Variable Transmission Ratio Research Articles

Coupled vibration modeling and dynamic characteristics of noncircular face gear drive system with time-varying instantaneous center excitation

Noncircular face gear drive is a new type of variable transmission ratio mechanism with advantages of light weight, high interchangeability, and convenient installation. Based on its transmission principle, the excitation pattern of the time-varying instantaneous center of the noncircular face gear drive system is investigated. A torsional–lateral–axial coupled dynamic model of the noncircular face gear system is presented under the compound parametric excitations of the time-varying instantaneous center and the mesh stiffness. By using Runge–Kutta numerical integration method, the dynamic responses of the system are derived to analyze the vibration features of the noncircular face gear under compound parametric excitations and the effect of the design parameters on the coupled vibration. The analytical results indicate that there exist multifrequency components in the dynamic responses of the system, including the instantaneous center frequency f1, the meshing one f2, nf1, mf2, and mf2 ± nf1. In addition, the dynamic performance of the noncircular face gear drive can be improved by decreasing the amplitude coefficient of the instantaneous center and the mesh stiffness or increasing their mean values.

Power Flows in Compound Transmissions for Hybrid Vehicles

Hybrid electric vehicle (HEV) traction systems are the most promising technologies being characterized by high performance, high fuel efficiency, low emissions and long operating range. Significant improvements can be achieved equipping transmissions with variable transmission ratio such as power-split transmission and a compound power-split electric continuously variable transmission (eCVT). These systems have been introduced to improve vehicle global efficiency since they can maximize the efficiency in different operating conditions. Optimal design and control of these systems leads improvements in vehicles performance and mathematical models, which support the preliminary design phase, can play a key role in this field. In this work, the internal power circulations of “four-port-mechanical-power split device are determined through a dynamic analysis.” Finally, the efficiency of the compound transmission is analytically evaluated, assuming that the overall losses are linked to the eCVT variator.

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.

A Novel Cold Rotary Forging Method of Producing Multiple Racks Using One Set of Punch

When producing racks by cold rotary forging, the top punch and the rack teeth definitely intervene and thus the top punch has to be amended, which makes the technical designing processes difficult and complex (Han et al., 2016, “Cold Orbital Forging of Gear Rack,” Int. J. Mech. Sci., 117(10), pp. 227–242). In this study, a novel cold rotary forging method of producing racks is put forward to avoid the interventions between the top punch and the racks. Thus, the top punch need not be amended and the technical designing processes correspondingly become simple. In light of this presented method, a novel idea for cold rotary forging of producing multiple racks using one set of punch is motivated. The concrete researches are as follows: First, the mathematical models are developed and three kinds of key forging conditions in cold rotary forging of racks are calculated to avoid the interventions between the top punch and the racks. The first one is the condition that the top punch and the rack teeth do not intervene. The second one is the condition that the top punch and cylindrical surfaces of racks do not intervene. The third one is the condition that the top punch can be successfully constructed. On the basis of these three kinds of key forging conditions, the workpiece is optimized and the cold rotary forging processes of racks with constant and variable transmission ratio are examined using finite element (FE) simulations. The experimental researches are also conducted. The results show that for both racks with constant and variable transmission ratio, the obtained key forging conditions are effective and the presented cold rotary forging principles of producing multiple racks using one set of punch are feasible.

Structural and kinematic analysis of a stirred tank planetary drive

Stirred tanks are used in many industries to intensify various physical and chemical processes. Currently, one of the most promising areas of research is the creation of rotationally reciprocating stirred tanks (RRST), which realize high mixing efficiency due to the difference in the velocities of the stirred liquid. As the actuator of RRST, we proposed to use a planetary gear with elliptical gears. Due to the variable transmission ratio of elliptical gearwheels, the rotationally reciprocating motion of the output shaft is ensured with rotational motion of the input shaft. We conducted a structural analysis of the planetary gear by means of the structural mathematical model of mechanisms and machines. A kinematic model of planetary gear has been constructed and studied, resulting in velocity analogue function of the mechanism output shaft.

