Modification Design Method for an Enveloping Hourglass Worm Gear with Consideration of Machining and Misalignment Errors

The influences of machining and misalignment errors play a very critical role in the performance of the anti-backlash double-roller enveloping hourglass worm gear(ADEHWG).However,a corresponding efficient method for eliminating or reducing these errors on the tooth profile of the ADEHWG is seldom reported.The gear engagement equation and tooth profile equation for considering six different errors that could arise from the machining and gear misalignment are derived from the theories of differential geometry and gear meshing.Also,the tooth contact analysis(TCA) is used to systematically investigate the influence of the machining and misalignment errors on the contact curves and the tooth profile by means of numerical analysis and three-dimensional solid modeling.The research results show that vertical angular misalignment of the worm wheel(Δβ) has the strongest influences while the tooth angle error(Δα) has the weakest influences on the contact curves and the tooth profile.A novel efficient approach is proposed and used to minimize the effect of the errors in manufacturing by changing the radius of the grinding wheel and the approaching point of contact.The results from the TCA and the experiment demonstrate that this tooth profile design modification method can indeed reduce the machining and misalignment errors.This modification design method is helpful in understanding the manufacturing technology of the ADEHWG.

Parametric Analysis of the End Face Engagement Worm Gear

A novel specific type of worm drive, so-called end face engagement worm gear（EFEWD）, is originally presented to minimize or overcome the gear backlash. Different factors, including the three different types, contact curves, tooth profile, lubrication angle and the induced normal curvature are taken into account to investigate the meshing characteristics and create the profile of a novel specific type of worm drive through mathematical models and theoretical analysis. The tooth of the worm wheel is very specific with the sine-shaped tooth which is located at the alveolus of the worm and the tooth profile of a worm is generated by the meshing movement of the worm wheel with the sine-shaped tooth, but just the end face of the worm（with three different typical meshing types） is adapted to meshing, and therefore an extraordinary manufacturing methods is used to generate the profile of the end face engagement worm. The research results indicates that the bearing contacts of the generated conjugate hourglass worm gear set are in line contacts, with certain advantages of no-backlash, high precision and high operating efficiency over other gears and gear systems besides the end face engagement worm gear drive may improve bearing contact, reduce the level of transmission errors and lessen the sensitivity to errors of alignment. Also, the end face engagement worm can be easily made with superior meshing and lubrication performance compared with the conventional techniques. In particular, the meshing and lubrication performance of the end face engagement worm gear by using the end face to meshing can be increased over 10% and 7%, respectively. This investigate is expect to provide a new insight on the design of the future no-backlash worm drive for industry.

Optimal Design for an End Face Engagement Worm Gear with Multiple Worm-wheel Meshing

To solve the problem for lacking a special mechanical transmission that could provide multiple outputs with high transmission efficiency and good lubrication in the modem industrial, a novel worm gear, named end face engagement worm gear, with multiple worm-wheel meshing is proposed for the first time. The essential parameters for the worm gear are optimized to enhance lubrication and meshing properties. Moreover, analysis of variance（ANOVA） is applied to determine the optimum levels and to determine the influence of parameters. The ANOVA results show that the novel end face engagement worm gear with multiple worm wheels provides high lubrication（the lubrication angle is more than 89~） and meshing performance（the induce normal curvature is less than 0.0002 mm ＇）. The interaction between center distance and roller slant distance most strongly influences the lubrication angle（contributed 51.6%）, followed by the parameters of center distance（contributed 25.0%）, roller slant distance（contributed 16.4%）, tooth angle of gear, gear ratio, and roller radius. In addition, roller radius most strongly influences the induced normal curvature（contributed 39.4%）, followed by roller slant distance（contributed 15.2%）, tooth angle of the gear（contributed 9.0%）, center distance, and gear ratio. The proposed worm gear helps to enrich the no-backlash high precision worm drive and the optimal design method can provide a useful reference on performance improvement of other worm gear.

Mathematical Model and Geometrical Model of Double Pitch ZN-type Worm Gear Set Based on Generation Mechanism

The current researches on the tooth surface mathematical equations and the theory of gearing mainly pay attention to the ordinary type worm gear set（e.g., ZN, ZA, or ZK）. The research of forming mechanism and three-dimensional modeling method for the double pitch worm gear set is not enough. So there are some difficulties in mathematical model deducing and geometry modeling of double pitch ZN-type worm gear set based on generation mechanism. In order to establish the mathematical model and the precise geometric model of double pitch ZN-type worm gear set, the structural characteristics and generation mechanism of the double pitch ZN-type worm gear set are investigated. Mathematical model of the ZN-type worm gear set is derived based on its generation mechanism and the theory of gearing. According to the mathematical model of the worm gear set which has been developed, a geometry modeling method of the double pitch ZN-type worm and worm gear is presented. Furthermore, a geometrical precision calculate method is proposed to evaluate the geometrical quality of the double pitch worm gear set. As a result, the maximum error is less than 6′10–4 mm in magnitude, thus the model of the double pitch ZN-type worm gear set is available to meet the requirements of finite element analysis and engineering application. The derived mathematical model and the proposed geometrical modeling method are helpful to guiding the design, manufacture and contact analysis of the worm gear set.

