Kinematic Modeling and Characteristic Analysis of Eccentric Conjugate Non-circular Gear & Crank-Rocker & Gears Train Weft Insertion Mechanism

A novel weft insertion mechanism named eccentric conjugate non-circular gear & crank-rocker & gears train weft insertion mechanism was proposed in order to better meet the requirements of rapier loom's weft insertion mechanism as well as reduce the manufacturing difficulty. Meanwhile, based on the working principle of this mechanism, kinematical mathematic models of this mechanism were established and an aided analysis and simulation software was compiled. The influences of eccentricity ratio, deformation coefficient, and other important parameters on the kinematics characteristics of this mechanism were analyzed by using the software. A group of preferable parameters which could meet the requirements of weft insertion technology were obtained by means of human-computer interactive optimization method. The maximum velocity, maximum acceleration, and variation of acceleration of this mechanism are smaller than those of the conjugate cam weft insertion mechanism applied on TT96 rapier loom under the conditions of the same unilateral total stroke of rapier head and the same rotary speed of loom spindle; meanwhile the other demands of weaving technology can be met by this novel weft insertion mechanism.

Reverse Design and Test of Non-circular Gear & Crank-Rocker & Gear Trains Weft Insertion Mechanism

For the purpose of obtaining satisfactory performance of the non-circular gear & crank-rocker & gear trains (NCCRG) weft insertion mechanism which was proposed in this paper, the ideal kinematic curve of this weft insertion mechanism was given, and the reverse solution models of this mechanism were established. A reverse design and simulation software was compiled based on Visual Basic 6.0 to obtain the mechanism parameters, including the pitch curves and tooth profiles of the non-circular gears. A test-bed of this mechanism was developed according to these parameters. The kinematic performance of this weft insertion mechanism was tested by high-speed video tape recorder with its corresponding video analytical software Blaster's MAS. And the test results were identical with the theoretical calculation. Compared with the conjugate cam weft insertion mechanism which is applied on TT96 rapier loom, under the condition of same weft insertion rate, the variation of acceleration of this mechanism is smaller. This novel weft insertion mechanism can meet the requirements of weft insertion on rapier looms with smooth and steady motion.

Matching between mechanics and thermodynamics among 4 individual strokes in a 4-stroke engine by non-circular gear mechanism

The relationship between engine mechanics and thermo-dynamics has been investigated by means of numerical simulation.The inherent mismatching between the mechanical behaviors and the thermodynamic process in internal combustion engine is identified,which is believed to be one of the important limiting factors of energy efficiency for conventional engines available in the current market.An approach for engine efficiency improvement through optimal matching between mechanics and thermodynamics(OMBMT)is proposed.An ideal matching model is defined and the conflicts due to the constraints among the mapping strokes in a 4-stroke engine are analyzed.A novel mechanical model is built for approaching optimal matching among all 4 individual strokes in a 4-stroke spark-ignition engine,which is composed of non-circular gears(NCG)and integrated with conventional slider crank engine mechanism.By means of digital mechanical model and numerical simulation,the matching gains among all 4 strokes are defined and calculated for quantifying the NCG engine efficiency improvement by comparing with a baseline engine.The potentials with the OMBMT implemented and the enhancements made by NCG mechanism for engines in terms of overall engine efficiency are reported.Based on the results achieved,it is recommended that the feasibility studies and the experimental validations should be conducted to verify the engine matching concept and effectiveness of the NCG mechanism engine model proposed,and the engine performance and NCG design parameters should be further optimized.

Calculating method of contact stress for non-circular gears

According to Hertz theory, the difference of contact stress for non-circular gears and equivalent gears is compared in the paper, a calculating method of contact stress for non-circular gears by using equivalent gears is researched, and computing formulas of power and rotation speed for equivalent gears are deduced. A numerical simulation of contact stress for non-circular gears has also been conducted based on the finite element method. By the comparison of fitting curves, the feasibility of using equivalent gears instead of non-circular gears to calculate the contact stress is testified.

