This paper proposes a method of directly designing the surface of action of a hypoid gear. In the proposed method, the characteristics of the gear meshing are independent of the manufacturing process. The conjugate gear surfaces can then be accurately obtained by coordinate transformation. A plane was selected as the surface of action to achieve hypoid gears with a higher performance than face gears. The proposed hypoid gear may have the same features as cylindrical involute gears that also mesh in the plane of action and are unaffected by translational assembly error. A design example is presented in this paper to verify that tooth surface meshing in the plane of action can be achieved for a high-reduction ratio hypoid gear. The influence of different types of assembly error on the tooth flank error was examined numerically by comparing with face gears.
Hypoid gears are used as the final reduction gear of vehicles to transmit and change direction torque. Plastic deformation of a hypoid gear tooth flank occurs when a load exceeding the yield stress acts on the tooth surface. This study analyzed the plastic deformation mechanism of hypoid gears. First, the relationship between plastic deformation and these stresses was identified by finite element analysis of approximated tooth contact. The results of this analysis found that local plastic deformation of the tooth flank is caused by internal stress under line of contact. The local plastic deformation expands to all the tooth section by movement of the line of contact. Particularly, the lines of contact near heel side contribute to the plastic deformation more than the other lines. Second, a plastic deformation index which was defined for simulation of the plastic deformation consists of three elements: 1) yield stress considering the hardness distribution of a case-hardened gear, 2) internal stress under the line of contact considering contact load by tooth contact analysis calculated by two cylinders Herzian contact model, and 3) correction coefficients both tooth profile direction and tooth trace direction at the contact point. The correlation between the plastic deformation index and plastic deformation was confirmed by a deformation test.
A new type of curve-face gear pair - high speed curve-face gear pair is proposed. It combines the high speed cam motion law and the curve-face gear transmission, and can transmit rotation/axial motion and power between intersecting axis. The meshing coordinate system of the gear transmission is established and the basic principle of engagement is expounded. The composite motion law and force of high speed curve-face gear drive are analyzed, and influences of the basic structural parameters on the pressure angle and the force are analyzed in detail. The comparison between the experimental results and the theoretical results shows that the basic principle and design of the gear transmission are verified.
Accompanying the improvement of vehicle interior quietness in recent years, there has been a need to manufacture low-noise transmission gears at low cost. In response to this need, we adopted a gear honing process as the finishing method following heat treatment in order to reduce the source of gear noise. Previously, gear manufacturing processes generally proceeded in the order of hobbing, gear shaving, heat treatment and gear honing. For the purpose of reducing manufacturing costs, however, there has been a trend in recent years to eliminate gear shaving, resulting in just the processes of hobbing, heat treatment and gear honing. However, with the manufacturing processes of hobbing, heat treatment and gear honing, there are several factors that make it necessary to improve the machining accuracy of the hobbing process. Therefore, this paper describes a hobbing simulation that has been conceived as a first step toward improving hobbing accuracy. This simulation was devised to make clear the effect of the positional relationship between the workpiece and the tool on gear accuracy, including workpiece pitch error and tooth runout. It has been verified on the basis of machining tests. The following results were confirmed by the simulation and machining tests. (1) Work piece positioning accuracy during hobbing has a large effect on pitch error and tooth runout. (2) Tool positioning accuracy greatly affects the tooth profile and helix undulation and also has a large effect on imparting periodic error to pitch error and tooth runout. These results confirmed the effectiveness of the hobbing simulation in determining hobbing process control values.
In this study, a measurement method of surface texture of tooth flanks with a CNC gear measuring instrument is validated. Especially, in order to inspect effect of probe profiles on the evaluation of surface texture, this paper proposes a numerical calculation method that simulates displacement of the probe contacting with tooth flanks of interest. The proposed method uncovers properties of profile curves of tooth flanks measured with different probes, which are installed on the gear measuring or surface roughness instruments. In the simulation, scanned data of a roughness standard test piece is used as tooth flanks, and ideal geometrical models of the different probes are used to calculate the probe motion. Finally, the statistical characteristic quantities of the simulated profile curves are evaluated to show the effect of the probe profile difference on the measurement results.
