Toothed Wheel Research Articles

ГЕОМЕТРИЧЕСКИЙ АНАЛИЗ И ТЕОРЕТИЧЕСКАЯ ОЦЕНКА КПД ПЛОСКО-КОНИЧЕСКОГО ЗАЦЕПЛЕНИЯ СФЕРИЧЕСКОЙ РОЛИКОВОЙ ПЕРЕДАЧИ

The study objective was to assess the influence of friction factors and geometric parameters of a spherical rolling screw motion drive on its efficiency. The load is transferred by means of a cone-and-plate engagement of two rows of rollers mounted on a satellite with fixed and driven plate central gears. With the help of a spherical rolling screw motion drive, it is possible to realize a wide range of gear ratios (16...200) and reduce the material capacity of the gearbox, ensuring the ratio of its mass to the nominal transmitted torque of less than 0.1 kg/(N•m). The main task of this research is to find out the ascent angle of the spatial closed center curves with the help of which the surfaces of the central wheel teeth are formed. The research methods are based on the application of the classical mechanics laws and computer modeling algorithms in NX system. The novelty of the research is in the novelty of the technical object under study, its low level of being studied, the lack of detailed methods of its calculation and design. As a result, based on the analysis of the geometric satellite model, the equations of the center curves are obtained and an algorithm for determining the ascent angle of the center curve in the middle section of the central wheel teeth is developed, which allows power analysis of the motion drive. The applicability of the formula for calculating the average ascent angle of a piecewise helical curve located on a cylindrical surface for spherical motion drives is evaluated and the necessity of its adjustment taking into account a given gear ratio and the inclination angle of the drive shaft crank is found out. An algorithm is developed for the theoretical study of the efficiency of spherical roller gears at the design stage.

Modelling and Experimental Study of Power Losses in Toothed Wheels

In recent decades, the request for more efficient performances in the aeronautical sector moved researchers to pay particular attention to all the related mechanisms and systems, especially with respect to the saving of power. In this context, the bearing modeling and design, as well as gear coupling, play a fundamental role. Moreover, the need for low power losses also concerns the study and the implementation of advanced lubrication systems, especially for high peripheral speed. With the previous aims, this paper presents a new validated model for toothed gears, added to a bearing model; with the link of these different submodels, the whole model describes the system’s dynamic behavior, taking into account the different kinds of power losses (windage losses, fluid dynamic losses, etc.) generated by the mechanical system parts (especially rolling bearings and gears). As the bearing model, the proposed model is characterized by high numerical efficiency and allows the investigation of different rolling bearings and gears with different lubrication conditions and frictions. A comparison between the experimental and simulated results is also presented in this paper. The analysis of the results is encouraging and shows a good agreement between experiments and model simulations, with particular attention to the power losses in the bearing and gears.

Research of the deformability of the cantilever axis of the satellite of a multi-satellite planetary gear and its influence on the load distribution over power flows

A mathematical model of the axis of the satellite, cantilevered in the cheek of the carrier of the planetary gear, is presented. The axis of the satellite is presented in the form of a beam on an elastic base. The influence of the flexibility of the axle and the drive elements mated with it on the distribution of the load over power flows is considered. The Leibniz formulas and the Euler method were used to obtain the model. The coefficient of uneven load distribution over power flows is obtained by solving a system of displacement compatibility equations, including deformations of the wheel teeth, rolling bearing, satellite axle and mating parts, taking into account the initial non-adherence of the teeth due to gear manufacturing errors. The load capacity of a planetary gear with cantilever axes of satellites is analyzed depending on the number of power flows. Keywords: planetary gear, deformation, cantilever axle, load distribution. fplehanov@list.ru, alexandrsun4009@gmail.com

Simulation of VERICUT-based Generating Grinding of Involute Beveloid Gears

Based on the principle of generating grinding, VERICUT is used for generating grinding of involute beveloid gears. Firstly, the tooth surface equation of the involute beveloid gears is derived according to the principle of involute beveloid gears forming and gear meshing theory, and the theoretical model of the involute beveloid gear is established; secondly, the CNC conical gear grinding machine model, grinding wheel tool model and tooth blank are built in UG and imported into VERICUT, and the CNC machining program of the generating grinding is written to carry out the generating grinding simulation; finally, the simulated involute beveloid gear is automatically compared with the design model to verify the accuracy of the generating grinding simulation machining method. This study provides theoretical guidance for the practical machining of involute beveloid gears, reduces costs and shortens machining cycles, thus improving the productivity of involute beveloid gears.

