Involute Worm Research Articles

Study on the vibration characteristics of toroidal involute worm meshing with different plastic gears

Toroidal involute worm (TI worm) meshing with plastic gear can serve as an efficient reducer for applications in smart home and automatic driving, owing to its stable transmission and high carrying capacity. This necessitates an in-depth analysis of the vibration and noise associated with TI worm drive to enhance the comfort in these scenarios. Utilizing the meshing characteristics of TI worm drive, a dynamic model including nonlinear factors such as time-varying meshing stiffness and meshing damping is established. The dynamic characteristics of TI worm meshing with different plastic helical gears are compared and analyzed. The TI worm drive experiments are carried out, and vibration signals are collected though accelerometers. The numerical analysis results align with the experimental findings. The results reveal that TI worm meshing with different plastics exhibits the maximum vibration amplitude in the axial direction of the worm. Specifically, PEEK demonstrates the highest amplitude, followed by POM, while Nylon has the smallest vibration amplitude. These findings serve as a valuable reference for mitigating vibration and noise of TI worm drives.

Gear Hob Base Worm Modelling from a Straight Toothed Generating Rack

The precision of a gear realized by hobbing is mainly influenced by the precision of the base worm, the adequate form of the rake face and the number of resharpenings. Gearing theory states that the base worm of a gear hob must be of involute type. Despite of this, manufacturing technology often admits a convolute worm as gear hob base worm. Due to the rake face grinding technology, there appears a difference between the theoretical and the real surface. On the other hand, the profile modification of the cutting edges occurs due to the re-sharpening. As a result, the cutting edges cannot reproduce that initial basic worm surface from which the gear hob was derived. In our opinion, the computing of the generating surfaces of the basic worm is still an unsolved problem. This paper deals with the study of a worm derived from a straight toothed generating rack. The incidence of an involute worm and that developed from the generating rack is investigated.

A method for point-contact conjugate tooth surfaces with a constant instantaneous transmission ratio generated by point-contact conjugate involute helicoids

Point-contact conjugate tooth surfaces are insensitive to manufacturing errors and assembly errors and have no transmission errors. However, design conditions for the current method of generating point-contact conjugate tooth surfaces are strict or lacking. This study proposed a method for point-contact conjugate tooth surfaces with a constant instantaneous transmission ratio generated by point-contact conjugate involute helicoids. According to relative motions of single- and two-degree-of-freedom in generating, design criteria were given and a mathematical model of the method was established. The mechanism of point-contact conjugate tooth surfaces was obtained by investigating the relationship between the engagement lines/surfaces, and kinematics was studied, in which the mechanism with a constant instantaneous transmission ratio was geometrically analysed. Based on this method, four types of point-contact conjugate worm drives were studied, in which two novel types of worm drives were developed, i.e., a point-contact conjugate toroidal involute (TI) worm drive, and a point-contact conjugate involute cylindrical (ZI) worm drive. The method was validated for correctness using numerical simulations and meshing tests and the influence of adjustable parameters on the meshing performance was outlined.

Meshing performance and error sensitivity of mismatched TI worm drive

Due to the characteristic of multi-tooth line contact, toroidal involute (TI) worm drive is characterized by high-loading capacity but sensitive to the assembly errors. This paper proposed a mismatched TI worm drive based on the media gear to reduce the assembly error sensitivity. According to spatial meshing theory, the design method and mathematical model are established. The geometric properties of TI worm flank can be fine-tuned and change the contact characteristics of the worm pair by adjusting the tooth number of media gear. The spatial point-contact analysis method is presented, and the effects of some design parameters on meshing performance are studied. The tooth contact analysis (TCA) is simulated to verify the carrying capacity and error adaptability. These results suggest that the mismatched TI worm pair remains the characteristics of multi-tooth contact and large carrying capacity. Compared with the standard TI worm drive, it has better error adaptability.

New method for determining singularities on enveloped surface and its application to study curvature interference theory of involute worm drive

In this paper, a more computationally convenient singularity condition of the enveloped surface is proposed using the theory of linear algebra. Its preconditions are only the tangential vector of the enveloping surface, the relative velocity vector, and the total differential of the meshing function. It avoids calculating the curvature parameters of the enveloping surface. It is proved that the singularity conditions of enveloped surface from different references are equivalent to each other and the relational equations among them are obtained. The curvature interference theory for the involute worm drive is established using the proposed singularity condition. The equation for the singularity trajectory is obtained. The calculation method for the singularity trajectory is proposed and its numerical result is obtained. The influence of the design parameters on the singularity trajectory is studied using the proposed curvature interference theory. The study results show that the risk of curvature interference is high when the transmission ratio is too small, especially in the case of the single-threaded worm and large modulus. The proposed singularity condition can also be applied to study the curvature interference mechanism in other types of the worm drive and to study the undercutting mechanism when machining the worm drive.