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 mixed H2/H∞ robust control strategy of four wheel steering system

Four wheel steering (4WS) technology can effectively improve the vehicle handling stability and driving safety. In order to fully consider the influence of the rear wheel steering, the vehicle dynamics model of 4WS vehicle, including the rear wheel steering by wire and two degrees of freedom vehicle model of 4WS vehicle, is established in this paper. The desired yaw rate is obtained according to the variable transmission ratio strategy. The yaw rate tracking strategy is applied to 4WS vehicle and rear wheel steering resistance moment is taken into account. Based on the robust control theory, H2/H∞ mixed robust controller design is carried to research the stability control of 4WS vehicle. Finally, the closed-loop simulation added driver model based on preview theory is carried out. The simulation results indicate that the designed H2/H∞ mixed robust controller can achieve the stability control.

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.

Optimisation and comparison of different powertrain layouts for parallel hybrid electric vehicles equipped with continuous transmission

The development of an efficient hybrid electric vehicle (HEV) platform needs an optimal design of its powertrain layout. This study is concerned with parallel HEVs (PHEVs) equipped with continuous transmission. First, different types of continuous transmissions, including continuously variable transmission (CVT), power-split CVT (PS-CVT) and multi-fixed ratio PS-CVT (MF-CVT), are discussed and their simulation models are presented. Also, various combinations of these continuous transmissions with PHEV configurations (namely, pre-transmission and post-transmission configurations) are introduced. Then, for a given PHEV model, several powertrain layouts resulting from combining the considered continuous transmissions and PHEV configurations are optimised over a standard drive cycle. The optimised powertrain layouts are compared from different perspectives, for instance the vehicle fuel consumption, emissions and some dynamic performance measures. In particular, the sensitivity of the PHEV performance characteristics to the driving cycle pattern, when it is equipped with each optimised layout, is investigated.

Geometric error detection of curve-face gear pairs

A new type of gear pair, the curve-face gear pair, composed of a curve-face gear and a non-circular gear with mutual engagement, was proposed to achieve variable ratio transmission of motion and power between the intersecting axes. Geometric error detection is required to evaluate the grade of the manufactured gears. Due to the complexity of the curve-face gear, direct detection has been conducted in a very limited way. In this article, a measurement method aimed at curve-face gear pair artifacts is presented based on the computer numerical control gear measuring center. By comparing the measured coordinate data of the surface points with the corresponding theoretical data, various errors such as tooth profile error and pitch deviation can be obtained, and accuracy grades are evaluated with reference to accuracy standards for cylindrical gear and bevel gear. The developed method is simple and robust without requiring a special measuring device; hence, it can be applied for the industrial practice as a means for measuring the tooth profile and pitch deviations which cannot be measured by conventional methods.

Research on Variable Transmission Ratio and Yaw Rate Control Strategy of Electric Forklift Steering-by-Wire System

Research on Variable Transmission Ratio and Yaw Rate Control Strategy of Electric Forklift Steering-by-Wire System

Analysis of vehicle static steering torque based on tire–road contact patch sliding model and variable transmission ratio

Static steering torque at parking is an important factor for steering portability of vehicle. At present, the most commonly used estimation method is empirical formula calculation, which, however, cannot explain the phenomenon that the steering torque increases rapidly when steering angle becomes very large (over 300°). This article proposes an estimation method of static steering torque on the basis of a mathematic model of tire-patch sliding torque, taking into account the changeable torque transmission ratio from steered wheel to steering wheel. Three components of static steering torque are modeled and analyzed, including the tire-patch sliding torque, gravity aligning torque, and internal friction torque of the steering system. In order to investigate the static steering torque at steering wheel, the transmission ratio of steering torque is obtained on the basis of rack-suspension mathematical analysis. An example of static steering torque estimation is conducted with the proposed method and is compared with experimental results. The comparison shows that the estimation results given by the proposed method are in better accordance with experimental results than other approaches.

Geometric design using undercutting and pointing conditions for a curve-face gear

Curve-face gear drive is a new type of variable transmission ratio gear pair between the intersecting axes based on the face gear pair. And tooth width is one of the main geometrical factors of curve-face gear which affects the intensity of tooth root. This article uses the method of boundary function and geometric approximate evaluation to investigate the undercutting and pointing conditions of curve-face gear considering the tooth profile difference. The equations of tooth profile distribution angle and engagement angle are derived using the coordinate transformation theory. On this basis, the equations of the theoretic undercutting and pointing conditions are deduced, and the undercutting inner diameter and pointing outer diameter of the tooth profile are simulated using mathematical software. Then, the corresponding phenomenon of undercutting and pointing of curve-face gear are analyzed. In the end, the feasibility of the theoretical calculation is received by the experiment of curve-face gear.