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.

Pattern and Analysis of Corrugation-Sand Retaining Seals for Tooth Wheel Drill Bits

The existing seal is not designed with a special sand retaining structure, and it is difficult to discharge the mud particles after entering, resulting in serious wear of the seal and premature failure. Therefore, a special-shaped sealing structure for sand blocking of roller cone bits is proposed to solve the problem of sealing wear. Starting from the structural principle, the structural parameters of the special-shaped seal of the sand-retaining flap are designed based on the O-ring, and the sealing principle is analyzed, the formula of grease leakage is derived, and the simulation and optimization analysis are completed with the aid of APDL. This proved the feasibility of the design. The influence law of structural parameters on contact pressure and leakage is obtained, and the formula of leakage is verified; The influence of structural parameters on the contact gap of the sand flap is obtained. Under the condition of optimal combination of structural parameters, the grease leakage is 43 mg/h, a decrease of 85%. Theoretically, it takes 580 h to exhaust the grease, and the contact gap of the sand flap is 0.00019479 mm, a decrease of 95%, which can greatly reduce the wear of the main seal. This study opens up a new idea for seal design.

СТРУКТУРНЫЙ АНАЛИЗ И УРАВНОВЕШИВАНИЕ МЕХАНИЗМА ВОЗВРАТНО-ПОСТУПАТЕЛЬНОГО ДВИЖЕНИЯ

The paper presents new mechanisms of reciprocating motion, built on the basis of a two-row planetary gear with non-circular gearwheels with two external gears. The desired type of the output link motion is realized by converting the rotationally reciprocating movement of the planetary mechanism output shaft using the transmission “toothed wheel — toothed rack”. The proposed mechanisms are balanced on the example of three planetary gear schemes, with one, two and three satellites. Structural analysis of gears with multiple satellites has shown that the addition of each extra satellite takes away one degree of freedom from the mechanism, as a result of which it becomes immobile. It is proposed to use a counterweight on each additional satellite instead of one two-moving kinematic pair, which leads to the elimination of redundant links. The conditions of static equilibrium for the developed schemes of planetary mechanisms are obtained, which make it possible to locate the centers of mass of the mechanisms on the axis of rotation and thereby significantly reduce noise and vibration in the gear developed on its basis.

Detect the stiffness transition in beam structures by using the passive tap-scan method

Damage detection of bridges through the response of a passing vehicle has drawn much attention in recent years. Most related researches focus on the impact of the bridge stiffness on vehicle responses. However, this paper demonstrates that the vehicle response is more sensitive to the stiffness transition in bridge girders. The theoretical basis is established on a vehicle-bridge interaction model, in which the change of an effective vehicle stiffness is introduced to represent the change of beam stiffness. The solution to this problem clearly shows that the acceleration of vehicle has an abrupt change at the stiffness transition point due to the discontinuity of the stiffness gradient. This effect will be enhanced when applying a tapping force near the vehicle resonance frequency. This tapping force can be economically generated by coordinating the vehicle velocity and the geometric pattern of toothed wheels, which was called the “passive tap-scan method” in a recent paper. This theory also reveals that the amplitude of the acceleration of vehicle is a quadratic function of the stiffness change ratio. Hence, a novel damage detection method is proposed to give a quantitative evaluation of the damage. These theoretical findings are quantitatively verified by numerical simulations and experimental tests on a standard pre-stressed concrete T-beam. Then, the practical capability of this damage detection method is further demonstrated through a field test on a real bridge.

