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.

Design and Experimental Research on Seedling Pick-Up Mechanism of Planetary Gear Train with Combined Non-circular Gear Transmission

Currently, transplanting mechanisms for dryland plug seedlings in China are mainly semiautomatic and have low efficiency. The rotary seedling pick-up mechanism with a planetary gear train for non-uniform intermittent transmission, and a concave and convex locking arc device, has a large rigid impact. To solve these problems, according to the design requirements for a dryland plug seedling transplanting mechanism, a rotary seedling pick-up mechanism of a planetary gear train with combined non-circular gear transmission of incomplete eccentric circular and noncircular gears was proposed. This has the characteristics of two-times greater fluctuation of the transmission ratio in a cycle, and can achieve a non-uniform continuous drive. Through analysis of the working principle of the seedling pick-up mechanism, its kinematics model was established. The human–computer interaction optimization method and self-developed computer-aided analysis and optimization software were used to obtain a set of parameters that satisfy the operation requirements of the seedling pick-up mechanism. According to the optimized parameters, the structure of the seedling pick-up mechanism was designed, a virtual prototype of the mechanism was created, and a physical prototype was manufactured. A virtual motion simulation of the mechanism was performed, high-speed photographic kinematics tests were conducted, and the kinematic properties of the physical prototype were investigated, whereby the correctness of the theoretical model and the optimized design of the mechanism were verified. Further, laboratory seedling pick-up tests were conducted. The success ratio of seedling pick-up was 93.8% when the seedling pick-up efficiency of the mechanism was 60 plants per minute per row, indicating that the mechanism has a high efficiency and success ratio for seedling pick-up and can be applied to a dryland plug seedling transplanter.

Kinematic Modeling and Characteristic Analysis of Eccentric Conjugate Non-circular Gear & Crank-Rocker & Gears Train Weft Insertion Mechanism

A novel weft insertion mechanism named eccentric conjugate non-circular gear & crank-rocker & gears train weft insertion mechanism was proposed in order to better meet the requirements of rapier loom's weft insertion mechanism as well as reduce the manufacturing difficulty. Meanwhile, based on the working principle of this mechanism, kinematical mathematic models of this mechanism were established and an aided analysis and simulation software was compiled. The influences of eccentricity ratio, deformation coefficient, and other important parameters on the kinematics characteristics of this mechanism were analyzed by using the software. A group of preferable parameters which could meet the requirements of weft insertion technology were obtained by means of human-computer interactive optimization method. The maximum velocity, maximum acceleration, and variation of acceleration of this mechanism are smaller than those of the conjugate cam weft insertion mechanism applied on TT96 rapier loom under the conditions of the same unilateral total stroke of rapier head and the same rotary speed of loom spindle; meanwhile the other demands of weaving technology can be met by this novel weft insertion mechanism.

Loaded multi-tooth contact analysis and calculation for contact stress of face-gear drive with spur involute pinion

The analytical method based on "Hertz theory on normal contact of elastic solids" and the numerical method based on finite element method (FEM) calculating the contact stress of face-gear drive with spur involute pinion were introduced, and their relative errors are below 10%, except edge contact, which turns out that these two methods can compute contact stress of face-gear drive correctly and effectively. An agreement of the localized bearing contact stress is gotten for these two methods, making sure that the calculation results of FEM are reliable. The loaded meshing simulations of multi-tooth FEM model were developed, and the determination of the transmission error and the maximal load distribution factor of face-gear drive under torques were given. A formula for the maximal load distribution factor was proposed. By introducing the maximal load distribution factor in multi-tooth contact zone, a method for calculating the maximal contact stress in multi-tooth contact can be given. Compared to FEM, the results of these formulae are proved to be reliable, and the relative errors are below 10%.