A variable-ratio line gear mechanism

Based on the previous studies of line gear (LG), which is also named as space curve meshing wheel (SCMW) in the published papers, a variable-ratio LG mechanism is proposed in this article. The formulae of contact curves of a variable-ratio LG pair were derived. Then prototypes of variable-ratio LG pairs were designed by these formulae and manufactured by 3D printing. Afterwards, kinematics experiments were conducted by measuring the transmission ratio. The result indicates that a variable transmission ratio is feasible to a variable-ratio LG mechanism designed by these derived formulae, and the change of the transmission ratio is steady according to a prescribed kinematic rule. It is capable of being employed to devices on demand of variable-ratio mechanical transmission mechanism in compact structure.

Pitch deviation measurement and analysis of curve-face gear pair

The curve-face gear pair is proposed as a new type of gear pair which was put forward in recent years. It can achieve variable ratio transmission of motion and power between the intersection axes. In the matter of the inspection of the pitch deviations of this gear pair, there is no practical possibility for a reliable metrological traceability to national or international measurement standards can be provided. Hence, a new method was proposed in this article, which was based on the CNC gear measuring center, aimed at the gear artefacts processed by the five-axis machining center. With the coordinate data which were obtained by the gear measuring center, the pitch deviations of the gear pair were obtained. In addition, based on the values of the pitch deviations, the angular deviations of curve-face gear pair can be worked out, and the results turn out that the measurement method is feasible.

The Research of Fuzzy Variable Transmission Ratio for Steer-by-wire System of Electric Forklift

Combining with the TE30 electric forklift produced by an enterprise, the principle of Steer-by-wire (SBW) system, steering motion state, ideal steering ratio are analyzed and studied. The biggest characteristic of SBW system is that the transmission ratio is free to design. Based on the establishment of two-degree-freedom linear model of Forklift, the paper designed the nonlinear transmission ratio function on vehicle speed and steering angle with the application of fuzzy control rules. The simulation results show that the fuzzy variable transmission ratio can make the yaw velocity gain tend to be constant, also can make Forklift light sensitive at low speeds and steady heavy at high speed. In order to ensure that the yaw velocity gain does not vary with the change of speed and steering angle, this paper presents a dynamic correction control strategy based on the steady-state control for Forklift. The simulation results show that the amplitudes of yaw velocity and sideslip angle are reduced with the dynamic correction of yaw velocity feedback, also the handling stability is improved.

Tooth Surface Design for Variable Transmission Ratio Bevel Gearing

A novel CAD method for tooth profile based on the gearing feature has been proposed in this paper, and this method could be applied to the variable transmission ratio and three-dimension situation. The two pitch curves of the two gears can be generated due to the given transmission ratio. The tooth profile curves are formed in each coordinate system of its pitch curve by the gearing process. Finally, the tooth profile could be extracted and translated into a real dimension by CAD method. It is provided a simply thought for tooth profile design to avoid so much complicated mathematical reasoning.

Vehicle Active Rear Wheel Steering Control Based on a Variable Transmission Ratio Control Strategy

In order to obtain the ideal steering performance, an active rear wheel steering (ARS) controller, based on the variable transmission ratio control strategy, is developed in this paper. ARS controller using sliding mode technique is designed to follow the desired yaw rate which is calculated by the ideal variable transmission ratio. Simulation result shows that, the proposed control strategy both obtains desired steering performance and provides the obvious benefits for the human driver.

Research on the Variable Ratio Gear Modeling and Transmission Ratio Test Method of Rack and Pinion Variable Ratio Steering Gear

A new modeling method for the variable ratio gear of the rack and pinion variable ratio steering gear was proposed in this paper. It was based on the characteristic that variable ratio gear pair meshing tooth profile surface are the envelope surface of each other and established a variable ratio gear three-dimensional model by simulating the gear machining process in CATIA and using Boolean subtraction operation. According to the related test standard of the variable ratio steering gear transmission ratio, a test bench was design and build, and the correctness of this modeling method was verified by comparing the designed variable ratio curve and the steering gear sample designed and processed by this method.