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The theory of calculating the curvature interference limit line of the offset involute cylindrical worm drive based on the singular point condition on the enveloping surface is established. The tooth surface equations and the meshing function of the worm drive are derived. Based on the singular point condition that the normal vector of the enveloping surface is zero, the equation of the curvature interference limit line is obtained. By employing the resultant elimination method and the geometric construction, the existence of the solutions of the curvature interference limit line is determined, and the reasonable initial values for the iteration program are afforded. The numerical outcomes show that there is one meaningful curvature interference limit line on each flank of single tooth of the worm gear, which usually does not enter the worm gear tooth surface. Both flanks of the worm gear are all settled in the side of the limit line, the curvature interference does not happen on the worm gear tooth surface. The undercutting of the cutting engagement process generally does not happen. The results also reveal that the curvature interference limit line is closer to the addendum and heel of the face worm gear on the i flank, which has the greatest potential venture inflict the undercutting. [ABSTRACT FROM AUTHOR]

The main purpose of this article is to establish the meshing theory for the offsetting Archimedes cylindrical worm drive, which consists of a cylindrical worm with asymmetric tooth profile and a plane worm gear. The equations of the tooth surfaces, the meshing function, the curvature interference limit function, and the curvature parameters are all obtained for the worm drive. By means of the developed reference-point-based meshing theory, the reference point located strictly on the tooth surfaces of a worm drive is determined via solving the system of nonlinear equations, in which no iteration is needed to perform this process. Based on the location of the reference point, the tooth surface boundaries are ascertained for the plane worm gear. The numerical case is carried out and the conjugate zone, the instantaneous contact lines, and the local meshing property parameters are acquired for the worm drive. The whole thread length of the cylindrical worm can almost be used and the conjugate zone can cover the whole tooth surface of the mating plane worm gear. In the meshing zone, not only the contact stress level between the tooth surfaces is relatively low, but also the lubrication condition is favorable. The comparative study on the meshing properties between the offsetting Archimedes cylindrical worm drive and the Archimedes conical worm drive is carried out. [ABSTRACT FROM AUTHOR]

Based on the lubrication angle field and the locus of lubricating weak point, the lubricating characteristic of the toroidal surface enveloping cylindrical worm drive is globally investigated. The nonlinear equation system to determine the lubricating weak point is established by utilising the lubrication angle. Generally speaking, the weak locus always exists roughly in the middle of the tooth surface of cylindrical wormgear and a zone with worse lubricating behaviour is around the locus. By increasing the number of worm thread, the locus of lubricating weak point can be completely removed from the wormgear tooth surface, and the locus approximately is in the shape of the inverse capital letter L. On this occasion, the entire wormgear tooth surface is half surrounded by the locus, and the overall lubrication performance of the worm drive is improved. The current research is an application of elastohydrodynamic lubrication (EHL) on worm drive. [ABSTRACT FROM AUTHOR]

The reliability and the reliability sensitivity of a cylindrical worm drive are considered in the present paper. To estimate them, some new mathematical methods are proposed. Depending on these approaches, a practical and simple technique to perform the estimation is taken shape. The application of such technique does not require knowing the probability distributions of the basic design parameters. The evaluation can be implemented so long as the mean values and the variances of the basic design arguments are known. In the bargain, the situation that the standardized random variable obeys an arbitrary probability distribution can be handled by taking advantage of the technique suggested as well. The numerical results show that the traditional excogitation methodology can in general give a favorable outcome with higher reliability. Generally speaking, as for an enclosed cylindrical worm gearing, the contact fatigue reliability is usually, more or less, higher than the bending fatigue reliability. In addition increasing the center distance and the module is beneficial to improve the reliability. Meanwhile the greater variance of the design parameters may lead to lower reliability as to a worm gear pair. [ABSTRACT FROM AUTHOR]

