Engineering topics
Publications and source records attributed to Anderson, W. J..
The equations for the displacement, velocity, and acceleration of a point in a nutating body are developed. These are used to derive equations for the inertial moment developed by a nutating body of arbitrary shape. Calculations made for a previously designed nutating plate transmission indicate that that device is severely speed limited because of the very high magnitude inertial moment.
Some of the research conducted which has brough rolling-element technology to its present state is discussed. Areas touched upon are material effects, processing variables, operating variables, design optimization, lubricant effects and lubrication methods. Finally, problem areas are discussed in relation to the present state-of-the-art and anticipated requirements.
A description is given of an antifriction bearing and a process by which its fatigue life may be extended. The method involves a rotating shaft supported by a fluid bearing and a rolling element bearing coupled in series. Each bearing turns at a fraction of the rotational speed of the shaft. The fluid bearing is preferably conical, thereby providing thrust and radial load support in a single bearing structure.
Some of the research conducted which has brought rolling-element technology to its present state is discussed. Areas touched upon are material effects, processing variables, operating variables, design optimization, lubricant effects and lubrication methods. Finally, problem areas are discussed in relation to the present state-of-the-art and anticipated requirements.
Foil bearings were designed and fabricated to replace pivoted-shoe journal bearings in a Brayton cycle turboalternator, within space limitations and constraints imposed by the existing machine. The foil bearings were integrated into a unified assembly with the rotor, housing, seals, and gimbal-mounted thrust bearing, without changes and modifications of machine components other than the journal bearings. The gas-lubricated foil bearings, which require no external pressure-source, furnished a stable support for a 21.9 pound rotor in the vertical attitude at speeds to 43,200 rpm. Excellent wipe-wear characteristics permitted well over 1000 start-stop cycles, without deterioration of performance in the entire speed range. The paper reviews salient aspects of design, fabrication, and performance. An account is given of rotor dynamics during starting, stopping, and traversing the region of resonances. The state of journal and foil surfaces is examined following intensive start-stop cycling and high-speed runs over extended periods of time.
Thrust-load analysis of a 150-mm angular contact ball bearing, taking into account centrifugal forces but omitting gyroscopics, elastohydrodynamics, and thermal effects. A Newton-Raphson method of iteration is used to evaluate the radial and axial projection of the distance between the ball center and the outer raceway groove curvature center. Fatigue life of the bearing is evaluated. Results for life, contact loads, and angles are given for a conventional bearing and two arched bearings.
A first-order thrust load analysis that considers centrifugal forces but which neglects gyroscopics, elastohydrodynamics, and thermal effects was performed. The analysis was applied to a 150-mm-bore angular-contact ball bearing. Fatigue life, contact loads, and contact angles are shown for conventional and arched bearings. The results indicate that an arched bearing is highly desirable for high-speed applications. In particular, at an applied load of 4448 n (1000 lb) and a DN value of 3 million (20,000 rpm) the arched bearing shows an improvement in life of 306 percent over that of a conventional bearing.
A Newton-Raphson method of iteration was used in evaluating the radial and axial projection of the distance between the ball center and the outer raceway groove curvature center (V and W). Fatigue life evaluations were made. The similar analysis of a conventional bearing can be directly obtained from the arched bearing analysis by simply letting the amount of arching be zero (g = 0) and not considering equations related to the unloaded half of the outer race. The analysis was applied to a 150-mm angular contact ball bearing. Results for life, contact loads, and angles are shown for a conventional bearing (g = 0) and two arched bearings (g = 0.127 mm (0.005 in.), and 0.254 mm (0.010 in.)). The results indicate that an arched bearing is highly desirable for high speed applications. In particular, for a DN value of 3 million (20,000 rpm) and an applied axial load of 4448 N (1000 lb), an arched bearing shows an improvement in life of 306 percent over that of a conventional bearing. At 4.2 million DN (28,000 rpm), the corresponding improvement is 340 percent. It was also found for low speeds, the arched bearing does not offer the advantages that it does for high speed applications.
Optimized series-hybrid fluid-film ball bearings are described and operating characteristics are calculated and discussed. It is predicted that a series-hybrid bearing may be constructed which will reduce ball-bearing speed by 30 percent thereby increasing bearing fatigue life by factors of up to 5.9. Flow rates required are less than 9 kilograms per minute.
The series-hybrid bearing couples a fluid-film bearing with a rolling-element bearing such that the rolling-element bearing inner race runs at a fraction of shaft speed. A series-hybrid bearing was analyzed and experiments were run at thrust loads from 100 to 300 lb and speeds from 4000 to 30,000 rpm. Agreement between theoretical and experimental speed sharing was good. The lowest speed ratio (ratio of ball bearing inner-race speed to shaft speed) obtained was 0.67. This corresponds to an approximate reduction in DN value of 1/3. For a ball bearing in a 3 million DN application, fatigue life would theoretically be improved by a factor as great as 8.
Equations for the flow rate, load capacity, and friction torque for a conical hydrostatic bearing were developed. These equations were solved by a digital computer program to determine bearing configurations for minimum friction torque. Design curves are presented that show optimal bearing dimensions for minimum friction torque as a function of dimensionless flow rate for a range of dimensionless load capacity. Results are shown for both laminar and turbulent flow conditions. The results indicate that hydrostatic pocket friction is a significant portion of the total friction torque. However, the bearing dimensions for a minimum friction design are affected very little by inclusion of pocket friction in the analysis. For laminar flow the values of the outer-land radius ratio X3 and outer bearing radius ratio X4 did not change significantly with increasing friction factor. For turbulent flow, the outer bearing radius ratio X4 did not change with increasing friction factor; therefore the value determined for X4 in the laminar flow case is valid for all turbulent flows.
Flexible rotor balancing by exact point speed influence coefficient method
Herringbone grooved gas lubricated journal bearing load capacity, attitude angle and power loss measurements
Fluid film bearing of hybrid device consists of orifice compensated annular thrust bearing and self-acting journal bearing. In series hybrid bearing, both ball bearing and annular thrust bearing carry full system thrust load, but two bearings share speed. Operation of system is stable and automatically fail-safe.
Equations for flow rate, load capacity, and friction torque for conical hydrostatic bearings under laminar and turbulent flow conditions
Performance of high speed bearings with cylindrically hollow balls
Conical hydrostatic bearing optimal dimensions for friction reduction based on laminar and turbulent flow velocity, load capacity, and friction torque calculations
Evaluating series hybrid bearing concept by testing lubricated fluid film thrust bearing at high speed