Formula For Friction Coefficient Research Articles

Simulation and experimental analysis on frictional vibration in the reversal process of a wiper-windscreen system

This paper studies the frictional vibration aspects of the automobile wiper-windscreen contact system and builds a numerical model that matches the test equipment. The reversal vibration of the contact system is examined by the dynamics part of a theoretical model with the derived analytical formulas. The fluid lubrication characteristics are investigated by the friction part of the model with solutions of the friction coefficient-negative slope formula for relative velocity and the friction coefficient formula in the time domain. The nonlinear dynamic response of the theoretical model of the wiper blade is calculated with the Runge-Kutta method and the results of the frictional vibration are well reproduced in real motions. The validity of the model is confirmed by parallel analyses of the simulated results and the experimental ones of the wiper-windscreen system. It is concluded that properly reducing the length of blade tip is an effective way to reduce vibrations of the system. The influences of the wiping speed and acceleration after reversal on the system vibrations are also analyzed through experimental investigations. The theoretical and experimental results presented in this paper can be reference to structural optimization of the wiper blade and vibration and noise control of the wiper-windscreen contact system.

Experimental Study on Shear Behavior of Interface between Different Soil Materials and Concrete under Variable Normal Stress

At present, the interface shear test is mainly used to evaluate the anti-sliding performance of the new foundation base. However, the traditional interface shear test has certain limitations in simulating the load change during the construction process and cannot accurately simulate the interface shear characteristics between the structure and the soil under the continuous change of the normal stress. Based on the self-developed large-scale interface shear equipment, this paper carried out the interface shear test and mechanism research of cement soil concrete, sand concrete, clay concrete and other materials in different curing cycles under the loading and unloading modes of variable normal stress repeated steps and continuous loading modes of variable normal stress steps. In addition, this paper deduced the formula of the minimum interface friction coefficient based on Mohr–Coulomb criterion. The experimental results show that the curing effect of cement soil can significantly improve the shear mechanical properties of the interface, and the friction coefficient of the cement soil concrete interface will also increase step by step with the increase of the curing time of the cement soil. The sliding shear surface can be remolded under the preloading of normal pressure, so that the interface shear characteristics of each shear material under repeated loading and unloading can be approximately equal to the interface shear characteristics of multiple equivalent materials under separate loading. In the case of a continuous change of normal stress, the rapid increase of normal stress will lead to accelerated entry into the limit shear state, resulting in plastic failure of the shear plane as a whole. In the engineering with a continuous change of stress, the interface shear friction coefficient of the material with high cohesion fluctuates greatly. The minimum interface friction coefficient formula and test proposed in this paper can be used to evaluate the interface friction coefficient range, and the sand concrete interface shear performance under the continuous normal stress loading mode showed good consistency. The self-developed large-scale interface shearing equipment and its test data provide theoretical basis and solutions for the improvement of traditional interface shearing equipment.

An in-plane dynamic tire model with real-time simulation capability

This article introduces an in-plane dynamic tire model with real-time simulation capabilities. The tire belt is discretized into uniformly distributed mass points, and numerous massless contact elements are added between adjacent mass points. The efficient bending force calculation method and Savkoor dynamic friction coefficient formula are included in the model. Newton’s method and the Newmark-beta method are combined to solve the dynamic equations of the tire model, and the simulation results show that a reasonable model structure could meet the real-time calculation requirements. Particle swarm algorithm was used to identify the model parameters under different conditions. Finally, the model is validated and compared with the test data, showing that the model can express the static, steady-state, and high-frequency dynamic mechanical characteristics of the tire with high accuracy and efficiency.

United computational model for predicting thermochemical-mechanical erosion in artillery barrel considering friction behavior

Artillery barrel erosion is mainly divided into two categories, namely thermochemical erosion and mechanical wear. However, most current research on this topic focuses on the former, and lacks sufficient attention to the latter. To describe the coupling relationship of thermochemical-mechanical erosion, this paper is inspired by the friction behavior between barrel and projectile, and proposes a material degradation model of thermochemical erosion considering frictional temperature rise. The change in the friction state caused by the temperature rise in a barrel is characterized by the friction coefficient formula, and updating the interior ballistic movement, results in a novel mechanical friction wear model. Moreover, a mechanical collision wear model is derived using the impact abrasion theory. The followed finite element simulations demonstrate that these proposed quantification models are capable of describing the artillery barrel erosion characteristics during the interior ballistic process more accurately. Good agreement between the numerical simulation and the actual rifling erosion conditions is achieved. The larger erosion is mainly located at the initial part of the rifling and the muzzle, which are about 1.50 mm and 0.45 mm respectively after launching 500 projectiles.

