Search Results (30)

The transmission accuracy and meshing performance of the gearbox is determined by the internal helical gears pair. Thermal deformation of internal helical gears pair is derived from sliding friction between the contacting teeth surface, resulting in shock, vibration, and misalignments. The purpose of this paper is to compare the influence of a modified gear and an unmodified gear on the temperature field and transmission characteristics of a planetary gear system under the same working conditions. This study presents an innovative temperature field model for gear pairs utilizing Surf152 elements, integrating Hertzian contact theory, tribological principles, and finite element analysis. For the first time, we quantitatively demonstrate the enhancement of thermo-mechanical performance through topological modification in helical gears. Under light-load conditions (200 rpm), the modified gear configuration exhibits a 6.38% reduction in tooth surface temperature and a 46.5% decrease in thermal deformation compared to conventional designs. Experimental validation confirms these improvements, showing an average 62.35% reduction in transmission error. These findings establish a novel methodology for high-precision gear design while providing critical theoretical foundations for planetary gear systems, ultimately leading to significant improvements in both transmission accuracy and operational lifespan. Full article

Ultra-high-pressure hydrogen solenoid valves face a fundamental design challenge of operating across a wide pressure range from 2 MPa to 87.5 MPa. To address the conflicting requirements of effective sealing at low pressures and structural integrity at high pressures, this study proposes a novel concave contact geometry based on Hertzian contact theory. Finite element analysis examines the mechanical relationships between plunger curvature radius (R_ₚ), seat curvature radius (Rₛ), and eccentricity (e). Optimization utilizing Latin hypercube sampling and kriging metamodeling yields an optimal design (Rₚ = 5.73 mm, Rₛ = 4.68 mm, e = 0.95 mm) with an Rₚ/Rₛ ratio of 1.22. The optimized concave contact geometry achieves 23.7% higher contact pressure at 2.0 MPa and 42.7% lower maximum equivalent stress at 87.5 MPa compared to conventional rectangular geometry. Experimental validation confirms the concave contact geometry seals at 1.7 ± 0.2 MPa, below the AIS-195 standard requirement of 2.0 MPa and 69.6% lower than the rectangular design (5.6 ± 0.7 MPa). Structural analysis after 87.5 MPa high-pressure exposure reveals no measurable deformation in the concave design, while the rectangular design exhibits permanent deformation of 0.0580 ± 0.007 mm. This integrated methodology provides a framework for optimizing contact geometries in fluid control components operating under extreme pressure conditions, successfully reconciling contradictory requirements across the entire pressure range. Full article

The intelligent bearing with an embedded sensor is a key technology to realize the running state monitoring of railway locomotive axle box bearings at the source end. To investigate the mechanical properties of axle box bearings with embedded sensor slots, based on nonlinear Hertzian contact theory and the bearing fatigue life theory, a mechanical equivalent analysis model with a virtual mandrel is established for double-row tapered roller bearings used in axle boxes with sensor-embedded slots, which integrally considers the effects of external forces. After verifying the mesh independence before and after embedding the sensor slots, the contact load of tapered rollers calculated by the mechanical model is compared with the theoretical solution based on Hertz contact which verifies the validity of the model from the perspective of contact load. The results show that adjusting the grooving depth and axial position has a significant effect on the local stress peak, and an excessive grooving depth or inappropriate axial position will trigger fatigue damage. This study provides a theoretical basis for analyzing the mechanical characteristics of sensor-embedded slots used in railway locomotive axle box bearings. Full article

