Gear Accuracy Research Articles

Research of the accuracy of 3D printed plastic gears

The best-known additive manufacturing process is 3D printing, which is increasingly used to manufacture various machine components. In this article, we investigate the accuracy of plastic gears made by 3D printing. The aim of the research was to study gears manufactured using 3D printing technology with m >0.6 mm module, to determine how the resulting gears differ from the initial geometry and how the manufacturing method affects the parameters of the gears.

A Mathematical Modeling of Computer Numerical Control Skiving Process for Manufacturing Helical Face Gears Using Sensitivity Matrix Combined With Levenberg–Marquardt Algorithm

Abstract Currently, numerous studies have applied gear skiving processes to produce face gear. However, there remains a significant challenge in achieving a flexible computing model for manufacturing a precise tooth surface for face gear. This study proposes a novel mathematical model that combines the cutter modification method and computer numerical control (CNC)-axis motion modification methods within a unified “closed-loop optimization.” This approach aims to enhance the tooth surface accuracy of skived helical face gears by determining optimal coefficients. Applying the Levenberg–Marquardt algorithm and sensitivity matrix enables the calculation of new polynomial coefficients, ensuring the attainment of gear surfaces with an accuracy grade of B6 (according to the ANSI/AGMA 2009-B01 standard) for each target surface. The proposed methodology involves the generation of a helical skiving cutter using a corrected rack. Subsequently, the cutting path on the CNC machine is optimized by incorporating additional motions expressed in polynomials. A comprehensive skiving simulation is conducted to achieve the desired face-gear surface, which is corrected by specified polynomial coefficients. The proposed model is validated through numerical and machining simulations using vericut software. The results affirm the practicality and efficacy of our approach in achieving the desired accuracy in producing helical face gears through power skiving processes.

Non-Newtonian thermal elastohydrodynamic mixed lubrication in elliptical contact for nutation-driven double circular-arc spiral bevel gear pair

The new type of nutation reducer with double circular-arc bevel gears as the core is characterized by advantages such as high load-bearing capacity, large transmission ratio, and simple structure. The existing research focuses on the machining methods of gears and the analysis of tooth contact. This article first time establishes an elastohydrodynamic mixed lubrication model for nutation double circular-arc bevel gear. The model's accuracy is verified by comparing it with existing test results. On this basis, combined with the finite element method and tooth contact analysis, the meshing characteristics, tooth contact characteristics, and lubrication characteristics of the double circular-arc bevel gear tooth surface are analyzed. The results show that the entrainment velocity at the contact point of the tooth surface during transmission is much higher than the sliding velocity. Consequently, the meshing motion is close to pure rolling. In constant-speed transmission, the oil film thickness at the engaging-in and exit points near the edge of the tooth surface is smaller than that at other meshing points on the tooth surface. This phenomenon can easily lead to mixed lubrication and lubrication failure, as well as tooth surface wear. During deceleration, i.e., when the speed drops to 50 r/min, the oil film thickness approaches zero, indicating that the gear has entered a mixed lubrication state. The proposed model can be used for lubrication analysis and improving transmission accuracy of nutation double circular-arc bevel gears.

Multi-Objective Optimization Design of Cycloid-Pin Gears Based on RV Reducer Precision Transmission Performance

This paper aims to realize multi-objective optimization of cycloid-pin gears to improve the positioning accuracy and load-carrying capacity of the rotary vector (RV) reducer, via the consideration of backlash, transmission error, and torsional stiffness. Initially, the analytical models of the RV transmission backlash and transmission error are developed by using both purely geometrical and equivalent model methods individually. Based on the generalized Hooke’s law, a torsion angle model is established to characterize the torsional stiffness of the system, utilizing methods such as Hertzian contact theory and bearing stiffness models. Subsequently, employing the Monte Carlo method, extremum method, and quality loss function, mapping objective functions for dimensional accuracy (tolerance) and transmission performance (backlash, transmission error, and torsional stiffness) are constructed. The geometry dimensions, dimensional accuracy, and modification of the cycloid-pin gear are considered as design variables to create a multi-objective optimization model. The improved Parallel Adaptive Genetic Algorithm using Deferential Evolution (PAGA-DE) is used for multi-objective solutions. Through example calculations, the impact of cycloid-pin gear parameters on transmission performance before and after optimization is determined. The reliability of backlash after optimization within 1.5′ reaches 99.99%, showing an increase of 8.24%. The reliability of transmission error within 1′ reaches 98.52%, demonstrating an increase of 1.35%. The torsional angle is reduced by 8.9% before optimization. The results indicate that the proposed multi-objective optimization design method for cycloid-pin gears can achieve the goal of improving the transmission performance of the RV reducer.