Meshing performance investigations of involute worm and helical gear drive based on counterpart rack

Meshing performance investigations of involute worm and helical gear drive based on counterpart rack

Meshing theory of involute worm drive

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.

Worm gear wear and coefficient of efficiency during their running-in period

The process of worm gear wear is considered. The reasons for the change in the coefficient of efficiency of worm gears during the running-in period are analyzed. Keywords: worm gear, line of engagement, contact surfaces, involute worm, velocity vector, friction coefficient. a-s-ivanov@yandex.ru

Research of Influence of Engagement Pairing of the Corrected Worm Gear with Involute Worm on the Life and Contact Pressure

Research of Influence of Engagement Pairing of the Corrected Worm Gear with Involute Worm on the Life and Contact Pressure

Geometric error modeling and compensation of horizontal CNC turning center for TI worm turning

This article proposes a method to compensate geometric errors of a horizontal CNC turning center for Toroidal Involute worm (TI worm) turning. TI worm is of great advantages for heavy duty transmission due to multi-tooth line contact. Contact situation and performance is influenced by the manufacturing accuracy of TI worm. However, few researches focused on the high-efficiency and high-precision turning method of TI worm. Therefore, tooth profile error prediction and compensation models for TI worm turning were built by the forward and actual inverse kinematics based on the multi-body theory. Firstly, the meshing system of TI worm was established according to the theory of gear meshing. The TI worm tooth surface was reconstructed via Non-Uniform Rational B-Splines (NURBS) fitting. Discrete points of toroidal spiral were calculated for NC turning code generation and correction. Secondly, spatial errors of the discrete points were predicted according to the forward kinematics model. The turning trajectories were modified in opposite direction of the spatial errors. Then, the compensated NC turning codes were obtained based on the instruction of variable pitch thread turning. Simulation and experiment verification of the accurate TI worm turning method and the geometric error compensation strategy were conducted on a three-axis horizontal CNC turning center. The tooth profile errors before and after compensation were compared to validate the effectiveness of the proposed method

ANALYSIS OF LOAD CAPACITY, WEAR AND LIFE WORM TRANSMISSION WITH INVOLUTE WORM CORRECTED WITH TWO- AND TREE PAIR ENGAGEMENT

ANALYSIS OF LOAD CAPACITY, WEAR AND LIFE WORM TRANSMISSION WITH INVOLUTE WORM CORRECTED WITH TWO- AND TREE PAIR ENGAGEMENT

Prediction Method of Contact Pressures, Wear and Life of Worm Gears with Archimedean and Involute Worm, Taking Tooth Correction into Account

This study evaluates the computation method of the study of worm gears with Archimedean and involute worms when engagement correction is presented, based on the contact pressures and the wheel teeth wear, as well as the gear life and the sliding speed in the engagement. The regularities of influence of correction on the stated gears parameters are stated. When there are positive values of the correction coefficient of wheel teeth, the maximal contact pressures and the linear wear of wheel teeth decrease as compared with the noncorrected gear, and when the correction coefficient is negative they increase. The stated regularities are represented in a diagram form.

A Method for Predicting Contact Strength and Life of Archimedes and Involute Worm Gears, Considering the Effect of Wear and Teeth Correction

A Method for Predicting Contact Strength and Life of Archimedes and Involute Worm Gears, Considering the Effect of Wear and Teeth Correction

The Deformaton of The Gear Hob’s Generating Surfaces Due to Re-Sharpening

Abstract The side relief faces of the monolithic involute gear hob are machined through relieving. The resulting surfaces are bevel helical surfaces in which the side cutting edges result from the intersection of these with the helical rake face. Theoretically, the gear hob is derived from an involute worm. Resharpening decreases the diameter of the hob, thus the edges became closer to the axis, and as a consequence they will be situated on a smaller worm than the original. The present paper analyses the deviation of the re-sharpened gear hob’s carrying worm from the theoretically perfect involute worm whose characteristic dimensions were adjusted considering the re-sharpened gear hob characteristic diameters. It was proven that the evolution of the errors is significantly different from that described in the literature. Thus, increasing the new gear hob diameters in comparison with the calculated dimensions is unnecessary, because it cannot reduce the error to half with this procedure. The mathematical model was built up accepting that the edges result from the intersection of an involute worm with a helical rake face and the side relief faces result from the rototranslation of the edges on a bevel helix leading curve dressed by the relieving parameter.