Research on Design Method of Non-Circular Gear Pair with Double Generating Angles

In order to enhance the bearing capacity of non-circular gear pair, the non-circular gear pair with double generating angles is proposed based on the design idea of unsymmetrical gear with double pressure angles. The tooth profile is designed by generating cutting theory, the pure rolling mathematic model that the center line of unsymmetrical rack roll along non-circular pitch curve is built, the digital model of non-circular gear with double generating angles is created through the second development method of CAD software, and then the drive characteristic and tooth strength are analyzed. The results show that the design method for double generating angles non-circular gear proposed in this paper is feasible, which is significant to improve the bearing capacity of non-circular gear pair.

Design and Experimental Research on Seedling Pick-Up Mechanism of Planetary Gear Train with Combined Non-circular Gear Transmission

Currently, transplanting mechanisms for dryland plug seedlings in China are mainly semiautomatic and have low efficiency. The rotary seedling pick-up mechanism with a planetary gear train for non-uniform intermittent transmission, and a concave and convex locking arc device, has a large rigid impact. To solve these problems, according to the design requirements for a dryland plug seedling transplanting mechanism, a rotary seedling pick-up mechanism of a planetary gear train with combined non-circular gear transmission of incomplete eccentric circular and noncircular gears was proposed. This has the characteristics of two-times greater fluctuation of the transmission ratio in a cycle, and can achieve a non-uniform continuous drive. Through analysis of the working principle of the seedling pick-up mechanism, its kinematics model was established. The human–computer interaction optimization method and self-developed computer-aided analysis and optimization software were used to obtain a set of parameters that satisfy the operation requirements of the seedling pick-up mechanism. According to the optimized parameters, the structure of the seedling pick-up mechanism was designed, a virtual prototype of the mechanism was created, and a physical prototype was manufactured. A virtual motion simulation of the mechanism was performed, high-speed photographic kinematics tests were conducted, and the kinematic properties of the physical prototype were investigated, whereby the correctness of the theoretical model and the optimized design of the mechanism were verified. Further, laboratory seedling pick-up tests were conducted. The success ratio of seedling pick-up was 93.8% when the seedling pick-up efficiency of the mechanism was 60 plants per minute per row, indicating that the mechanism has a high efficiency and success ratio for seedling pick-up and can be applied to a dryland plug seedling transplanter.

Reverse design and tests of vegetable plug seedling pick-up mechanism of planetary gear train with non-circular gears

In the previous research,the seedling pick-up mechanism of the planetary gear train with incomplete eccentric circular gear and non-circular gears for vegetable plug seedlings still has two shortcomings.One is that not enough seedling pick-up depth leads to a low success ratio of seedling pick-up at high rotation speeds,the other is that the smaller seedling pushing angle results in poor seedling pushing effect.Therefore,the reverse design of the seedling pick-up mechanism based on its motion trajectory was carried out.The local trajectory of seedling pick-up and seedling pushing sections was adjusted to obtain the theoretical motion trajectory of the seedling pick-up mechanism.The cubic non-uniform B-spline curve was used to fit the adjusted trajectory.A novel seedling pick-up mechanism of the planetary gear train with non-circular gears was proposed,including three combined non-circular gears,four non-circular gears,one planetary carrier,and two seedling pick-up arms.The reverse design model of the mechanism was established.The analysis and design software of the mechanism was developed to obtain the mechanism parameters meeting design requirements.The virtual prototype of the mechanism was established and its physical prototype was manufactured.Through the virtual motion simulation and high-speed photographic kinematics bench tests of the mechanism,the kinematic model and results of reverse design of the mechanism were verified,with the kinematic performances of the mechanism prototype studied.The seedling pick-up tests of the mechanism were conducted in the laboratory.The success ratios of seedling pick-up were 94.2%,95.6% and 90.2% while the seedling pick-up efficiencies of the mechanism were 60,80 and 100 plants per minute per row,respectively.Besides,the seedling pushing effect was improved mush because of the greater seedling pushing angle.The seedling pick-up mechanism through revise design is of high value to be applied in the practical vegetable plug seedling transplanters.