In this study, sintered and powder-forged rollers and gears with different densities and nickel contents were fatigue-tested using a roller testing machine and a gear testing machine in order to elucidate their fatigue strength. The densities of the sintered and powder-forged rollers and gears were in the range 7.01 g/cm3 to 7.84 g/cm3, and the nickel contents of the metal powders were chosen as 0.5 % and 3.0 %. These experimental results were compared with the results for ingot steel ones. The hardness near the surface of the test specimens with a nickel content of 3.0 % was lower than that of the other ones. The pores in the sintered rollers became smaller or disappeared upon hot forging. The failure modes of the rollers and gears were mainly spalling due to subsurface cracking and pitting due to surface cracking, respectively. The fatigue strength of the sintered rollers and gears was the lowest in this experimental range. The fatigue strength of the powder-forged rollers and gears was roughly equivalent to that of the ingot steel ones, respectively. The fatigue strength of the test specimens increased as their density increased. It was clear that the fatigue strength of the sintered and powder-forged rollers and gears was proportional to the hardness at the failure depth for nickel contents of 0.5 % and 3.0 %. In other words, the fatigue strength of the rollers and gears with a nickel content of 3.0 % was similar to those of the others because of the toughness effect of nickel under the same material density.
Due to better material qualities, new surface finishing methods and better heat-treatment process reliability, flank surface damages, such as pitting or micropitting, can be prevented in a reliable manner. This results in an increase of unexpected flank damages with crack initiation below the surface of the loaded gear flank, for example tooth flank fracture. Tooth flank fracture is characterized by a crack initiation below the active surface due to shear stresses caused by the Hertzian flank contact and crack propagation in direction of both the active flank surface and the core area. Damages caused by tooth flank fracture usually result in a total breakdown of the gear unit. The main mechanisms leading to tooth flank fracture have been investigated in different research projects. By now, an ISO technical specification for calculation of tooth flank fracture load capacity for case hardened spur and helical gears is in preparation. Based on the available draft technical specification, a parameter study on the load capacity calculation of the damage mechanism tooth flank fracture has been performed in order to identify characteristic influence factors. Furthermore, the tooth flank fracture load capacity was compared to the pitting load carrying capacity for different example gearings. Based on the parameter study, the influence of surface hardness, hardness gradient and core hardness on the damage mechanism tooth flank fracture is characterized. With these findings, different heat treatment processes and material characteristics can be quantified regarding their susceptibility for tooth flank fracture damages. Besides the properties of the heat influenced near-surface zone, different residual stress profiles and geometrical parameters (radii of curvature, module …) have been analyzed, too. Based on the performed parameter study, design limits for practical application have been derived and are presented in the present paper. These derived design limits allow a fast estimation of the exposure concerning tooth flank fracture for a given gear unit design.
The grinding of case-hardened gears after the heat treatment ensures a high quality regarding the gear geometry and tooth surface topography. If the limits of the gear material are exceeded during this process, the mechanical and thermal influence from the grinding operation can lead to tempering effects and re-hardening of the gear teeth. As part of the research project FVA (Forschungsvereinigung Antriebstechnik e.V.) 453 (Schwienbacher et al., 2007), the influence of grinding burn on the flank load carrying capacity has been investigated. As a result, a surface factor has been proposed to allow a consideration of the negative influence on the flank load carrying capacity due to grinding burn. However, for most applications, the flank load carrying capacity of the unimpaired tooth flank must be provided to ensure a safe operation. Within the project FVA 453 II (Koller et al., 2012b), the potential of superfinishing, shot peening and re-grinding, respectively, as a repairing method were evaluated experimentally. The main results of this project will be summarized in this paper.
Precise information about the load distribution in the tooth contact can improve the quality of calculation results regarding strength and durability of spur and helical gear stages. A method of measuring the load distribution of spur gear stages in lab conditions has been developed. The basic idea is, that tangential deformations on the backside of a loaded tooth flank are directly linked to the load distribution on the tooth flank. A measuring procedure to detect the aforementioned tangential deformations has been developed. The measurement results can be compared to calculated load distributions with two methods. The first method is to generate tangential deformations out of a calculated load distribution by using the finite element method (FEM). The measurement results can be compared to the so determined tangential deformations. The second method is to directly generate a load distribution out of the measurement results. Calculated load distributions can be directly compared to a so determined load distribution. Therefore, an iterative calculation approach using the FEM has been developed. Using the methods mentioned before, calculated load distributions can be validated.
