Meshing Efficiency Research Articles

Research on friction and meshing efficiency of ADC12-POM gear pair considering off-line meshing

Metal-plastic gear pairs, due to their combination of the advantages of both materials, have been widely promoted and applied in many industries. However, research on their transmission performance is not yet complete, especially regarding the tribological properties of metal-plastic gear pairs. The study focus on ADC12-POM gear pairs. Based on the principle of potential energy, the study considers significant elastic deformation during POM meshing, resulting in obvious off-line meshing. Consequently, the study establishes a stiffness model for ADC12-POM gear pairs with off-line meshing. Using this stiffness model and a load distribution model, to calculate the tooth surface load distribution coefficient for the gear pairs. Building upon previous research on friction coefficient models, the study develop a friction coefficient model that accounts for off-line meshing and compare it with the friction coefficient model that does not consider off-line meshing. To validate the accuracy of the friction coefficient model, the study design and create an efficiency test rig for ADC12-POM gear pairs, conducting theoretical and experimental studies on gear mesh efficiency. The study analyzes the distribution of mesh efficiency along the meshing line and its relationship with the friction coefficient. By comparing experimental measurements with theoretical calculations, the study verifies the proposed friction coefficient model, providing a theoretical basis for the study of metal-plastic gears.

Theoretical modeling and transmission characteristics analysis of a novel double-roller hourglass worm drive based on enveloping principle

Traditional planar double-enveloping hourglass worm pairs have the characteristics such as the strong bearing capacity, high transmission efficiency and long life-span. However, the high relative sliding velocity and the serious agglutination or abrasion may also occur at the contact point on tooth surfaces. In this paper, a novel type of double-roller hourglass worm pair is proposed and analyzed, wherein, the worm part adopts from the planar double-enveloping worm pair, the corresponding meshing tooth surface of worm gear is replaced by two rows of cylinder rollers for reducing friction and enhancing meshing efficiency. That is, the original meshing tooth surfaces in worm gear are replaced by the common tangent plane of rollers to form a special type of meshing drive, the original line-contact form between tooth surfaces was changed to point-contact so that the sliding friction was transformed into rolling friction, and the meshing efficiency can be greatly improved. The theoretical model of double-roller hourglass worm pair was established based on spatial enveloping principle, the meshing equation and tooth surface equations were derived. The solid models of worm and gear were established and assembled. The parameters of enveloping surface angle, roller radius and friction coefficient, which affecting relative motion velocity at meshing contact point and efficiency during the whole transmission process was analyzed and discussed systematically. The results showed that comparing to the traditional worm pair, the roller’s rotation greatly reduced the relative sliding velocity and improved meshing efficiency at the contact point in this double-roller hourglass worm pair.

Computerized Simulation of Meshing of S-gears and Modification Geometry

S-gear is a new type of gear with the advantages of small sliding coefficient, high meshing efficiency and large load-bearing capacity due to the concave-convex contact in a vicinity of the meshing start and end. In view of the excellent characteristics and potential value of S-gears, this paper deeply studies the designation and meshing characteristics of the S-gears. First, based on the relationship of S-shaped rack-cutter and machining motion, the tooth surface of the S-gears is generated. Second, by superimposing the surface of modified volume with the standard tooth surface, the modified tooth surface of S-gears is constructed. On this basis, using MATLAB programming, the coordinates of 3D grid node of modified S-gears are calculated. Third, loaded tooth contact analysis (LTCA) is used to study the meshing characteristics of the S-gears with longitudinal modifications and misalignment angle errors. Ultimately, one example is presented and the result shows that after tooth surface modification, the load distribution of S-gears is effectively improved and error sensitivity is greatly reduced. S-gear is a new type of gear which is different from involute gears and has great potential application prospect in large load-bearing field, which will be further studied in the future.

Study of Gear Meshing Efficiency of Electric Drive Axle with Considering System Deformation

Study of Gear Meshing Efficiency of Electric Drive Axle with Considering System Deformation

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.

