Before Calculating the Teeth of Spur gears on the Bend

2020 ◽  
pp. 151-158
Author(s):  
Yurii Nevdakha ◽  
◽  
Viktor Dubovyk ◽  
Nataliia Nevdakha ◽  
Fedir Zlatopolskiy ◽  
...  
Keyword(s):  
Stress Distribution ◽  
Cross Section ◽  
Bending Strength ◽  
Fatigue Cracks ◽  
Local Stress ◽  
Transition Curve ◽  
Variable Cross ◽  
The Real ◽  
Calculated Dependence ◽  
Number Of Teeth

The aim of the work is to improve the calculations of spur cylindrical wheels per bend, due to the fact that the existing formulas do not give the actual value of the maximum stress, and the diagram does not correspond to the real law of stress distribution. In order to obtain satisfactory results, it is more correct to calculate the teeth at the maximum local stress. Combining the coefficients and substantiating the calculated dependence to determine the value of the coefficient of the shape of the tooth under load, applied at any point of the working profile of the tooth, to obtain formulas for the bending strength of the teeth of the gear and wheel. When calculating the bending teeth, the calculation is based on the stresses arising at the base of the tooth, under the load applied at the top of the tooth. Consider first the most common calculation scheme. Dangerous section of the tooth as seen from the plot of total stresses indicates that the maximum normal stress occurs on the non-working side of the tooth - the compression side, however, since fatigue cracks occur at the base of the tooth on the stretching side, the calculation is based on tensile stress on the working side. The hypothesis of non-curvature of flat sections is unfair for short beams of variable cross section, so the total diagram does not correspond to the real law of stress distribution. But at the base of the tooth near the transition curve is the place of stress concentration. The actual dangerous cross-section lies below the cross-section of the depression, this is confirmed by the fact that the fatigue cracks form an angle with the load curve close to straight, and the fracture of the tooth has a convex shape. In this case, it is more correct to calculate the teeth at the maximum local stress. Combining the coefficients obtained a calculated dependence to determine the value of the coefficient of the shape of the tooth under load, applied at any point of the working profile of the tooth. As a result of the study it was found that the coefficient of tooth shape decreases with increasing number of teeth. This result was expected because as the number of teeth increases, the angle between the teeth decreases, and neighboring teeth perceive part of the stress that occurs in the loaded tooth. The formulas for checking the bending strength of gear teeth and wheels are obtained. The above refinement calculations of the teeth on the bend reflect the beneficial effect of improving the accuracy of the manufacture of teeth.

The Analysis of Longitudinal Impact Response for Variable Cross-Section Rod

2016 ◽  
Vol 693 ◽  
pp. 504-510
Author(s):  
Xiao Juan Jiao ◽  
Jian Min Ma
Keyword(s):  
Stress Distribution ◽  
Cross Section ◽  
Influencing Factor ◽  
Variable Cross Section ◽  
Longitudinal Impact ◽  
Variable Cross ◽  
Elastic Rod ◽  
Distribution Law ◽  
Change Rate ◽  
Cross Section Change

s The longitudinal impact between rigid body and variable cross-section elastic rod with fixed boundary condition was studied, the velocity and stress distribution law during 1st impact wave period was derived for the variable cross-section rod, the influence of cross-section change rate on rod response was discussed. Some examples calculations were carried on, It is shown that the cross-section change rate is a significant influencing factor for the velocity and stress distribution in the rod during impact.

Dynamical Stress Distribution Analysis of a Non-Uniform Cross-Section Beam Under Moving Mass

2006 ◽  
Author(s):  
M. T. Ahmadian ◽  
E. Esmailzadeh ◽  
M. Asgari
Keyword(s):  
Stress Distribution ◽  
Cross Section ◽  
Natural Frequencies ◽  
Moving Load ◽  
Variable Cross Section ◽  
Moving Mass ◽  
Variable Cross ◽  
Distribution Analysis ◽  
Concentrated Force ◽  
Direct Integration Method

One of the engineers concern in designing bridges and structures under moving load is the uniformity of stress distribution. In this paper the analysis of a variable cross-section beam subjected to a moving concentrated force and mass is investigated. Finite element method with cubic Hermitian interpolation functions is used to model the structure based on Euler-Bernoulli beam and Wilson-Θ direct integration method is implemented to solve time dependent equations. Effects of cross-section area variation, boundary conditions, and moving mass inertia on the deflection, natural frequencies and longitudinal stresses of beam are investigated. Results indicates using a beam of parabolically varying thickness with constant mass can decrease maximum deflection and stresses along the beam while increasing natural frequencies of the beam. The effect of moving mass inertia of moving load is found to be significant at high velocity.