Influence of Setting Error of Tool on Tooth Profile and Contact Point of Face Gear Drive

In order to analyze the influence of setting error of tool on both tooth profile and contact characteristic of orthogonal face gear drive,the coordinate systems with and without setting error are established.Moreover,the equations of tooth profile and contact points of face gear drive are derived by envelope principle.According to the equations,the change of tooth profile and the contact points position on face gear are analyzed.The tooth surface and contact points are obtained by numerical simulation.Results show that the tooth profile and contact characteristic of face gear drive are not sensitive to the setting error of tool.

A precision generating hobbing method for face gear with assembly spherical hob

In order to improve the processing precision and shorten the hob manufacturing cycle of the face gear,a precision generating hobbing method for face gear with the assembly spherical hob is proposed.Firstly,the evolution of the cylindrical gear to spherical hob basic worm is analyzed,then the spherical hob basic worm is designed,thus the basic worm and spiral angle equation of spherical hob are obtained.Secondly,based on the design method of the existing hob,the development method of the assembly spherical hob is analyzed,the cutter tooth and the cutter substrate of the assembly hob are designed,and the whole assembly is finished.Thirdly,based on the need of face gear hobbing,a numerical control machine for gear hobbing is developed,and the equation of the face gear is obtained.Fourth,for reducing the face gear processing errors induced by equivalent installation errors,the error analysis model is established and the impacts of each error on the gear tooth surface are analyzed.Finally,the assembly spherical hob is manufactured and the gear hobbing test is completed.According to the measurement results,the processing parameters of face gear hobbing are modified,and the deviation of tooth surface is significantly reduced.

Mathematical Model and Machining Method for Spiral Flute Rake Faces of Hourglass Worm Gear Hob

To improve the cutting performance of an hourglass worm gear hob and the accuracy of the resulting worm gear,the rake angles of the teeth on the pitch circle should be reduced.A method of forming the spiral flutes by using a variable transmission ratio was developed.This method ensures that the rake angles on the indexing torus of each tooth are approximately 0°.Based on the gear meshing theory and the hourglass worm forming method,the discretization mathematical model of the rake face of a planar double enveloping worm gear hob was established by using cylindrical generating surface,and the feed parameters for machining the rake face for a variable transmission ratio were obtained.The spiral flute was simulated and the hob was machined on a four axis CNC milling machine.A contourgraph was used to measure the rake angle.The measurement results showed that the proposed method can reduce the absolute value of the rake angle on both sides of the cutting teeth,which can be used for machining the spiral flute rake face of an hourglass worm gear hob.

Influence Predictions of Contact Effects on Mesh Stiffness of Face Gear Drives with Spur Gear

Mesh stiffness is one of important base parameters of face gear dynamic studies.However,a calculation solution of mesh stiffness of face gear drives is not to be constructed due to complex geometric flakes of face gear teeth.Thus,a calculation solution of mesh stiffness of face gear drives with a spur gear,which is based on the proposed equivalent face gear teeth and Ishikawa model,is constructed,and the influence of contact effects on mesh stiffness of face gear drives is investigated.The results indicate the mesh stiffness of face gear drives is sensitive to contact effects under heavy loaded operating conditions,specially.These contributions will benefit to improve dynamic studies of face gear drives.

Reverse Design and Test of Non-circular Gear & Crank-Rocker & Gear Trains Weft Insertion Mechanism

For the purpose of obtaining satisfactory performance of the non-circular gear & crank-rocker & gear trains (NCCRG) weft insertion mechanism which was proposed in this paper, the ideal kinematic curve of this weft insertion mechanism was given, and the reverse solution models of this mechanism were established. A reverse design and simulation software was compiled based on Visual Basic 6.0 to obtain the mechanism parameters, including the pitch curves and tooth profiles of the non-circular gears. A test-bed of this mechanism was developed according to these parameters. The kinematic performance of this weft insertion mechanism was tested by high-speed video tape recorder with its corresponding video analytical software Blaster's MAS. And the test results were identical with the theoretical calculation. Compared with the conjugate cam weft insertion mechanism which is applied on TT96 rapier loom, under the condition of same weft insertion rate, the variation of acceleration of this mechanism is smaller. This novel weft insertion mechanism can meet the requirements of weft insertion on rapier looms with smooth and steady motion.