The dynamic and economic performance study of a new Simpson planetary gearset based dual motor powertrain for electric vehicles

The dual motor powertrain is superior to the single motor powertrain in terms of economic performance for electric vehicles. To further improve the dynamic and economic performance of dual motor powertrain, a new Simpson planetary gearset based dual motor powertrain (SPGDMP) is proposed. The SPGDMP can realize six driving modes, including four single motor driving modes and two dual-motor driving modes. A simplified dynamic model which considers the gear meshing efficiency is built to implement the parameters design and formulate the energy management strategy (EMS). The genetic algorithm is used to optimize the parameters of SPGDMP to minimize the total power of the drive motor and meet the predetermined dynamic performance requirements at the same time. The EMS is formulated by minimizing the instantaneous consumed power of two motors. To demonstrate the performance of SPGDMP, the parallel axle based dual motor powertrain (PADMP) that meets the same dynamic performance requirement is used as the reference. The simulation results show that the proposed SPGDMP requires lower total power of driving motors to achieve the same dynamic performance and has much better economic performance.

Structure Design and Experimental Study of Pin-Cycloidal Planetary Reducer for the Pitch of High-Power Wind Turbine

In recent years, with the development of manufacturing technology and production capacity, wind power industry has been developed rapidly.A new type of pin-cycloidal planetary reducer was proposed in this studyfor the actuator of the pitch of high-power wind turbines. Based on the transformation mechanism method, the transmission efficiency of the reducer was calculated by analyzing the pin-cycloidal meshing efficiency, bearing efficiency, and output mechanism efficiency. Prototype testing were combined to systematically and deeply study the design theory of the reducer for the pitch of high-power wind turbines. Finally, a new design was proposed for a reliable two-stage pin-cycloidal planetary reducer with a strong bearing capacity and multi-tooth meshing on the hard gear surface that can be applied to the pitch system of high-power wind turbines.

Meshing efficiency analysis of double helical gears considering tribo-dynamic coupling effect

In order to obtain accurate meshing efficiency of double helical gears, a calculation method of sliding friction power loss is proposed considering the tribo-dynamic coupling effect. Based on the mixed elastohydrodynamic lubrication (EHL) theory, the initial friction coefficient of tooth surface is obtained and the friction excitation is calculated. Considering the tribo-dynamic coupling effect, a sixteen-degree-of-freedom tribo-dynamic model of double helical gear pair is established, including time-varying mesh stiffness, friction excitation, backlash and transmission error. The tribo-dynamic behaviours of gear pair are analysed before and after coupling, and then the sliding friction power loss and meshing efficiency of double helical gears are obtained. The research results show that after tribo-dynamic coupling, the friction coefficient and friction excitation of double helical gear pair increase, and the meshing efficiency decreases. The meshing efficiency of gear pair increases with the increase of helix angle and pressure angle, and decreases with the increase of surface roughness.

Influence of rotational speed and torque on meshing efficiency of double helical gear transmission system

The accuracy of gear meshing efficiency model is the key to study the influence factors of gear meshing efficiency. Experiment is an effective method to verify the theory model. Therefore, the acquisition of experimental value of gear meshing efficiency is particularly important. Taken double helical gears as the research object, on the analysis of a large number of experimental data, the experimental value of gear meshing efficiency for double helical gears are calculated and then the influence of rotational speed and torque on meshing efficiency of double helical gears is studied. Firstly, the calculation method of transmission efficiency for experimental value in different layout of gear test-rigs with closed power flow is summarized. Secondly, the calculation method of meshing efficiency for experimental value in gear test-rig with closed power flow is introduced. Thirdly, the calculation method of load-dependent bearing loss is given. Finally, the experimental value of meshing efficiency for double helical gears is calculated and the influence of rotational speed and torque on meshing efficiency of double helical gears is obtained, which lays a theoretical foundation for the further improvement of the transmission efficiency of double helical gears.

Optimal structural pattern for maximal compliance using topology optimization based on phasefields: Application to improve skin graft meshing efficiency.

This article focuses on the problem of maximal compliance design of a hyper-elastic solid with the optimal design of human skin grafts as the application in mind. The solution method is a phasefield-based topology optimization method that supposes multiple local phasefields and a minimum distance constraint in order to prevent the phasefields from merging. Consequently, structurally disintegrating solutions such as by the coalescence of voids can be prevented. The method is used to find an optimal graft meshing pattern for a sample that is subjected to a biaxial extension of up to 150%, which corresponds to an expansion ratio of 1 : 2.25. Three prospective unitcell solutions that exhibit meta-material behavior are proposed for a periodic graft pattern. The results are a step toward improving the skin graft meshing efficiency. This work does not cover experimental validation.