Research on Cavitation Characteristics and Influencing Factors of Herringbone Gear Pump

Cavitation is a common issue in pumps,causing a decrease in pump head,a fall in volumetric efficiency,and an intensification of outlet flow pulsation.It is one of the main hazards that affect the regular operation of the pump.Research on pump cavitation mainly focuses on mixed flow pumps,jet pumps,external spur gear pumps,etc.However,there are few cavitation studies on external herringbone gear pumps.In addition,pumps with different working principles significantly differ in the flow and complexity of the internal flow field.Therefore,it is urgent to study the cavitation characteristics of external herringbone gear pumps.Compared with experimentalmethods,visual research and cavitation area identification are achieved through computation fluid dynamic(CFD),and changing the boundary conditions and shape of the gear rotor is easier.The simulation yields a head error of only 0.003%under different grid numbers,and the deviation between experimental and simulation results is less than 5%.The study revealed that cavitation causes flow pulsation at the outlet,and the cavitation serious area is mainly distributed in the meshing gap and meshing area.Cavitation can be inhibited by reducing the speed,increasing the inlet pressure,and changing the helix angle can be achieved.For example,when the inlet pressure is 5 bar,the maximumgas volume fraction in themeshing area is less than 50%.These results provide a reference for optimizing the design and finding the optimal design parameters to reduce or eliminate cavitation.

Application of Isogeometric Analysis Method in Three-Dimensional Gear Contact Analysis

Gears are pivotal in mechanical drives,and gear contact analysis is a typically difficult problem to solve.Emerging isogeometric analysis(IGA)methods have developed new ideas to solve this problem.In this paper,a threedimensional body parametric gear model of IGA is established,and a theoretical formula is derived to realize single-tooth contact analysis.Results were benchmarked against those obtained from commercial software utilizing the finite element analysis(FEA)method to validate the accuracy of our approach.Our findings indicate that the IGA-based contact algorithmsuccessfullymet theHertz contact test.When juxtaposed with the FEA approach,the IGAmethod demonstrated fewer node degrees of freedomand reduced computational units,all whilemaintaining comparable accuracy.Notably,the IGA method appeared to exhibit consistency in analysis accuracy irrespective of computational unit density,and also significantlymitigated non-physical oscillations in contact stress across the tooth width.This underscores the prowess of IGA in contact analysis.In conclusion,IGA emerges as a potent tool for addressing contact analysis challenges and holds significant promise for 3D gear modeling,simulation,and optimization of various mechanical components.

Contact Stress Reliability Analysis Model for Cylindrical Gear with Circular Arc Tooth Trace Based on an Improved Metamodel

Although there is currently no unified standard theoretical formula for calculating the contact stress of cylindrical gears with a circular arc tooth trace(referred to as CATT gear),a mathematical model for determining the contact stress of CATT gear is essential for studying how parameters affect its contact stress and building the contact stress limit state equation for contact stress reliability analysis.In this study,a mathematical relationship between design parameters and contact stress is formulated using the KrigingMetamodel.To enhance the model’s accuracy,we propose a new hybrid algorithm that merges the genetic algorithm with the Quantum Particle Swarm optimization algorithm,leveraging the strengths of each.Additionally,the“parental inheritance+self-learning”optimization model is used to fine-tune the KrigingMetamodel’s parameters.Following this,amathematicalmodel for calculating the contact stress of Variable Hyperbolic Circular-Arc-Tooth-Trace(VH-CATT)gears using the optimized Kriging model was developed.We then examined how different gear parameters affect the VH-CATT gears’contact stress.Our simulation results show:(1)Improvements in R2,RMSE,and RMAE.R2 rose from0.9852 to 0.9974(a 1.22%increase),nearing 1,suggesting the optimized Kriging Metamodel’s global error is minimized.Meanwhile,RMSE dropped from3.9210 to 1.6492,a decline of 57.94%.The global error of the GA-IQPSO-Kriging algorithm was also reduced,with RMAE decreasing by 58.69%from 0.1823 to 0.0753,showing the algorithm’s enhanced precision.In a comparison of ten experimental groups selected randomly,the GA-IQPSO-Kriging and FEM-based contact analysis methods were used to measure contact stress.Results revealed a maximum error of 12.11667 MPA,which represents 2.85%of the real value.(2)Several factors,including the pressure angle,tooth width,modulus,and tooth line radius,are inversely related to contact stress.The descending order of their impact on the contact stress is:tooth line radius>modulus>pressure angle>tooth width.(3)Complex interactions are noted among various parameters.Specifically,when the tooth line radius interacts with parameters such as pressure angle,tooth width,and modulus,the resulting stress contour is nonlinear,showcasing amultifaceted contour plane.However,when tooth width,modulus,and pressure angle interact,the stress contour is nearly linear,and the contour plane is simpler,indicating a weaker coupling among these factors.

