Curve-face Gear Research Articles

Pattern Classification and Gear Design of Spatial Noncircular Gear Continuously Variable Transmission

Noncircular gear and curve face gear are collectively referred to as spatial noncircular gear. Combined with the transmission characteristics of spatial noncircular gear, a new classification design method of spatial noncircular gear continuously variable transmission (CVT) pattern was proposed, including two categories named addition type and multiplication type, with a total of five subcategories. Through the combination of the transmission ratio changing mechanism and transmission selection mechanism, it can realize the CVT. The overall transmission ratio depends on the phase angle between the spatial noncircular gear pairs and is independent of the input rotation angle. Firstly, the CVT principle and transmission ratio characteristics of each pattern were analyzed. Then the tooth profile classification design of spatial noncircular gear was carried out, and the general parametric design equations of the tooth surface with different tooth profiles were obtained. Finally, through simulation, the overall transmission ratio of each pattern was compared between theory and simulation, which verified the correctness of the CVT classification design method. The advantages and disadvantages of the two categories were analyzed. Moreover, through the transmission experiments of curve face gear pairs with different tooth profiles, the transmission ratios were compared between theory and experiment. Considering the influencing factors such as machining error, assembly error and measurement error, the experimental error is within a reasonable error range, which verified the correctness of the tooth profile classification design method. This study provides a new idea for the further research and application of spatial noncircular gear CVT.

Compound transmission principle analysis of eccentric curve-face gear pair with curvilinear-shaped teeth based on tooth contact analysis

A new type of compound transmission gear pair was put forward, called eccentric curve-face gear pair with curvilinear-shaped teeth. It could realize reciprocating motion of the gear shaft when the intersecting shafts achieve transferring motion and power through its unique tooth profile. The compound transmission principle of this gear pair was fully established based on the profile-closure process of axial direction and meshing process of the end face. The tooth surfaces of the eccentric curve-face gear and non-circular gear were generated. The contact paths of different teeth were obtained, and the compound transmission principle of eccentric curve-face gear pair with curvilinear-shaped teeth was verified by tooth contact analysis. By analyzing the mechanical characteristics of time-varying contact points, the changing rule of contact force was studied, and the compound transmission principle of the gear pair was further revealed from mechanics. Moreover, the experimental platform for transmission of eccentric curve-face gear pair with curvilinear-shaped teeth was set up to measure the motion law and contact area, and the correctness of the analysis results was verified.

Nonlinear Dynamic Analysis of Eccentric Curve-face Gear Transmission System

This paper establishes a dynamic model and a Lagrange bond diagram model for the eccentric curve-face gear transmission system. The dynamic model includes a gear meshing model, a lumped-parameter supporting model, a drive and a load, etc. Considering the impact of cam effect and inertia force caused by gear eccentricity, the dynamic equations are established based on the Lagrange bond diagram model. Moreover, the parameters of the model are analyzed deeply, the effects of gear eccentricity, helical angle, tooth profile of gear pairs, and input velocity on the vibration response in time and frequency domain are studied. It is found that the dynamic response of the eccentric curve-face gear transmission system is a highly nonlinear process. The gear eccentricity can modulate both amplitude and frequency. Introducing a force-locking spring in the eccentric curve-face gear transmission system with helical-teeth will negatively affect the system, resulting in the increase of vibration amplitude. The time-varying helical angle of the eccentric curve-face gear transmission system with circle-arc teeth will also have a negative effect on the dynamic characteristics and cause more small pulses. The axial dynamic response, bending dynamic response, and torsion dynamic response are more sensitive than the radical dynamic response to the change of helical angle. Finally, the correctness of numerical analysis was verified through experimental studies.

The Mathematical Model of Curve-Face Gear and Time-Varying Meshing Characteristics of Compound Transmission

The curve-face gear pair is a new type of gear pair with variable transmission ratio for spatial finite helical motion. In this paper, mathematical models of a new developed curve-face gear were simplified and obtained directly by the standard shaper. The subsequent studies on the curve-face gear compound transmission characteristics were further analyzed by the combinations of the principle of space gearing and screw theory. Firstly, the conjugate tooth surface geometry as well the point contact traces of curve-face gears were derived. Secondly, the geometric relationships between gear pair and the corresponding meshing characteristics were evaluated by several basic geometric elements, including instantaneous screw, axodes, striction curve, and conjugate pitch surface. Based on that analysis, it was found that the tooth contact normal was reciprocal to the instantaneous twist, which demonstrated that the conjugate motion with the desired transmission ratio could be realized in current curve-face gear compound transmission. Moreover, the time-varying slip characteristics of the curve-face gear pair were also revealed, that is, rolling and sliding action coexist at all contact on the tooth surfaces. In brief, this work provided the theoretical basis for following researches on machining curve-face gear with standard shaper.

