Worm Gear Set Research Articles

113 高性能小型鼓形ウォームギヤの研究(第 1 報)

Theory and production method of Hourglass worm gear of small size with a high performance are proposed. Wheel tooth is involute helical gear of this worm gear and pinion cutter generates worm tooth. This worm gear set is produced and contact mark is coinciding well with the theory.

Effects of profile shifted factor and pressure angle on the ZK-type dual-lead worm gear drives

In the light of a mathematical model of the ZK-type dual-lead worm gear set proposed in the authors’ recent work, this study adopts tooth contact analysis to compute the kinematic errors, instantaneous contact teeth (ICT) and average contact ratios (ACR). An elastic deformation of 3 μm is allowed while calculating ICT and ACR. In addition, increasing the ICT from three to four or from four to five reduces the root stress of the gear set due to its multiple contact teeth. Although a worm gear driven with a small pressure angle can increase the ICT, a worm gear with a small pressure angle incurs a more serious undercutting phenomena. Undercutting can also be averted by applying a positive-shifted modification of the hob cutter during the worm gear generation. Moreover, the boundary of conjugate and non-conjugate surface regions appears on the worm gear tooth surface when the worm gear has a low pressure angle. The non-conjugate region also influences the transmission efficiency, operational life time and noise of the worm gear drive. Furthermore, worm gear generation with a negative-shifted modification can decrease the unfavorable non-conjugate region.

GDS-9 A STUDY ON THE MANUFACTURING OF THE HOURGLASS WORM GEAR SET(GEAR DESIGN AND SYNTHESIS)

GDS-9 A STUDY ON THE MANUFACTURING OF THE HOURGLASS WORM GEAR SET(GEAR DESIGN AND SYNTHESIS)

Mathematical model and bearing contacts of the ZN-type worm gear set cut by oversize hob cutters

The ZN-type oversize hob cutter for cutting of worm gears is investigated. The mathematical model of the ZN-type worm gear set is developed based on the cutting mechanism and hob cutter parameters. Influences of oversize hob cutter regrinding, worm-thread number and assembly errors on the bearing contacts and kinematical errors of the ZN-type worm gear set are investigated. A numerical example is given to demonstrate the bearing contacts and kinematical errors of the worm gear set.

Object-Oriented Modelling Technique Applicable To Worm Gear Set Development

This paper investigates how the object-oriented modelling technique can be applied to simulate the worm gear set design procedure, man-ufacturing process, and tooth contact analysis (TCA). An abstract worm base class containing some basic worm dimensions is constructed, and then an abstract worm gear class is derived from the worm class. Based on the developed abstract worm and worm gear classes, classes for the ZN-type, ZE-type, and ZK-type worm and worm gear can be generated. By exploiting object-oriented technique, the authors also develop a TCA program to simulate all possible worm gear set combinations. Finally, the TCA for any type worm and worm gear combination can be simulated by suitably setting worm and worm gear objects into the TCA program. The operating system Windows 95 is the designated platform and Visual C++ 4.0 is the implementation language.

ZK-Type Dual-Lead Worm and Worm Gear Drives: Contact Teeth, Contact Ratios and Kinematic Errors

Contact ratio is an important gear design parameter for gear bending and contact stresses. A higher contact ratio may reduce the stresses and kinematic errors of the gear set. In this study, we calculate the kinematic error of the ZK-type dual-lead worm gear set by applying the tooth contact analysis (TCA) method. Two kinds of contact ratios, the instantaneous contact teeth (ICT) and the average contact ratio (ACR), are investigated and calculated by applying TCA method. ICT is an important design parameter for a dual-lead worm gear set when the gear set is used in a machine subjected to large impact forces. ACR is also a useful design factor for assessing gear tooth strength and dynamic load. If gear surface elastic deformation 3μm is allowed for the worm gear set, the ICT may have 2, 3 or 4 teeth and the ACR reveals that the ZK-type dual-lead worm gear drive is a high-contact-ratio gear set. It is found that this type of worm gear set with a shorter center distance assembly can increase the value of ACR during the gear meshing. Illustrative examples presented herein demonstrate the effects of gear parameters on contact teeth, contact ratios, average contact ratios and kinematic errors under various conditions.