The cycloid planetary gear drives designed in the so-called RV-type play an important role in precision power transmission. Not only the high reduction ratio, but also the shock absorbability is the significant advantage. However, the load analysis of such the drive is complicated, because the contact problem of the multiple tooth pairs is statically indeterminate. The aim of the paper is thus to propose a computerized approach of loaded tooth contact analysis (LTCA) based on the influence coefficient method, either for the contact tooth pairs of the involute stage or of the cycloid stage. The contact points are determined based on the instant center of velocity in the model. On the other hand, the shared loads of multiple contact tooth pairs are calculated numerically with a set of equations according to the relations of deformation-displacement and load equilibrium. The coupled influences of the loads acting on the involute and the cycloid tooth pairs are also analyzed considering the friction on the contact tooth flanks as well as the stiffness of the supporting bearings for the cycloid discs. With an industrial example, the contact pattern with distributed contact stresses and the shared load of each contact tooth pair during operation are simulated with aid of the proposed approach. The transmitted torques on the crankshaft, the displacements of the main components and the efficiency of each stage calculated accordingly are also illustrated in the paper.
The gear rolling densification of Powder Metal (PM) gears leads to better mechanical properties due to the selectively closed porosity of some hundreds of a micrometer under the surface of the tooth. The optimization of this process is critical in order to reduce the overall design time of the process and to increase the quality of the rolled gear. One way to optimize the process, tool design and gear with stock is to conduct Finite Element (FE) simulations with a plasticity material model for porous metals. The simulations should be able to predict the resulted geometry and densification, after that the opposite procedure can be conducted and by using simulations as a design tool to predict the process parameters. In this paper, FE simulations are being performed for the gear rolling densification process. The aim is to investigate how such simulations can be used to improve the quality of the rolled gear. Moreover, to identify how more advanced plasticity material models such as the anisotropic model of Ponte-Castaneda Kailasam and coworkers can help and increase the accuracy of the calculations, compared to more commonly used models such as the one suggested by Gurson-Tveergard-Needleman (GTN). Furthermore, the results from the simulations in densification and involute profile are also correlated with experimental results to validate the accuracy of the simulations. Finally, the accuracy of the simulations in densification and involute profile will define if the target of optimizing the gear rolling densification process through FE simulations is realistic.
This study aims to experimentally investigate churning power losses generated by a planetary gear set which is splash lubricated. To this end, a specific test rig has been used to operate a planetary gear train under unloaded conditions in various configurations within a range of the planet-carrier rotational speed. Churning loss is isolated from the measured drag torque and the effects of several parameters (rotational speed, temperature, oil sump level, planet number…) on this source of dissipation are quantified. Beyond the influence of speed or oil level, it is concluded that the number of planets is of primary importance on churning power losses. Moreover, a first assumption is made concerning the oil sump behavior regarding the experiments: an oil ring is created explaining the evolution of the churning losses measured. In addition, this study compares the churning phenomenon occurring in cylindrical gear trains with the one observed during the experiments. It is shown that the approach used for conventional gear trains cannot be used for epicyclic ones: in planetary gear sets the centrifugal effects are predominant whereas the gravity forces have a larger influence on the free surface flows which occur in cylindrical gear sets.
In this study, steady-state mechanical power loss model of an automatic transmission gear train consisting of multiple stages of planetary gear sets is developed. Load dependent (mechanical) power losses at the internal (ring-planet) and external (sun-planet) gear meshes and planet bearing interfaces are included through elastohydrodynamic lubrication (EHL) based power loss formulations. At the end, efficiency of an 8-speed automatic transmission is studied under representative operating conditions to quantify the contribution of various loss mechanisms to the total loss under variable speed, load and temperature conditions. Impact of gear surface roughness amplitudes on the resultant power losses is also described.
The strength of plastic greatly varies with temperature; that is, the strength increases as the temperature decreases. Therefore, the lifetime of a plastic gear can be increased by reducing the meshing-teeth temperature of the gear. The meshing-teeth temperature can be reduced by changing the material of the mating gear from plastic to metal considering that a metal gear will have high thermal conductivity. In this study, we investigated the load-carrying characteristics of an unlubricated crossed helical gear consisting of a plastic gear meshed with a metal gear. We performed gear lifetime experiments and meshing-teeth temperature survey experiments. The results showed that the failure mode of the plastic crossed helical gear was caused by the breakage of the tooth and the rim. Then, we confirmed that the stress ratio could be an index for the lifetime evaluation of the plastic crossed helical gear that could fail by tooth breakage. Additionally, by testing gear pairs with several dimensions, we confirmed that the mean flash temperature could be an index for the meshing-teeth temperature evaluation of the plastic crossed helical gear. Furthermore, we proposed a lifetime estimation method for the plastic crossed helical gear that could fail by tooth breakage and verified the validity of the proposed method based on the experimental results.