About the Profile Accuracy of the Involute Gear Hob

Abstract Gear hobs are the most widely and frequently used gear cutting tools. During the time passed between the moment of invention (Schiele, 1876) and the present, gear hobs reached a considerable evolution regarding the geometry, the profile of the edge, the relieving technologies finalizing in the latest constructive and design solutions. This paper deals with the calculus of the edge profile in the case the basic worm of the hob has involute helicoid surfaces. In order to obtain a constant grinding allowance on the relief faces of the gear hob teeth it is necessary to compute the edge of the roughing relieving cutter. The equations are deduced considering that the provenience involute worm is a one teethed helical gear with shifted profile. The presented mathematical model proves that linearizing the relieving cutter profile is not an adequate solution if aspiring to higher precision.

Machining of an involute worm gear drive using the surface definition procedure

Abstract There is a need for special machines and methods for machining of an involute worm gear drive. Due to these necessities, the machines for involute profile machining are limited and the production costs are also excessive. There are general approaches applicable for various types of gearwheel machining. As known, involute worm gears are generally machined in two ways, namely by the rolling method and by form milling. The rolling method is the most widely used one. In this study, the aim is to develop a novel machining method for involute worm gear drive production, which can be more often used in industrial production. Furthermore, this method should reduce machining costs andsimplify the manufacturing process for involute gear drives. Thus, theoretical calculations for the involute form of worm gear drive have been done and an analytical model has been set up using Matlab M file. Machining coordinates of involute worm gear have been created and transformed to G codes. So, the involute curve has been formed. Accuracy of those derived machining codes has been tested by using a CNC Simulator program. Finally, an involute worm gear drive has been machined in a CNC lathe (with two axes) machine using grooving tool and the newly designed special tool holder.

The Mesh Property of the Steel Involute Cylindrical Worm with a Plastic Involute Helical Gear

ABSTRACTWith the increasing use of plastic gears in substitution of conventional steel ones, a plastic involute helical gear has been introduced to engage with a steel involute worm thus forming a novel plastic-steel worm-gear pair. The geometry and kinematics of this kind of worm-gear pair has been established first to derive its meshing properties which have been further verified by the finite element simulation. And it turns out that the contact area of this worm-gear pair is a point or an ellipse instead of a line. Further, a discrete dynamic model has been applied to investigate the dynamic transmission of motion and power of this worm-gear pair through the dynamic mesh force and the driven plastic involute helical gear. And the effects of angular and distance assembling errors have also been included.

The Derivation and Simulation of Curved Tooth Face Gear Tooth Theoretical Contract-Point Trace Line Equations

The face gear tooth surface theoretical equation, based on the mesh of curved tooth face gear and involute worm, was deduced by means of differential geometry, meshing theory and so on. According to the conditions of the gear meshing, studying the ideal contract-point trace line theoretical equation under the conditions of no machining errors, installation errors and so on. By solving the equations and simulating in SOLIDWORKS, finally the tooth contact situation of face gear and cylindrical worm in the meshing process was got.

An Analysis on Contact Line Performance of Offset Cylindrical Worm Gearing

Based on the theory of gear mesh, the contact line equation of involute offset cylindrical worm gearing, which is consisted of an involute helical gear with few teeth and a face gear in substance, is obtained. Furthermore, in order to investigate the influence of design parameters on the performance of contact line, numerical simulation of which is carried out. Analysis results indicate that an appropriate increase in helix angle and modulus as well as the teeth number of worm, reduction in the teeth number of worm gear can make the contact line performance better.

Effects of Boundary Condition and Helix Angle on Meshing Performance of TI Worm Gearing

To exactly describe the contact state and contact area of tooth surface of toroidal involute (TI) worm gearing, the authors introduced boundary condition into contact line analysis. With helix angle chosen as parameter, the criterion for the existence of meshing boundary line on the surface of TI worm gearing is derived. Results show that there can be four situations for meshing boundary line on the tooth surface of gear, namely, inexistence of meshing boundary line, a unique line, two lines, and two coincident lines. If the helix angle is equal to or slightly smaller than the bigger angle, which makes two meshing boundary lines superpose, a preferable meshing performance is obtained. Computer simulation proves the validity of the above conclusion.