Heat treatment process optimization for face gears based on deformation and residual stress control

In this paper, based on the principle of heat transfer and thermal elastic-plastic theory, the heat treatment process optimization scheme for face gears is proposed according to the structural characteristics of the face gear and material properties of 12Cr2Ni4 steel. To simulate the effect of carburizing and quenching process on tooth deformation and residual stress distribution, a heat treatment analysis model of face gears is established, and the microstructure, stress and deformation of face gear teeth changing with time are analyzed. The simulation results show that face gear tooth hardness increases, tooth surface residual compressive stress increases and tooth deformation decreases after heat treatment process optimization. It is beneficial to improving the fatigue strength and performance of face gears.

Design and Experiment of Non-circular Combined Gear Train Beating-up Mechanism

The most important performance of a beating-up mechanism is that the dwelling time of the sley must ensure the completion of the weft insertion. To meet this requirement, a new non-circular combined gear train beating-up mechanism which is composed of two-stage planetary gear trains is proposed. The first-stage is a Fourier planetary gear train and the second-stage is a non-circular planetary gear train. For designing of this new mechanism, the ideal kinematic equations of the sley are constructed first. Then the kinematic model of the first-stage Fourier planetary gear train is established and the reverse solution for the pitch curves of the second-stage non-circular gears is deduced. With a computer-aided design program, the influences of several important parameters on the pitch curves of the second-stage non-circular gears are analyzed, and a set of preferable structural parameters are obtained. Finally, a test bed of this mechanism is developed and the experimental results show that this new beating-up mechanism can achieve the designed dwelling time, namely it can meet the requirements of beating-up process.

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.

Efficient and accurate worm grinding of spur face gears according to an advanced geometrical analysis and a closed-loop manufacturing process

Worm grinding has been applied to manufacture gears to pursue high accuracy and fine surface finish.When the worm used to grind face gears is manufactured with multi-axis computer numerical control(CNC)machining,the machining accuracy is usually improved by increasing the number of tool paths with more time cost.Differently,this work proposes a generated method to improve the efficiency by dressing the worm surface with only one path,and a closed-loop manufacturing process is applied to ensure the machining accuracy.According to an advanced geometric analysis,the worm surface is practically approximated as a swept surface generated by a planar curve.Meanwhile,this curve is applied as the profile of a dressing wheel,which is used to dress the worm surface.The practical machining is carried out in a CNC machine tool,which was originally used to grind helical gears.Finally,a closed-loop manufacturing process including machining,measurement,and modification is proposed to compensate the machining errors.The proposed method is validated with simulations and practical experiments.

Research on cutting vibration characteristics of face-milling involute gear

Traditional machining methods, such as gear hobbing, gear shaping and gear milling, etc, are commonly used for cutting machining of gear tooth profile, which cannot meet huge machining demand of gears to a certain extent. This article proposes to utilize a face-milling machining method in involute gear machining, which can be used to reduce production cost effectively. Cutting vibration generated during cutting machining has a direct effect on the machining accuracy and machined surface quality of workpiece. Therefore, it is desiderated to perform in-depth research regarding this issue. ADAMS software was used to establish a rigid-flexible coupling virtual prototyping model of face-milling gear milling system and a cutting vibration system model. Cutting vibration analysis was performed for face-milling gear by adopting quick sine frequency sweep method, so that the frequency response characteristics of workpiece in three directions X, Y and Z and space were acquired. The research results will provide reference and theoretical foundation for actual application of face-milling gear machining technology.