Temperature Field Simulation and Experimental Study of Anti‑backlash Single‑Roller Enveloping Hourglass Worm Gear

In gear transmission,temperature rise has a non-negligible impact on the accuracy,noise and transmission efficiency.However,there is no relevant research on the temperature rise of the anti-backlash single-roller enveloping hourglass worm(ASEHW)gear.To solve this problem,based on tribology principle and Hertz contact theory,the thermal power calculation method of the ASEHW gear was proposed for the first time and thermal analysis was carried out by Ansys software.The bulk temperature of the ASEHW gear under four different rotating speed(300 r/min,600 r/min,900 r/min,1200 r/min)is calculated.The main factors causing temperature rise of the ASEHW gear are analyzed theoretically.Meanwhile,an experimental study is performed to verify the simulation results and validate the theory methods.The theory presented in this paper provides a solution for the thermal power calculation of ASEHW gear.This research provides a theoretical basis for further optimization of ASEHW gear.

New method for calculating face gear tooth surface involving worm wheel installation errors

The machining principle and realization method for the continuous generative grinding face gear by a worm wheel are introduced. Based on a five-axis linked CNC grinding machine, a new method is presented to deprive the equation of face gear error tooth surface by assuming the tool surface as the error surface, where actual tool installation position error is introduced into the equation of virtual shaper cutter. Surface equations and 3-D models for the face gear and the worm wheel involving four kinds of tool installation errors are established. When compared, the face gear tooth surface machined in VERICUT software for simulation based on this new method and the one obtained based on real process(grinding face gear by using a theoretical worm wheel with actual position errors) are found to be coincident, which proves the validity and feasibility of this new method. By using mesh planning for the rotating projection plane of the face gear work tooth surface, the deviation values of the tooth surface and the difference surface are acquired, and the influence of four kinds of errors on the face gear tooth surface is analyzed. Accordingly, this work provides a theoretical reference for assembly craft of worm wheel, improvement of face gear machining accuracy and modification of error tooth surface.

Parametric 3D Modeling of Worm and Worm Gear Based on AutoCAD

Worm and worm gear are modeled under development environment in AutoCAD based on the principle of ordinary cylindrical worm drive. The drawing commands available in AutoCAD are used to develop worm blank and cutter models. The solid models of worm and worm gear are obtained through the use of the commands, move, rotate and subtract, to simulate the generating cutting movement on the gear cutting machine. Autolisp language is utilized in programming for parametric modeling of worm and worm gear. The developed program can automatically draw worm and worm gear when users load the wlwg program, input the modulus and the number of threads, handedness, and other parameters. The operation is simple and accurate, providing potentials to speed up product design process and improve efficiency.

A New Manufacturing Method for Hourglass Worm Gear Hob Based on a Semi⁃automatic CAD

The top relief surfaces of an hourglass worm gear hob are ground manually in the traditional manufacturing process,which cannot ensure the width of the land surfaces of the hob.Moreover,each geometric feature of the hob has been produced through different manufacturing techniques and machine tools,which results in low efficiency.To solve this problem,we propose a semi-automatic computer aided design(CAD)method for hobs.The point clouds of each feature surface of a hob are calculated by combing mathematical equations of the top relief surfaces built by the proposed method with other existing equations of hob surfaces.According to the point clouds,the method can achieve the automatic modeling for the hob in three-dimensional(3D)software by classifying and extracting the parameter information of the feature-hierarchical knowledge of the hob.Based on the generated 3D model,the entire surfaces of the hob can be manufactured on a four-axis computer numerical control(CNC)milling machine through only twice clamping.Verification of the width of the land surface of the hob manufactured by semi-automatic CAD method on a measuring projector proved the precision of the designed width can be ensured.The edge of the contact area on the worm wheel in a meshing experiment is clear and distinct,which means the worm gear drive is meshed well and the hob manufactured by the proposed method has improved machinability.The method simplifies the processing technique,and improves the design efficiency and production accuracy.

Contact analysis and load distribution of double-envelop hourglass worm gearing affected by errors and load

An approach for the contact analysis and load distribution of double-envelop hourglass worm gearing is presented, which is based on a 3-D elastic contact finite element method (FEM) model that accommodates the influence of errors and load. As compared with existing tooth contact analysis model that assumes rigidity for the contacting surfaces, the proposed model provides a more realistic analysis on the contact patterns, the distribution of contact load and transmission errors. It is also capable of exploring the influence of different errors on meshing performances, the contact deformation, the shift of the contact zone and load share among the meshing tooth-pairs under different load.

YK7232——GEAR GRINDING MACHINE WITH WORM GRINDING WHEEL

The machine is used for precisiongrinding of hardened cylindricalgears with medium module inbatches for the industries ofaircraft,automobile,machine tool,gear box and various transmissiondevices.

STUDY ON CONTROLLABLE MISMAT－CHED ENGAGEMENT OF CONE－GEN－ERATED CYLINDRIC WORM GEARING

Controllable modification of cone-generated cylindric worm gearing has been carriedout. The tooth contact state of modified gearing can be controlled by selecting the positions of con-tact points of worm surfaee and the correction amount of curvature. The modification machiningcan be conveniently implemented by changing the geometrical sizes and setting parameters of grind-ing wheel. Therefore the research has better scientific basis and practical value.

EXPERIMENTAL STUDY ON LUBRICATION BEHAVIOR OF DOUBLE ENVELOPING HOUK GLASSWOKM GEARING

The lubrication behavior of double enveloping hourglass worm gearing is studied experimently. The effects of rotational speed of the worm and load on the formation of the fluid film between engagement tooth surfaces are investigated in detail. and working angle of this worm gearing is also analyzed. Some beneficial results are obtained。