The present paper describes the tooth surface temperature and the power transmission efficiency of plastic sinecurve gears in the running condition. The plastic sine-curve and involute gears were manufactured by injection molding. The running tests for sine-curve and involute gears were performed under no-lubrication and grease-lubrication conditions, and the tooth surface temperature and the power transmission efficiency were measured. Test results show that the sine-curve gears for operating condition had lower tooth surface temperatures and higher power transmission efficiencies than involute gears under no-lubrication conditions, but in the grease-lubrication condition the superiority of sine-curve gears was not observed.
This article presents a lifespan testing analysis of polymer gears manufactured by cutting. Compared to injection molding, machine cutting provides higher accuracy of gear geometry. Two different tooth flank geometries were tested; i.e. involute and S-gears. In theory, S-gears have several advantages over involute gears due to the convex/concave contact between the matching flanks. The theoretical tooth flank geometry of S-gears provides more rolling and less sliding between the matching flanks, compared to involute gears. The convex/concave contact leads to lower contact stress, which in combination with less sliding means lower losses due to sliding friction and consequently less heat generated. The goal of our research was to prove that tooth flank geometry affects the lifetime of polymer gears, and to find the mechanisms and quantitative differences in the performance of both analyzed geometries. The gears were tested on specially designed testing equipment, which allows exact adjustment of the central axis distance. Two different material pairs (POM/POM and POM/PA66) of the drive and driven gears were tested. Each test was done at a constant moment load and a constant rotational speed. Several tests were conducted using the same conditions due to repeatability analysis. All the tests were performed till the failure of the gear pair and without lubrication. In lifespan testing, the polymer S-gears showed better performance and longer lifespan than involute polymer gears.
Splined joints are commonly used to transmit rotary motion from a shaft to machine elements such as gears. While computationally efficient spline load distribution models have recently been proposed, there is no validated load distribution model of a splined joint due to lack of high-fidelity experimental data. Accordingly, this study aims to establish an extensive experimental database on load distributions of splined joints subject to both spur and helical gear loading conditions. A quasi-static, spline-specific test setup is developed and instrumented. A test matrix covering various loading conditions is executed in order to form a spline load distribution database. The experimental data illustrates the cyclic nature of loads and resultant stresses on spline teeth caused by rotation of the spline teeth in relation to the gear mesh that loads the splined joint. A nonlinear relationship between torque applied and resultant stress is revealed, as well as the relationship between the location of maximum stress along the face width and the amount of lead crown modification applied. Lastly, simulation results from the model of Hong et al. (2014b) are compared to the experimental data under spur and helical gear loading conditions to assess the premise of such models.
A simulation software is being developed for predicting the power losses in poly-V belt transmissions. For this purpose, some theoretical models have been implemented considering different types of power losses taking place in a Front Engine Accessory Drive (FEAD). Even though these power losses come from different phenomena, the analysis in this paper is focused on the elastomeric belt hysteresis losses due to dynamic bending, stretching, shear, flank and radial compression of the belt rubber. Experimental tests are performed in order to determine the intrinsic loss modulus of the belt elastomeric constituent causing the loss of energy. This study permits determining a hysteresis power loss map of a belt transmission.
This paper investigated the influence of pulley tilting on slip ratio (s) of the commercially available continuously variable transmissions (CVTs). Two types of pulleys (tiltable pulley and untiltable pulley) were prepared to investigate the influence of the tilt of pulley on the slip properties. The tilt of the driving pulley was prevented for simple comparisons when untiltable driving pulley was applied, while tiltable pulleys were conventionally used. The maximum transmitting efficiency (η) and the maximum transmitting torque were increased when untiltable pulleys were used, while slip ratio (s) was decreased. The radial displacement of contacting point due to the tilt of pulley was much affected to the penetration of the belt about max 70 times compared with that by rolling, when pulley surface was tilted. The remarkable penetration was prevented by applying untiltable pulley. In current type of CVT, practical CVT unit for commercial uses was usually driven with the slip in circumferential direction due to the tilt of pulley accompanying with radial displacement of the belt. This paper found that about 33% of slip was counted due to the tilt of pulley in observed total slip between driving and driven pulley by the specific reason where the driving pulley should be tiltable for the motion of the shift in axial direction on the shaft. The observed slip was dominantly caused by the penetration of the belt when the driven pulley was tilted.
