High Gear Ratio Research Articles

Innovations in Engineering and Technology of Worm-Type Gears

Relatively small changes in engineering and technology of traditional established products turn over time into a series of milestones that determine both technical characteristics and production methods, and as a consequence - the competitiveness of the final product. Accordingly, it is relevant to periodically look at the evolution of the accumulated solutions and make some conclusions on it. For this purpose, the paper reviews innovations in design and production of worm-type gears obtained in Izhevsk scientific school in the field of gears for the last two decades: spiroid gears operating at low rotational speeds and transmitting high loads, leading to plastic deformations due to compactness of gears; spiroid gears with small gear ratios (3...8) competing with more expensive in production bevel and hypoid ones; worm gears with steel hardened gearwheels with increased strength and manufacturability; planetary spiroid gears providing extremely high gear ratio, improved methods and techniques of design and preproduction of gear cutting. The paper presents the review of innovations in design of worm-type gears made in Izhevsk scientific school in the field of gears for the last two decades: spiroid gears for cases of low speeds and small gear ratios, worm gears with steel hardened gearwheels, planetary and spiroid gears, improved methods and techniques of design and preparation of gear cutting.

The new constructive design of the planetary gearbox winches

Although the constructions of planetary reducers are complex, their technical indicators are higher than other gear boxes, and their overall dimensions are smaller. In this article, the constructions of planetary gearboxes were investigated, and an in-depth literature analysis was conducted on their modernization. Application of these gearboxes with high technical indicators and compact dimensions in lifting mechanisms would be suitable for the purpose. Thus, small overall size, large efficiency, and high reliability are the main requirements for winches, and planetary gearboxes can also provide these features. But for some reason, traditionally, geared elevator winches are mainly made with worm gearboxes. This is mainly due to the fact that they provide a high gear ratio in single stage and self-braking. But the efficiency of worm gear box is small, and the friction losses are larger. Therefore, it is time and necessity to replace them with other progressive designed gearboxes in the lifing winches. Taking these into account, in the article, as a result of structural and kinematic analysis and synthesis of planetary gearboxes, new constructions were developed and structural schemes were proposed for their application in the lifting mechanisms. For each of these schemes, the transmission ratio and efficiency were evaluated and compared with each other. The proposed schemes can be applied in the different types of lifting winches. The application fields of winches are different. Winches are more commonly used in drilling equipment and elevators. Winches are the main units of these equipments. Winches and their braking systems must meet operational requirements and operating conditions. Their strength and traction must be sufficient to perform the most demanding technological operations. Lifting and lowering speeds should ensure accident-free operations, be economically efficient and highly productive.

An exact system of generation for face-milled hypoid gears with uniform depth taper: Application to hypoid gear drives with high gear ratio

An exact system of generation for face-milled hypoid gears with uniform depth taper is proposed. This system defines the location of pinion and wheel, their respective cutting (or grinding) cutters, and the relations of motion in their respective reference coordinate systems attached to the cutting machine. As a result, the grinding cutter geometric parameters and basic machine-tool settings are analytically determined without the need of any further optimization process. The appropriate selection of the mean cutter radius is addressed following the recommendations of the Information Sheet AGMA ISO 22849-A12. The tooth contact analysis of the gear drive shows a localized bearing contact with no unloaded transmission errors in the absence of misalignments. A lower sensitivity of the contact pattern to errors of alignment is observed as the mean cutter radius is decreased. Stress analysis shows that only the application of a tip relief is needed to avoid edge contacts at the tip of the gear tooth surfaces, being the point width of the cutting blades a key parameter to balance bending stresses in the pinion and the wheel.

Design and Analysis of Harmonic Drive Reduction Pump Jack for Dynamic Performance in Oil Extraction

The purpose of this study is to provide a high gear ratio reducing pump jack system, utilizing the characteristics of high transmission ratio and precision of harmonic drives, in order to improve the efficiency of low-permeability oil field extraction. A comparison was made between the new system and the conventional walking beam pump jack. The results showed that at a stroke length of 1.5 m and pumping frequencies of 4.5 min-1, 3.5 min-1, 2.5 min-1, 1.5 min-1, and 0.5 min-1, the maximum acceleration of the suspended load in the harmonic reducing pump jack was reduced by 20.79% compared to the conventional walking beam pump jack.