Experimental study on motion and mechanical characteristics of the vertical wheel in the rock-breaking process

Polycrystalline diamond compact (PDC) drill bit often performs with low ROP, short service life and poor stability under complicated and difficult to drill formations. Therefore, a vertical wheel PDC bit is proposed, which is a new drill bit technology applying an integrated unit combining the tooth wheel and the rotary shaft thereof. Besides, the experiments on motion and mechanical characteristics of the vertical wheel under the conditions of tooth shape and number of teeth, normal deflection angle of the wheel, and different cutting depth were carried out using variable parameter experimental device, and the movement, force law, and crushing specific work of vertical wheel under different experimental conditions were obtained. The comparative experiments of PDC cutting rock breaking under the conditions of parallel cutting of PDC unit and pre-damage of the wheel were also carried out, and the cutting load of PDC teeth under pre-damage conditions is between 38.72% and 70.95% lower than that of parallel cutting was obtained. Finally, a comparative experiment of indoor drilling between vertical wheel PDC bit and conventional PDC bit was carried out. Results show than when drilling in gravel rock, under the same WOB, the torque response of vertical wheel PDC bit is equivalent to that of the PDC bit, while the ROP of vertical wheel PDC bit is 22.94%–53.33% higher than that of conventional PDC bit, and the three-dimensional acceleration of the vertical wheel PDC bit is 19.17%–76.23% of that of the PDC bit. The experimental results contribute to a better understanding of vertical wheels and provide technical support for their use in PDC bits.

Расчет геометро-кинематических характеристик зацепления арочных зубьев цилиндрической передачи при погрешностях взаимного расположения

The use of cylindrical gears with arched teeth in the drives of energy-saturated machines (locomotives, final drives of tractors, top drives of drilling rigs, helicopters) makes it possible to multiply the durability of gears compared to spur and helical gears. To date, a dozen and a half different techniques and methods for designing and manufacturing arched teeth of cylindrical wheels have been proposed. Among them, the most promising is the method of cutting arched teeth on CNC machines with circular cutter heads using the running-in method with a single division. The purpose of the article is to implement the construction of mathematical models for the formation of arched teeth on the basis of the theory of spatial gearing and to study the geometric and kinematic characteristics of their gearing under conditions of non-zero errors in the relative position of the wheel and gear in the transmission. The object of study is a cylindrical gear with arched teeth. In the article, dependencies for radius-vectors and unit vectors of the normals of the surfaces of arched teeth of cylindrical wheels are obtained, a mathematical model is developed for calculating the points of contact of arched teeth in engagement in the presence of a misalignment angle, a non-parallelism angle and wheel displacement. On the example of the final transmission of a locomotive, for the first time, the influence of the density of fit of the surfaces of the teeth in engagement on the displacement of the working lines from the average section of the tooth due to errors in the position of the transmission elements was studied for the first time. By calculating the error of the position function in the transmission, the procedure for quantifying its nonconjugacy is considered. It has been established that the geometry of the arched teeth of the method under study, under conditions of deviation of the positions of the transmission elements from the nominal ones, leads to a mismatch of the engagement, the position error function has a sawtooth shape, as a result of which impacts are inevitable when the teeth enter the engagement. Ways are proposed to achieve, within the framework of the considered method of manufacturing arched teeth, an approximate nature of the engagement of the teeth in the gear

ANALYSIS OF THE INFLUENCE OF THE DISPLACEMENT OF THE GEAR RACK PROFILE OF THE PAIR EVOLUTION GEARING ON THE QUALITY INDICATORS OF THE TRANSMISSION