Meshing Efficiency Analysis of Modified Cycloidal Gear Used in the RV Reducer

Cycloidal gears play an important role in the performance of rotate vector (RV) reducers. In this article, numerical analysis of mixed elastohydrodynamic lubrication (EHL) is applied to establish a meshing efficiency model for a modified cycloidal gear. A theoretical efficiency formula is derived and the effects of modification amount and short-amplitude coefficient on efficiency parameters are analyzed, including contact load, relative speed, oil film pressure and thickness, and friction coefficient. The simulation results show that the meshing efficiency is almost unchanged when the modification amount changes, whereas it increases with an increase in the short-amplitude coefficient. Efficiency experiments for an RV reducer with different cycloidal gears are carried out to verify the simulation results. The meshing efficiency analysis in this article contributes to the optimal design of cycloidal gears used in RV reducers.

Research on the sliding friction associated spur-face gear meshing efficiency based on the loaded tooth contact analysis.

In order to solve the problem of Meshing Efficiency of spur-face gear sliding friction, a method for calculating the Meshing Efficiency of Spur-Face gear is proposed based on Elastohydrodynamic lubrication (EHL) theory. Through the Tooth Contact Analysis (TCA) and Loaded Tooth Contact Analysis technique (LTCA) method, the meshing process of the Spur-Face gear was simulated. The calculation model of Sliding friction coefficient was established by using non Newtonian quasi steady thermal Elastohydrodynamic lubrication (TEHL) theory, and the calculation model of Meshing Efficiency of Spur-Face gear was established. The influence of input torque and rotational speed on Meshing Efficiency is analyzed. The results show that Sliding friction coefficient is an important factor affecting the Meshing Efficiency of gears. Sliding friction coefficient is not the same at different positions of the tooth surface. Sliding friction coefficient is affected by input speed and input torque. This method provides a theoretical basis for further optimization calculation of Spur-Face gear.

A method for calculating gear meshing efficiency by measured data from gear test machine

Gear meshing efficiency is an important component of gear transmission efficiency, and the meshing efficiency of gear is directly related to device performance and energy consumption. The gear meshing efficiency can’t be obtained directly from the measurement results of gear test machine. It is rarely reported effective method to calculate the gear meshing efficiency with measured data from gear test machine, which limits the verification of theoretical calculation method of gear meshing efficiency. Therefore, a method for calculating gear meshing efficiency by measured data from gear test machine is proposed in the paper. It is suitable for power closed type gear test machine, and suitable for power open one as well. Firstly, according to the type of gear test machine, the corresponding calculation method of gear transmission efficiency is confirmed. Secondly, the gear transmission efficiency under both unloaded and loaded conditions, the total power under loaded conditions and friction-related losses at the bearings are calculated at a given speed, respectively. Finally, substituting the calculation results of friction-related losses at the bearings, total power under loaded conditions and the gear transmission efficiency both unloaded and loaded conditions into the gear meshing efficiency calculation formula, and gear meshing efficiency by measured data from gear test machine is obtained. An example is presented to verify the proposed method.

POWER FLOW AND EFFICIENCY ANALYSES OF DUAL PLANETARY COUPLING MECHANISM BASED ON BOND GRAPH THEORY

This paper concentrates on the power flow and transmission efficiency of a two-side motors driving transmission system used in tracked vehicle. Based on the theoretical analysis of tracked vehicle's steering process, the theory of bond graph was applied in the efficiency analyses due to the properties of energy conservation and power fluxion. A bond graph model of dual planetary platoon power coupling mechanism was established. The kinematic and the dynamic characteristics of all components and the constraints between components were obtained with the constraint conditions of turning radius and speed. According to the criterion of power flow, the power flows of the transmission system were got under six different driving conditions. Based on the power flows, the transmission efficiency was obtained by the calculation method of planetary gear train's meshing efficiency, which was proposed by this paper. The results show that by using the bond graph theory, we can get all the possible power flows of the transmission system and its corresponding transmission efficiency. This method is more systematic and universal than the traditional methods, especially suitable for complex multi input and multi output gear transmission system.

THE ENGINEERING DESIGN AND TRANSMISSION EFFICIENCY VERIFICATION OF HELICAL SPUR GEAR TRANSMISSION WITH A SINGLE GEAR PAIR

The transmission efficiency of a gear reducer (ηT) can be expressed as ηT = ηm × ηb × ηs, where ηm is the meshing efficiency of gear pairs, ηb is the efficiency of bearings, and ηs is efficiency of oil seals. Based on the research of Hsieh, et al., the meshing efficiencies of a helical spur gear pair (4, 77) are between 96.13 and 99.20%. The purpose of this article is to analyze the theoretical transmission efficiencies of non-standard helical spur gear pair and verify the theorem. According to the gear data, the theoretical transmission efficiencies are calculated to be 90.13–97.85%. And its test values of transmission efficiencies are between 82.3 and 91.9% (acceptable values). There are only 5.39–14.14% errors between these two values. This manuscript verifies that a helical spur gear pair can have a high reduction ratio (20–30) and acceptable real transmission efficiencies.