ОЦЕНКА ЭНЕРГЕТИЧЕСКИХ ПОКАЗАТЕЛЕЙ УСОВЕРШЕНСТВОВАННОГО ПРИВОДА МНОГООПОРНЫХ ДОЖДЕВАЛЬНЫХ МАШИН, ТИПА «КУБАНЬ-ЛК1»

The issues of assessing the energy performance of the improved drive of a multi-support irrigation machine (DM) operating in motion in the Kuban-LK1 circle are described. It is noted that in order to increase the efficiency of DM cart drives and increase the speed of their movement, it is necessary to develop geared motors with a high gear ratio. The most promising option seems to be the use of energy-intensive gearmotors equipped with wave transmission. The rationale for the use of highly efficient gearing is given through theoretical studies. It is indicated that today, in the design of machines of this type, wheel gears with ineffective worm gears are used, as a result of which a blocked connection and uneven peripheral wheel speeds are formed in the transmission of running systems, which leads to a decrease in efficiency. operation of gear motors. It is possible to eliminate such negative qualities of the operation of the Kuban-LK DM by equipping it with gearmotors with wave transmission. Experimental studies of the machine were carried out at Ozery JSC, Kolomensky district, Moscow region, on a prototype of an 8-bogie electrified multi-support DM “Kuban-LK1”. On four trolleys (No. 2, No. 3, No. 7 and No. 8), gear motors with wave transmission were installed on each wheel. Potatoes were watered. Agricultural background is a field planted with potatoes. The slope of the field along the water supply pipeline and in the direction of movement of the carts did not exceed ± 0.01. As a result of the research, operational indicators were obtained, presented in Table 1, which allowed us to draw the following conclusions: power consumption of the support trolley with a modernized drive when operating; two electric motors, is 300 - 370 W. Under the same conditions, a serial drive consumes 630 – 670 W. Thus, power savings occur due to increased efficiency. drive (η) from 0.5 to 0.8 and its unlocking, on average, by approximately 1.8 times.

Exact Analytical Magnetic Field Analysis, Optimization Design and Realization of an Eccentric Magnetic Harmonic Gear

The eccentric magnetic harmonic gear (EMHG) has a high efficiency and high gear ratio capability for large torque transmission. The air gap magnetic field can be calculated using an exact analytical model. The analytical approach is based on the theoretically accurate hyperbolic cotangent transformation method. The relative permeance function, which is derived from the impact of rotor eccentricity, can be used to find the eccentric air gap magnetic field solution. The proposed analytical approach is employed as the basis for a genetic algorithm that is used to develop and optimize the EMHG. The analytical results are in good agreement with the finite element method results, which verifies the correctness and validity of the proposed analytical model. The experimental measurements on the dual-stage EMHG confirm the validity of the analytical prediction.

A cycloidal magnetic gear with a novel flux shield (“moon”) achieving higher torque density and lower unbalanced electromagnetic forces

Magnetic gears’ numerous potential advantages, such as contactless operation, reduced maintenance requirements, lack of lubrication, and inherent overload protection, have led to significant interest in the technology. The cycloidal magnetic gear (CyMG) is an enticing option for applications requiring high gear ratios. CyMGs do not require the modulators used in coaxial magnetic gears, but CyMGs have disadvantages, including counterproductive torque developed in the larger air gap region and unbalanced magnetic forces, which must be supported by the bearings. This paper introduces a novel “moon” structure, which serves as a flux shield, for CyMGs. The moon is made out of ferromagnetic material and is located in the larger region of the air gap. The moon increases torque density by providing a leakage path for the flux that would otherwise create counterproductive torque. The moon also reduces the unbalanced magnetic forces. This structure’s benefits are investigated using finite element analysis. The results show that, within the evaluated design space, the proposed moon can increase the maximum achievable active volumetric torque density (VTD) by 7.6% to 8.6% for each of the considered gear ratios or it can reduce the no-load eccentric force of the maximum VTD moon-free 20:1 CyMG by as much as ∼86% without decreasing the VTD.