Triad-displaced ULAs configuration for non-circular sources with larger continuous virtual aperture and enhanced degrees of freedom

Non-uniform linear array(NULA)configurations are well renowned due to their structural ability for providing increased degrees of freedom(DOF)and wider array aperture than uniform linear arrays(ULAs).These characteristics play a significant role in improving the direction-of-arrival(DOA)estimation accuracy.However,most of the existing NULA geometries are primarily applicable to circular sources(CSs),while they limitedly improve the DOF and continuous virtual aperture for noncircular sources(NCSs).Toward this purpose,we present a triaddisplaced ULAs(Tdis-ULAs)configuration for NCS.The TdisULAs structure generally consists of three ULAs,which are appropriately placed.The proposed antenna array approach fully exploits the non-circular characteristics of the sources.Given the same number of elements,the Tdis-ULAs design achieves more DOF and larger hole-free co-array aperture than its sparse array competitors.Advantageously,the number of uniform DOF,optimal distribution of elements among the ULAs,and precise element positions are uniquely determined by the closed-form expressions.Moreover,the proposed array also produces a filled resulting co-array.Numerical simulations are conducted to show the performance advantages of the proposed Tdis-ULAs configuration over its counterpart designs.

Stability Analysis of Nonlinear Models of Nose Landing Gear Shimmy

Shimmy can reduce the service life of the nose landing gear, affect ride comfort, and even cause fuselage damage leading to aircraft crashes. Taking a light aircraft as the research object, the torsional freedom of landing gear around strut axis and lateral deformation of tire are considered. Since the landing gear shimmy is a nonlinear system, a nonlinear mechanical model of the front landing gear shimmy is established. Sobol index method is proposed to analyze the influence of structural parameters on the stability region of the nose landing gear, and Routh-Huritz criterion is used to verify the reliability of the analysis results of Sobol index method. We analyse the effect of torsional stiffness of strut, caster length, rated initial tire inflation pressure, rake angle, and vertical force on the stability region of theront landing gear. And the research shows that the optimization of the torsional stiffness of the strut and the caster length of the nose landing gear should be emphasized, and the influence of vertical force on the stability region of the nose landing gear should be paid attention to.

Research on Instantaneous Angular Speed Signal Separation Method for Planetary Gear Fault Diagnosis

Planetary gear train is a critical transmission component in large equipment such as helicopters and wind turbines. Conducting damage perception of planetary gear trains is of great significance for the safe operation of equipment. Existing methods for damage perception of planetary gear trains mainly rely on linear vibration analysis. However, these methods based on linear vibration signal analysis face challenges such as rich vibration sources, complex signal coupling and modulation mechanisms, significant influence of transmission paths, and difficulties in separating damage information. This paper proposes a method for separating instantaneous angular speed (IAS) signals for planetary gear fault diagnosis. Firstly, this method obtains encoder pulse signals through a built-in encoder. Based on this, it calculates the IAS signals using the Hilbert transform, and obtains the time-domain synchronous average signal of the IAS of the planetary gear through time-domain synchronous averaging technology, thus realizing the fault diagnosis of the planetary gear train. Experimental results validate the effectiveness of the calculated IAS signals, demonstrating that the time-domain synchronous averaging technology can highlight impact characteristics, effectively separate and extract fault impacts, greatly reduce the testing cost of experiments, and provide an effective tool for the fault diagnosis of planetary gear trains.