Efficient Grinding Method for Face Gear with Long Radius Disk Wheel

In order to improve the machining efficiency of the dish wheel grinding face gear, two changes are proposed:a disk wheel grinding face gear with a long radius and a multi-axis movement optimization method for tooth surface correction. Based on the grinding principle of face gears, the equation of the long radius disk wheel is deduced. Based on the structure of the machining tool, the tooth surface equations of the face gear shaped by the long radius disk wheel are established. Furthermore, an optimization model of face gear tooth surface correction is established, and the machine tool motion optimization of face gear tooth surface correction is completed;Finally, a long radius disk wheel grinding face gear test is performed. After the face gear tooth surface correction, the maximum value of the tooth surface deviation is reduced from 180 μm to 16 μm which verified the correctness of the machining method.

Calculating method of contact stress for non-circular gears

According to Hertz theory, the difference of contact stress for non-circular gears and equivalent gears is compared in the paper, a calculating method of contact stress for non-circular gears by using equivalent gears is researched, and computing formulas of power and rotation speed for equivalent gears are deduced. A numerical simulation of contact stress for non-circular gears has also been conducted based on the finite element method. By the comparison of fitting curves, the feasibility of using equivalent gears instead of non-circular gears to calculate the contact stress is testified.

Simulation Analysis on Quasistatic Characteristics of Multistage Face Gears with Double Crown Surfac

The multistage face gears are the core component of the planetary gear train,which is symmetrically meshed by multiple single-stage face gear and multiple cylindrical gears.However,it is difficult to synchronize the contact between face gears and cylindrical gear due to the tooth number differences.Thus,the interference problems between two stages and big stress concentration are obvious.The crown surface configuration technology and structure design were introduced to optimize the meshing condition.To improve the double crown design feasibility and meshing stability,it is necessary to establish a reasonable multistage face gears pair simulation model to evaluate various influence factors on the contact condition and quasi-static characteristics of multistage face gears structure.The relevant scatter plots are fitted by comparing the contact results with different crown quantities and friction coefficients to intuitively obtain the variation regularity of maximum deformation,maximum strain,maximum stress and maximum strain energy.The natural frequency and mode coefficient are also determined by modal analysis under these two conditions.All the above mentioned studies verified the contact conjugate properties of double crown surface configuration were suitable.The results can provide a foundation for structure optimization and transmission reliability of multistage face gears.

Grinding-Hardening of Face Gears Under Minimum Quantity Lubrication with Disc Wheels

To shorten the process of face gears,the grinding-hardening effect experiment of face gears under minimum quantity lubrication(MQL)was carried out.Firstly,the grinding method of face gears was analyzed based on the envelope principle,and the control equation of grinding movement was constructed.Secondly,the distribution ratio equation of heat flux density was established,and the theoretical calculation formula of triangle heat source was derived.Thirdly,since a MATLAB calculation program was compiled,the temperature change law under MQL grinding was analyzed.In the end,the influence of grinding parameters on the grinding-hardening layer depth was analyzed.The results demonstrate that MQL grinding achieves the grinding-hardening effect.

Effects of Temperature and Centrifugal Force on Fretting Wear of Contact Interface of Face Gear

Taking the typical face gear connection structure of the combined rotor as the research object,this paper studies the distribution rules of the contact state,contact stress and slip distance of the contact tooth surface of face gear under different centrifugal force and temperature conditions by using the finite element method,in order to improve the reliability of face gear connection structure.And the influence of centrifugal force and temperature on the maximum wear depth of the tooth surface is studied based on the fretting wear model proposed by McColl.Results show that:(1)The external diameter has an opening phenomenon on the contact surface of the face gear under the centrifugal effect,which reduces the load-bearing area;(2)The contact stress at the inner root of the face gear is the largest and the wear is the most serious;(3)The temperature field causes the contact surface to be thermally expanded,resulting in the large uneven deformation,and the tooth surface appears drum-shape;(4)The maximum contact stress and the maximum wear depth occur in the middle of the tooth root;(5)As the temperature increases,the maximum wear depth of the tooth surface increases significantly.Consequently,reducing temperature of the combined rotor plays an important role in effectively reducing the wear of the face gear and improving the connection life of face gear connection structure.