Studies on the Noncircular Planetary Gear Mechanisms

The non-circular internal gears and non-circular external gears of concave pitch curve can not be processed by gear hobbing currently. Gear shaping, compared with gear hobbing, is a more general method which can solve all the problems above. Unlike previous geometric algorithms, by using the normal vector of gear pitch curve and in combination with the processing feed of shape cutter in this paper, a three-axis linkage mathematical model of non-circular gear shaping based on the model of the envelope is obtained. At the same time, through MATLAB and Visual C++ mixed programming, a non-circular gear shaping system is developed according to the linkage model. Finally, with a pair of three order elliptic gears, and via the computer-aided manufacturing, the whole non-circular gear shaping processing in three-axis linkage CNC gear shaping machine is shown in this paper, and then proving the correctness of the linkage shaping model and the shaping method of non-circular gear.

A non-circular planetary gears train beating-up mechanism was proposed, the ideal kinematic curve of beating-up rockshaft was constructed and the reverse model of the pitch curve of non-circular gears was established based on the ideal kinematic curve. When the first-level non-circular gears were set as elliptical gears, the maximum swinging angle of the sley and the influence of the elliptical gears' eccentricity on the concavo-convex characteristic of the second-level non-circular gears were analyzed. Provided with a set of parameters, the pitch curves and tooth profiles of the second-level non-circular gears were determined by reverse method. The result has shown that non-circular planetary gears train beating-up mechanism can meet the requirements of beating-up process.

This study aimed at the problems of unequal speed transmission ratio mutual restriction and side gap accumulation of the transplanting mechanism with single-degree-of-freedom K-H-V non-circular planetary gear train, which leads to poor trajectory and attitude, and poor precision of movement. This study has proposed a simple structure of transplanting mechanism with differential internal engagement non-circular planetary gear trains, which reconstructs the complex transplanting trajectory and attitude of the planting arm through single-stage unequal speed transmission. The working principle of the transplanting mechanism was analysed, and the kinematic theoretical model of the transplanting mechanism was established. The optimal design software for the transplanting mechanism was developed based on the visual platform. The dimensions optimisation on the transplanting mechanism was completed considering the requirements with strong coupling, and multi-objective and a set of superior mechanism parameters were obtained. The design theory and method of the internal engagement non-circular gear pair were proposed based on the generating principle. The correctness and accuracy of the trajectory and attitude of the transplanting mechanism were verified through virtual simulation experiments. The experiments show that the designed transplanting mechanism with internal engagement non-circular planetary gear trains was compact in structure, the trajectory meets the requirements of multi-objective transplanting, and the trajectory and attitude can be accurately reproduced, which provides a new feasible solution for the innovative design of the transplanting mechanism.

The effect on dynamics of using a new transmission design for eccentric speed reducers

Study on an internal gear with asymmetric involute teeth

Continuously variable transmission (CVT) of noncircular gear has the technical advantages of large bearing capacity and high transmission efficiency. The key technology of CVT with noncircular gear has been broken through some countries, and is in the stage of deep application research. Although the characteristics and design methods of noncircular gear pairs have been continuously studied in China, the noncircular gear CVT is still in the preliminary exploration and research stage. The linear functional noncircular gear pair, whose transmission ratio is a linear function in the working section, to realize continuously variable transmission was the research object in this paper. According to the required transmission ratio in the working section, the transmission ratio function in the non-working section was constructed by using a polynomial. And then the influence of pitch curve parameters in the working section on which in the non-working section was also analyzed to obtain the pitch curve suitable for transmission of this gear pair. In addition, for improving the stability and bearing capacity of gear transmission, the noncircular gear pair transmission with high contact ratio was designed. Furthermore, the accurate value of the contact tooth length was calculated based on the gear principle and the characteristics of the involute tooth profile, from this the contact tooth length error was calculated by comparing the accurate value with its actual value obtained by the rolling experiment. Finally, an indirect method to verify the contact ratio by detecting the contact length error of the tooth profile was proposed.

The present study is part of a series aimed at enhancing the reliability of JIS B 1759, ”Estimation of tooth bending strength of cylindrical plastic gears.” This study examined the stress correction factor converting the nominal tooth bending stress into the local one. The current version has a problem with underestimating the load capacity of internal gears, but considering the contact ratio under load has alleviated the problem. Nevertheless, some issues remain, which led the present paper to determine an alternative stress correction factor through finite element analyses of internal virtual spur gears. Before discussing the alternative factor, examining the fillet profile of injection-molded internal spur gears led to proposing a single circular arc as the standard fillet. Based on that, FEAs of internal virtual spur gears with a single circular fillet determined the modified stress correction factor, which can relieve JIS B 1759 of the underestimations. The modified factor enables the standard to estimate load capacity regardless of external or internal gears, which improves the reliability of the standard.