Tooth bending stress analysis of high speed curve face gear of composite transmission

To promote the engineering application of composite transmission of high speed curve face gear, which consists of a cylindrical gear and a high speed curve face gear, the analysis of tooth bending stress should be taken into consideration. High speed curve face gear pair is a new type of curve face gear pair. Combined with the principle of high speed cam and curve face gear pair transmission, it can transfer the axial/rotation composite motion and power between two intersecting shafts. Based on the gear engagement principle, the gear meshing coordinate system was established and the fundamental of the high speed composite transmission was expounded. Combined with the tooth profile equation of generating gear, the tooth surface equation of high speed curve face gear was gained. Tooth force, contact ratio and normal load distribution were calculated. Then the tooth bending stress of high speed curve face gear during the transmission was calculated and analyzed in detail. Influence of basic parameters on tooth bending stress was discussed. Finally, the simulation and measurement experiment of tooth bending stress was carried out. By the comparison analysis of simulation, experiment and theory, the correctness of tooth bending stress calculation method was verified, which has important guiding significance for the further research of high speed curve face gear of composite transmission.

Contact fatigue model and life prediction of the compound motion curve-face gear pair

Different from the common face gear pair fixed rotation motion between intersecting axes, the compound transmission of the curve-face gear is a new motion form, which can convert rotational motion into rotation and movement motion. To solve the contact fatigue life problem of this new motion form gear pair, a new contact fatigue life calculation method of the compound transmission curve-face gear pair was proposed. Based on the space gear engagement principle and the fracture mechanics theory, the theoretical contact fatigue model of the curve-face gear composite transmission was established. Considering that the contact load for every tooth is time-varying in the half-period of the curve-face gear, the contact fatigue life stage of the curve-face gear was divided into crack initiation and crack growth, and the crack growth fatigue life for each tooth was calculated using the finite element method. The curve-face gear pair was processed in the five-axis NC machining center and the compound transmission experiment platform of the curve-face gear was set up to measure the tooth surface dynamic contact stress, and the overall life of the curve-face gear was predicted. The comparison analysis between theoretical and experimental results verified the correctness of the theoretical contact fatigue calculation model.

Analysis and calculation of bending fatigue life of curve-face gear

The curve-face gear pair is a new type of gear pair, and it has not been widely applied in many occasions as other kinds of gear pairs. In order to solve the bending fatigue life problem of this new gear pair with time-varying characteristics, a new theoretical calculation model was established. According to the loading state in actual operation, the single-tooth force model of curve-face gear pair was built, the effective loading of curve-face gear was analyzed, and loading spectrum in a period tooth was obtained. By building tooth equivalent cantilever beam model, the single-tooth bending stress calculation formula was derived, and the bending stress spectrums in tooth different sections were analyzed, meanwhile stress spectrum of bending fatigue hazard section in a period tooth was obtained. Combining the Miner’s rule and bending stress spectrum of dangerous section position, the bending fatigue life calculation method of curve-face gear was proposed. Through concrete example analysis, the bending fatigue life of curve-face gear was calculated. According to dynamic load spectrum extracted by ADAMS and bending stress calculated by ANSYS Workbench, the fatigue damage distribution of curve-face gear was obtained by nCode DesignLife. By constructing curve-face gear pair running experimental platform, the dynamic tooth root bending stress was measured. Comparing the theoretical calculation, simulation, and experimental results, the error between experiment and theory is within 10%, so the theoretical calculation method of bending fatigue life of curve-face gear was verified.

Research on the Discrete Algorithm of Tooth Surface for a Curve-Face Gear

Abstract The curve-face gear pair is a new type of face gear pair with a variable transmission ratio. Concerning the complexity of its tooth surface, based on the coordinate transformation principle and the spatial meshing theory, a discrete algorithm of this tooth surface was proposed. The determination rule of the limiting points on the tooth surface was analyzed by introducing the generating method and tooth surface characteristics of this gear tooth. Through the corresponding limiting angles and the distribution law of the contact line, the gear tooth surface was discretized, and the theoretical data points of the tooth surface were obtained. The variations in gear tooth surface in a meshing cycle and under different parameters were analyzed. By comparing the virtual tooth model and the corresponding rolling experiment, the correctness of the tooth surface discrete algorithm of the curve-face gear was verified.

