The Dynamic Behavior of Surface Grinding: Part 1—A Mathematical Treatment of Surface Grinding

1971 ◽  
Vol 93 (2) ◽  
pp. 485-491 ◽  
Author(s):  
R. A. Thompson
Keyword(s):  
Steady State ◽  
Dynamic Behavior ◽  
Ground Surface ◽  
Steady State Solution ◽  
Surface Grinding ◽  
Mathematical Representation ◽  
Mathematical Treatment ◽  
Test Results ◽  
Wheel Wear ◽  
Insight Into

A mathematical representation for surface grinding is developed. The main feature of the model is that it takes into account the reversing motion of the workpiece, typical to surface grinding. The most general steady state solution is applied to the governing equations to give insight into the dynamic behavior of surface grinding. The theory predicts that steady state surface grinding vibrations can exist. They occur at a frequency which is always higher than the system’s uncoupled resonant frequency and slightly dependent on the workpiece’s direction of motion. Further, the model predicts the existence of wheel lobes. The lobes precess around the wheel according to their size, the wheel wear coefficient, and the chatter amplitude. The model suggests that the lobes can produce a rough ground surface even in the absence of dynamic grinding forces. As Part 2 of the presentation, some test results are offered in support of the mathematical theory of Part 1.

Analysis of the Primary and Secondary Resonances of Viscoelastic Beams Made of Zener Material

2019 ◽  
Vol 14 (9) ◽  
Author(s):  
Przemysław Wielentejczyk ◽  
Roman Lewandowski
Keyword(s):  
Steady State ◽  
Dynamic Behavior ◽  
Harmonic Balance ◽  
Virtual Work ◽  
Continuation Method ◽  
Harmonic Balance Method ◽  
Steady State Solution ◽  
Response Curves ◽  
Zener Model ◽  
Secondary Resonances

The problem of geometrically nonlinear, steady-state vibrations of beams made of viscoelastic (VE) materials is considered in this paper. The Euler–Bernoulli and the von Kármán theories are used to describe the dynamic behavior of beams. The VE material of the beams is modeled using the Zener model. Two harmonics are present in the assumed steady-state solution of the problem at hand, which enables an analysis of both the primary and secondary resonances. The virtual work equation and the harmonic balance method are used to derive the amplitude equations in the explicit form. The response curves are determined using the continuation method and treating the frequency of excitation as the main parameter. The results of several examples, which illustrate the dynamic behavior of the considered beams, are presented and discussed.

Calculation of Effective Ground Depth of Cut by Means of Grinding Process Model

2011 ◽  
Vol 496 ◽  
pp. 7-12 ◽  
Author(s):  
Takazo Yamada ◽  
Michael N. Morgan ◽  
Hwa Soo Lee ◽  
Kohichi Miura
Keyword(s):  
Process Model ◽  
Ground Surface ◽  
Depth Of Cut ◽  
Grinding Wheel ◽  
Grinding Process ◽  
Wheel Wear ◽  
Elastic Deformations ◽  
Proposed Model ◽  
Effective Depth ◽  
Grinding Machine

In order to obtain the effective depth of cut on the ground surface, a new grinding process model taking into account thermal expansions of the grinding wheel and the workpiece, elastic deformations of the grinding machine, the grinding wheel and the workpiece and the wheel wear was proposed. Using proposed model, the effective depth of cut was calculated using measured results of the applied depth of cut and the normal grinding force.

An airfoil theory of bifurcating laminar separation from thin obstacles

1990 ◽  
Vol 216 ◽  
pp. 255-284 ◽  
Author(s):  
C. J. Lee ◽  
H. K. Cheng
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Steady State ◽  
Steady State Solution ◽  
Equation System ◽  
Branch Points ◽  
Laminar Separation ◽  
Kutta Condition ◽  
Numerical Studies ◽  
Steady State Solutions

Global interaction of the boundary layer separating from an obstacle with resulting open/closed wakes is studied for a thin airfoil in a steady flow. Replacing the Kutta condition of the classical theory is the breakaway criterion of the laminar triple-deck interaction (Sychev 1972; Smith 1977), which, together with the assumption of a uniform wake/eddy pressure, leads to a nonlinear equation system for the breakaway location and wake shape. The solutions depend on a Reynolds numberReand an airfoil thickness ratio or incidence τ and, in the domain$Re^{\frac{1}{16}}\tau = O(1)$considered, the separation locations are found to be far removed from the classical Brillouin–Villat point for the breakaway from a smooth shape. Bifurcations of the steady-state solution are found among examples of symmetrical and asymmetrical flows, allowing open and closed wakes, as well as symmetry breaking in an otherwise symmetrical flow. Accordingly, the influence of thickness and incidence, as well as Reynolds number is critical in the vicinity of branch points and cut-off points where steady-state solutions can/must change branches/types. The study suggests a correspondence of this bifurcation feature with the lift hysteresis and other aerodynamic anomalies observed from wind-tunnel and numerical studies in subcritical and high-subcriticalReflows.