와전류 효과에 따른 버니어 모터와 동기기의 전자계 성능 및 손실 특성 비교 분석

In this article, the analysis of electromagnetic performances and loss according to the operating ranges are conducted through the comparative study with surfaced mounted permanent magnet synchronous machine(SPMSM) and vernier PM machine(VPMM), which is classified into flux modulation pole and no flux modulation pole types. We investigated SPMSM and VPMM show different flux weakening capability at high speed, VPMM can maintain high torque due to the flux modulation effect but SPMSM was not. We revealed that high torque and power factor are related with the gear ratio closely for VPMM and SPMSM. Furthermore, VPMM with high gear ratio model is subjected to the influence of eddy current which causes degradation of the output torque and the loss of rotor core tends to be increased depending on levels of flux modulation.

Optimal Design of a Compound Planetary Reducer Using a Nonlinear Optimization Method

The growth of the robotics industry has led to rising demand for reducers that increase torque efficiently while reducing motor speed. Among them, compound planetary reducers can be effectively used in robots because they can achieve high gear ratios with smaller volume. The design of conventional reducers comprises the method of setting a gear ratio to design the gear dimensions and calculating efficiency through dynamic analysis. However, this method suffers from repeated designing and analysis, which makes it very time-consuming. Therefore, this study defines the problem of reducer design as the problem of optimization by setting an objective function, constraints, and boundary conditions, and proposes to obtain the results in a short period of time using the Sequential Least Squares Programming(SLSQP) method. Using the SLSQP method, optimization results can be obtained as real numbers, making it suitable for use in compound planetary friction reducers with no constraints on the selection of gear dimension. For the design problem of the conventional compound planetary gear reducer in which the module value exists, an additional optimal design method considering the module is proposed. To compare the optimal results, we have made a 30:1 compound planetary friction reducer and a 50:1 compound planetary gear reducer using 3D printing. A gear ratio evaluation experiment was conducted to evaluate the performance of the actual manufactured prototype reducers.

A new three-stage gearbox concept for high reduction ratios: Use of a nested-cycloidal architecture to increase the power density

Increasing the Gear Ratio (GR) while decreasing the gearbox dimension is a contradiction that mechanical designers are challenged to solve. The increasing importance of fine-tuning high power density designs has led to the development of innovative solutions involving cycloidal and hypocycloidal gears. However, when the required GR increases and the number of the stages raises, the gearbox architecture plays a key role in minimizing the overall dimensions. In the present paper, an innovative gearbox architecture is presented. The new design combines three cycloidal and hypocycloidal gearing stages to achieve a higher GR with respect to a traditional two-stage cycloidal gearbox with the same overall dimension. This architecture is called Nested since it involves stages with internal and external gears arranged one inside the other. A comparison of the proposed solution with the more compact two-stage cycloidal architecture (Wolfrom) is shown. The GRs as a function of the total number of meshing features are discussed as well as the torques acting on each component. Eventually, a design solution is illustrated.

Cycloidal Reluctance Magnetic Gears for High Gear Ratio Applications

At high gear ratios, surface permanent magnet (SPM) cycloidal magnetic gears (CyMGs) can achieve higher torque densities than SPM coaxial magnetic gears (CoMGs). This article introduces the radial flux reluctance CyMG (Rel CyMG) topology and its operating principles. The Rel CyMG replaces the permanent magnets (PMs) on an SPM CyMG’s inner rotor with salient teeth. Additionally, the Rel CyMG only requires half of the SPM CyMG’s outer rotor PM count to achieve the same gear ratio, which simplifies assembly and allows the use of wider magnets. This may improve high gear ratio designs’ manufacturability. A genetic algorithm (GA) was used with 2-D finite element analysis (FEA) to optimize Rel CyMGs, SPM CyMGs, and SPM CoMGs and demonstrate that SPM CyMGs significantly outperform the other topologies at higher gear ratios in terms of specific torque (ST) and PM ST. However, Rel CyMGs outperform SPM CoMGs at higher gear ratios, with respect to ST and PM ST. Rel CyMGs also eliminate the need for a PM retention sleeve and potentially enable the use of smaller air gaps, which can allow them to achieve slightly higher PM STs than SPM CyMGs at ultrahigh gear ratios. Employing Halbach arrays significantly improves both CyMG topologies’ ST.