Bending stress analysis of eccentric straight and helical curve-face gear pair

As a new type of gear transmission developed in recent years, curve-face gear transmission has not appeared before. In order to solve the problem of root bending strength of the eccentric straight and helical curve face gear, a calculating method of the tooth root bending strength was proposed. According to the principle of space meshing, differential geometry and design of machinery, the parametric equations of pitch curve was obtained, the pressure angle and the contact ratio in the meshing process were derived. The plane equivalent pitch curve was obtained, and the formula for calculating the equivalent tooth form factor and the equivalent stress correction factor was acquired. The calculation method of the bending strength of the gear pair was established, and the influence of the basic structural parameters on the bending stress was also analyzed in detail. The position of the stress hazard of the eccentric curve-face gear was determined. Through the finite element analysis and transmission experiment, the accuracy of the calculation method of strength of the gear pair was verified.

Calculation and analysis of meshing efficiency of composite motion of the curve-face gear pair

The curve-face gear is a new type of composite motion mechanism. The calculation of meshing efficiency of composite motion is proposed in this paper. According to the gear meshing principle, the force state of the curve-face gear pair and the motion law of the composite motion are revealed. The theoretical method of the transmission efficiency of the curve-face gear composite motion is established, and the formula for calculating the transmission efficiency of compound motion of the curve-face gear pair is obtained. Using the control variable method, the factors affecting the meshing efficiency of the curve-face gear pair are discussed. A comprehensive experimental platform is designed. The relevant experiments are carried out. The experimental data under different conditions are obtained. The experimental data are compared with the theoretical data to verify the related inference. Finally, the related measures to increase the transmission efficiency of the curve-face gear composite motion are proposed.

Tooth Surface Design and Sliding Characteristics Analysis of Compound Motion Curve Face Gear Pair

Tooth Surface Design and Sliding Characteristics Analysis of Compound Motion Curve Face Gear Pair

Tooth contact analysis of elliptical bevel gear with different misalignment

Considering the wide use of bevel gear, a new bevel gear type with variable transmission ratio has been proposed. Based on the manufacturing and generating theory of gear, the mathematical equations for the tooth surface of this gear type has been established with two different methods: lead crowning, which meets the commonly used industrial methods with higher efficiency, lower cost and the method with rack cutter shows much clear relationship of gear meshing process. The contact points and characteristics of transmission errors with different misalignment conditions have been presented. Also the feature of contact area on the tooth surface in a whole cycle was developed in this paper. Compared the contact results of elliptical bevel gear with curve face gear, the former has less misalignments sensitivity and better loaded capability.

Calculation and Characteristic Analysis of Tooth Width of Eccentric Helical Curve-Face Gear

Eccentric helical curve-face gear pair is a new type of gear pair consisting of a helical non-circular gear and an eccentric helical curve-face gear, which can implement the rotation of intersected axes as well as the movement of output axes. According to the conjugate surface theory and the spatial coordinate transformation theory, the coordinate system, the meshing equation and the tooth surface equation of eccentric helical curve-face gear are obtained. Based on the spatial gear engagement theory, the undercutting and pointing phenomenon of eccentric helical curve-face gear are analyzed, and equations of tooth width of eccentric helical curve-face gear are proposed. By changing the different parameters of eccentric helical curve-face gear pair, the influencing factors and variation of undercutting radius, pointing radius and tooth width are derived. Furthermore, by building the experiment devices of the roll testing and the transmission, the correctness of the calculation method of tooth width of eccentric helical curve-face gear is verified by using the contact analysis and the experimental verification.

Loaded tooth contact analysis of curve-face gear pair

As a new gear pair with variable transmission ratio, curve-face gear can be applied to percussion drill to simplify the structure. For the application of curve-face gear pair, the loaded tooth cont...

Study on the compound transmission mechanism of the curve-face gear based on screw theory

The compound transmission mechanism of curve-face gear is a new type of gear transmission based on the cam mechanism and the curve-face gear pair. It combines the transmission characteristics of the cam mechanism and noncircular bevel gear. When the compound transmission mechanism of curve-face gear is engaged in the meshing transmission, the rotating center of the cylindrical gear is fixed and used as the driving wheel, and the curve-face gear can generate the helical motion around the axis. In this paper, the meshing characteristics and motion laws of the compound transmission mechanism of the curve-face gear are studied based on the theory of screw. Based on the meshing theory of gears, the coordinate system of conjugate surfaces is established, the basic meshing theory and equation are obtained. On this basis, combined with the principle of the cam, the transmission principle is analyzed by the screw theory. The tooth surface equation of the compound transmission mechanism of curve-face gear is deduced based on the meshing theory and the related knowledge of geometry. The motion law of the curve-face gear and the change of the motion law with the change of the basic parameters of the gear pair with different design parameters are calculated and analyzed. An experimental platform is built to verify the law of motion, and the experimental results are compared with the theoretical values. The correctness of the theoretical analysis is verified, which provides a new way for the research of the compound transmission mechanism of the curve-face gear.