A new method of machining ultrasonic cavitation abrasive flow based on phase control technology was proposed for improving the machining efficiency of the inner wall of TC4 (Ti-6Al-4V) titanium alloy tubes. According to ultrasonic phase control theory and Hertzian contact theory, a model of ultrasonic abrasive material removal rate under phase control technology was established. Using COMSOL Multiphysics 6.1 software, the phase control deflection effect, acoustic field distribution, and the size of the phase control cavitation domain on the inner wall surface were examined at different transducer frequencies and transducer spacings. The results show that the inner wall polishing has the most excellent effect at a transducer frequency of 21 kHz and spacing of 100 mm. In addition, the phased deflection limit was explored under the optimal parameters, and predictive analyses were performed for voltage control under uniform inner wall polishing. Finally, the effect of processing time on polishing was experimented with, and the results showed that the polishing efficiency was highest from 0 to 30 min and stabilized after 60 min. In addition, the change in surface roughness and material removal of the workpiece were analyzed under the control of the voltage applied, and the experimental results corresponded to the voltage prediction analysis results of the simulation, which proved the viability of phase control abrasive flow polishing for the uniformity of material removal of the inner wall of the tube. Full article

Peeling wheat yields higher-quality flour. During processing in a flaking machine, wheat kernels undergo continuous compression within the machine’s chamber. As this compression persists, damage to the kernels intensifies and accumulates, eventually leading to kernel breakage. To study the damage characteristics of wheat kernels during peeling, this study established a continuous damage model based on Hertzian contact theory and continuous damage theory. The model’s accuracy was validated through experiments, culminating in the calculation of critical parameters for wheat peeling. This study focused on different wheat varieties (Ningmai 22 and Jichun 1) and kernel sizes (the thicknesses of the small, medium, and large kernels were standardized as follows: Ningmai 22—2.67 ± 0.07 mm, 2.81 ± 0.07 mm, and 2.95 ± 0.07 mm; Jichun 1—2.98 ± 0.11 mm, 3.20 ± 0.11 mm, and 3.42 ± 0.11 mm). Continuous compression tests were conducted using a mass spectrometer, and critical damage parameters were analyzed and calculated by integrating the theoretical model with experimental data. The test results showed that the average maximum crushing force (F_c) for small, medium, and large-sized kernels of Ningmai 22 was 96.71 ± 2.27 N, 110.17 ± 2.68 N, and 128.41 ± 2.85 N, respectively. The average maximum crushing deformation (α_c) was 0.65 ± 0.08 mm, 0.68 ± 0.13 mm, and 0.77 ± 0.17 mm, respectively. The average elastic–plastic critical pressure (F_s) was 50.21 N, 60.13 N, and 59.08 N, respectively, and the average critical values of elastic–plastic deformation (α_s) were 0.37 mm, 0.38 mm, and 0.39 mm, respectively. For Jichun 1, the average maximum crushing force (F_c) for small-, medium-, and large-sized kernels was 113.34 ± 3.15 N, 125.28 ± 3.64 N, and 136.15 ± 3.29 N, respectively. The average maximum crushing deformation (α_c) was 0.75 ± 0.11 mm, 0.83 ± 0.15 mm, and 0.88 ± 0.18 mm, respectively. The average elastic–plastic critical pressure (F_s) was 58.11 N, 64.17 N, and 85.05 N, respectively, and the average critical values of elastic–plastic deformation (α_s) were 0.45 mm, 0.47 mm, and 0.52 mm, respectively. The test results indicated that during mechanical compression, if the deformation is less than α_s, the continued application of the compression load will not result in kernel crushing. However, if the deformation exceeds α_s, continued compression will lead to kernel crushing, with the required number of compressions decreasing as the deformation increases. If the deformation surpasses α_c, a single compression load is sufficient to cause kernel crushing. Since smaller wheat kernels are more susceptible to breakage during processing, the peeling pressure (F) within the chamber should be controlled to remain below the average elastic–plastic critical pressure (F_s) of small-sized wheat kernels. Additionally, the kernel deformation (α) induced by the flow rate and loading in the chamber should be kept below the average elastic–plastic critical deformation (α_s) of small-sized wheat kernels. This paper provides a theoretical foundation for the structural design and optimization of processing parameters for wheat peeling machines. Full article