Fatigue failure of 45# steel in dry sliding against Kevlar/PTFE hybrid composite under elevated load

2017 ◽  
Vol 232 (4) ◽  
pp. 391-400
Author(s):  
Bingli Fan ◽  
Yulin Yang ◽  
Shicheng Yan ◽  
Jian Ma ◽  
Dapeng Gu ◽  
...  
Keyword(s):  
Stress Distribution ◽  
Cross Section ◽  
Fatigue Failure ◽  
Hybrid Composite ◽  
Friction Pair ◽  
Fatigue Cracks ◽  
Wear Characteristics ◽  
Opposite Case ◽  
Fabric Composite ◽  
Final Failure

Frictional failure is inevitable for friction pairs. A common sense about the frictional failure of steel-polymer composite friction pair is that the polymer composites are the primary failure part rather than the steel counterpart. However, an opposite case was newly found in the case of fabric self-lubricating liner (Kevlar/PTFE hybrid composite) spherical plain-bearing under elevated load: the steel counterbody suffered a fatigue failure before the fabric composite fails, which resulted in the final failure of the bearing. This paper investigated such fatigue failure of surface chrome plated 45# steel by systematically studying the wear characteristics of 45# steel and fabric composite, the stress distribution of the 45# steel and fatigue features within cross section of the 45# steel. Results showed that wear characteristics of both fabric composite and 45# steel exhibited regional characters. Failure mechanism of the 45# steel was found to be fatigue failure (mainly fatigue pitting), which was revealed by mathematical analysis of the stress distribution of the 45# steel and the fatigue cracks found within subsurface of the cross section of the 45# steel.

Boundary element method in numerical study of three-dimensional Stokes flows in channels of arbitrary shape

2012 ◽  
Vol 9 (1) ◽  
pp. 94-97
Author(s):  
Yu.A. Itkulova
Keyword(s):  
Boundary Element Method ◽  
Boundary Element ◽  
Cross Section ◽  
Numerical Study ◽  
Three Dimensional ◽  
Cylindrical Tube ◽  
Variable Cross Section ◽  
Variable Cross ◽  
Periodic Flows ◽  
Element Method

In the present work creeping three-dimensional flows of a viscous liquid in a cylindrical tube and a channel of variable cross-section are studied. A qualitative triangulation of the surface of a cylindrical tube, a smoothed and experimental channel of a variable cross section is constructed. The problem is solved numerically using boundary element method in several modifications for a periodic and non-periodic flows. The obtained numerical results are compared with the analytical solution for the Poiseuille flow.

Longitudinal oscillation of a rod with a variable cross section

2019 ◽  
Vol 14 (2) ◽  
pp. 138-141
Author(s):  
I.M. Utyashev
Keyword(s):  
Cross Section ◽  
Natural Frequencies ◽  
Liouville Problem ◽  
Variable Cross Section ◽  
Variable Cross ◽  
Longitudinal Vibrations ◽  
Cross Sectional ◽  
Independent Functions ◽  
The Cross ◽  
The Right

Variable cross-section rods are used in many parts and mechanisms. For example, conical rods are widely used in percussion mechanisms. The strength of such parts directly depends on the natural frequencies of longitudinal vibrations. The paper presents a method that allows numerically finding the natural frequencies of longitudinal vibrations of an elastic rod with a variable cross section. This method is based on representing the cross-sectional area as an exponential function of a polynomial of degree n. Based on this idea, it was possible to formulate the Sturm-Liouville problem with boundary conditions of the third kind. The linearly independent functions of the general solution have the form of a power series in the variables x and λ, as a result of which the order of the characteristic equation depends on the choice of the number of terms in the series. The presented approach differs from the works of other authors both in the formulation and in the solution method. In the work, a rod with a rigidly fixed left end is considered, fixing on the right end can be either free, or elastic or rigid. The first three natural frequencies for various cross-sectional profiles are given. From the analysis of the numerical results it follows that in a rigidly fixed rod with thinning in the middle part, the first natural frequency is noticeably higher than that of a conical rod. It is shown that with an increase in the rigidity of fixation at the right end, the natural frequencies increase for all cross section profiles. The results of the study can be used to solve inverse problems of restoring the cross-sectional profile from a finite set of natural frequencies.

scholarly journals Theoretical and Experimental Studies on MEMS Variable Cross-Section Cantilever Beam Based Piezoelectric Vibration Energy Harvester

Micromachines ◽  
2021 ◽  
Vol 12 (7) ◽  
pp. 772
Author(s):  
Xianming He ◽  
Dongxiao Li ◽  
Hong Zhou ◽  
Xindan Hui ◽  
Xiaojing Mu
Keyword(s):  
Power Density ◽  
Cantilever Beam ◽  
Cross Section ◽  
Energy Harvester ◽  
Variable Cross Section ◽  
Vibration Energy ◽  
Variable Cross ◽  
Vibration Energy Harvester ◽  
Piezoelectric Vibration Energy Harvester ◽  
Piezoelectric Vibration

The piezoelectric vibration energy harvester (PVEH) based on the variable cross-section cantilever beam (VCSCB) structure has the advantages of uniform axial strain distribution and high output power density, so it has become a research hotspot of the PVEH. However, its electromechanical model needs to be further studied. In this paper, the bidirectional coupled distributed parameter electromechanical model of the MEMS VCSCB based PVEH is constructed, analytically solved, and verified, which laid an important theoretical foundation for structural design and optimization, performance improvement, and output prediction of the PVEH. Based on the constructed model, the output performances of five kinds of VCSCB based PVEHs with different cross-sectional shapes were compared and analyzed. The results show that the PVEH with the concave quadratic beam shape has the best output due to the uniform surface stress distribution. Additionally, the influence of the main structural parameters of the MEMS trapezoidal cantilever beam (TCB) based PVEH on the output performance of the device is theoretically analyzed. Finally, a prototype of the Aluminum Nitride (AlN) TCB based PVEH is designed and developed. The peak open-circuit voltage and normalized power density of the device can reach 5.64 V and 742 μW/cm3/g2, which is in good agreement with the theoretical model value. The prototype has wide application prospects in the power supply of the wireless sensor network node such as the structural health monitoring system and the Internet of Things.

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