Contact Pressure Distribution Research Articles

Sensitive misalignment oriented loaded contact pressure regulation model for spiral bevel gears

In full consideration of misalignment having strong sensitivity with respect to meshing transmission performances, an innovative data-oriented loaded contact pressure regulation model is established for spiral bevel gears by fine-modifying the optimal selected misalignment. Here, accurate loaded contact pressure evaluations includes: i) geometric boundary considering size, direction, and position; ii) loaded contact pressure distribution; iii) the maximum loaded contact pressure. Firstly, an improved tooth contact analysis with error (eTCA) is developed to establish data-oriented functional relationships. Loaded contact pressure prediction considering the different evaluations is performed for the initial misalignments and its performances. Moreover, considering accurate prediction and feedback, data-oriented regulation model is established by using numerical loaded tooth contact analysis (NLTCA). Focusing on accurate loaded contact pressure distribution, the constrained sub-objectives are the geometric boundary and the maximum one. Finally, the sensitivity coefficients of each misalignment to each loaded contact pressure evaluation at each contact point are calculated. The sensitivity analysis strategy is provided to get an accurate and effective data-oriented loaded contact pressure regulation model. Given numerical instances can verify that the proposed method get an important access to the meshing transmission performance monitoring and optimization for complex spiral bevel gears.

Optimization of electrode positions for equalizing local spatial performance of a tomographic tactile sensor.

A tomographic tactile sensor based on the contact resistance of conductors is a high sensitive pressure distribution imaging method and has advantages on the flexibility and scalability of device. While the addition of internal electrodes improves the sensor's spatial resolution, there still remain variations in resolution that depend on the contact position. In this study, we propose an optimization algorithm for electrode positions that improves entire spatial resolution by compensating for local variations in spatial resolution. Simulation results for sensors with 16 or 64 electrodes show that the proposed algorithm improves performance to 0.81 times and 0.93 times in the worst spatial resolution region of the detection area compared to equally spaced grid electrodes. The proposed methods enable tomographic tactile sensors to detect contact pressure distribution more accurately than the conventional methods, providing high-performance tactile sensing for many applications.

An Improved Slicing Technique for Finite Line Contacts in the Modeling of Rolling Element Bearings

Abstract Mechanical system often involves the finite line contact of key components such as rolling element bearings and gear pairs. Different contact models have been developed to predict the load–displacement relationship and contact pressure distribution, but there usually exists a tradeoff between the accuracy of simulation results and computational cost. An improved slicing technique is presented in this work. According to the half-space theory, a tri-linear fitting model is developed to express the load–displacement relationship and coupling behavior in slices of contact region, which is originally controlled by a spatial convolution. The improved slicing technique is thus formulated based on the tri-linear model. A modified Newton–Raphson algorithm is adopted to solve the free boundary problem of the improved slicing technique. The improved slicing technique is validated to be able to correctly predict the load–displacement relationships and the contact pressure distributions of different contact profiles, especially for contact pressure concentrations which other slicing techniques are unable to predict accurately. The computation speed of the proposed method is much faster than the semi-analytical method and is of the same order of other slicing technique. The high accuracy and low computational cost enable the proposed method to be applied in the on-line calculation of rolling element bearings and other sophisticated mechanical systems.

Modelling tangential friction considering contact pressure distribution of rough surfaces

Frictional interfaces play an important role on the dynamic response of jointed structures. To accurately predict the dynamics of jointed structures, the phenomenological Iwan-type models, which consist of many spring-slider elements in parallel or series, are often used to describe interface frictional behavior. In this paper, a novel tangential friction modelling approach based on the framework of Iwan model is proposed. Specifically, the density function of slider critical slip force, which is vital to deduce the final form of Iwan model, is determined by a new method. The method is based on the real rough surface and contact pressure results due to rough contact are introduced to derive the form of Iwan model. This provides a physical method to derive the density function of slider critical slip force, while in the past the density function is usually assumed artificially without a clear physical meaning. In the proposed method, twofold Weibull mixture model is used to represent the contact pressure distribution of actual rough surfaces. Following this, the corresponding Iwan density function is derived based on the local Coulomb friction. Then substituting Iwan density function into Iwan model, the explicit relationship between the tangential force and the relative displacement is deduced. The proposed modelling approach is applied to sphere-on-sphere contact and the comparison between the simulation and theoretical results shows perfect agreement. Then, the proposed modelling approach is validated against published experimental results for a flat-on-flat contact and a bolted joint. Compared to the classic Iwan model, the proposed model can better match the experimental results at the transition from microslip to macroslip. This study considers the influence of real rough contact characteristics on tangential friction behavior and provides a new tangential friction model deriving method.