A calculation method for friction coefficient and meshing efficiency of plastic line gear pair under dry friction conditions

A calculation method for the friction coefficient and meshing efficiency of plastic line gear (LG) pair under dry friction conditions was studied theoretically and experimentally, taking a polyoxymethylene parallel line gear pair (POM PLGP) as an example. Firstly, the geometric and mechanical models of PLGP were built by considering the effects of misalignment and loaded deformation under the actual operating condition. Then, the friction coefficient of POM specimens was obtained via the ball-on-disk experiment, of which the value varies between 0.35 and 0.45 under the experimental conditions. The calculation formula for the friction coefficient of POM LG pair was obtained by fitting the friction coefficient of the POM specimens, and the meshing efficiency of POM LG pair was calculated based on the calculation formula for friction coefficient and the meshing efficiency calculation approach. Finally, the meshing efficiency of POM PLGP specimens was measured using a homemade gear meshing efficiency test rig. The experimental results validated the feasibility of the proposed calculation method for the friction coefficient and meshing efficiency of the plastic LG pair. This study provides a method for the calculation of the friction coefficient and meshing efficiency of plastic gear pairs under dry friction conditions. It also provides the basis for the wear calculation of plastic LG pair under dry friction conditions.

Flow patterns and pressure gradient correlation for oil–water core–annular flow in horizontal pipes

The water-lubricated transportation of heavy oil seems to be an attractive method for crude oil production with significant savings in pumping power. With oil surrounded by water along the pipe, oil–water core–annular flow forms. In this paper, the characteristics of oil–water core–annular flow in a horizontal acrylic pipe were investigated. Plexiglas pipes (internal diameter = 14 mm and length = 7.5 m) and two types of white oil (viscosity = 0.237 and 0.456 Pa·s) were used. Flow patterns were observed with a high-speed camera and rules of flow pattern transition were discussed. A pressure loss model was modified by changing the friction coefficient formula with empirical value added. Totally 224 groups of experimental data were used to evaluate pressure loss theoretical models. It was found the modified model has been improved significantly in terms of precision compared to the original one. With 87.4% of the data fallen within the deviation of ± 15%, the new model performed best among the five models.

A Dynamic Analysis of Cage Instability in Ball Bearings

Cage motions in ball bearings are investigated using a dynamic analysis program. Increases in the cage friction coefficient induce unstable motions of the cage. The instability is more likely to occur under high load and low‐speed conditions due to less ball-race sliding. A simple theory of cage instability is developed, and a critical cage friction coefficient formula is proposed, which is a function of the cage mass, ball-race traction, ball-cage contact stiffness, cage rotational speed, and number of balls. The prediction of this formula agrees with the results of the dynamic analysis. With a nonuniform separation between the balls, a high-speed whirl is superimposed on the normal whirl with the ball group speed. The direction of the high-speed whirl is the same as the cage rotational direction in inner race rotation (IR), but they are opposite in outer race rotation (OR). These results agree with some experimental results in the literature and validate the dynamic analysis.

Research on the dynamic response of high-contact-ratio spur gears influenced by surface roughness under EHL condition

Employing high-contact-ratio (HCR) gear is an effective method of decreasing the load on a single tooth, as well as reducing vibration and noise. While the spindlier tooth leads to greater relative sliding, having more teeth participate in contact at the same time makes the HCR gear more sensitive to the surface quality. Available literature regarding HCR gear primarily investigates the geometrical optimization, load distribution, or efficiency calculation. Limited work has been conducted on the effect of rough surfaces on the dynamic performance of HCR gear. For this reason, a multi-degree-of-freedom (MDOF) model is presented mathematically to characterize the static transmission error based on fractal theory, investigate the relative sliding friction using an EHL-based friction coefficient formula, and detail the time-varying friction coefficient suitable for HCR gear. Based on numerical results, the surface roughness has little influence on system response in terms of the dynamic transmission error but has a large effect on the motion in off-line-of-action (OLOA) direction and friction force. The impact of shaft-bearing stiffness and damping ratio is also explored with results revealing that a greater shaft-bearing stiffness is beneficial in obtaining a more stable motion in OLOA direction, and a larger damping ratio results in a smaller effective friction force. The theory presented in this report outlines a new method of analyzing the dynamics of HCR gear in respect of introducing surface roughness into MDOF model directly, as well as establishing an indirect relationship between dynamic responses and surface roughness. This method is expected to guide surface roughness design and manufacturing in the future.

