Helical Gear Meshing Research Articles

An investigation into the effects of profile shifts on helical gear mesh stiffness

Time-varying meshing stiffness (TVMS) is a significant nonlinear periodic excitation in helical gears, it poses significant impacts on gear system’s dynamic characteristics and fatigue life. However, the specific impact of profile shift on it remains unclear. This article establishes an analytical model for the TVMS of helical gears by utilizing the slicing method to address this gap based on the potential energy method, and quantitatively analyze the TVMS with different modification coefficients. The research found that the helical gear’s TVMS decreases with the increase of modification coefficient for individual profile shifts. For the equal compound profile shifts, it rises with the increase of modification coefficient of pinion. For the unequal compound profile shifts, the positive drive increases the TVMS, but the negative drive to the contrary. The research achievements provide valuable guidelines for dynamic design and structure optimization for helical gears.

An improved approach for tooth contact analysis of mismatched involute spiroid gears

The theoretical contact type of involute spiroid gears (IS) is line contact. The line contact will be turned out into point contact, even edge contact, due to errors. An improved algorithm for tooth contact analysis of mismatched IS is presented. The algorithm can be generally applied to the gears with point contact, whether edge contact occurs or not. Three methods are used in the algorithm: clearance method, edge rule and numerical method. Edge rule is provided to predict the contact type. The numerical method is used to solve nonlinear equations to obtain the precise contact point and contact path. The guess point can be estimated by the clearance method or the known contact point near the solution. In addition, the clearance method with high precision is utilized to avoid the invalidation of numerical method to ensure the robustness. Finally, the proposed algorithm is applied to simulating the meshing of helical gears and IS. The results are compared with those obtained by published literature or finite element method to verify the accuracy and efficiency.

Analytical algorithm for time-varying friction force and torque of pitting helical gear

Friction excitation is an important factor affecting gear vibration and noise. This paper analyzes the variation law of sliding friction during helical gear meshing, and the calculation algorithm of friction force and torque of helical gear is derived. The effects of working parameters on the friction force and torque are analyzed based on the time-varying friction factor model. The calculation method of the friction force and friction torque of pitting helical gear is given by establishing the quadrilateral pitting model on the tooth surface of the helical gear. The influence of pitting parameters on the friction force and torque is analyzed, which can provide the research basis for the dynamic response analysis of pitting gear.

Study on the meshing stiffness of plastic helical gear meshing with metal worm via point-contact

Time-varying meshing stiffness is the main internal excitation source for gear dynamic responses. A calculation method for meshing stiffness of point-contact transmission pairs is proposed to analysis the dynamic responses of the plastic helical gear metal worm drive. Based on the curvilinear motion trajectories and the contact ellipse changes of helical gear worm drive, a method of equivalent area rectangle is introduced to convert the contact ellipse into contact line, and the relationship between the contact line and the worm angle is established. The meshing stiffness of plastic helical gear metal worm drive is calculated and compared with the finite element method (FEM) to verify its accuracy. The results show that the meshing stiffness of plastic helical gear metal worm drive is affected by the meshing impact, and the time-varying meshing stiffness value of double-tooth meshing will be close to or even lower than that of single-tooth meshing. In the plastic helical gear metal worm drive, there is no stable stiffness value whether it is single-tooth meshing or double-tooth meshing. The single-tooth meshing stiffness has an upward trend under the influence of the pressure angle. The calculation results of theoretical model are basically consistent with the FEM results, but the theoretical model cannot fully reflect the stiffness change during meshing impact.