Influence of Top Seal Damage on Contact Seal in Ram Blowout Preventer.

Top seal failure of ram blowout preventer (BOP) is one of the main factors leading to well control risk. The constitutive model and parameters of nitrile butadiene rubber (NBR) were optimized by compression and tensile tests, and the failure analysis model of the contact seal of the ram BOP top seal was built. The nonlinear contact mechanical behavior of the connection part of the BOP top seal was analyzed by the finite element method. Then, the influence of corrosion and wear defects at the top seal position of the 2FZ35-70 BOP under rated working pressure on the contact seal were studied, and the results showed that the overall contact pressure distribution of the top seal corrosion defects was uniform, the local contact pressure of the corrosion pit edge increased, and the top contact pressure decreased. The overall contact pressure of the wear defect of the top seal decreased linearly, the contact pressure at the maximum depth of the wear defect was the smallest, and the contact pressure gradually decreased to both sides. Ultimately, to guarantee the safety and reliability of the ram BOP, it is suggested that the acceptable depths of the seal corrosion pit and the wear at the top of the ram BOP are 4.0 mm and 0.2 mm, respectively, thus the reliability evaluation problem of the quantitative seal of the ram BOP top seal is solved.

An approach of micro-slip modeling based on asymmetric contact pressure distribution and its application in nonlinear boundary beam system

A novel micro-slip friction modeling approach based on the Iwan model is presented here. The normal load and tangential stiffness are reassigned reasonably to obtain the tangential force–displacement expression, and the relationship between the asymmetry of contact pressure distribution and the Iwan density function is established. The micro-slip model depends on the distribution of contact pressure, and has the ability to degenerate into a macro-slip model. Based on the model, a simplified non-linear dynamics model of a rotating blade with a dovetail joint is developed, and its effectiveness is verified by comparing it with a relevant reference. The first-order bending vibration of the blade under distributed excitation is analyzed. The results indicate that the pressure distribution of the contact interface has a significant effect on the amplitude–frequency response of the blade and the contact behavior on the joint interface. Compared with the proposed micro-slip model, the single point contact model overestimates the response amplitude. The amplitude–frequency curve obtained by this model is obviously different from the macro-slip model. It is proved that the micro-slip model can more accurately simulate the nonlinear vibration characteristics of tenoned blades, which provides new insights for the study of the vibration characteristics of tenoned blades.

Modeling and in-depth analysis of the mid-spatial-frequency error influenced by actual contact pressure distribution in sub-aperture polishing.

In ultra-precision optical processing, the sub-aperture polishing is prone to produce a mid-spatial-frequency (MSF) error. However, the generation mechanism of the MSF error is still not fully clarified, which seriously affects the further improvement of optical component performance. In this paper, it is proved that the actual contact pressure distribution between the workpiece and tool is a crucial source which affects the MSF error characteristics. A rotational periodic convolution (RPC) model is proposed to reveal the quantitative relationship among the contact pressure distribution, speed ratio (spin velocity/feed speed) and MSF error distribution. In-depth analyses show that the MSF error is linearly related to the symmetry level of contact pressure distribution and inversely proportional to the speed ratio, where the symmetry level is effectively evaluated by the proposed method based on Zernike polynomials. In the experiments, according to the actual contact pressure distribution obtained from the pressure-sensitive paper, the error rate of modeling results under different processing conditions is around 15%, which proves the validity of the proposed model. The influence of contact pressure distribution on the MSF error is further clarified through the establishment of RPC model, which can further promote the development of sub-aperture polishing.

Elastohydrodynamic lubrication model and failure test for micro-contact thermodynamic characteristics of friction interface

A micro-contact thermodynamic model is proposed to study the interfacial characteristics in wet friction pair based on Elastohydrodynamic Lubrication (EHL) theory. The study takes into account the asperity elastic-plastic deformation, establishing an improved model with high accuracy in verifications with experimental data and existing model. With this optimized micro-contact thermodynamic model, we systematically discussed the influence of sliding speed, oil temperature, and average surface pressure on thermodynamic behaviors such as rough contact area, pressure distribution, and temperature distribution. Additionally, experimental investigations revealed the complex failure mechanism of the friction disc. Specifically, during the failure process, the friction coefficient and the radial temperature difference gradually increase. The metal oxides form on the surface, and the graphite distribution is gradually dispersed.