Surface undulation parameters of continuously variable transmission friction during turning

City traffic conditions contain frequent starts and stops. Thus, Single-Stage Continuously Variable Transmissions are subject to high loads when operating at high gear ratios, leading to excessive friction that cause slipping and heating of friction elements. This study proposes a microprofile with undulation on the surface of the pulley. A mathematical dependence on the technological quality assurance of the surface layer of the V-belt transmission parts formed during turning is proposed, enabling the prediction of height parameters of undulation depending on the change in the spindle speed, feed, and cutting speed. Estimating the error in the field experiment data and calculating values of the proposed methodology showed that the height parameters of the undulation of pulleys have a relative error of 6.3%.

AC Losses in Form-Wound Coils of Surface Mounted Permanent Magnet Vernier Machines

Surface mounted permanent magnet Vernier (SPM-V) machines, because of their high torque density and multi-pole structure, are promising candidates for low-speed direct-drive applications. To achieve high torque density, the SPM-V machines are generally designed with high gear ratios. Therefore, their operating frequencies can be much higher than those of the conventional SPM machines. This potentially increases the alternating current (AC) winding losses, especially those with form-wound coils proposed for high-power applications. This article investigates the AC losses (including skin effect, proximity effect, rotor PM induced, and circulating current losses) in form-wound stator coils of a 3 MW direct-drive SPM-V machine with different slot/pole number combinations. The study reveals that the SPM-V machines have significantly higher AC winding losses than their conventional SPM counterparts for similar operating conditions. To reduce the AC winding losses in SPM-V machines, a novel flux shunt concept is proposed along with other conventional techniques such as increasing the number of turns/coil (with terminal voltage being kept constant) and parallel strands/turn, providing extra clearance at slot opening. With the loss reduction techniques implemented, the SPM-V machines can achieve comparable efficiency but much higher torque density than their conventional counterparts. Moreover, the proposed flux shunt was also found to be very effective in reducing the potential risk of permanent magnet (PM) irreversible demagnetization, a key issue for SPM-V machines at high power ratings.

Modeling and Stiffness-based Continuous Torque Control of Lightweight Quasi-Direct-Drive Knee Exoskeletons for Versatile Walking Assistance.

State-of-the-art exoskeletons are typically limited by low control bandwidth and small range stiffness of actuators which are based on high gear ratios and elastic components (e.g., series elastic actuators). Furthermore, most exoskeletons are based on discrete gait phase detection and/or discrete stiffness control resulting in discontinuous torque profiles. To fill these two gaps, we developed a portable lightweight knee exoskeleton using quasi-direct drive (QDD) actuation that provides 14 Nm torque (36.8% biological joint moment for overground walking). This paper presents 1) stiffness modeling of torque-controlled QDD exoskeletons and 2) stiffness-based continuous torque controller that estimates knee joint moment in real-time. Experimental tests found the exoskeleton had high bandwidth of stiffness control (16 Hz under 100 Nm/rad) and high torque tracking accuracy with 0.34 Nm Root Mean Square (RMS) error (6.22%) across 0-350 Nm/rad large range stiffness. The continuous controller was able to estimate knee moments accurately and smoothly for three walking speeds and their transitions. Experimental results with 8 able-bodied subjects demonstrated that our exoskeleton was able to reduce the muscle activities of all 8 measured knee and ankle muscles by 8.60%-15.22% relative to unpowered condition, and two knee flexors and one ankle plantar flexor by 1.92%-10.24% relative to baseline (no exoskeleton) condition.

Influence of meshing stiffness on load distribution between planets of planetary gear drives

Planetary gear sets are suitable for high power density and gear ratio, but this means high torques and stress levels. Though the torque is transmitted between multiple planets, it is not evenly distributed among them due to manufacturing and assembly errors. The torque is greater than the average value in some planets, and smaller in the others, which will have to be considered for strength calculations. In addition, this uneven load distribution among planets can also be affected by the meshing stiffness, if the planets are not at the same relative meshing position at any moment. In this paper, the condition for uneven distribution of the load between planets due to the meshing stiffness is established, and the calculation method of the corresponding influence factor is proposed.