Study on a novel backlash-adjustable worm drive via the involute helical beveloid gear meshing with dual-lead involute cylindrical worm

This paper focuses on a novel backlash-adjustable worm drive, and it is composed of a dual-lead involute cylindrical (DIC) worm and an involute helical beveloid (IHB) gear. It is characterized by the low error sensitivity, easy to manufacture and with the backlash-adjustable. The design criteria for the novel worm drive are presented based on a variable-lead and variable-thickness media rack. Then the mathematical model and meshing performance analysis model are deduced and established, and the theory of backlash-adjustable is proposed. The tooth contact analysis (TCA) is conducted by the numerical calculation and stress analysis. Moreover, the experimental gearbox is manufactured, and the contact tests and transmission accuracy tests are completed. These results indicate that the novel worm drive can effectively adjust backlash without affecting the transmission accuracy. This theoretical research provides the theoretical support for further analysis and application of the novel backlash-adjustable worm drive.

Experimental investigation of helical gear tooth crack location and depth detection using moving average method on transmission error

Gear systems are the most useful and essential power transmission systems in the high-speed industry due to their accuracy. It is necessary to make sure that these systems work without defects such as tooth cracks. Therefore, detecting the location and depth of cracks in gear systems is very important. In this research, a new approach is proposed to detect the crack location, and accordingly, some statistical indicators are used to estimate the crack depth in the helical gear tooth. To this end, after explaining the helical gear mesh stiffness and tooth-root crack modeling, the helical gear pair dynamic is modeled. Then, the vibration data of a helical gear system is obtained by an experimental test rig, and the moving average method is undertaken to precisely detect the crack location. The crack depth ratio is estimated using the crest factor, impulse factor, clearance factor, and [Formula: see text] and [Formula: see text] which are applied to the simulation results and the experimental signal. According to these results, the crest factor, impulse factor, and clearance factor calculated the crack depth ratio with a good agreement, and the indicators [Formula: see text] and [Formula: see text] estimated it with a more significant error. Also, the average of estimated values is calculated, indicating a better result than each indicator alone.

Dynanic Simulation of Helical Gears with Crack Propagating In to Gear Body*

The change of mesh stiffness induced by tooth crack will change the vibration characteristic of gear system. In this paper, an analytical model is proposed to investigate the helical gear mesh stiffness with tooth crack propagating into gear body. The developed model is validated by comparison with the FEA method. Hereafter, the mesh stiffness of helical gears with different crack depths is obtained and the effect of the crack depth on the mesh stiffness is studied. Afterwards, a 6 DOF helical gear dynamic model is established and the effects of crack depth on the dynamic response are investigated. The results indicated that the mesh stiffness of the helical gears reduced significantly with the present of tooth crack, the amplitude of periodical impulses increased as the crack depth increased, the rotate frequency and its harmonic frequencies are sensitive to the tooth crack.

Measurements and theoretical analysis of a helical gear meshing impact signal

Meshing impact is an important factor that affects gear vibration and noise. Therefore, it is of great theoretical and practical significance to study the characteristics of offline meshing impact to reduce the vibration caused by meshing impact. Currently, a single-pair gear is the research goal, ignoring complex coupling relationships between systems, and the established numerical solution formula of the meshing impact cannot be verified. By using Hilbert demodulation and instantaneous frequency, this study obtained the meshing impact signal from the dynamic transmission error signal of the experiment and obtained the maximum deformation caused by the meshing impact. The meshing stiffness of a single tooth was obtained by loaded tooth contact analysis and tooth contact analysis, and the meshing impact force was calculated. The dynamic model of the meshing impact considering the contact ratio was established to compare with the obtained force in the experiment. The method of measuring the meshing impact signal from experiments has not been reported in relevant literature. The method has the advantages of being extensive, accurate and convenient, and it is not affected by the complexity of the system. At the same time, this method can be used to determine the gear teeth with meshing impact in the course of operation and provide a basis for real-time shape modification and design. Therefore, it is of great significance.