A unified optimization design method for multi-stage non-circular gear transmission based on periodic B-spline interpolation

Bu makalede iç ve dış dişlilerdeki girişimi belirleyen analitik yaklaşımlar araştırılmaktadır. Dış helisel dişliler için fonksiyonel ve imalat tipi girişimler dikkate alınmaktadır. İç düz dişliler için evolvent ve takılma girişimleri ele alınmıştır. Girişim limitleri için literatürde bulunan denklemler incelenmiştir. Ayrıca iç düz dişliler için evolvent girişimi profil kaydırma ile önlemek için bir denklem önerilmiştir. Tasarım parametrelerinin etkisini araştırmak için hem kremayer tipi hem de pinyon tipi dişli imalatı için bilgisayar programları geliştirilmiştir. Geliştirilen programlara dayalı olarak sayısal örnekler verilmiştir. Bu çalışma dişli tasarım sürecinin ilk aşamalarında girişim olup olmadığını belirlemek için kullanılabilir.

In this paper, the authors evaluate the influence of the centrodes coefficients on the gear ratio function characteristics of the compound non-circular gear (CNCG) train formed by two pairs of external non-circular gears (NCGs). First, a mathematical model describing the mating centrodes for the CNCG train has been establishing. From there, evaluate the influence of centrode coefficients μ1 and μ2 of NCGs in the CNCG train on the gear ratio function characteristic for the CNCG train. A design of a CNCG train with an improved cycloid tooth profile by a rack cutter. The evaluation results show that when increasing μ1, transmission size tends to decrease, but the speed and torque variation range rises to 54.31%. While reducing μ2, the speed variation and torque range increase, but the mating centrodes of NCGs 4 is a concave curve that cannot gear shaping by a rack cutter or hob cutter must be by shaper cutter.KeywordsCentrode coefficientGear ratio functionNon- circular gearCompound non- circular gear train

The internal gear grinding machine, ZI20A is the first of its kind that is applicable for mass production of internal gears. It is suitable for grinding planetary gears, heat-treated internal or external gears at high speeds with high accuracy. One of the features of this machine is its ability to grind stepped workpieces. In case of stepped workpieces, it is difficult to determine the axial stroke required to achieve proper grinding of the entire tooth surface without causing any interference of the stepped region with the machine parts or grinding wheel. During the grinding test of such workpieces, sometimes the tooth flank remains unground at the ends due to inadequate axial stroke. A new simulation tool has been developed to visualize and analyse the internal gear grinding process. Using this simulation tool, the axial stroke required for grinding can be estimated without performing actual grinding tests.

Little research has been done so far on the development of a simplified design technique for noncircular gears. Such a technique should take into consideration various kinematic constraints that exist in the noncircular gear pitch curve design process, to obtain appropriate gearing on the basis of a given angular velocity ratio curve. It seems that no generalized design technique has yet been established. This study used design specifications such as an angular velocity ratio curve (types of curves in individual segments and their coefficients) and center distance to design a pair of noncircular gears. The center distance was kept constant. The design process for the pitch curve was obtained and extracted from various kinematic constraints. Based on thses results, We developed a design automation technique for the pitch curve for noncircular gears, with given arbitrary angular velocity ratio curve.

Prevention of resonance oscillations in gear mechanisms using non-circular gears

This paper describes a new steering mechanism proposed by one of the authors(T.E.). This steering mechanism using noncircular gears has the capability of turning a carrier with a small radius. In order to facilitate the analysis of the steering mechanism, the concept of a virtual two-wheeled vehicle was introduced. As a result of analysis made by the other author (A.A.), it was proven that the noncircular gear for the steering mechanism is an elliptical gear of which the pitch curve can be represented by a simple equation. In addition, a method to apply this mechanism to wheeled robots, such as the carrier robots used in industrial production lines, was studied. It was confirmed that the concept of the virtual two-wheeled vehicle is very useful in the design of the steering mechanism.

Applying the non-circular gear to transplanting mechanism can get more desirable planting work locus, which is a hot research topic recently. Pascal curve gear was obtained by researching features of Pascal curve in this paper, the non-circular gear planetary transplanting mechanism was designed using Pascal curve gear. Mathematical modeling of the various gears was carried out. Software for dynamic simulation and parameter optimization of non-circular gear transplanting mechanism was developed. Using the software, users input a set of parameters, and the software instantly calculates and shows the work locus and motion simulation, then users can judge whether the parameters are reasonable and get the appropriate planting work locus, validating that Pascal curve gear can be used in rice transplanter. Optimization parameters obtained from software are of guiding significance for the manufacture and testing of physical prototypes.