Cycloidal Magnetic Gear Combining Axial and Radial Topologies

Axial flux and radial flux cycloidal permanent magnetic gears are characterized by high gear ratios and high torque densities; however, their rotors experience large unbalanced forces, which stress the bearings used in the gear. This paper presents a new cycloidal magnetic gear topology that combines the radial and axial flux topologies. The paper analyzes the forces and torques contributed by the axial and radial magnets in this topology using 3D finite element analysis. It was found that the perpendicular force is necessary to transfer torque to the high-speed shaft and, thus, cannot be cancelled out, but the eccentric component of the magnetic forces can be largely cancelled out, potentially reducing bearing losses and increasing the lifespan of the bearings used in the gear. A proof-of-concept prototype was constructed. Experimental slip torque results matched 3D finite element analysis (FEA) simulations to within 15%, and testing showed that no-load losses were reduced and the slip torque was increased by combining both axial and radial topologies, compared to using an axial configuration alone.

Improving load capacity parameters of worm gears

Worm gear drives possess several advantages in comparison to other types of transmissions. Some of the most important advantages are: high gear ratio, compact design and vibration damping. Therefore, the author’s team focused within the framework of research presented on creating opportunities to improve another very important characteristic feature of worm gears: the load capacity. During the process of investigation, optimization procedures have been created aiming to improve the load capacity parameters of worm gear trains. Different functional parameters and certain geometry parameters have been taken into account such as rotational frequency of the worm shaft, gear ratio, module and geometry dimensions of the worm gear set. The research methodology applied includes several stages. The research results obtained are presented and discussed. Conclusions and recommendations are made.

Research of gear drives

Worm gear drives possess important advantages such as: compact design, high power density due to a high gear ratio within a single gear stage. However, these gear drives often show high sliding speeds within the tooth contact, resulting in relative low efficiency coefficient in the meshing. Therefore, an exact calculation regarding efficiency in the meshing and load capacity is important during the beginning stage of the machine design process. Currently, no calculation method is available to analyze worm gears considering efficiency in meshing and contact strength. The objective of the research implemented was to analyze extensively the meshing efficiency and the contact stress behavior of various geometry designs of worm gears drives. Optimization research has been implemented considering the criteria mentioned. All calculations and theoretical analysis have been implemented for different center distances, different modules, gear ratios and rotational speeds of the worm shaft. Simulation results are shown and discussed. Important conclusions and recommendations are suggested.

A novel cylindrical skiving tool with error-free flank faces for internal circular splines

Strain wave gearing is widely applied in robotics and aerospace because of its zero-backlash and high gear ratio. Its circular spline (CS) is a rigid internal gear engaged with a flex spline (FS), driven by the wave generator's rotation. Obtaining the CS's tooth profile is difficult because the FS has a deformed ellipse shape caused by the wave generator. Furthermore, most CSs are manufactured by gear shaping and thus are lower precision and productivity comparing to external gears produced by gear hobbing. Power skiving is recently applied to overcome this problem. Mathematical models of CS and its skiving tool are established here. Moreover, a cylindrical tool is submitted to make tool manufacturing easier than a conical tool. A novel design for the error-free cylindrical tool and the skived gear is eventually derived. By modifying machine settings of the skiving process, it provides a relief angle to avoid the cylindrical tool rubbing with the internal gear. This manufacturing process is conducted on a six-axis CNC bevel gear cutting machine. An error analysis of the VERICUT cutting simulation result confirms the correctness of the proposed models.

The influence of the cycloid disc bearing type on the cycloidal speed reducer efficiency

The robotics industry has experienced a rapid expansion in the last decade. As a result, the market of speed reducers with high gear ratios, high precision and a compact design is growing rapidly. In addition to these characteristics, it is very important for gear trains to have high efficiency. Because of their compact design, cycloidal speed reducers are not exposed to axial forces, which is their important characteristic. This means that radial bearings can be used in their supports. The bearing type has significant effects not only on the design and dimensions of the cycloid speed reducer but also on its efficiency. In this paper, an analysis of power losses for different types of rolling bearings of a cycloid disc has been performed. At the end of the paper, concrete conclusions are presented as well as directions for future research.