Multi crack detection in helical gear teeth using transmission error ratio

Gear systems are used to transmit power in the industry when accuracy and synchrony are needed and helical gear systems are used in more accurate and high-speed industries. It is important to ensure that these systems work faultlessly, therefore the detection of the crack location and situation is very efficient in the gear systems. In this research, a new approach is proposed to detect the multi crack location and length in the helical gear teeth. To this end, after giving an explanation of helical gear mesh stiffness and demonstrating the helical gear pair dynamic modeling, the transmission error ratio method is used to detect the cracks locations and lengths. Then, according to solved examples, when the cracks locations are far enough that their effects on the transmission error are completely separated, the cracked teeth and the lengths of cracks can be detected exactly, and when the cracks are in adjacent teeth, according to the cracks lengths and depths and their effects overlap, the number of cracks and their lengths can be detected exactly, approximately or absolutely undetectable.

Load Distribution Analysis for The Plastic Helical Gear Meshing with Steel Worm

This paper presents an approach for the analysis of load distribution of plastic helical gear meshing with steel worm. Based on the deformation compatibility assumption in the gear mesh process, the load on the contact point of each gear is calculated. By calculating the applied load on each gear tooth in a meshing cycle, the load distribution on the gear tooth is obtained. As compared with the finite element method, the presented method result correlates well with the simulation result with the ANSYS Workbench. The method presented in this paper realizes the fast calculation of meshing force between plastic helical gear and steel worm, which can provide some references for gear design and gear loading capacity improved in engineering.

Dual lead-crowning for helical gears with long face width on a CNC internal gear honing machine

Gear tooth surfaces are usually crowned to meet various needs, including enhanced of the load capacity, avoidance of edge contact and longer service life. However, the traditional single lead-crowning method is less adequate for a long face-width helical gear meshing with two gears simultaneously. This study proposes a novel method for dual lead-crowning for helical gears with long face-widths using a CNC internal gear honing machine. The anti-twist tooth modification is carried out by controlling the swivel angle and the rotation angle of work gear. Dual lead-crowning with different crowning amounts for different tooth proportions, anti-twist tooth modification and tooth contact analysis (TCA) are presented in the numerical examples to demonstrate the validity and advantages of the proposed method.

Calculation of time dependent mesh stiffness of helical planetary gear system using analytical approach

Time-dependent mesh stiffness is a most important reason of vibration and dynamic excitation in gear sets. In this research, analytical formulas of the helical gear set and the planetary gear system are combined to calculate the time-dependent mesh stiffness of the helical planetary gear system. For this purpose, at the first step, the analytical equations are derived for the spur gear pair. Then by dividing a helical tooth into the several independent thin spur tooth slices, the helical gear pair mesh stiffness is extracted. Finally, these equations are extended to the helical planetary gear system. The suggested analytical results and those which obtained by the finite element method (FEM) are compared and are in good agreement when the helix angle is less than 15 degrees. Also, the helical planetary gear system mesh stiffness in different cases such as fixed carrier, fixed sun gear and fixed ring gears is calculated. These results show that the value of mesh frequency ratio in each case scales the mesh stiffness shapes in the rotation angle direction. In other words, mesh frequency ratio parameter determines the number of meshing period in each rotation of planets.

Measurement and Simulation of Loss Torque Generated by Meshing of Helical Gears

Measurement and Simulation of Loss Torque Generated by Meshing of Helical Gears

Research on vibration characteristics of gear-coupled multi-shaft rotor-bearing systems under the excitation of unbalance

To find out the effect of eccentricity of a gear wheel on inherent characteristics of a gear-rotor system, this paper establishes a pair of general transverse-rotational-axial-swinging multi degrees of freedom coupling helical gear meshing dynamic model based on the finite element method (FEM). Considering the influence of the azimuth, the meshing angle, the helix angle and the rotation direction of driving shaft on mesh stiffness matrix, it analyzes the effect of mesh stiffness and mesh damping on the inherent characteristics and the transient response of the system. It obtains the displacement response curve and the dynamic meshing force curve of all nodes responding to the incentives of static transmission error and unbalance while considering mesh damping. It concludes that the effects of gear coupling and eccentricity of gear wheel should be taken into account in a multi-parallel-shaft gear meshing rotor system.