The article is devoted to the study of the influence of the modification of the paired evolute gearing with convex-concave contact on the quality indicators of transmission, namely, the contact pressure and the speed of slippage in the engagement. Previous studies of evolute gears showed the presence of characteristic zones on the side surface of the tooth, which have worse values of quality indicators than in similar involute gear. One of the ways to remove these zones or to reduce their impact on the load capacity of the transmission is to modify the tooth profile, which will be implemented by shifting the profile of the processing gear rack. A displacement factor is added to the equation of the rail profile curve, which has the same value for the gear and wheel teeth, but the opposite sign. On the basis of the developed equation, the side profiles of the teeth of the gear and the wheel were constructed. Several values of the rack displacement coefficient with a positive and negative sign for the gear teeth are considered. The results of the research allow us to evaluate the influence of the amount and direction of the rail displacement on the curvature of the tooth profiles, the contact pressure in engagement along the height of the tooth, and the relative and absolute speed of sliding. The modifications of the profile of the processing toothed rack proposed in this work will expand the existence of paired evolute gears with a different set of quality indicators. This will make it possible to design gears with rational values of contact pressures and slip speeds when they are used in heavily loaded transmissions created for specific operating conditions. Gears with relatively high slip speeds can be used in road and construction equipment transmissions, which are characterized by low shaft rotation frequency, in which the speed of slip between the teeth does not have a significant effect on the life or efficiency of the transmission. Otherwise, gears with relatively low slip speeds are very relevant when they are implemented in the transmission of modern and promising vehicles with a hybrid or fully electric power unit, especially in the case of passenger cars with high-speed electric motors.

ОБҐРУНТУВАННЯ ВИБОРУ ФОРМИ ІНДУКТОРА ДЛЯ МАГНІТНО-ІМПУЛЬСНОЇ ОБРОБКИ ВЕЛИКОГАБАРИТНОГО ЗУБЧАСТОГО КОЛЕСА

Reducing products cost, and currently increasing the environmental friendliness of technological processes, is the main goal of machine-building production. Achieving these goals can be, in particular, due to the introduction of new processing methods. One of which is magnetic pulse processing(MPP). Using this method requires the use of special equipment, such as a magnetic inductor.The article proposes the use of a specially shaped inductor to strengthen the surface layer of the teeth of a large-sized gear wheel. The considered types of winding for the manufacture of a production coil of inductance from the point of view of the direct effect on the areas of the tooth with the greatest wear. Applying the Biot -Savart -Laplace law to calculate the magnetic fields of linear conductors, a detailed calculation of the inductor was carried out. It showed that the proposed design cannot provide strengthening over the entire plane of the contact spot of the tooth, where the greatest wear occurs during the operation of the wheel. When applying magnetic pulse processing, it is necessary to pay great attention to the shape and type of inductor winding. The type of winding and the turns arrangement of the inductor coil are also limited by the design of thepart. Special design restrictions are established where it is necessary to process internal cavities. Such cavities include the spaces between teeth of gear wheels.The article states that the magnetic field of the inductor, which has a parallel winding and covers a tooth, has the greatestforce on the edges of the tooth, and not on the area of the contact patch. It is also calculated that the magnetic field cannot exceed 1800 kA/m with the given parameters of the electric generator. Optimizing inductor shape and winding makes it possible to significantly reduce the requirements for generators while keeping the quality of the output at the same level.

ОЦЕНКА РИСКОВ И ПОТЕНЦИАЛЬНЫХ ОТКАЗОВ ПРИ ПРОЕКТИРОВАНИИ ПРОЦЕССА ИЗГОТОВЛЕНИЯ ГИБКИХ КОЛЕС ВОЛНОВЫХ ЗУБЧАТЫХ ПЕРЕДАЧ НА ОСНОВЕ МЕТОДИКИ PFMEA

The article presents a model for assessing the risks of potential failures of the machining process of flexible wheels of wave gears (WG). The constructed model is based on the methodology for analyzing the types and consequences of potential process inconsistencies (PFMEA). Structural, functional analysis and analysis of failures arising in the process of turning, grinding and cutting the teeth of a flexible wheel are carried out. As a result of the analysis, a risk assessment was carried out and a list of measures aimed at improving the quality of the machining process of flexible wheels of the WG was established.