A coaxial multi-ring detection method for measuring the pitch and thickness accuracy of cylindrical gears

Performance of gear transmissions affects the performance of mechanical equipment. It is necessary to develop more reliable gear pitch and tooth thickness accuracy detection methods in order to evaluate gear transmission performance and detect gear pitch and tooth thickness accuracy more accurately. Based on the basic theory of gears, binocular vision technology, and statistical principles, a new method that measures gear pitch and tooth thickness using machine vision is proposed: coaxial multi-ring detection (MCD). There is no contact, no damage, and a high degree of efficiency with this method. Using this method, we are able to detect the pitch and thickness accuracy of each gear tooth multiple times within the tooth width range and in multiple directions perpendicular to the gear axis. We statistically analyze the measurement results to determine the gear’s most accurate detection results. The measurement method for gear machining accuracy is investigated using the coaxial multi-ring detection method. The statistical analysis of multiple measurement results is carried out, and the measurement results obtained are highly consistent with those of the gear detection center. In conclusion, the measurement results of this method are highly reliable, and they can be used as a reliable basis for evaluating gear transmission performance.

Research on the Hobbing Processing Method of Marine Beveloid Gear

Due to the particular structure of the beveloid gear, it cannot be directly hobbed by an ordinary gear hobbing machine. The existing processing method is complex and has a high cost. Therefore, the mass production and industrialization of beveloid gears are limited. To improve the machining efficiency and accuracy of processing beveloid gears, we proposed a hobbing method via the modification of ordinary hobbing machines. At first, we completed the derivation and calculation of the relevant processing parameters of the beveloid gear based on the study of the structural characteristics of the beveloid gear and the principle of hobbing machining. Then, we proposed and designed a beveloid gear hobbing method, and the modification of the ordinary hobbing machine was completed by using a hanging wheel mechanism in synchronous belt type. Finally, we completed the actual hobbing of the beveloid gear, and the feasibility of the proposed method was verified. After that, we analyzed the machining error of the trial-produced beveloid gear; the results showed that the accuracy of the trial-produced beveloid gear met the 6-level standard, which also verified the accuracy of the proposed method.

Features of using the over-skiving method for multi-pass cutting of external gears

Problem. There is a problem of determining the working parameters, including axial feed and cutting speed, as well as the helix angle of the teeth of the disc cutter and the tool spindle, the geometry of the cutting part, and the cutting depth per pass in Power skiving technology.Objective. It is necessary to investigate the cutting process using the Power Skiving method for generating external gears over multiple passes and develop recommendations for selecting its optimal parameters.Implementation methodology. The cutting force and its tangential component acting on the cutter are presented based on the fundamental principles of cutting theory, using the function of the cross-sectional area of the cut, the material strength limits of the workpiece for shear, and the intensity of plastic deformation of the chip. Calculations of the cut area are based on a graphoanalytical 3D model of the undeformed chip. The coefficient of shear intensity is determined depending on the thickness of the cut layers using the Deform 2D system. The study of the force factors is conducted in the initial stage for single-tooth cutting, considering the operation of a single tooth of the tool, and for multi-tooth cutting conditions, corresponding to real cutting and forming conditions in this method.Results. Analysis of harmonic vibrations with different frequencies of the investigated forces indicates that, under average loading, the maximum principal component of the cutting force occurs on the third pass, and the tangential force on the tool axis occurs on the first pass. The variation in the frequency of these signals is explained by changes in the contact angle between the tool and the gear wheel in the machine engagement and the different number of teeth involved in cutting.Conclusions. The obtained data allowed the development of a methodology for selecting rational parameters - axial feed values, the number of passes with different cutting depths to minimize time consumption, and achieve the desired accuracy of gears. It has been demonstrated that to reduce processing errors, it is most rational to decrease cutting force by increasing the number of passes, rather than reducing the axial feed.