Calculation of Meshing Efficiency of Helical Gear Based on Double Integral Method

The meshing efficiency of helical gear transmission is calculated by using the method of double integral. The external involute helical gear meshing is taken and the model of helical gears is simplified by the idea of differential. The instantaneous efficiency equation of a meshing point is derived, and further more the rectangular coordinate system of meshing zone of helical gears is established. The average meshing efficiency of helical gears is achieved by using double integral method. Then, the influence of design parameters is studied and the efficiency formula is verified by comparing the theoretical results with relevant experimental data, which can provide a theoretical basis for decide the design parameters.

THE DESIGN AND MESHING EFFICIENCY ANALYSIS OF HELICAL SPUR GEAR REDUCER WITH SINGLE GEAR PAIR FOR ELECTRIC SCOOTERS

To achieve reduced costs and energy conservation, this paper proposes non-standard helical spur gear reducer with one gear pair (having reduction ratio 19.25) to be the gear reducer for electric scooter. This paper also focuses on the meshing efficiency analysis of non-standard helical spur gear pair. According to Buckingham’s research, the theoretical meshing efficiency formula of non-standard helical spur gear pair is derived. Three design cases of non-standard helical spur gear pair (4, 77) are proposed as examples for analyzing their meshing efficiencies at widely rotation speed range. The theoretical meshing efficiencies for the helical spur gear pair (4, 77) are between 96.47–99.26%. Its best meshing efficiency occurs at 800–1000 rpm of pinion. The meshing efficiencies of these three design cases are almost same, and their differences are less than 0.5%. Considering the root strength of pinion, Cases II and III are better than Case I.

THE EQUATION DERIVATION AND ANALYSIS OF MESHING EFFICIENCY FOR A STRAIGHT SPUR GEAR PAIR

According to the concept of “Stribeck Curve” proposed by Downson, this paper proposes modified coefficients for the calculation of average friction coefficients for approach and recess. Based on the research of Buckingham, this paper derives the theoretical meshing efficiency equation of straight spur gear pair. And, based on the involute theorem, the average sliding velocities for approach and recess are obtained. The corresponding modified average friction coefficients for approach and recess are obtained. Finally, according to modified average friction coefficients and meshing efficiency equation, the meshing efficiencies for straight spur gear pair (15, 79) are analyzed to be 99.04–99.62%. The best meshing efficiency occurs at pinion speed 800–1500 rpm. Based on the proposed approach, the meshing efficiencies of all spur gear pairs can be analyzed. The results of this paper will contribute to engineers in the design of straight spur gear reducers.

Meshing Efficiency Analysis of Straight Spur Gear Pair

Due to shortage of energy, the meshing efficiency of gear train becomes an important factor of power system. This paper focuses on the meshing efficiency of straight spur gear pair. The analysis of gear meshing efficiency involves the involute theorem of gears, friction and lubrication, and other related issues. According to Buckingham’s research, the theoretical meshing efficiency equation of straight spur gear pair is proposed. One straight spur gear pair (15, 79) is proposed to be the example for analyzing meshing efficiencies at each rotation speed. The theoretical meshing efficiencies for the straight spur gear pair (15, 79) are between 98.36% ~ 99.79 %. Its best meshing efficiency occurs at pinion speed 600 rpm.

Modeling and analysis of the dynamic efficiency of manual transmission/reducer

To analyze and model the dynamic efficiency of vehicle transmission system, the theoretical power losses formulas of the spur/helical gear under the condition of elastohydrodynamic lubrication (EHL) were deduced. The spur gear meshing efficiency model was validated by comparing the predicted models with measured data. The formulas of oil churning, windage, and bearing power losses, which are widely applied and fit the experimental results well, were employed to analyze the efficiency of manual transmission system. In terms of formulas of power losses of each part in the transmission, the dynamic transmission efficiency model of manual transmission/reducer based on Matlab/Simulink was established. The efficiency map of each shift of a specific five-speed manual transmission was simulated under new European Driving Cycle (NEDC). Finally, in terms of simulation results, a new type gearbox was proposed and analyzed, which is capable of improving transmission efficiency significantly.