Investigation of a Design Modification for Double Helical Gears Reducing Vibration and Noise

To reduce vibration and noise and increase transmission efficiency, a three segment method for modifying the pinion profile was proposed. Cutter surface equations were deduced by changing the shape of the cutter-edge, substituting three segment parabolas for the line. The influence of longitudinal tooth modifications on tooth surface load distributions was discussed. Transmission error minimization and uniformity of tooth surface load distribution were chosen as optimization goals and the modified parameters were obtained by applying the complex method. Finally, an experiment comparing the loaded transmission error, vibration, and noise both before and after modifications was carried out. The results indicate that the modified design is reliable.

Quasi-static-model-based wear analysis of helical gears

A quasi-static wear model for helical gears is proposed based on finite element method and Archard's formula to investigate the wear characteristics of tooth surface in real operation conditions. The numerical simulation reveals that the wear depth distributes unevenly along the tooth lead and varies along the tooth profile. The surface wear depth claims its minimal value at the pitch circle and reaches its maximal value near the tooth root of the pinion. The effects of misalignment on wear depth are further investigated to provide useful information for gear designers. The numerical simulation reveals that the vertical misalignment is more influential than the parallel misalignment on the gear wear depth. Therefore, to eliminate the negative effects of misalignment, the misalignment should be strictly controlled.

Effects of parameters on rotational fine blanking of helical gears

The application of fine blanking to the manufacturing of helical gears directly from a strip has been restricted due to the traditional linear cutting stroke of the punch and die.In this work,rotational fine blanking which combined the linear and rotational motion of punch and counterpunch was applied for the forming of helical gears.A three-dimensional(3D) rigid-plastic finite element model was developed on the DEFORM-3D platform.By finite element simulation and analysis,the influences of key parameters on the punch load and cut surface were investigated.It is shown that: 1) with increasing the counterforce or helical angle,the punch load and the depth of die roll increase; 2) with increasing blank holder force,the punch load increases while the depth of die roll decreases; 3) V-ring indenter facilitates an improvement in the quality.The results of this research reveal the deformation mechanism of rotational fine blanking of helical gears,and provide valuable guidelines for further experimental studies.

Fabrication of miniature helical gears by powder extrusion using gas atomized Zn-22%Al powder

Powder extrusion, which is based on the superplastic behavior of Zn-22%A1 eutectoid alloy, was proposed to reduce the forming load and promises to provide fine microstructures in the manufacture of miniature helical gears. The specifications of the helical gears were as follows： module, 0.3; number of teeth, 12; and helix angle, 15°. Compacted powders were consolidated by sintering and solution heat treatment. The consolidated billets consisted of lamellar and fine-grained microstructures. Extrusion experiments were carried out under the following conditions： temperature, 250 ℃; strain rates, 2.36× 10-3 s^-1 and 1.18× 10^-1 s-1. The mechanical properties of the extruded helical gears were investigated by measurement of the Vickers hardness and extrusion load, and by scanning electron microscopy.

Analysis and correction of the machining errors of small plastic helical gears by ball-end milling

Many small-size precise plastic helical involutes gears are used in electrical appliances to transmit rotary movements con- tinuously and smoothly. Ball-end milling is an effective method for trial manufacture or small batch production of this type of gear, but the precision of the gear is usually low. In this research, the main sources of the errors of the gear, machining errors of the tooth profile and trace of the gear obtained were analyzed. The correction amounts for these errors are then determined by using a CNC gear tester. They are used to generate a new 3D-CAD model for gear machining with better nrecision.

Advancing high-speed train gearbox durability:enhanced bearing load and contact stress through transition from helical to herringbone gears

High-speed trains typically utilize helical gear transmissions,which significantly impact the bearing load capacity and fatigue service performance of the gearbox bearings.This paper focuses on the gearbox bearings,establishing dynamic models for both helical gear and herringbone gear transmissions in high-speed trains.The modeling particularly emphasizes the precision of the bearings at the gearbox's pinion and gear wheels.Using this model,a comparative analysis is conducted on the bearing loads and contact stresses of the gearbox bearings under uniform-speed operation between the two gear transmissions.The findings reveal that the helical gear transmission generates axial forces leading to severe load imbalance on the bearings at both sides of the large gear,and this imbalance intensifies with the increase in train speed.Consequently,this results in a significant increase in contact stress on the bearings on one side.The adoption of herringbone gear transmission effectively suppresses axial forces,resolving the load imbalance issue and substantially reducing the contact stress on the originally biased side of the bearings.The study demonstrates that employing herringbone gear transmission can significantly enhance the service performance of high-speed train gearbox bearings,thereby extending their service life.