New Software (Multi-flowCAD) Development for Sub-Main Line Hydraulic Design: Computational Algorithm, Computer Visualization and Implementation

Hydraulic design of multiple outlets sub-mains in a distribution network system, often referred to as manifolds, laterals or gated pipes, which are extensively used in practice, has been a major problem tackled by many authors. The increasing progress in computer technology has led to the development of the improved solutions of analytical and numerical methods. This paper aims to present the new software simulation model based on the stepwise computation algorithm with software application. This model is based on discrete nonuniform outflow distribution approach for evaluating different forms of pressure head-discharge distributions along the sub-main line. In the procedure, the required hydraulic flow characteristics along the energy-grade line, the velocity head change and variation of the Reynolds number, which affects the selection of the proper friction coefficient formula to be applied along the different reaches of the pipeline, are sensitively determined. Based on certain hydraulic parameters and uniformity criteria, an improved user-friendly computer program in Visual Basic 6.0 language named “Multi-flowCAD” was developed for hydraulic analysis and design of multiple outlets sub-main lines. The present computer-aided computing technique was successfully implemented with the highest accuracy for different forms of pressure head profiles covering various design configurations regarding different flow regimes and uniform line slope situations with respect to alternative computing techniques. In professional practice, the present improved software simulation model is the most suitable, because only the basic equations of the hydraulics of steady-state pipe flow condition were sensitively used in each pipe section between successive outlets. The present model can be efficiently used for hydraulic analysis and design of various types of multiple outlets pipelines in sub-main distribution networks, for all performed simulations.

Analytical and Experimental Investigation of Parameters Affecting Sliding Loss in a Spur Gear Pair

The effects of gear module, pressure angle and gear ratio on the sliding losses of a spur gear pair have been investigated analytically and experimentally in this paper. The analytical investigations were done by using the gear meshing model proposed in the authors' former work. The various empirical formulas of friction coefficient are used in the calculation process. The estimated results are compared with the experimental results done by using back-to-back gear test rig. The analytical results agree well with the experimental results. The sliding losses of gears having larger module are higher than the gears having smaller module. The larger pressure angle gears have lower sliding losses, and increasing the gear ratio causes the increase in sliding loss. The estimated results calculated by using the friction coefficient formula proposed by ISO TC60 are the most accurate comparing with the experimental results.

An empirical formula for friction coefficient of a perforated wall with vertical slits

The friction coefficient in the permeability parameter of a perforated wall has been estimated on the basis of a best fit between measured and predicted values of such hydrodynamic coefficients as reflection and transmission coefficients. In the present study, an empirical formula for the friction coefficient is proposed in terms of known variables, i.e., the porosity and thickness of the perforated wall and the water depth. This enables direct estimation of the friction coefficient without invoking a best fit procedure. To obtain the empirical formula, hydraulic experiments are carried out, the results of which are used along with other researchers' results. The proposed formula is used to predict the reflection and transmission coefficients of various types of structures including a perforated wall. The concurrence between the experimental data and calculated results is good, verifying the appropriateness of the proposed formula. It is also shown that the proposed formula can be used for irregular waves as well.

Field-Scale Assessment of Uncertainties in Drip Irrigation Lateral Parameters

Grass establishment on railway embankment steep slopes for erosion control in Central Queensland, Australia, is aided by drip lateral irrigation systems. The effective field values of the lateral parameters may be different from the manufacturer supplied ones due to manufacturing variations of the emitters, environmental factors, and water quality. This paper has provided a methodology for estimating drip lateral effective parameter values under field conditions. The hydraulic model takes into account the velocity head change and a proper selection of the friction coefficient formula based on the Reynolds number. Fittings and emitter insertion head losses were incorporated into the hydraulic model. Pressure measurements at some locations within the irrigation system, and the inlet discharges, were used to calibrate the lateral parameters in a statistical framework that allows estimation of parameter uncertainties using the Metropolis algorithm. It is observed that the manufacturer’s supplied parameters were significantly different from the calibrated ones, underestimating pressures within the irrigation system for a given inlet discharge, stressing the need for field testing. The parameter posterior distributions were found to be unimodal and nearly normally distributed. The emitter head loss coefficient distribution being very significant suggests the need to incorporate it into the hydraulic modeling. Although the example given in this paper relates to steep slopes, the methodologies are general and can be applied to any use of drip laterals.