Probability estimate of the strength reliability of toothed wheel gear

An improved calculation method for the strength reliability of surface-hardened cylindrical gears, based on determining the probability of safe operation of the gear is presented in the paper. The calculation of probability of fault-free operation according to the criterion of depth contact endurance is implemented and the tools of non-parametric statistics are applied. When calculating contact stresses, the twist angle caused by deformations of the shafts gear is taken into account. The reliability of the toothed wheel gear was evaluated using the developed technique.

OPTIMAL DESIGN OF INVOLUTE SPUR GEARS WITH INCREASED CONTACT RATIO: OBJECTIVE FUNCTION, VARIABLES PLANNING AND CONSTRAINTS

Reducing the mass and dimensions of involute spur gears is an actual task of modern mechanical engineering. One of the perspective ways to solve it is the use of gearing with an increased working tooth depth and profile contact ratio εα ≥ 2. The study is devoted to the development of optimal design methods for such gears. Optimality criteria is formulated as follows: the contact stresses in the pitch point must take a minimum value when all constructive, geometric, kinematic, and technological constraints are met, first, when the profile contact ratio εα ≥ 2 is ensured. Variables planning are defined. These are addendum coefficients of the basic racks tooth for pinion and wheel , ; profile angle of the basic rack α; addendum modification coefficient of the pinion x1. Formed a system of constraints for the variables planning: the main functional constraint of the minimum value of the profile contact ratio: εα ≥ 2; constraint for the addendum coefficients of the basic racks tooth for pinion and wheel , ; constraint for profile angle of the basic rack α; constraint for addendum modification coefficients x1, x2; absence of the cutter interference for tooth dedendum; absence of the sharpening for tooth addendum; absence of the mesh interference; ensuring the bending strength of pinion and wheel teeth. A method for solving the problem of optimal design is chosen. The method of probing the space of design parameters was chosen from all the variety. The points of the LPτ-sequence are used as test points. The method allows you to operate with a significant number of parameters – up to 51, provides a sufficiently large number of evenly distributed test points – up to 220. In further studies, it is planned developing of methods and algorithms for solving the problem. Also carry out test and verification calculations to confirm and evaluate the theoretical results. Keywords: spur gear, profile contact ratio, contact stress, optimal design, objective function, variables planning, constraints of the variables planning.

Research on Generating Gear Grinding Machining Error Based on Mapping Relationship between Grinding Wheel Surface and Tooth Flank

This paper proposes a method to study the machining error when one is generating gear grinding based on the mapping relationship between the grinding wheel surface and the tooth flank. The profile of the grinding wheel after grinding is collected, and the theoretical tooth flank is derived according to a model of generating gear grinding. By comparing the normal deviation of the theoretical tooth flank with the measured tooth flank, the machining error characteristics are identified. Firstly, the mathematical model of generating gear grinding is established according to a multi-body theory and coordinate transformation. Secondly, the experiments of the lead modification for helical gear were performed on a YW7232 CNC gear grinding machine. The tooth flank twist compensation function was turned off in experiments No. 1–No. 3, and it was turned on in experiments No. 4–No. 6, while the other process parameters kept the same. Then, the corresponding theoretical tooth flank data were derived from the grinding wheel surface which were measured using the laser profilometer LJ-V7000. Finally, the machining error characteristics were obtained by analyzing the difference between the theoretical and measured tooth flank deviations. The result of this paper can provide theoretical and practical references for the improvement of the gear grinding accuracy and gear modification design.

Electrospun Nanofiber/Textile Supported Composite Membranes with Improved Mechanical Performance for Biomedical Applications.