Statistical Modification Analysis of Helical Planetary Gears based on Response Surface Method and Monte Carlo Simulation

Tooth modification technique is widely used in gear industry to improve the meshing performance of gearings. However, few of the present studies on tooth modification considers the influence of inevitable random errors on gear modification effects. In order to investigate the uncertainties of tooth modification amount variations on system＇s dynamic behaviors of a helical planetary gears, an analytical dynamic model including tooth modification parameters is proposed to carry out a deterministic analysis on the dynamics of a helical planetary gear. The dynamic meshing forces as well as the dynamic transmission errors of the sun-planet 1 gear pair with and without tooth modifications are computed and compared to show the effectiveness of tooth modifications on gear dynamics enhancement. By using response surface method, a fitted regression model for the dynamic transmission error（DTE） fluctuations is established to quantify the relationship between modification amounts and DTE fluctuations. By shifting the inevitable random errors arousing from manufacturing and installing process to tooth modification amount variations, a statistical tooth modification model is developed and a methodology combining Monte Carlo simulation and response surface method is presented for uncertainty analysis of tooth modifications. The uncertainly analysis reveals that the system＇s dynamic behaviors do not obey the normal distribution rule even though the design variables are normally distributed. In addition, a deterministic modification amount will not definitely achieve an optimal result for both static and dynamic transmission error fluctuation reduction simultaneously.

Finite element analysis and simulation for cold precision forging of a helical gear

To investigate the effects of billet geometry on the cold precision forging process of a helical gear, six different billet geometries were designed utilizing the relief-hole principle. And the influences of the billet geometry on the forming load and the deformation uniformity were analyzed by three-dimensional （3D） finite element method （FEM） under the commercial software DEFORM 3D. The billet geometry was optimized to meet lower forming load and better deformation uniformity requirement. Deformation mechanism was studied through the distribution of flow velocity field and effective strain field. The forging experiments of the helical gear were successfully performed using lead material as a model material under the same process conditions used in the FE simulations. The results show that the forming load decreases as the diameter of relief-hole do increases, but the effect of do on the deformation uniformity is very complicated. The forming load is lower and the deformation is more uniform when do is 10 mm.

A distributed dynamic mesh model of a helical gear pair with tooth profile errors

A dynamic model of a helical gear rotor system is proposed.Firstly,a generally distributed dynamic model of a helical gear pair with tooth profile errors is developed.The gear mesh is represented by a pair of cylinders connected by a series of springs and the stiffness of each spring is equal to the effective mesh stiffness.Combining the gear dynamic model with the rotor-bearing system model,the gear-rotor-bearing dynamic model is developed.Then three cases are presented to analyze the dynamic responses of gear systems.The results reveal that the gear dynamic model is effective and advanced for general gear systems,narrow-faced gear,wide-faced gear and gear with tooth profile errors.Finally,the responses of an example helical gear system are also studied to demonstrate the influence of the lead crown reliefs and misalignments.The results show that both of the lead crown relief and misalignment soften the gear mesh stiffness and the responses of the gear system increase with the increasing lead crown reliefs and misalignments.

Analysis of axial force of double circular arc helical gear hydraulic pump and design of its balancing device

In view of the axial force produced in the working process of double arc helical gear hydraulic pump,the theory of differential equation of curve and curved surface was utilized so that the calculation formula of axial force was obtained and the relationship between the axial force and structure parameters of gears was clarified.In order to balance the axial force,the pressure oil in the high pressure area was introduced into the end face of the plunger to press the plunger against the gear shaft,and the hydrostatic bearing whose type is plunger at the end of the shaft was designed.In order to verify the balance effect of axial force,the leakage owing to end clearance and volume efficiency of gear hydraulic pump before and after the balancing process was analyzed.This paper provides a new analysis idea and balance scheme for the axial force produced in the working process of the double arc helical gear hydraulic pump,which can reduce the leakage owing to end clearance caused by the axial force and improve the volume efficiency of the gear hydraulic pump.

EFFECT OF GEAR WIDTH AND HELIX ANGLE ON FACTOR OF DYNAMIC LOAD OF DOUBLE CIRCULAR ARC HELICAL GEARING

Based on theory of mechanical dynamics, meshing characteristic as well as thedynamic model of double circular arc helical gearing, an analysis approach and a computer programhave been developed for studying the state of dynamic load and factor of dynamic load of thegearing, the changing situation of dynamic load and dynamic load factor vs some affecting factorssuch as gear width, helix angle and accuracy grade etc are investigated. A series of conclusions areobtained: ①With the increasing in the values of gear width, the dynamic load factor appears slowdecreasing tendency in most region of gear width. ②When the accuracy grades of the gearing areimproved, the values of dynamic load factor decrease. ③The value of dynamic load factor appears adecreasing tendency with the increasing of value of helix angle at the same ratio of criticalrotational speed.

Excitation Prediction by Dynamic Transmission Error under Sliding Friction in Helical Gear System

Monte Carlo method was adopted to calculate the meshing error considering the manufacture error and assembly error of the meshing point along the time-varying contact line for helical gear pair. The flexural-torsion-axis dynamic model coupled was established under the tooth friction force and solved by the perturbation method to compute real dynamic tooth load. The change laws of the friction force and friction torque were obtained in a meshing period. The transmission error formulation was analyzed to introduce meshing excitations. The maximum dynamic transmission error, the maximum meshing force and the maximum dynamic factor were calculated under different speeds, external loads and damping factors. The conclusions can provide theoretical basis for the gear design especially in tooth profile correction.