Research on Three-Dimensional Simulation of the Internal Arc Gear Skiving

Aiming at the problems that the simulation accuracy which is reduced due to the simplification of the model,a three-dimensional simulation method based on solid modeling is being proposed.By analyzing the motion relationship and positional relationship between the caries knife and the workpiece,the coordinate system of the caries machining was established.With the MATLAB software,the cutting edge model and the blade sweeping surface model of the boring cutter are sequentially established.Boolean operation is performed on the blade swept surface formed by the tooth cutter teeth with time t and the workpiece tooth geometry as well as the undeformed three-dimensional chip geometry model and the instantaneous cogging geometry model are obtained at different times.Through the compare between gear end face simulation tooth profile and the theoretical inner arc tooth profile,we verified the accuracy and rationality of the proposed method.

Time-Varying Mesh Stiffness Calculation and Dynamic Modeling of Spiral Bevel Gear with Spalling Defects

Time-varying mesh stiffness(TVMS)is a vital internal excitation source for the spiral bevel gear(SBG)transmission system.Spalling defect often causes decrease in gear mesh stiffness and changes the dynamic characteristics of the gear system,which further increases noise and vibration.This paper aims to calculate the TVMS and establish dynamic model of SBG with spalling defect.In this study,a novel analytical model based on slice method is proposed to calculate the TVMS of SBG considering spalling defect.Subsequently,the influence of spalling defect on the TVMS is studied through a numerical simulation,and the proposed analytical model is verified by a finite element model.Besides,an 8-degrees-of-freedom dynamic model is established for SBG transmission system.Incorporating the spalling defect into TVMS,the dynamic responses of spalled SBG are analyzed.The numerical results indicate that spalling defect would cause periodic impact in time domain.Finally,an experiment is designed to verify the proposed dynamic model.The experimental results show that the spalling defect makes the response characterized by periodic impact with the rotating frequency of spalled pinion.

Optimization design and test of rice plug seedling transplanting mechanism of planetary gear train with incomplete eccentric circular gear and non-circular gears

In order to solve the problem of the high-speed mechanized transplanting of rice plug seedlings,the design requirements of transplanting mechanism for rice plug seedlings were analyzed and a kind of rice plug seedling transplanting mechanism of planetary gear train based on the drive with incomplete eccentric circular gear and non-circular gears was designed innovatively.The laboratory kinematics was examined.The working principle of the transplanting mechanism for rice plug seedlings was studied,kinematics analysis of the transplanting mechanism was carried out and its kinematic model was set up.A human-computer interaction optimization method was used to optimize the parameters of the transplanting mechanism.The computer aided analysis and optimization software of the transplanting mechanism based on Visual Basic 6.0 was developed.Through analyzing the influence of design variables on the optimization objectives of the transplanting mechanism,a set of parameters of the transplanting mechanism which meet the requirements of transplanting trajectory and posture for transplanting rice seedlings were obtained by means of human-computer interaction.The structure of the transplanting mechanism was designed according to this set of parameters,and its virtual prototype and physical prototype were set up and manufactured,respectively.The kinematic simulation test and high-speed photography kinematic test of the transplanting mechanism were conducted to obtain its kinematic performances,such as transplanting trajectory and posture.The results of bench test,simulation analysis and theoretical analysis were almost in agreement,which verified the correctness of the theoretical model and design results of the transplanting mechanism,indicating that the optimized transplanting mechanism can satisfy the requirements of transplanting rice seedlings and be applied in the rice plug seedling transplanter.