The traction drive - integrated drive generator (T-IDG®) has been developed since 1999 to replace current hydrostatic transmission drive generators mounted on Japanese military aircrafts. The T-IDG® consists of a generator and a half-toroidal traction-drive continuously variable transmission (CVT), which maintains a constant output speed of 24,000 rpm. In terms of coping with recent trends of high-power electric drive aircraft (MEA) and the need for weight reduction, a high-speed traction-drive CVT is advantageous over current hydro-static drive transmissions. The high-speed half-toroidal CVT has a fundamental issue regarding the thrust ball bearing, which must support a large loading force at a high rotational speed. The gyroscopic effect of the thrust ball bearing causes a serious slip called gyroscopic sliding at the insufficient preload and it damages the bearing. This paper describes the theoretical criteria and the design method for suppressing gyroscopic sliding. The test to validate the theory is also conducted with a prototype T-CVT up to 20,000 rpm with a peripheral speed of the traction contact of 70 m/s.
Due to the growing elderly population in many developed countries like Japan, assistive devices are increasingly needed to overcome the difficulties of their activities of daily living (ADL). The motion of standing up places a particular burden on the ankle and knee joints and connects static motions (e.g., sitting and lying) and kinetic motions (e.g., walking and climbing up/down the stairs). In our previous research, two types of standing-up assistance apparatuses were introduced according to the suitable standing-up motions. However, these devices are bulky and cannot be widely used in practical settings such as bus terminals. Regarding the suitable standing-up motions of the elderly in the previous literature, a standing-up apparatus with a pantograph mechanism is introduced to diminish the size of the mechanism based on three design principles: (1) the trajectory of the user's COG is an arc; (2) the trajectory of the user's hip joint while standing up is a straight line at an angle of 45 [deg] from the horizon; and (3) the user is supported until the knee angle reaches 60 [deg]. Simulations showed that the load on knee and ankle joint is decreased, and user may stand up easily with our proposed apparatus. A prototype of the apparatus that may be installed on various chairs in public was fabricated. Considering that the apparatus may be used in places without electric power supply, the apparatus is made simply with links and a gas spring instead of electric actuators. Experimental measurements of the trajectories of the center of gravity (COG) and hip joints show that the proposed apparatus may help users to stand in a way that minimizes stress on their lower-body joints.
Wearable assistive devices have been receiving considerable attention in academic circles. To make these devices efficient, we need additional research on the service lives of the mechanical elements used in these devices. The wearers of these devices frequently encounter unexpected movements that lead to motor failure in the devices. The purpose of this study is to develop an overload protection mechanism using a torque limiter, which can eliminate the overload torque delivered in the reverse direction to effectively prevent the device from breaking and ensure the safety of the user. To improve the service life of assistive walking devices, we designed a sandwich mechanism for the final gear of the servo motor. We made the material from rubber and configured it between a pair of circular plates. The surface tractive force delivered the required torque. When the surface load exceeded the maximum friction force, the circular plates slipped and protected the device. In this paper, we implement a torque limiter and prove its durability by performing experiments using two circular plate designs, one with grooves type and another without grooves type. We also use various materials to assess the applicability of the assistive walking device. The findings indicate that the with grooves type gives better torque performance; it achieves the same rated torque as the servo motor. Thus, this study recommends that with grooves type is particularly suitable for the elderly who require high assistive power. On the other hand, without grooves type is suitable for users who employ the device for extended periods because this type has an excellent service life. Our experiment proves that the torque limiter that we developed can withstand the load torque over 300 times for situations involving the loss of balance such as stumbling and slipping. Finally, we experimentally validate the improvement of walking performance by using this torque limiter.
This article intends to discuss the possibility of how to quickly improve the functions of in-situ sensing gear conditions. This study proposes a new manufacturing method of the sensors by using a laser beam machine sinters conductive inks sprayed on gear surfaces as a crack sensor. For this purpose, we have developed a three-axis laser-printing machine. The developed three-axis laser printer was based on a three-axis CNC machine, and a 1.6W laser module (445nm wave length) was mounted on the principal axis of the CNC machine. However, the laser power was not enough for sintering the conductive ink sprayed on a 5-micrometer-thick polyimide as an insulated layer on steel plates. Thus, the 1.6W laser module is replaced with a 3.5W laser module, which has the same wavelength. This paper shows laser sintering conditions for the new laser module. In addition, a simple sensor, which is able to detect cracks at roots of gear teeth, is proposed. The sensor is formed of an involute spur gear. The electrical property, such as resistance, of the proposed crack sensors was investigated in this paper, and it was concluded that the relation between the resistance and module of gears was linear, when the number of teeth was fixed.