Research on the wear characteristics of magnetorheological fluid in sealing interface considering the interaction between surface roughness and magnetic particles

In this paper, the influence of magnetorheological fluid (MRF) on the wear mechanism of sealing pairs under different surface roughness is studied from the perspective of theoretical analysis and experimental verification. Simulation analysis shows that the coupling of roughness and microparticles changes contact pressure and frictional stress distribution on O-ring acted by asperities. Combined with wear morphologies, it is further proved that roughness affects the movement pattern of particles in the sealing gap, thereby determining the tribodynamic behavior of MRF. Specifically, the roughest sample shows low friction coefficient and best wear resistance, while the smoothest sample exhibits worse tribological performance. The above analysis is the reason for the sealing wear under MRF is completely opposite to that of base oil.

Stress-adaptive design of 2D contact interfaces with uniform pressure: A bio-inspired approach

In this article, a bio-mimetic approach to the generative design of contact interfaces with uniform pressure distribution is explored. During the morphogenesis process, biological joints grow depending on the states of stress generating a shape adapted to the mechanical loads. This adaptation is driven by two main rules: shear stress inhibits growth, whereas cyclic hydrostatic compressive stress promotes it. In this work, we demonstrate that the stress-dependent growth rules of synovial joint morphogenesis can be applied to generate contact interfaces with uniform pressure in engineering applications. For that, we present a mathematical model that comprises a contact formulation and a bio-inspired growth function; the model is solved numerically using finite element methods. We analyse the impact of the growth rules of synovial joint development on the contact pressure distribution of two-dimensional contact interfaces. We study the parameter space of the bio-inspired growth function to fine-tune the model parameters. The model is tested in several cases with different boundary conditions and material properties. The results show that the proposed generative design process leads to contact interfaces that provide uniform contact pressure. A quantitative metric of the uniformity of the contact pressure is also defined. This metric indicates that the bio-inspired process generates geometries as good as those obtained with other methods present in the literature without the need of an initial shape close to the final one. Thus, this work demonstrates that synovial joint morphogenesis can be adapted for generative design in engineering.

Vibrations of joined conical-cylindrical shells with bolt connections: Theory and experiment

This paper investigated the vibration characteristics of joined conical-cylindrical shells (JCCSs) with bolt loosening boundary conditions both theoretically and experimentally. The non-uniform arc constraint model is established to simulate the bolt loosening boundary conditions by the artificial spring technology, which can describe the actual bolt contact pressure distribution. Continuously distributed artificial springs are introduced to realize the connection of the conical and cylindrical shells. Donnell's shell theory and Chebyshev polynomials are adopted to establish the theoretical model, and the dynamic equation is derived from the Lagrange equation. The validity of the present model is verified by the available literature, hammer test and vibration shaker test. The results indicate that the maximum errors of natural frequencies and resonant displacements are less than 4.41% and 18.6%, respectively. It is found that bolt loosening has a significant effect on the fundamental frequency, but it gradually weakens with the increase of the mode order. Increasing bolt loosening degree can lead to an increment of resonant displacement. The developed model is reliable in estimating the dynamic behaviors of bolted JCCSs with different loosening degrees, and it contributes to providing guidance in the design and service process of combined shell structures.

An effective equivalent stiffness model combined with equivalent beam model to predict the contact pressure distribution for a large PEM fuel cell stack

The contact pressure distribution plays a key role to the proton exchange membrane (PEM) fuel cell performance. The purpose of this study is to propose an equivalent stiffness model combined with an equivalent beam model to predict the contact pressure distribution for a large fuel cell stack. With the established equivalent stiffness model, the equivalent values of contact pressure is revealed. Moreover, these equivalent values are extended by an iterative calculation for contact pressure distribution with an established equivalent beam model. Finally, the presented model is compared to a three-dimensional FEA model. This equivalent stiffness model has high accuracy only with a 4.1% tolerance and the correlation coefficient of FEA and equivalent beam model for the contact pressure distribution at transverse and longitudinal direction is 0.976 and 0.998. This presented equivalent model is effective and can provide a direction for future work on high-performance fuel cell stack design and optimization.

