Simulation of Random Surface Roughness-Induced Contact Vibrations at Hertzian Contacts During Steady Sliding

1986 ◽  
Vol 108 (1) ◽  
pp. 123-127 ◽  
Author(s):  
Andres Soom ◽  
Jern-Wen Chen
Keyword(s):  
Contact Stiffness ◽  
Contact Region ◽  
Digital Simulation ◽  
Hertzian Contact ◽  
Random Surface ◽  
Normal Contact ◽  
Simulation Techniques ◽  
Frequency Domains ◽  
Surface Irregularities ◽  
Contact Vibrations

Random normal contact vibrations, excited by surface irregularities swept through the contact region of Hertzian contacts during sliding, are studied using digital simulation techniques. The input disturbances are modeled as random time processes with specified spectral content in the spatial wavenumber and frequency domains. The Hertzian contact stiffness is modeled directly or through a bilinear approximation. The contact vibration spectra and resulting mean square contact loading are obtained from the simulations. A comparison with previous measurements shows good agreement between the simulation and experimental results.

Interaction Model for “Shelled Particles” and Small-Strain Modulus of Granular Materials

2018 ◽  
Vol 85 (10) ◽  
Author(s):  
Shun-hua Zhou ◽  
Peijun Guo ◽  
Dieter F. E. Stolle
Keyword(s):  
Elastic Modulus ◽  
Contact Stiffness ◽  
Scaling Law ◽  
Interaction Model ◽  
Contact Problems ◽  
Hertzian Contact ◽  
Spherical Particles ◽  
Thin Coating ◽  
Normal Contact ◽  
Laboratory Test Results

The elastic modulus of a granular assembly composed of spherical particles in Hertzian contact usually has a scaling law with the mean effective pressure p as K∼G∼p1/3. Laboratory test results, however, reveal that the value of the exponent is generally around 1/2 for most sands and gravels, but it is much higher for reclaimed asphalt concrete composed of particles coated by a thin layer of asphalt binder and even approaching unity for aggregates consisting of crushed stone. By assuming that a particle is coated with a thin soft deteriorated layer, an energy-based simple approach is proposed for thin-coating contact problems. Based on the features of the surface layer, the normal contact stiffness between two spheres varies with the contact force following kn∼Fnm and m∈[1/3,  1], with m=1/3 for Hertzian contact, m=1/2 soft thin-coating contact, m=2/3 for incompressible soft thin-coating, and m=1 for spheres with rough surfaces. Correspondingly, the elastic modulus of a random granular packing is proportional to pm with m∈[1/3,  1].

Motion of a Ball in a Ball Bearing

1973 ◽  
Vol 95 (1) ◽  
pp. 263-268
Author(s):  
H. Portig ◽  
H. G. Rylander
Keyword(s):  
Deformation Theory ◽  
Coulomb Friction ◽  
Ball Bearing ◽  
Digital Simulation ◽  
Equations Of Motion ◽  
Unsteady Motion ◽  
Hertzian Contact ◽  
Contact Deformation ◽  
Normal Forces ◽  
Simulation Language

A method is developed which allows the digital simulation of the unsteady motion of a single ball constrained only by two moving bearing races. Any desired motion of the races can be simulated. Normal forces acting on the ball are calculated by Hertzian contact deformation theory. If there is slippage between ball and races, Coulomb friction is assumed to occur. Solutions to the differential equations of motion were obtained on a computer with the digital simulation language MIMIC. The phenomenon of ball control as well as the behavior of the ball as it reached a controlled state from rest were observed. This analysis can produce more realistic results than methods that assume that the ball is controlled at all times, especially when the races are radially or angularly displaced with respect to each other.

The Effect of Thermo-Hydrodynamics on Manual Automotive Transmissions Gear Rattle

2009 ◽  
Author(s):  
Miguel De la Cruz ◽  
Stephanos Theodossiades ◽  
Homer Rahnejat ◽  
Patrick Kelly
Keyword(s):  
Contact Stiffness ◽  
Hertzian Contact ◽  
Transmission Model ◽  
System Response ◽  
Common Denominator ◽  
Gear Teeth ◽  
Lubricated Contacts ◽  
Engine Order ◽  
Dynamic Transmission Model ◽  
Gear Rattle

Manual transmission gear rattle is the result of repetitive impacts of gear meshing teeth within their backlash. This NVH phenomenon is a major industrial concern and can occur under various loaded or unloaded conditions. It fundamentally differs from other transient NVH phenomena, such as clonk or thud, which are due to impulsive actions. However, they all have their lowest common denominator in the action of contact/impact forces through lubricated contacts. Various forms of rattle have, therefore, been defined: idle rattle, drive rattle, creep rattle and over-run rattle. This paper presents a dynamic transmission model for creep rattle conditions (engaged gear at low engine RPM). The model takes into account the lubricated impact force between a gear teeth pair during a meshing cycle as well as the friction between their flanks. Hertzian contact conditions are applied to the gear pair along the torque path. Additionally, isoviscous hydrodynamic regime of lubrication is assumed for unselected (loose gear pairs) with lightly loaded impact conditions. The highly non-linear impacts induce a range of system response frequencies. These include engine order harmonics, harmonics of meshing frequency and natural frequencies related to contact stiffness. The last of these are dependent on the contact geometry and lubricant rheology. The analysis includes lubricant viscosity variation due to generated contact pressures as well as temperature. For loose gears, subject to oscillations on their retaining bearings, bearing friction is also considered.