An efficient vectorization solution to cutting dynamics modeling for face-hobbing of hypoid gears

The cutting vibration generated by cutting forces is critical to the accuracy and efficiency of face-hobbed hypoid gears. However, few relevant works are currently on cutting dynamics modeling for the face-hobbing process due to its complex spatial relationships. This study developed an efficient cutting dynamics model considering comprehensive characteristics of the non-generated face-hobbed hypoid gear machining process. A concise and efficient analytical solution to cutting dynamics modeling for face-hobbing of hypoid gears is obtained by using a vectorization method to characterize chip regenerating mechanisms. The machine tool vibration caused by cutting forces is predicted and validated according to an industrial case study. The proposed cutting dynamic model is 36.11% more efficient than the semi-analytical dynamic model derived from other cutting force prediction methods, and its accuracy is also improved with an error of less than 15%. Furthermore, the proposed vectorization solution to face-hobbing cutting dynamics modeling will be a practicable and effective method for analyzing the chatter in the machining of complex surfaces.

Selection of abrasive tools and cutting modes to improve the quality of gears and gear blocks

The paper analyzes the advantages and disadvantages of tools for tooth grinding and tooth honing, the areas of their application are noted. The issues of correction and restoration of grinding wheels and hones are considered in detail, recommendations are given when choosing coolant and oils. It is noted that the accuracy and quality of gears and gear blocks depend on the correct choice of tools for finishing operations. A comparative analysis of the effect of the processing method on the surface quality of the teeth is carried out.

Investigation of Spatial Symmetry Error Measurement, Evaluation and Compensation Model for Herringbone Gears

In the machining process for herringbone gears manufactured by numerical control gear-shaping machines, out-of-tolerance problems of symmetry error generally exist. This paper proposed a high-precision control of spatial symmetry error in the one-time forming machining for herringbone gear. To improve the machining symmetry accuracy and quality of herringbone gear, a mathematical model of measurement, evaluation and compensation for spatial symmetry error was established based on the least square method. Meanwhile, a new shaping machining method based on spatial symmetry error detection and compensation was proposed. The test results indicated that the proposed method can maintain symmetry within 0.02 mm. This study provided a novel spatial symmetry error detection and compensation machining method for herringbone gear that has advantages compared to traditional methods in terms of machining accuracy, efficiency, and continuous machining type.

A novel geometric error compensation method for improving machining accuracy of spiral bevel gear based on inverse kinematic model

A novel geometric error compensation method for improving machining accuracy of spiral bevel gear based on inverse kinematic model

Algebraic Modeling of Cylindrical Interference-Free Power-Skiving Tool for Involute Internal Gear Cutting With Tilt Angle

Abstract The development of feasible methods for the design of power-skiving tools without cutting interference is essential in ensuring the accuracy of involute internal machined gears. One of the most crucial points in obtaining interference-free and resharpenable power-skiving tools is that of determining the cutting-edge and clearance surface. The present study introduces a tilt angle during the power-skiving process to design a simple cylindrical interference-free tool shape, in which the shape of the cutting edge remains unchanged after resharpening. The relative position between the new tool center point and gear during machining is similarly unchanged after resharpening. In addition, the clearance angle between the tool and the gear can be easily adjusted simply by changing the tilt angle of the tool during power-skiving. The validity of the proposed design method is demonstrated through a simple numerical example. The simulation results confirm the feasibility of the proposed method.