Prediction of friction-related power losses of hypoid gear pairs

A model to predict friction-related mechanical efficiency losses of hypoid gear pairs is proposed in this study. The model includes a gear contact model, a friction prediction model, and a mechanical efficiency formulation. The friction model uses a friction coefficient formula obtained by applying multiple linear regression analysis to a large number of elastohydrodynamic lubrication analyses covering typical ranges of key parameters associated with surface roughness, geometry, load, kinematics, and the lubricant. Formulations regarding the kinematic and geometric properties of the hypoid gear contact are presented. The load and friction coefficient distribution predictions are used to compute instantaneous torque/power losses and the mechanical efficiency of a hypoid gear pair at any given position. Results of a parametric study are presented at the end to highlight the influence of key operating conditions, surface finish, and lubricant properties on mechanical efficiency losses of hypoid gears.

Prediction of Mechanical Efficiency of Parallel-Axis Gear Pairs

AbstractA computational model is proposed for the prediction of friction-related mechanical efficiency losses of parallel-axis gear pairs. The model incorporates a gear load distribution model, a friction model, and a mechanical efficiency formulation to predict the instantaneous mechanical efficiency of a gear pair under typical operating, surface, and lubrication conditions. The friction model uses a new friction coefficient formula obtained by using a validated non-Newtonian thermal elastohydrodynamic lubrication (EHL) model in conjunction with a multiple linear regression analysis. The load and friction coefficient distribution predictions are used to compute instantaneous torque/power losses and the mechanical efficiency of a gear pair at any given rotational position. Efficiency measurements from gear pairs having various gear designs and surface treatments are compared to model predictions. Mechanical efficiency predictions are shown to be within 0.1% of the measured values, indicating that the proposed efficiency model is accurate. Results of a parametric study are presented at the end to highlight the influence of key basic gear geometric parameters, tooth modifications, operating conditions, surface finish, and lubricant properties on mechanical efficiency losses.

Initial motion of sediment under waves and wave-current combined motions

Recently, one of the authors proposed a very convenient formula to evaluate the friction coefficient induced by wave-current combined motion, which spans all flow regimes including the transitional regime and requires no iteration. This formula is applied to an analysis of existing experimental data regarding initial motion of sediment particles under pure waves and wave-current combined motion. It was found that most of the data analyzed here were located in the transitional regime. Thus, the full-range friction coefficient formula can be conveniently applied as compared with previous implicit formulae and graphical friction laws. The formula of general motion under pure wave motion can be modified to compute the critical water depth of sediment movement. Some discontinuities in the former work in the transitional regime now can be overcome in the present study.

Analysis and Design of Trickle‐Irrigation Laterals

The problem of a lateral pipe with equally spaced emitters and uniform slope is investigated. Individual emitters are considered in discharge and pressure estimations along the lateral. The friction head loss between successive emitters is estimated by the Darcy‐Weisbach formula, taking into account the variation of the Reynolds number, the different zones on Moody diagram, and the friction coefficient formula corresponding to each zone. In addition, the change of the velocity head is accounted for at different emitters. As the net pressure head at each emitter is evaluated, the corresponding emitter discharge is estimated accordingly. A computer program is presented for analyzing and designing trickle‐irrigation laterals. The results of two numerical examples solved using the presented technique are in close agreement with those of other rational analysis. Laminar flow prevails in a considerable length at the downstream end of the lateral, whereas an upstream length may be subject to fully turbulent flow. The estimation of the lower‐quarter distribution uniformity shows that considering individual emitters rather than longitudinal slot is of practical importance. Design criteria for trickle‐irrigation laterals are provided.

Energy loss of pipe flows stratified with suspended-load and bed-load

The problem of energy loss for pipe flows stratified with suspended-load and bedload is discussed in this paper. It is postulated that for two-phase flows with coarse particles at high concentrations, the impact force on particles plays an important role in suspending the particles. On this basis, formulas for friction coefficients are derived and substantiated by the measured data. Experiments reveal that the classical diffusion theory is not sufficient for describing two-phase flows with coarse particles at high concentrations. Whether the suspension of coarse particles increases the dissipation of flow energy mainly depends on the relative importance of the impact force as compared with the turbulent force acting on the particles. However, at high concentrations of coarse suspensions, dissipation of flow energy will be increased significantly. The presence of bed-load will undoubtedly increase the energy loss of the flow. A quantitative relationship for additional loss due to the presence of the bed-load in terms of flow conditions and particle properties is suggested and a limiting concentration for the bed-road is proposed.