scholarly journals Modeling and Dynamic Analysis of Spherical Roller Bearing with Localized Defects: Analytical Formulation to Calculate Defect Depth and Stiffness

2016 ◽  
Vol 2016 ◽  
pp. 1-11 ◽  
Author(s):  
Behnam Ghalamchi ◽  
Jussi Sopanen ◽  
Aki Mikkola
Keyword(s):  
Dynamic Model ◽  
Contact Stiffness ◽  
Roller Bearing ◽  
Measurement Data ◽  
Contact Forces ◽  
Hertzian Contact ◽  
Radial Clearance ◽  
Outer Race ◽  
Rolling Elements ◽  
Localized Defects

Since spherical roller bearings can carry high load in both axial and radial direction, they are increasingly used in industrial machineries and it is becoming important to understand the dynamic behavior of SRBs, especially when they are affected by internal imperfections. This paper introduces a dynamic model for an SRB that includes an inner and outer race surface defect. The proposed model shows the behavior of the bearing as a function of defect location and size. The new dynamic model describes the contact forces between bearing rolling elements and race surfaces as nonlinear Hertzian contact deformations, taking radial clearance into account. Two defect cases were simulated: an elliptical surface on the inner and outer races. In elliptical surface concavity, it is assumed that roller-to-race-surface contact is continuous as each roller passes over the defect. Contact stiffness in the defect area varies as a function of the defect contact geometry. Compared to measurement data, the results obtained using the simulation are highly accurate.

Normal Contact Stiffness Fractal Geometric Model Based on the Gamma Distribution of Rough Joint Surface

2013 ◽  
Vol 760-762 ◽  
pp. 2064-2067 ◽  
Author(s):  
Jing Fang Shen ◽  
Ke Xiang Wu ◽  
Fei Yang
Keyword(s):  
Convex Body ◽  
Gamma Distribution ◽  
Contact Stiffness ◽  
Geometric Model ◽  
Fractal Theory ◽  
Fractal Model ◽  
Joint Surface ◽  
Engineering Practice ◽  
Normal Contact ◽  
Normal Contact Stiffness

In this article, according to WenShuHua and Zhangxueniang fractal model, we point out the deficiency. Based on the fractal theory and Zhang, Wens contact stiffness fractal model, this paper puts forward Gamma distribution of rough joint surface normal contact stiffness. This paper considers micro convex body for ellipsoid, contact area for elliptic. This is slightly convex body for sphere hypothesis is more close to the actual situation. At the same time by using statistics theory, considering the contact ellipse long, short axis a and b are greater than zero, the assumption of a and b to two-dimensional Gamma distribution, it is more suitable for engineering practice.

Multisensory Virtual Reality for delivering training content to machinery operators

2021 ◽  
pp. 1-39
Author(s):  
Monica Bordegoni ◽  
Marina Carulli ◽  
Elena Spadoni
Keyword(s):  
Virtual Reality ◽  
Digital Simulation ◽  
Research Work ◽  
Learning By Doing ◽  
Protective Equipment ◽  
Training Method ◽  
Simulation Techniques ◽  
Machine Operators ◽  
Negative Factors ◽  
University Laboratory

Abstract The issue of training operators in the use of machinery is topical in the industrial field and in many other contexts, such as university laboratories. Training is about learning how to use machinery properly and safely. Beyond the possibility of studying manuals to learn how to use a machine, operators typically learn through on-the-job training. Indeed, learning by doing is in general more effective, tasks done practically are remembered more easily, and the training is more motivating and less tiresome. On the other hand, this training method has several negative factors. In particular, safety may be a major issue in some training situations. An approach that may contribute overcoming negative factors is using Virtual Reality and digital simulation techniques for operators training. The research work presented in this paper concerns the development of a multisensory Virtual Reality application for training operators to properly use machinery and Personal Protective Equipment (PPE). The context selected for the study is a university laboratory hosting manufacturing machinery. The application allows user to navigate the laboratory, to approach a machine and learn about how to operate it, and also to use proper PPE while operating a machine. Specifically, the paper describes the design and implementation of the application and presents the results of preliminary testing sessions.

Analysis of load distribution and contact stiffness of the single-nut ball screw based on the whole rolling elements model

2019 ◽  
Vol 43 (3) ◽  
pp. 344-365 ◽  
Author(s):  
Ye Chen ◽  
Chun-yu Zhao ◽  
Si-yu Zhang ◽  
Xian-li Meng
Keyword(s):  
Load Distribution ◽  
Contact Stiffness ◽  
Structural Parameters ◽  
Contact Angles ◽  
Ball Screw ◽  
Distribution Model ◽  
Axial Stiffness ◽  
Feed System ◽  
Normal Contact ◽  
Rolling Elements

This paper aims to investigate the load distribution and contact stiffness characteristics of the single-nut ball screw pair (SNBSP). First, the transformed relationship of coordinate systems is established. Then, the whole rolling elements load distribution model of the SNBSP is presented. Based on this, the whole rolling elements contact stiffness model is obtained. Applying the Newton–Raphson iterative method to solve the model, the normal force of rolling elements and the contact angles between balls and raceway surface are determined. The calculation results are reasonably consistent with those of the half pitch model. Then, the local contact stiffness and global contact stiffness are obtained. Furthermore, the effects of axial load and structural parameters of the SNBSP on the normal contact force, contact angle, and local and global contact stiffness are discussed using numeric analysis. Finally, a dynamic model of the z-axis feed system with time-varying axial stiffness is established, and the accuracy of the model is verified by experiments.

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