Faults Analysis and Diagnosis of DRJ-460 Dish Centrifugal Separator′s Helical Gear

The main faults of dish centrifugal separator's helical gear are described inthis paper. In order to diagnose the DRJ-460 dish centrifugal separator correctly, the vibration istested with a helical gear under both normal and abnormal conditions. After comparing severalgeneral methods of the gear's fault feature extraction, a new convenient and effective method ispresented on the basis of analyzing the vibration spectrum under different rotary velocities.

Investigation on Mesh and Sideband Vibrations of Helical Planetary Ring Gear Using Structure, Excitation and Deformation Symmetries

Time?variant excitations in planetary gear trains can cause excessive noise and vibration and even damage the system on a permanent basis. This paper focuses on the elastic vibrations of a helical planetary ring gear subjected to mesh and planet?pass excitations. Motivated by the structure, excitation and deformation symmetries, this paper proposes dual?frequency superposition and modulation methods to capture the mesh and sideband vibrations. The transi?tion between ring gear tooth and planet is introduced to address the excitations and vibrations. The phasing e ect of ring gear tooth and planet on various deformations is formulated. The inherent connections between the two types of vibrations are identified. The vibrations share identical exciting rules and the wavenumber and modulating signal order both equal the linear combination of tooth and planet counts. The results cover in?plane bending and extensional, out?of?plane bending and torsional deformations. Main findings are verified by numerical calculation and comparisons with the open literature. The analytical expressions can be used to determine whether the sideband is caused by component fault or only by elastic vibration. The methods can be extended to other power?transmission systems because little restriction is imposed during the analysis.

Microstructures and Mechanical Properties of Helical Bevel Gears Made by Mn-Cu Alloyed Austempered Ductile Iron

Austempered ductile iron （ADI） has several advantages of replacing cast steel and forged steel in many engineering fields. A new Mn-Cu alloyed ADI with excellent mechanical properties has been developed in order to cut the cost and enlarge the application of ADI. The helical bevel gears were made of the new-developed Mn-Cu alloyed ADI. The microstructure and mechanical properties of the standard sample were investigated by optical microscope （OM）, scanning electron microscope （SEM） and performance measurement. The results showed that after a series of treatments, the mechanical properties （Rm 1007. 4 to 1200 MPa, A 5.2% to 8. 8%, HRC 32 to HRC 35, O^K 70 to 120 J/cmz ） of the Mn-Cu alloyed ADI standard sample could reach European standard EN1564-97/ EN-CJS-1000-5. The surface hardness after helical bevel gears meshing was significantly increased due to the formation of martensite. The bench test and traffic running testing results suggested that the new Mn-Cu alloyed ADI with ultimate life and median life respectively exceeding 30×104 and 50 × 10^4 times could replace 20CrMnTi forged steel for manufacturing the EQ140 helical bevel gears.

Improved analytical model for mesh stiffness calculation of cracked helical gear considering interactions between neighboring teeth

As one of the most typical fault forms of the helical gear,the crack will change the dynamic excitation and further affect the dynamic behaviors of the transmission systems.Due to the complicated structure of the helical gears,the coupling effect between the neighboring loaded teeth is usually ignored in the mesh stiffness calculation,making it considerably overestimated especially in the case of the crack fault.An improved mesh stiffness calculation method of helical gear with spatial crack is proposed to make up this gap.The interactions between the loaded neighboring teeth induced by the gear body flexibility were considered to improve the calculation accuracy and applicability.Besides,the load distribution law for the engaged cracked tooth along the tooth width and profile can be obtained.The results indicated that the mesh stiffness of the multi-tooth engagement calculation using this model could be further improved compared with the traditional methods.Finally,the effects of the helix angle,crack depth,and crack propagation length on the mesh stiffness and load distribution were investigated using the proposed method.

Novel Concentric Tube Robot Based on Double-Threaded Helical Gear Tube

Nasopharyngeal carcinoma is a malignant tumor originating from the nasal mucosa. It is a malignanttumor of the head and neck. Concentric tube robot (CTR), as it can form a complicated shape and access hardto-reach lesions, is often used in minimally invasive surgeries. However, some CTRs are bulky because of theirtransmission design. In this paper, a light CTR based on double-threaded helical gear tube is proposed. Sucha CTR is less cumbersome than the traditional CTR as its actuation unit is compact and miniaturized. Themapping relationship between the gear tube attitude and motor output angle is obtained by kinematic analysis.The precision, stability, and repeatability of the driving mechanism are tested. The experimental results showthat the positioning error in the translation test is less than 0.3 mm, the rolling angle error in the stability testis less than 0.6◦, and the error in the translation repeatability test is less than 0.005 mm. Finally, a tip-targetingtest is performed using the new CTR, which verifies the feasibility of the CTR for surgeries.