The temperature field distribution of high-speed double-helical gears under oil injection lubrication is investigated by obtaining heat flux density and convective heat transfer coefficients through theoretical calculations and CFD (computational fluid dynamics) simulations. Based on the CFD method, fluid simulations are performed to obtain the distribution of lubricating oil on the surface of the double-helical gears, the velocity streamline diagram of the lubricating oil, and the convective heat transfer coefficients of different surfaces of the gears. The friction heat flux density is calculated using Hertzian contact theory and theoretical formula of heat generation. The double-helical gears’ steady-state temperature field simulation uses this heat flux density as a boundary condition. The correctness of the calculation method is verified through experiments. The study shows that increasing the jet velocity allows the jet to reach the tooth surface more effectively, improving the cooling effect and reducing the maximum gear temperature. However, the relationship between the jet velocity and the minimum gear temperature is non-linear. Within a certain range, increasing the jet diameter makes the jet wider, and the area covered by the lubricating oil becomes larger as the jet spreads around the gear teeth, enhancing the cooling effect. An increase in gear speed leads to an increase in frictional heat flux density; moreover, the high-velocity airflow generated by the increased speed reduces the amount of lubricant entering the mesh zone, which in turn causes the maximum temperature of the gears to continue to rise. Full article

Machines operate under increasingly harsher contact conditions, causing significant wear and contact fatigue. Sub-surface stresses are responsible for the premature contact fatigue of rolling element bearings, meshing gears, and cam–follower pairs. Surface protection measures include hard, wear-resistant coatings. Traditionally, contact integrity has been predicted using classical Hertzian contact mechanics. However, the theory is only applicable when the contact between a pair of ellipsoidal solids of revolution may be considered as a rigid indenter penetrating a semi-infinite elastic half-space. Many coatings act as thin bonded elastic layers that undergo considerably higher pressures than those predicted by the classical theory. Furthermore, inelastic deformation of bonded solids can cause plastic flow, work-hardening, and elastoplastic behaviour. This paper presents a comprehensive, integrated contact mechanics analysis that includes induced sub-surface stresses in concentrated counterformal finite line contacts for all the aforementioned cases. Generated pressures and deformation are predicted for hard coated surfaces, for which there is a dearth of relevant analysis. The contact characteristics, which are of particular practical significance, of many hard, wear-resistant advanced coatings are also studied. The paper clearly demonstrates the importance of using efficient semi-analytical, detailed holistic contact mechanics rather than the classical idealised methods or empirical numerical ones such as FEA. The novel approach presented for the finite line contact of thin-layered bonded solids has not hitherto been reported in the open literature. Full article

Structural vibration has always been a major concern in the engineering field. A dynamic vibration absorber in the form of contacts with adjustable stiffness (CDVA) offers effective vibration suppression and can improve conventional dynamic vibration absorbers with high sensitivity to frequency deviation and difficulty in adjusting the frequency. In this research, first, based on the theoretical model of the contact between a rubber ball and an inner cone, the feasibility of changing the axial contact state to change the structure’s natural frequency was verified using an ANSYS simulation. A theoretical model of the static contact stiffness between the ball and the inner cone was constructed using Hertzian contact theory and Hooke’s law, and a theoretical model of the cubic nonlinear elastic restoring force was used to characterize the stiffness properties of the rubber ball during compressive rebound. The steady-state frequency response equations of the main vibration structure were derived using the averaging method in conjunction with the two-degree-of-freedom dynamics model, and the stability of the solutions to the frequency response equations was obtained in conjunction with the stability determination criterion. Then, the impact of the CDVA’s design parameters on the nonlinear dynamic response of the primary vibration structure was simulated and analyzed. The resulting findings can serve as guidance for designing dynamic vibration absorber parameters. Based on the principles of ball-inner cone contact, a dynamic vibration absorber structure was proposed. A design test was conducted to verify the correctness of the contact stiffness model, and an experimental study was carried out to investigate the law of change in the dynamic stiffness and damping of the principle structure of CDVA under dynamic excitation conditions. Finally, the vibration test platform of the solidly supported beam structure was constructed, and vibration suppression tests of the CDVA in different compression states were conducted to investigate the tunability and feasibility of CDVA vibration suppression. The results showed that the dynamic vibration absorber had good vibration absorption characteristics and could be used for single-mode vibration suppression of multimodal main structures. Full article