Numerical Calculation and Experiment of Coupled Dynamics of the Differential Velocity Vane Pump Driven by the Hybrid Higher-order Fourier Non-circular Gears

The transmission systems of the differential velocity vane pumps （DVVP） have periodic vibrations under loads. And it is not easy to find the reason. In order to optimize the performance of the pump, the authors proposed DVVP driven by the hybrid Higher-order Fourier non-circular gears and tested it. There were also simi- lar periodic vibrations and noises under loads. Taking into account this phenomenon, the paper proposes fluid mechanics and solid mechanics simulation methodology to analyze the coupling dynamics between fluid and transmission system and reveals the reason. The results show that the pump has the reverse drive phenomenon, which is that the blades drive the non-circular gears when the suction and discharge is alternating. The reverse drive phenomenon leads the sign of the shaft torque to be changed in positive and negative way. So the transmis- sion system produces torsional vibrations. In order to confirm the simulation results, micro strains of the input shaft of the pump impeller are measured by the Wheatstone bridge and wireless sensor technology. The relation- ships between strain and torque are obtained by experimental calibration, and then the （rue torque of input shaft is calculated indirectly. The experimental results are consistent to the simulation results. It is proven that the peri- odic vibrations are mainly caused by fluid solid coupling, which leads to periodic torsional vibration of the trans- mission system.

Method for generating non-circular gear with addendum modification and its application in transplanting mechanism

With a focus on the design of tooth profiles of non-circular gears with addendum modifications that conform to the given complex transmission ratio curves and based on a series of discrete point sets on the pitch curves,the criteria for tooth profile distortion and undercut in non-circular gears were proposed.With the constraint of no tooth profile distortion and undercut,the addendum modification coefficient was introduced into the calculation of the distorted and undercut segments of the tooth profile of a non-circular gear,and the addendum modification coefficient of each contact point of the non-circular gear was obtained.Based on the generating principle for gear shaping with gear cutters,a theoretical model for calculating the tooth profile of non-circular gears with addendum modification was derived.The cutting and radial feeding motions of the pinion cutter were ignored,and only the meshing motion was considered.The involute tooth profiles of the pinion cutter enveloped the tooth profile of the non-circular gear.3D automatic non-circular gear model generation software was developed,which was a secondary development product of the software UG.A non-circular gear in a rice potted seedling transplanting mechanism was designed,and the transplanter was developed and tested.The test results showed that the designed tooth profile of non-circular gear achieved the variable transmission ratios required by the transplanting mechanism.When the transplanting efficiencies were 140 plants/min,160 plants/min and 180 plants/min,the transplanter completed the rice potted seedling transplanting operation with high quality.

Design and Experiment of Non-circular Combined Gear Train Beating-up Mechanism

The most important performance of a beating-up mechanism is that the dwelling time of the sley must ensure the completion of the weft insertion. To meet this requirement, a new non-circular combined gear train beating-up mechanism which is composed of two-stage planetary gear trains is proposed. The first-stage is a Fourier planetary gear train and the second-stage is a non-circular planetary gear train. For designing of this new mechanism, the ideal kinematic equations of the sley are constructed first. Then the kinematic model of the first-stage Fourier planetary gear train is established and the reverse solution for the pitch curves of the second-stage non-circular gears is deduced. With a computer-aided design program, the influences of several important parameters on the pitch curves of the second-stage non-circular gears are analyzed, and a set of preferable structural parameters are obtained. Finally, a test bed of this mechanism is developed and the experimental results show that this new beating-up mechanism can achieve the designed dwelling time, namely it can meet the requirements of beating-up process.

Mathematic model and tooth contact analysis of a new spiral non-circular bevel gear

A novel spiral non-circular bevel gear that could be applied to variable-speed driving in intersecting axes was proposed by combining the design principles of non-circular bevel gears and the manufacturing principles of face-milling spiral bevel gears.Unlike straight non-circular bevel gears,spiral non-circular bevel gears have numerous advantages,such as a high contact ratio,high intensity,good dynamic performance,and an adjustable contact region.In addition,while manufacturing straight non-circular bevel gears is difficult,spiral non-circular bevel gears can be efficiently and precisely fabricated with a 6-axis bevel gear cutting machine.First,the generating principles of spiral non-circular bevel gears were introduced.Next,a mathematical model,including a generating tooth profile,tooth spiral,pressure angle,and generated tooth profile for this gear type was established.Then the precision of the model was verified by a tooth contact analysis using FEA,and the contact patterns and stress distributions of the spiral non-circular bevel gears were investigated.