Measurement and Evaluation Method Study of Alignment Deviation of Double-helical Gear

The alignment deviation of the V-vertex of two symmetrically arranged gears with different rotation directions is a unique geometric parameter of double helical gears, which has an important effect on the vibration, noise, and double helical gear service life. Aiming to more accurately represent the manufacturing accuracy of double helical gears and their transmission performance, this paper proposes the meaning of the v-vertex basis the contact line of tooth surface based on the apex characteristics of double helical gears. First, the mathematical model of tooth flank is established based on gear meshing theory. Secondly, a method for measuring and evaluating the alignment deviation of double helical gear v-vertex (full tooth contact line method) is proposed. Eventually, the validity and convenience of the proposed measurement method are verified by the experiment. Experimental results showed that the total alignment deviation of double helical gears evaluated by the full tooth contact line method is 0.0082 mm, which meets the design requirements in Reference 16. This paper provides a new measurement and evaluation method for the comprehensive and accurate evaluation of double helical gears, which has significant implications for the design and manufacture of high-precision double helical gears.

Thermal Error Modelling for the Parallelism Between the Gear Axis and the Z-axis of GMI

Gear measuring instrument (GMI) is the mainstream equipment for gear measurement. As the measurement accuracy of gears improves and GMI is gradually used in production, thermal errors are becoming an important factor affecting the measurement accuracy of GMI. In the precision measurement of the gears, the parallelism errors between the gear axis and the Z-axis of the GMI are the major error source. This error is usually reduced by mechanical adjustment when a GMI is assembled. When the temperature of the GMI and its environment changes, the thermal deformation will lead to new parallelism errors between the gear axis and the Z-axis of the GMI, which will further cause errors in the GMI. In this paper, the effect of the parallelism thermal errors of the GMI is studied, and the parallelism thermal errors model under room temperature environment was established. First, the temperature field of the GMI and its environment and the parallelism thermal errors were measured; then, the TMP are grouped using the FCM, and the key TMP were selected by optimizing the group of the measurement points using Pearson correlation coefficient method; finally, the parallelism thermal errors were established by RBF (Radial Basis Function) neural network and tested by using the measured data. The experimental results show that the predictive accuracy of the established parallelism thermal error model can reach 60.89% in the X direction and 82.26% in the Y direction, indicating good generalization ability and robustness. The model can be used for subsequent thermal error compensation.

Effect of Chill Plate Thickness on Surface Hardening and Dimensional Accuracy of Nodular Cast Iron Gears Manufactured by the Chill Casting Method

The gear manufacturing method is an important determinant of their performance and service life. Surface hardness and dimensional accuracy play a significant influence in determining wear and contact fatigue in gears. This study’s goal was to measure the gear profile dimensions and surface behavior of nodular cast iron made using the chill casting technique. Chill plates made of 304 stainless steel with thicknesses of 0.2, 0.4, and 0.6 mm were used to provide good surface cooling rates during the chill casting of gears performed using open molds of silica sand. Chill plates are plated onto the walls of the mold, and then the molten material is poured at 1400 °C. The obtained gears were tested using photographs, microstructures, SEM-EDX, microhardness, wear, and dimensional measurements. The thickness of the chill plate can affect the hardening process of the gear surface. Thicker chill plates result in slower cooling rates, resulting in a more homogeneous microstructure and increasing the hardness level of the hardened layer. Whereas thinner chill plates result in a faster cooling rate, which results in a higher hardness and wear resistance of the hardened layer. Reducing the thickness of the chill plate from 0.6 mm to 0.2 mm increases the cooling rate and increases the amount of diffusion that can occur. The results showed that M7C3 and the (FeCrC)7C3 matrices were formed, with an average hardness within a range of 700–994.96 HV. A chill plate with a thickness of 0.4 mm produces gear with the best accuracy and precision.

A Theoretical-Experimental Study on the Influence of FDM Parameters on the Dimensions of Cylindrical Spur Gears Made of PLA

This paper presents the results of a theoretical-experimental study on the influence of FDM parameters (height of the deposited layer at one pass Hs and percentage of filling Pu) on the dimensions of cylindrical spur gears made of PLA (shaft diameter d and bore diameter D). In this context, we designed the 3D model of a cylindrical gear with module m= 1 and z= 60 spur teeth, which we used for FDM 3D printing of 27 PLA parts with different values of coating height deposited at a pitch Hs of 0.10, 0.15, 0.20mm and different values 50, 75, and 100% of filling percentage Pu. The 324 values obtained from measuring the diameters d and D of 27 cylindrical spur gears made of PLA and the calculated values of statistical indicators (arithmetic mean, standard deviation, dispersion) were used to determine the dimensional accuracy of the analyzed parts. The study results show that the percentage of filling has a greater influence than the shaft diameter on the dimensional accuracy of cylindrical spur gears made of PLA.