This paper aims to realize multi-objective optimization of cycloid-pin gears to improve the positioning accuracy and load-carrying capacity of the rotary vector (RV) reducer, via the consideration of backlash, transmission error, and torsional stiffness. Initially, the analytical models of the RV transmission backlash and transmission error are developed by using both purely geometrical and equivalent model methods individually. Based on the generalized Hooke’s law, a torsion angle model is established to characterize the torsional stiffness of the system, utilizing methods such as Hertzian contact theory and bearing stiffness models. Subsequently, employing the Monte Carlo method, extremum method, and quality loss function, mapping objective functions for dimensional accuracy (tolerance) and transmission performance (backlash, transmission error, and torsional stiffness) are constructed. The geometry dimensions, dimensional accuracy, and modification of the cycloid-pin gear are considered as design variables to create a multi-objective optimization model. The improved Parallel Adaptive Genetic Algorithm using Deferential Evolution (PAGA-DE) is used for multi-objective solutions. Through example calculations, the impact of cycloid-pin gear parameters on transmission performance before and after optimization is determined. The reliability of backlash after optimization within 1.5′ reaches 99.99%, showing an increase of 8.24%. The reliability of transmission error within 1′ reaches 98.52%, demonstrating an increase of 1.35%. The torsional angle is reduced by 8.9% before optimization. The results indicate that the proposed multi-objective optimization design method for cycloid-pin gears can achieve the goal of improving the transmission performance of the RV reducer. Full article

The sealing reliability of collet connectors is essential within underwater production systems. This paper is based on the lens gasket sealing mechanism and Hertzian contact theory, establishing mechanical models for the core sealing components in preloaded and working states and analyzing the minimum required axial preload force for sealing. According to the sealing principles of the connector, the force characteristics of each sealing element are analyzed in both preloaded and working states. The interplay of forces between these elements is subsequently determined. Furthermore, the amplification of axial preload force within the sealing structure is confirmed through simulations of contact characteristics. Finally, the accuracy of theoretical and simulated results is confirmed through experimental validation. Full article

The modeling of tilting-pad journal and thrust bearings presents a level of complexity beyond that of bearings with a fixed-arc geometry, particularly with regard to their dynamic influences. With tilting-pad bearings, the theory surrounding their fluid film must be complemented with the representative modeling of the pad dynamics. What has been recognized in recent decades is the significance of the pad support, in particular the flexibility of the pivot region of the pad. The typical model for including the stiffness of the pivot is based on the Hertzian contact theory. Some researchers have noted that the Hertzian theory does not permit sufficient flexibility in the pivot region. It has been suggested that the contact mechanics at the pivot would be better represented as a pairing of rough surfaces. The modeling used here is based on a statistical asperity micro-contact theory for rough surface line contact that has been extended to include contact stiffness. This model has been applied to the determination of the effective dynamic properties of tilting-pad bearings. The results show that pivot stiffness can be as low as one third of the stiffness determined by the Hertzian theory. A comparison to published experimental results confirms the significance of the rough surface modeling, particularly for the line contacts associated with rocker-back tilting pads. Full article