Research on the method to calculate deformation of curve-face gear

As a new type of face gear, the tooth deformation of curve-face gear has always been one of the research focuses. The conventional method of calculating the tooth deformation of face gear is widely focused on the basis of Buckingham's opinion, without considering the actual contact status. Therefore, in order to resolve this problem, a new calculation of curve-face gear tooth deformation is proposed. Firstly, the tooth distribution regularity of curve-face gear was analyzed. Then, a model for predicting the tooth elastic deformation of curve-face gear, taking into account the equivalent teeth, cross-section property, actual contact status and load distribution, was presented. Finally, the deformation variations were analyzed by taking into account the specific parameters such as eccentricity e, order number n1 and n2, and the correctness of the proposed mathematical model was verified by the results of the related experiment.

Analysis of loaded characteristics of helical curve face gear

As a new gear pair, the helical curve face gear pair have not been widely applied as normal face gear. It can be used to substitute crank-slider mechanism to achieve variable transmission ratio and improve the structure and characteristics to some extent, such as grinders, planers and so on. The mathematical model of the helical curve face gear pair and the tooth contact analysis are necessary for the theoretical analysis of this gear pair. Based on the theory of gear meshing and coordinate transmission, the meshing equations for non-circular gear contacting with helical curve face gear without misalignment are obtained. On the basis of Hertz's theory, the principal curvatures at contact point are represented. And the contact area on every tooth and the half cycle of helical curve face gear have been established separately. As well as the contact stress on every tooth and half cycle of helical curve face gear. However, there may be misalignment during the meshing of this gear pair, this paper also covers the contact path and the functions of transmission errors with misalignment, includes the comparison of helical curve face gear and straight curve face gear. The developed theories for complex tooth surface are verified by experiment. These analysis show the contact characteristics of this gear pair during the meshing process and provide the theoretical support for further analysis and application of helical curve face gear pair.

Calculation and analysis of contact ratio of helical curve-face gear pair

Helical curve-face gear pair is a new type of gear pair consisting of a helical non-circular gear and a helical curve-face gear, which can transfer the movement of variable transmission ratio between intersecting axes. According to the spatial gear engagement theory and the spatial coordinate transformation theory, the transformation matrix of helical curve-face gear pair and the unit normal of helical cutter are deduced. Based on the meshing theory, the meshing equation of helical curve-face gear pair is built. Equations of instantaneous contact ratio of helical curve-face gear pair are proposed by transforming helical curve-face gear pair into helical non-circular rack and pinion. Besides, the influences of basic parameters of helical cutter and helical curve-face gear pair on contact ratio are analyzed. The tooth surface coordinate data of helical curve-face gear pair is obtained by using the gear measuring center, and the comparison findings between experimental and theoretical results are the experiment data basically agree with the theoretical calculation value, and error is within 5%, so the calculation method of contact ratio is verified.

Dynamic Model and Analysis of Nonlinear Vibration Characteristic of a Curve-Face Gear Drive

To study the nonlinear dynamic characteristics of curve-face gear drive, a generalized nonlinear dynamic model based on Lagrange Bondgraphs was presented. The model considered the effects of the basic parameters of curve-face gear, such as meshing frequency, eccentricity k and the order number n1 of non-cylindrical gears. Utilizing this simulation model, the vibration characteristics of curve-face gears were analysed. It is indicated that the vibration response of the curve-face gear is more complex than that of the face gear due to the influence of external excitation. These characteristics determine that this gear pair cannot be applied directly to a transmission system with high speed. Finally, a related experiment was proposed to present the validation of the numerical model.

RESEARCH ON THE MANUFACTURING AND EVALUATION METHOD FOR A CURVE-FACE GEAR

Curve-face gear is a new type transmission device combining the common transmission characteristics of non-circular gears and face gears, which can transfer the motion and power between the intersecting shaft and staggered shaft. Given the complexity of the tooth generation of curve-face gear, 1) some machining methods, including three axis NC machining method , five-axis CNC machining method and the combined processing method of additive manufacturing and five-axis CNC machining, were introduced. 2) Based on space gear meshing theory and the machining principle, the machining models of curve-face gear were established.In order to verify the accuracy of the obtained gear, tooth surface measurement was applied, a new accuracy evaluation method for pitch deviations and tooth profile deviation of curve-face gear was processed. The results show that the tooth surface accuracy of the curve-face gear is high. The design of the curve-face gear, and its processing methods have been verified.