Study of the influence mechanism of pitch deviation on cylindrical helical gear meshing stiffness and vibration noise

To analyze the influence mechanism of pitch deviation on cylindrical helical gear meshing stiffness and vibration noise, the calculation methods about meshing stiffness and engaging vibration of helical gear which consider actual pitch deviations are proposed. The numbering rules of gear meshing teeth in LTCA (Load Tooth Contact Analysis) were rearranged according to the contact ratio and tooth pitch deviation, and the time-varying meshing stiffness and the axial degree of freedom were considered in the helical gear vibration model. A numerical simulation of example based on helical gears with the given pitch deviation is performed, which proves that load transmission error and RMS (root mean square) value of meshing vibration acceleration with tooth pitch deviation are bigger than that with standard pitch. The percent deviation of meshing stiffness increased with the increase in contact ratio, but decreased gradually with increase in load. The resonant frequency of vibration acceleration with pitch deviation becomes smaller comparing to the frequency with standard pitch. This study provides evidence that it is essential to consider the influence of pitch deviation when we design the parameters and predict vibration of cylindrical helical gear transmission system.

Measurement of loss torque generated by meshing of helical gears

Measurement of loss torque generated by meshing of helical gears

A model for analyzing stiffness and stress in a helical gear pair with tooth profile errors

A model is introduced for analyzing the influence of tooth shape deviations and assembly errors on the helical gear mesh stiffness, loaded transmission error, tooth contact stress and tooth root stress. The helical gear is approximated as a series of independent spur gear slices along axial direction whose face-width is relatively small. The relative position relationships among those sliced teeth in mesh are developed with tooth profile errors and the stiffness of the sliced tooth is calculated by the potential energy method. From the equilibriums of the forces, gear mesh stiffness, loaded transmission error, tooth contact stress and tooth root stress are calculated. Then two cases are presented for validation of the model. It is demonstrated that the model is effective for calculating the stiffness of helical gear pairs. Finally, the effects of the tooth tip reliefs, lead crown reliefs and misalignments on the gear mesh stiffness, transmission error, tooth contact stress and tooth root stress are analyzed. The results show that mesh stiffness decreases, loaded transmission error, the maximum tooth contact stress and the maximum tooth root stress grow with the increasing tooth tip relief, lead crown relief and misalignment. And tooth edge has concentrated tooth contact stresses with a gear misalignment.

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.

Helical gear multi-contact tooth mesh load analysis with flexible bearings and shafts

A multi-contact tooth meshing model for helical gear pairs considering bearing and shaft deformations is proposed. First, to easily incorporate into the system model, the complicated Harris\'s bearing force-displacement relationship is simplified applying a linear least square curve fit. Then, effects of shaft and bearing flexibilities on the helical gear meshing behavior are implemented through transformation matrices which contain the helical gear orientation and spatial displacement under loads. Finally, true contact lines between conjugated teeth are approximated applying a modified meshing equation that includes the influence of tooth flank displacement on the tooth contact induced by shaft and bearing displacements. Based on the model, the bearing\'s force-displacement relation is examined, and the effects of shaft deformation and external load on the multi-contact tooth mesh load distribution are also analyzed. The advantage of this work is, unlike previous works to search true contact lines through time-consuming iterative strategy, to determine true contact lines between conjugated teeth directly with presentation of deformations of bearings and shafts.

Contact stress analysis for a pair of aluminum matrix composite helical gear and steel worm

This paper presents a contact stress analysis for a pair of aluminum matrix composite helical gear and steel worm during rotation. The material of helical gear is 10% SiC particulate-reinforced Al matrix composite. Contact stress analysis for helical gear and worm are performed at different contact positions during rotation based on finite element analysis. Three different conditions are designed to investigate the contact stress of 40Cr, POM and aluminum matrix composite helical gear mesh with worm. Through contrast contact stress between different material helical gear, it was found that the load performance of aluminum matrix composite helical gear is close to steel and better than plastic gear.