Optimising the performance of materials requires, among other things, the characterisation of residual stresses during the design stage. Raman spectroscopy offers access to these residual stresses at the micrometre scale when this inelastic light scattering is active in these materials. In this case, the relationship between the Raman mode shift and the pressure must be known. High-pressure cells with diamond anvils or bending instruments coupled to Raman spectrometers are habitually used to determine this relationship. In this article, we propose a new method that involves a Hertzian contact to obtain this relationship. A device that compresses an alumina ball against a transparent glass plane is connected to a Raman spectrometer. Under these conditions, the contact pressure can be as high as 1.5 GPa. The contact between the glass plane and the ball is observed through a diaphragm. Several hundred Raman spectra are recorded depending on the contact diameter. The spectral profiles obtained represent the shift in the Raman modes of alumina and glass along the contact diameter. Hertz’s theory accurately describes the pressure profile as a function of position for elastic materials. Therefore, the contact diameter can be measured by fitting the spectral profile with a function identical to the Hertz profile. We then deduce the maximum pressure. Next, the calculated pressure profile along the contact diameter is correlated with the spectral profile. We obtain a pressure dependence of the Raman mode with a coefficient equal to 2.07 cm${}^{-1}$/GPa for the Eg modes of alumina at 417 cm${}^{-1}$, which is in good agreement with the literature. In the case of glass, we refine the measurement of the Q3 mode shift at 1096 cm${}^{-1}$ in the studied pressure range compared to the literature. We find a coefficient of 4.31 cm${}^{-1}$/GPa. This work on static contacts opens up promising prospects for investigations into dynamic contacts in tribology. Full article

Hertzian formulas are commonly used for the evaluation of deformation and pressure distribution of non-conformal and slightly conformal mechanical pairs to estimate component stiffness and durability. For the sake of simplicity, their use is extended even to those cases in which Hertz’s hypotheses do not hold. This paper summarizes Hertz’s theory and compares the results obtained with theoretical and finite element analysis of the point contact of non-conformal and conformal pairs made of spheres, caps, and spherical seats. This study was motivated by the non-Hertzian behavior of a tilting pad bearing ball-and-socket pivot conforming contact observed by the authors in previous experiments. In particular, the displacement and force relation were investigated by varying the geometrical parameters, the materials, the boundary conditions, and the friction coefficient. In the case of non-conformal contact, the parameter variations had negligible effect in agreement with Hertz’s theory while for conformal contact, the cap and seat height and width and the relative clearance were the most influential parameters on the non-Hertzian behavior. These novel results indicate that in conformal pairs, such as for tilting pad bearing ball-and-socket pivots, whenever Hertz’s hypotheses are not satisfied and the assessment of contact stiffness is crucial, Hertzian formulas should not be applied as done in common practice, instead more accurate numerical or experimental evaluation should be made. Full article

This paper focuses on the influence of radial internal clearance on the dynamics of a rolling-element bearing. In the beginning, the 2—Degree of Freedom (DOF) model was studied, in which the clearance was treated as a bifurcation parameter. The derived nonlinear mathematical model is based on Hertzian contact theory and takes into consideration shape errors of rolling surfaces and eccentricity reflecting real operating conditions. The analysis showed characteristic dynamical behavior by specific clearance range, which reflects others in a low or high amplitude and can refer to the optimal clearance. The experimental validation was conducted with the use of a double row self-aligning ball bearing (SABB) NTN 2309SK in which the acceleration response was measured by various rotational velocities. The time series obtained from the mathematical model and the experiment were analyzed with the recurrence quantification analysis. Full article

The goal of this study was to explore the self-guided machining mechanism of boring and trepanning association (BTA) deep hole drilling and realize precise control of the machining quality. The motion analysis method was used to analyze the center motion trajectory of the drill during the entrance, and the self-guiding mechanism and hole-forming mechanism of BTA deep hole drilling were revealed. Considering the bending deformation of the drilling tube and the tool structure parameters, according to the elastic-plastic deformation theory and Hertzian contact theory, a novel analytical model of the extrusion contact between the guide pads and the hole wall of the BTA deep hole drilling was established for the theoretical prediction of the extrusion deformation and the machining hole diameter. Combined with the finite element method (FEM) simulation model, the variation law of the contact inclination angle, contact stress, and extrusion deformation of the guide pads and the hole wall with the drilling conditions were studied. The total extrusion deformation between the guide pad and the hole wall was between 10 and 50 μm. The maximum error between the FEM simulation results and the test results was 18.1%, and the maximum error between the analytical model results and the test results was 23.6%. The simulation and experimental results showed that the established extrusion contact model could accurately predict the extrusion deformation of the hole wall and the machining hole diameter. Full article