Theoretical and experimental studies on vibration characteristics of bolted joint multi-plate structures

The bolted joint multi-plate structures are widely used in practical engineering, but their theoretical dynamic model is hard to find in literature. The main purpose of this paper is to establish a general dynamic model of bolted joint multi-plate structures with flanges, and to investigate its vibration characteristics from both theoretical and experimental aspects. Both the flange effect and contact pressure distribution in the bolted joint affected region (BJAR) are considered. Artificial spring sets with variable stiffness are adopted to simulate the non-uniform distributed contact pressure in BJAR. The governing equations are derived based on the Kirchhoff plate theory and Euler-Bernoulli beam theory. The Chebyshev polynomials are used as admissible displacement functions. Then, the free vibration and forced vibration under base excitation are solved by means of the Rayleigh-Ritz method and Newmark-beta method, respectively. The experimental studies, including modal test and vibration response test, are conducted on a bolted joint two-plate specimen to verify the accuracy of the theoretical model. Results show that the present model is capable of realizing reliable vibration prediction and can be conveniently extended to the structure with an arbitrary number of plates and bolts. For the bolted structures, considering the pressure distribution in the connection interfaces can significantly improve the accuracy of theoretical results.

Smoothing tool design and performance during subaperture glass polishing.

During subaperture tool grinding and polishing, overlaps of the tool influence function can result in undesirable mid-spatial frequency (MSF) errors in the form of surface ripples, which are often corrected using a smoothing polishing step. In this study, flat multi-layer smoothing polishing tools are designed and tested to simultaneously (1)reduce or remove MSF errors, (2)minimize surface figure degradation, and (3)maximize the material removal rate. A time-dependent convergence model in which spatial material removal varies with a workpiece-tool height mismatch, combined with a finite element mechanical analysis to determine the interface contact pressure distribution, was developed to evaluate various smoothing tool designs as a function of tool material properties, thicknesses, pad textures, and displacements. An improvement in smoothing tool performance is achieved when the gap pressure constant, h¯ (which describes the inverse rate at which the pressure drops with a workpiece-tool height mismatch), is minimized for smaller spatial scale length surface features (namely, MSF errors) and maximized for large spatial scale length features (i.e.,surface figure). Five specific smoothing tool designs were experimentally evaluated. A two-layer smoothing tool using a thin, grooved IC1000 polyurethane pad (with a high elastic modulus, E p a d =360M P a), thicker blue foam (with an intermediate modulus, E f o a m =5.3M P a) underlayer, and an optimized displacement (d t=1m m) provided the best overall performance (namely, high MSF error convergence, minimal surface figure degradation, and high material removal rate).

Numerical prediction of influence of chain length on contact pressure distribution on polymer composite sprocket

Numerical prediction of influence of chain length on contact pressure distribution on polymer composite sprocket

Mixed Lubrication Analysis of Tapered Roller Bearings and Crowning Profile Optimization Based on Numerical Running-In Method

Tapered roller bearings (TRBs) are widely used in heavy-load rotating machinery. One of the technical problems in TRBs is the existence of sharp spikes of the contact pressure in the vicinity of the two ends of the tapered rollers. To suppress the pressure spikes at the roller ends, a straight roller profile is crowned in cylindrical and tapered roller bearings. However, compared to cylindrical roller bearings, there are few studies on the profile modification of TRBs in the literature, and most of the publications on the EHD analysis of tapered rollers focused on a single roller, using traditional profiles such as logarithmic profiles, dub-off profiles and chamfer profiles. By using the numerical running-in method proposed and used in crowning profiles of cylindrical rollers by the authors, this paper provides the first ever asymmetric optimized profile solution for all TRBs rather than for just a single roller. The results show that the optimized profile has the best performance in smoothing contact pressure distribution in the axial direction compared with the conventional logarithmic profile and is a useful profile form with respect to the elimination of sharp pressure spikes. In addition, considering the effect of temperature and mixed lubrication, this paper analyzes the influences of different axial profiles under radial load (Fr), rotation speed (N) and standard deviation of roughness (Rq) conditions.

Insulated rail joint (IRJ) contact characterisation-an ultrasonic reflectometry approach for a cross-material interface

Vehicle–track interaction at insulated rail joints (IRJs) plays a significant role in the wear evolvement and damage of the IRJ components. It is, however, challenging to characterise the contact conditions within the region non-destructively and accurately using experimental tools, especially when the IRJ contact involves both wheel–rail and wheel–endpost contact pairs. This study presents an ultrasonic technique to monitor and characterise static IRJ contacts in a non-invasive manner. The proposed ultrasonic reflectometry technique can realise high-resolution visualisation of contact patch and contact pressure distribution for both wheel–rail contact and wheel–endpost contact, by striking a beam of focused ultrasonic signals at the contact interface. Different data post-processing strategies are applied for the two types of contacts and a deconvolution algorithm is applied to rectify the measurements near the rail–endpost boundary. The ultrasonic measurements are verified through finite element simulations and the results show good agreement with each other in terms of both contact area and contact pressure level. It is expected that the proposed ultrasonic approach can be a reliable tool to assist in revealing the contact behaviour of IRJs more profoundly.

