Changhou Lu

Averaging Effect on Pitch Errors in Hydrostatic Lead Screws With Continuous Helical Recesses

The motion errors of hydrostatic lead screws can be smaller than the pitch errors due to the averaging effect of oil films, which is the so-called averaging effect on the pitch errors (AEPE). This paper investigates the factors influencing AEPE under low speeds and a constant external load. An equivalent model of hydrostatic lead screws with continuous helical recesses is established, and the axial motion errors of the nut are obtained by combining the dichotomy and finite difference methods. The results show that (a) the motion errors caused by the pitch errors of the lead screw have additivity, and the pitch errors of the nut have little influence on the motion errors, (b) when the lead screw only has cumulative pitch errors, the motion errors are equal to the average value of the cumulative pitch errors located on the two flank surfaces of the lead screw, and (c) when the lead screw only has periodic pitch errors, the number of nut threads with helical recesses n and the period of the pitch errors of the lead screw T are the main influencing factors on AEPE.

Study on movement forming methods for the machining of elliptic-shaped holes

The movement forming methods for the machining of elliptic-shaped holes are presented. These methods can make the tool nose orbit, which is the synthesis of revolution of the hydrostatic shaft center around bearing center and rotation of the tool nose around shaft center, become an ellipse. Thus, the machining of elliptical holes can be achieved. Necessary conditions and sufficient conditions for forming elliptic tool nose orbit, under the condition that multiple shaft center orbits and the tool nose’s rotation orbit take synchronous forward synthesis and synchronous backward synthesis, are studied. The influence of initial phase angle of the tool nose on the formation of elliptic tool nose orbit has also been investigated. Characteristics and control equations of elliptic tool nose orbit under the conditions of multiple shaft center orbits and different initial phase angles of the tool nose are given. These studies will lay a theoretical foundation for the realization of the movement forming methods. Traditional machining methods for elliptic-shaped holes require auxiliary feed mechanism installed on the machine tool, and machining efficiency is limited by the frequency response characteristic of the servo bar. The forming methods presented in this article can overcome these shortcomings and provide a new approach for precision machining of elliptic-shaped holes.

Numerical analysis on the static performance of a new piezoelectric membrane restrictor

Purpose This paper aims to establish an accurate mathematical model of a piezoelectric membrane restrictor that can be applied to control the shaft’s centerline orbit. Design/methodology/approach The methodology uses three coupled equations to establish a mathematical model of the piezoelectric membrane restrictor – Reynolds equation, the membrane deformation equation and the flow rate equation. A data identification method is used to propose the flow rate formulas for the piezoelectric membrane restrictor. Findings It has been found that the structural parameters, the membrane center deformation and the inlet and outlet pressures of the piezoelectric membrane restrictor have an effect on the static performance of the restrictor. The identified flow rate result of the piezoelectric membrane restrictor is consistent with the models. Originality/value The paper provides an accurate mathematical model of the piezoelectric membrane restrictor which can also be applied to other membrane restrictors.

Open-loop control of elliptical shaft center orbit:

In order to realize the machining of elliptical holes, the article researches control simulation of shaft center movement orbit using Eulerian method. A new hydrostatic bearing and a hydraulic control system are proposed, and quantitative relation between the expected shaft center coordinates and spool displacement of electro-hydraulic servo valve is studied. With the Eulerian method, open-loop control orbit of shaft center is simulated. And the simulation results indicate that open-loop control method not only controls shaft center movement to form ellipse orbits but also has strong robustness against dynamic disturbing force or instantaneous static disturbing force. This article lays theoretical basis for machining of elliptical holes.

An accurate method for determination of the performance characteristics of membrane-type restrictors:

The determination of flow rate and fluid resistance for membrane-type restrictors is modified in this paper, and it can be more accurate and confident from the measurements in experiments. Three coupled equations including Reynolds equation, membrane deformation equation of large axisymmetric deflection and flow rate equation have been used to establish the mathematical model of membrane-type restrictor and solved simultaneously. Several cases are simulated by the traditional method and the modified numerical method, and the simulation results are compared with experimental data for flow rates and fluid resistances. It has been found that the determination of the performance characteristics of membrane-type restrictors is significantly affected by the hypotheses of membrane deflection scales, the pressures distribution and the gap height between the sill and membrane. The numerical results of the modified method are much more approximated to the actual flow rate measured in Kang et al.’s work than those of the traditional formula, and the proposed method can increase the determination accuracy of the flow rate and restriction coefficient in the design of membrane-type restrictors distinctly.

Performance Analysis of Capillary-Compensated Hydrostatic Lead Screws with Discontinuous Helical Recesses Including Influence of Pitch Errors in Nut

ABSTRACT This article investigates the axial static and dynamic characteristics of capillary-compensated hydrostatic lead screws with discontinuous helical recesses considering the influence of the pitch errors of the nut. The mathematical model is based on the Reynolds equation, including rotational lubricant inertia and the flow continuity equation. The finite difference method and the perturbation technique are applied. The results show that the pitch errors cause the inequality of recess pressures on the same flank surface of the nut thread; the influence of pitch errors on the axial load capacity is not significant within the dimensionless axial displacement of the nut of 0.6, but the effect on the axial stiffness and damping coefficients is significant under larger axial displacement.