Accuracy of Worm Gear–Worm Engagement in Gearboxes

Accuracy of Worm Gear–Worm Engagement in Gearboxes

A Novel Analytical Explicit Method to Calculate Formed Wheel and Tooth Flank of Involute Gears in Profile Grinding Process

AbstractGear drive is a common and efficient way to transfer power and motion. To ensure the machining accuracy of gears, the tooth flanks are formed by profile grinding technology in some cases. In the profile grinding process, the calculation of wheels using the information of gears named as the forward-calculation process and obtaining gears based on wheels (the backward-calculation process) traditionally adopt numerical ways. It is always time consuming and large code quantity. To conquer these drawbacks, this article presents an analytical method using the envelope theory to compute the contacting curves that are the basis of getting tooth flanks or wheels in the forward- or the backward-calculation process. For the forward-calculation process, the tooth flank is expressed in the form of an extended straight-line surface that can be taken as the generating line moving along the helix curve. The normal vector for an arbitrary point on the generating line is the same. By using this characteristic, the contacting curve can be explicitly gained as the function of only one parameter. Similarly, in the backward-calculation process, the formed wheel is expressed by a cross section rotating about its axis. For this type of surface, the guide curve is a circle, and the normal vectors of points on the guideline insect with the axis at the same point. Taking advantage of this principle, the contacting curve can be analytically expressed by only one unknown parameter. To verify the validity of the proposed method, some examples and comparative experiments are performed. The results show that the presented method is correct. When compared with the classical numerical way, the time span for the proposed method is 15 times less than that for the numerical way. When compared with the practical grinding wheel and the practical gear, the maximum errors are 0.18 mm and 0.0099 mm, respectively. The proposed method can be served as one of the universal ways to generate formed wheels or involute gears in the profile grinding process.

Face gear generating grinding residual model based on the normal cutting depth iterative method

The generating grinding method has the characteristics of high machining accuracy and high efficiency. Therefore, it is widely used in the finishing process of the face gear tooth surface. The physical performance of the grinding process is an important factor that influences the machining accuracy of the face gear tooth surface. Therefore, to improve the manufacturing accuracy of the face gear, it is necessary to accurately simulate the grinding process of the face gear. Owing to the influence of the complex spatial geometric characteristics of the face gear tooth surface and the grinding wheel, establishing a surface residual modeling method for the face gear is a key challenge in simulating the generating grinding process. To address the aforementioned issues, this study proposes a normal cutting depth iterative method to calculate the grinding residual in the face gear generating grinding process. This method considers the complex 3D spatial characteristics of the face gear tooth surface and establishes the spatial residual model of each node of the face gear surface in the process of generating grinding. Compared with other residual algorithms based on 2D truncation or Boolean operation of face gears, this algorithm has higher computational accuracy and efficiency. Thus, it lays the foundation for accurately establishing the complex spatial microscopic surface topography in the face gear generating grinding process.

Simulation and Experimental Verification of Die Quenching Deformation of Aviation Carburized Face Gear.

The tooth width and length of face gear limit control the strength of face gear, and heat treatments are often used to improve the hardness and strength of face gear. However, heat treatments will often cause additional deformations, which will affect the dimensional accuracy of the face gear. In this paper, to effectively control the deformation and ensure the accuracy of the face gear, the finite element method was used to establish the calculation model of the face gear die quenching method, and thus, the influence of die on the gear quenching deformation was analyzed. Next, the accuracy of the calculation model was verified by the pressure quenching experiment. The results demonstrated that the inconsistent phase transformation between the surface and the center of the face gear was the key factor affecting the deformation due to the influence of the carbon content. Compared with die-less quenching, the inner hole-die can effectively limit the radial shrinkage deformation of the face gear. With the increase of the upper-die pressure, the axial and radial deformations of the face gear gradually became stable. In the actual production, the load of dies should be reasonably selected based on the gear accuracy requirements.