Textile-supported nanocomposite as a scaffold has been extensively used in the medical field, mainly to give support to weak or harmed tissues. However, there are some challenges in fabricating the nanofiber/textile composite, i.e., suitable porous structure with defined pore size, less skin contact area, biocompatibility, and availability of degradable materials. Herein, polyamide-6 (PA) nanofibers were synthesized using needleless electrospinning with the toothed wheel as a spinneret. The electrospinning process was optimized using different process and solution parameters. In the next phase, optimized PA nanofiber membranes of optimum fiber diameter with uniform distribution and thickness were used in making nanofiber membrane-textile composite. Different textile fabrics (woven, non-woven, knitted) were developed. The optimized nanofiber membranes were combined with non-woven, woven, and knitted fabrics to make fabric-supported nanocomposite. The nanofiber/fabric composites were compared with available market woven and knitted meshes for mechanical properties, morphology, structure, and chemical interaction analysis. It was found that the tear strength of the nanofiber/woven composite was three times higher than market woven mesh, and the nanofiber/knitted composite was 2.5 times higher than market knitted mesh. The developed composite structures with woven and knitted fabric exhibited improved bursting strength (613.1 and 751.1 Kpa), tensile strength (195.76 and 227.85 N), and puncture resistance (68.76 and 57.47 N), respectively, than market available meshes. All these properties showed that PA nanofibers/textile structures could be utilized as a composite with multifunctional properties.

Measurement Method of Temperature of the Face Gear Rim of a Spiroid Gear.

Spiroid gears are used to transfer heavy loads with a significant reduction in input speed. Like most toothed gears, they are lubricated with oil whose physical properties change with temperature fluctuations, affecting the durability and reliability of the gear. Bearing this in mind, gear designers plan systems for measuring oil temperature during gear operation at the design stage. The authors of this paper are of the opinion that, in the case of spiroid gears, it may be insufficient to measure only oil temperature during gear operation. It seems that the working temperature of a pair of mating wheels has a decisive impact on the durability and reliability of the gear. The measurement of oil temperature in a tested gear should be treated as a supplementary measurement with the measurement of temperature on the toothed wheels as the basic measurement. Taking into consideration the above, an innovative test bench was designed and built, making it possible to observe how working parameters of the gear (torque and rotational speed) affect the temperature of the lubricating oil, but most of all, the working temperature of the pair of mating wheels. This paper presents, among others, the results of research on the impact of the rotational speed of the input shaft and load on the distribution of temperature on the toothed rim of the face gear.

COMPARATIVE SERVICE LIFE ANALYSIS FOR WORM GEARS ACCORDING TO DIFFERENT FAILURE CRITERIA

In this paper, a comparative analysis of the service life of worm gear wheels for various failure criteria is carried out. Based on this analysis, a method is proposed for selecting the worm gear wheel material, the values of the modulus, on which the bending strength of the teeth depends. Research has shown that increasing the bending strength of teeth is of great practical importance, both for one-sided and two-sided loads. This also makes it possible to significantly increase the lifetime of one-side loaded gear wheels by replacing their working flanks with non-working ones. it was proposed to replace the working surfaces of the teeth of worm wheels after a certain service life.

Kinematic Characteristics of Vertical Runner and Numerical Simulation Analysis of Rock Breaking

In order to solve the problems of PDC teeth easy to collapse and fail in hard, hard and soft interlaced formations and gravel bearing formations, low mechanical speed, and difficult orientation caused by high torque response of pdc bits in directional drilling, this paper proposes a new type of composite bit with vertical wheels on the blade. Through theoretical analysis, the rotating conditions of the vertical wheel are obtained, that is, the contact angle of the cutting teeth of the vertical wheel must be greater than the center angle of its two adjacent teeth. At the same time, the cutting tracks generated by the previous vertical wheel unit experiments are analyzed, and the causes of different cutting tracks are obtained. Finally, the rock breaking of the PDC teeth under the pre damage of the vertical wheel is numerically simulated and analyzed, and it is concluded that the force on the PDC teeth is closely related to the relative height between the cutting teeth of the vertical wheel, It increases with the increase of relative height. When the relative height is 2mm, the tangential force on the PDC tooth is 4.78 times that when the relative height is 0mm, and the axial force is 2.47 times that when the relative height is 0mm. At the same time, the relationship between the force on the PDC teeth and the normal deflection angle and the rake angle of the vertical roller is not obvious.