ZK-Type Dual-Lead Worm and Worm Gear Drives: Geometry

A dual-lead worm gear set is frequently used for machines to operate without backlash, which can be adjusted along the worm’s axial direction. The ZK-type dual-lead worm is generated by a cone-type straight-edged grinding wheel while an oversize worm-type hob cutter cuts the worm gear. The dual-lead worm gear set has two different axial modules and helix angles for the right- and left-side tooth surfaces. The mathematical model involving ZK-type dual-lead worm and worm gear surface geometries is developed based on the theory of gearing and gear cutting mechanism. According to the proposed mathematical model, computer graphs of the ZK-type dual-lead worm gear drives have been presented. Coordinates of the meshed grid-point on gear drive surfaces can thus be determined by applying the numerical method. Undercutting of the worm gear surface has been investigated based on the theory of gearing and the developed gear set mathematical model. The gear set mathematical model developed herein can facilitate gear set tooth contact analysis, contact teeth, contact ratio and other advanced investigations.

Effects of the hob cutter regrinding and setting on ZE-type worm gear manufacture

A mathematical model for a ZE-type worm gear set is proposed. The characteristics of a ZE-type worm gear cut with an oversize hob cutter are investigated. Bearing contacts and kinematic errors in the ZE-type worm gear set due to regrinding of oversize hob cutters are also studied. Bearing contacts in the worm gear set were obtained using surface separation topology techniques and tooth contact analysis. It was found that bearing contact locations are sensitive to the hob cutter setting angle and setting distance. Kinematic error minimization was achieved modifying worm normal tooth angle. By applying the optimization theorem and computer simulation programs, optimum hob cutter settings and worm normal tooth angle were determined to improve bearing contact location and minimize the worm gear set kinematic errors. A numerical example is given to demonstrate the results of the investigation. The developed computer-aided manufacture program has successfully been applied to the worm gear manufacture and hob cutter design.

Mathematical model and bearing contacts of the ZK-type worm gear set cut by oversize hob cutters

An oversize worm-type hob cutter is used to cut worm gears in this study. A mathematical model of the ZK-type worm gear set is developed based on the cutting mechanism and its tool parameters. Variations in bearing contact due to pitch diameter variations of oversize hob cutters and center distance variations of worm gear sets are also investigated. A numerical example is given to demonstrate the paths and dimensions of the bearing contacts of worm gear sets.

A mathematical model of the ZE-type worm gear set

The mathematical model of the ZE-type worm gear set derived here is based on tool design parameters, machine tool settings, and worm and worm-gear cutting mechanisms. The backlash of the worm gear set is considered into the developed mathematical model. The developed mathematical model is most helpful in designing, contact and stress analyzing, manufacturing, measuring and optimizing worm gear sets. The profile of the fly cutter for small-lot worm-gear cutting is also investigated. Three-dimensional computer graphs of the worm gear set are presented to demonstrate the developed mathematical model.

Design of Involute Worm Gears with Entry Gaps.

In a worm gear set which consists of an involute helicoid worm and its conjugate worm wheel, theoretical line contact occurs when the set is assembled at the nominal center distance. This study first proves that theoretical tooth contact occurs only on the plane perpendicular to the worm wheel axis and tangent to the base cylinder of the worm, when the worm and the original conjugate worm wheel is set up at a center distance shorter than the nominal one. Namely, such a worm gear set makes the point contact only on the above mentioned plane and on the other places, there are gaps between the worm and wheel tooth surfaces. These gaps indicate a possibility of realizing the so-called "entry gaps" which are necessary for favorable lubricating condition. Then, two numerical examples of worm gear sets endowed with the entry gaps are introduced. In the examples, the worms are designed to have the outside and root diameters smaller than the original ones while the base cylinder and the helix on it are unchanged.

A Study of the Efficiency of a Double-Action Worm Gear Set

A double-action worm gear set—so called because the worm has both rotational and longitudinal degrees of freedom—has been invented primarily for use in a motorized spacecraft hinge. This paper presents an analysis of the mechanical efficiency of the double-action worm gear set, together with preliminary test results. Results of analysis and test show that the double-action feature of the worm makes it possible to control the forward and backward driving efficiency of the gear set. Compared to a standard worm gear set, the double-action worm gear set has the advantages of the ability to absorb small applied displacements to the wormwheel shaft in an unlocked position, the ability to be non-backdrivable with a high degree of certainty when locked against an end stop and the ability to maintain a specific preload in a locked position.

Kinematic Errors In Precision Worm Gears

This paper describes the measurement of error sources in a worm gear set and assesses their effects when developing a computer model to synthesise behaviour. To do this several test gears have been made and the process monitored by controlled measurement at several stages using some of the most sensitive and accurate equipment available. A computer program has been written to model the characteristics of these worm and wheel gear pairs under a range of conditions. The predictions have been validated using a test rig measuring rotary accuracy of the input and output shafts under a torque load.