• The formation principle of the conjugate tooth surface couple is fully investigated. • The kinematic theory is established for the point-conjugate gear drive. • The mixed mismatched conical worm drive that is easy to be machined is proposed. • The kinematic meshing quality is investigated for the worm drive systematically. • The vibration and impact caused by the mismatch are weak for the worm drive. The kinematics is developed and investigated deeply for the point-conjugate tooth surface couple. The formation principle of the conjugate tooth surface couple is studied by means of the kinematics, and the formation mechanism and law are revealed. The kinematic theory is established for the point-conjugate gear drive to measure its motion stability, in which the method to compute the angular acceleration of the driven gear is presented in detail. A novel kind of crossed-axis gearing that is convenient to be machined is proposed and named the mixed mismatched conical worm drive. The kinematic meshing quality is investigated for the worm drive by applying the established kinematic theory. The numerical results reflect that the transmission error of the worm drive is little and the adjacent error curves are intersectant. The angular acceleration of the worm gear is extremely small, and therefore the vibration and impact caused by the mismatch are weak for the worm drive. It is more reasonable that the curve of transmission error of the worm drive is a high-order polynomial curve since the angular acceleration is not constant. [ABSTRACT FROM AUTHOR]

Abstract: In the present paper, the tooth contact characteristics and the error sensitivity of the ease-off dual-torus double-enveloping hourglass worm drive (the DTT worm drive) are considered. The ease-off hourglass worm drive is composed of a standard hourglass worm and a modified worm wheel. In order to determine the instantaneous contact point of the mismatched worm pair, the two-stage downhill secant method (the TSDS method) is proposed to be used for solving the nonlinear contact equations. Roughly speaking, the main merits of the TSDS method are lower sensitivity to the initial guess, without a request for computing the Jacobi matrix and no singularity near the genuine solution. After ascertaining the transient contact point, the momentary contact ellipse, the instantaneous transmission ratio and some other tooth contact features are worked out by means of an improved local synthesis approach, which is proposed for point contact gear drives in this article. The results of computerized simulation show that, the mismatched worm gear set is able to accomplish desirable point contact, and has respectable load carrying capacity. On the other hand, the mismatched worm gearing is insensitive to the alignment errors, and its property of the transmission error is advantageous to reduce the noise and vibration. [Copyright &y& Elsevier]

The present study is an application of elastohydrodynamiclubrication (EHL) theory on a new type of toroidal worm drive with concave worm profile, ground by a grinding wheel whose profile consists of two circular arcs. The EHL analysis is focused on the minimum oil-film thickness and entraining geometry. When a primary geometric design is made for a worm set, many factors, except speed and contact geometry, are very difficult to know exactly. For this reason, a method is proposed to evaluate the minimum EHL oil-film thickness indirectly but conveniently in the whole contact area. Parallel research of the entraining geometry for this type of worm pair has been accurately carried out by using the theory of gearing. On the basis of the theory established, the EHL characteristics of the recommended worm pair are discussed in detail by means of computerized simulation approach. Obtained results show that this kind of hourglass worm pair has preferable EHL performance because favorable unification is embodied in terms of the forming condition of oil-film and its thickness within the whole contact area. [ABSTRACT FROM AUTHOR]

• A novel meshing theory of the involute worm drive is built by geometry. • It is proved that the helical surface with constant helix parameter ground by plane is an involute helical surface. • The prove complements the principle for grinding the involute worm with the planar grinding wheel. • The meshing performance of the involute worm drive is studied in depth. • The calculation methods of meshing performance for involute worm drive are proposed. The subject of this paper is the establishment of a new meshing theory applicable to the involute worm drive. The method is proposed for determining the meshing characteristic parameters of the involute worm drive using the principal frame on the involute helicoid. A rigorous proof is presented to prove that a helicoid with constant helix parameter ground by a planar grinding wheel is an involute helicoid employing the uniqueness theorem for surfaces in differential geometry. The relationship among the helix angle of base circle, normal pressure angle and helix angle for the involute worm is proved. Using the proposed meshing theory, the numerical simulation of the involute worm drive is carried out to investigate the meshing performance of the involute worm drive. The numerical results reflect that the conjugate zone covers almost the entire worm gear tooth surface. The contact frequency is higher on one side of the worm gear tooth surface. The contact stress is higher near the end face of worm gear. An area of poor lubrication exists in the middle of the worm gear tooth surface. [ABSTRACT FROM AUTHOR]