Volatile Lubricants Injected Through Laser Drilled Micro Holes Enable Efficiently Hydrocarbon-Free Lubrication for Deep Drawing Processes

In order to reduce the use of classic lubricants such as synthetic or mineral oils, emulsions or waxes in the deep drawing process, a new tribological system based on volatile lubricants was investigated. In this system, a volatile medium is injected under high pressure through laser drilled micro holes directly into the contact zone between the tool and the sheet metal and serves as a temporary lubricant. In order to investigate this tribological system under realistic conditions, strip drawing experiments with different volatile lubricants (air, nitrogen, carbon dioxide and argon) were performed on galvanized sheets. Therefore, a new generation of strip drawing tools was designed and numerically calculated for low elastic deformations to ensure a uniform contact pressure distribution over the entire friction contact area. To obtain a homogeneous distribution of the volatile lubricants, a number of micro holes with a depth of several millimeters were drilled into the hardened strip drawing jaws using ultrashort pulsed laser radiation. Taking into account the capabilities of this laser drilling technique in terms of size and shape of the micro holes, computational fluid dynamics simulations were performed to predict the flow behavior of the lubricant within the micro hole as well as the contact zone and were compared with observable effects in outflow tests. The chemical composition of the acting tribological layers was characterized by means of X-ray photoelectron spectroscopy and their changes during the deep drawing process were correlated with the lubricants used as well as the measured wear and friction values.

Study on the VCRplus Back-Up Roll Contour of 1500 mm CVC Mill

The back-up rolls of hot strip mills wear considerably under the conditions of high temperature and heavy load, which affects the roll service period and the stability of strip profile control. Serious uneven wear, short service periods, and spalling problems occurred on conventional back-up rolls of upstream stand CVC mills in 1500 mm continuous hot rolling production lines. Through finite element simulations, the problems are determined to be caused by the configuration of a flat roll contour of the back-up roll and the CVC roll contour of the work roll, which leads to uneven contact pressure between the rolls. The wear distribution form is ‘anti-CVC’ shape, and there is peak contact pressure between the rolls on both sides of the roll body. In particular, the long-term negative shifting of CVC on site further increases the peak contact pressure between the rolls, resulting in uneven wear and spalling accident. Based on the design technology of VCR back-up roll contours with variable contact lengths, and considering the cooperation between the middle of the back-up roll and the CVC work roll contour, the roll contour of the back-up roll has been improved. The designed VCRplus roll contour was analyzed and evaluated by finite element simulation, including the distribution of contact pressure between rolls, the control effect of bending force, and the transverse stiffness of the roll gap. The simulation results show that the VCRplus roll contour can effectively improve the uneven distribution of contact pressure between the rolls, and effectively improve the control effect of bending force and the transverse stiffness of the roll gap. Industrial tests demonstrate that VCRplus back-up roll contours have the advantages of uniform back-up roll wear, enhanced self-sustaining of the roll contour, and further extension of the back-up roll service life. The roll contour has now stably been put into industrial production, and the rolling capacity during the back-up roll service period has been extended from 150,000,000 kg to 250,000,000 kg.

Leakage Model of Tubing and Casing Premium Connection Based on Sinusoidal Contact Simulation between Rough Surfaces

This paper proposed a semi-theoretical model to quantitatively predict leakage rate of tubing and casing premium connections. The geometric parameters of the sealing surface profile approximated by a sinusoidal micro-convex surface were first obtained based on the random normal distribution sampling method. With the actual area prediction formula for elastic–plastic contact of an axisymmetric sinusoidal micro-convex body based on the equivalent simulation principle, the circumferential leakage width and radial average leakage height of the micro-leakage channel between sealing surfaces were then acquired with the surface roughness and geometric mean contact pressure. At last, the actual micro-leakage rate of the premium connection was derived by considering the non-uniform contact pressure distribution between sealing surfaces. An example was investigated to validate the model and reveal the sealing and leakage characteristics, and anti-leakage measures were proposed. The results show that average contact pressure, circumferential leakage width, and radial average leakage height between sealing surfaces were non-uniformly distributed. The leakage rate of a premium connection decreases exponentially with an increase in radial interference between sealing surfaces. In order to reduce leakage rate, it is beneficial to increase radial interference and lower sealing surface roughness.