Engine Testing of an Advanced Alloy for Microturbine Primary Surface Recuperators

2005 ◽  
Author(s):  
Wendy J. Matthews ◽  
Terry Bartel ◽  
Dwaine L. Klarstrom ◽  
Larry R. Walker
Keyword(s):  
Steady State ◽  
Oxide Scale ◽  
Engine Test ◽  
Test Results ◽  
Protective Oxide ◽  
Protective Oxide Scale ◽  
Cyclic Operation ◽  
Engine Testing

HAYNES® alloy HR-120® has been identified as a potential alloy for the manufacture of primary surface recuperators. Primary surface recuperator components have been manufactured from HR-120, and actual microturbine testing is on going. Initial engine test results indicate the formation of a protective oxide scale that is resistant to both steady-state and cyclic operation with no evidence of accelerated attack, and which is likely to meet or exceed the desired 80,000 hour component life.

Experimental and Numerical Study on Grinding Temperature during Surface Grinding with Different Cooling Methods

2009 ◽  
Vol 416 ◽  
pp. 514-518 ◽  
Author(s):  
Qing Long An ◽  
Yu Can Fu ◽  
Jiu Hua Xu
Keyword(s):  
Numerical Study ◽  
Specific Energy Consumption ◽  
Ground Surface ◽  
Numerical Results ◽  
Surface Grinding ◽  
Grinding Temperature ◽  
Air Jet ◽  
The Difference ◽  
High Specific Energy ◽  
Cooling Methods

Grinding, characterized by its high specific energy consumption, may generate high grinding zone temperature. These can cause thermal damage to the ground surface and poor surface integrity, especially in the grinding of difficult-to-machine materials. In this paper, experimental and fem study on grinding temperature during surface grinding of Ti-6Al-4V with different cooling methods. A comparison between the experimental and numerical results is made. It is indicated that the difference between experimental and numerical results is below 15% and the numerical results can be considered reliable. Grinding temperature can be more effectively reduced with CPMJ than that with cold air jet and flood cooling method.

Dependency of Unsteady Time-Linearized Flutter Investigations on the Steady State Flow Field

2011 ◽  
Author(s):  
Michael Blocher ◽  
Markus May ◽  
Harald Schoenenborn
Keyword(s):  
Steady State ◽  
Steady State Solution ◽  
Elastic Stability ◽  
Compressor Cascade ◽  
Steady State Flow ◽  
State Flow ◽  
Flow Parameters ◽  
Pressure Distributions ◽  
German Aerospace ◽  
École Polytechnique

The influence of the steady state flow solution on the aero-elastic stability behaviour of an annular compressor cascade shall be studied in order to determine sensitivities of the aero-dynamic damping with respect to characteristic flow parameters. In this context two different flow regimes — a subsonic and a transonic case — are subject to the analysis. The pressure distributions, steady as well as unsteady, on the blade surface of the NACA3506 profile are compared to experimental data that has been gained by the Institute of Aeroelasticity of the German Aerospace Center (DLR) during several wind tunnel tests at the annular compressor cascade facility RGP-400 of the Ecole Polytechnique Fe´de´rale de Lausanne (EPFL). Whereas a certain robustness of the unsteady CFD results can be stated for the subsonic flow regime, the transonic regime proves to be very sensitive with respect to the steady state solution.

On the steady-state solution of the M/G/2 queue

1979 ◽  
Vol 11 (01) ◽  
pp. 240-255 ◽  
Author(s):  
Per Hokstad
Keyword(s):  
Steady State ◽  
General Solution ◽  
Laplace Transform ◽  
Queue Length ◽  
Joint Distribution ◽  
Length Distribution ◽  
Steady State Solution ◽  
Queue Length Distribution ◽  
The Difference ◽  
Number Of Customers

The asymptotic behaviour of the M/G/2 queue is studied. The difference-differential equations for the joint distribution of the number of customers present and of the remaining holding times for services in progress were obtained in Hokstad (1978a) (for M/G/m). In the present paper it is found that the general solution of these equations involves an arbitrary function. In order to decide which of the possible solutions is the answer to the queueing problem one has to consider the singularities of the Laplace transforms involved. When the service time has a rational Laplace transform, a method of obtaining the queue length distribution is outlined. For a couple of examples the explicit form of the generating function of the queue length is obtained.

Observations on the Steady-State Solution of an Extremely Flexible Spinning Disk With a Transverse Load

1983 ◽  
Vol 50 (3) ◽  
pp. 525-530 ◽  
Author(s):  
R. C. Benson
Keyword(s):  
Steady State ◽  
Hybrid System ◽  
Fourth Order ◽  
Steady State Solution ◽  
Transverse Load ◽  
System Of Differential Equations ◽  
Membrane Theory ◽  
Small Disk ◽  
Spinning Disk ◽  
Flexible Disk

The steady deflection of a transversely loaded, extremely flexible, spinning disk is studied. Membrane theory is used to predict the shapes and locations of waves that dominate the response. It is found that waves in disconnected regions are possible. Some results are presented to show how disk stiffness moderates the membrane waves, the most important result being an upper bound on the highest ordered wave of significant amplitude. A hybrid system of differential equations and boundary conditions is developed to replace the pure membrane formulation that is singular, and the full fourth-order plate formulation that is numerically sensitive. The hybrid formulation retains the salient features of the flexible disk response and facilitates calculations for very small disk stiffnesses.

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