Experimental investigation of helical gear tooth crack location and depth detection using moving average method on transmission error

Gear systems are the most useful and essential power transmission systems in the high-speed industry due to their accuracy. It is necessary to make sure that these systems work without defects such as tooth cracks. Therefore, detecting the location and depth of cracks in gear systems is very important. In this research, a new approach is proposed to detect the crack location, and accordingly, some statistical indicators are used to estimate the crack depth in the helical gear tooth. To this end, after explaining the helical gear mesh stiffness and tooth-root crack modeling, the helical gear pair dynamic is modeled. Then, the vibration data of a helical gear system is obtained by an experimental test rig, and the moving average method is undertaken to precisely detect the crack location. The crack depth ratio is estimated using the crest factor, impulse factor, clearance factor, and [Formula: see text] and [Formula: see text] which are applied to the simulation results and the experimental signal. According to these results, the crest factor, impulse factor, and clearance factor calculated the crack depth ratio with a good agreement, and the indicators [Formula: see text] and [Formula: see text] estimated it with a more significant error. Also, the average of estimated values is calculated, indicating a better result than each indicator alone.

Stiffness Estimation of Cracked Beams Based on Nonlinear Stress Distributions Near the Crack

The crack presence causes nonlinear stress distributions along the sections of a beam, which change the neutral axis of the sections and further affect the beam stiffness. Thus, this paper presents a method for the stiffness estimation of cracked beams based on the stress distributions. First, regions whose stresses are affected by the crack are analyzed, and according to the distance to the crack, different nonlinear stress distributions are modeled for the effect regions. The inertia moments of section are evaluated by substituting these stress distributions into the internal force equilibrium of section. Then the finite-element technique is adopted to estimate the stiffness of the cracked beam. The estimated stiffness is used to predict the displacements of simply supported beams with a crack, and the results show that both static and vibrational displacements are accurately predicted, which indicates that the estimated stiffness is precise enough. Besides, as the section shape of beam is not limited in the process of modeling the stress distributions, the method could be applicable not only to the stiffness estimation of cracked beams with a rectangular section, but also to that of the beams with a T-shaped section if the crack depth ratio is not larger than 0.7.

Stress Intensity Factor Solutions for Circumferential Surface Cracks With Large Aspect Ratios in Pipes Subjected to Global Bending

In some cracks attributed to primary water stress corrosion cracking, the crack depth a was greater than half-length of the crack 0.5ℓ. This paper presents details of stress intensity factor solutions for circumferential surface cracks with large aspect ratios a/ℓ in piping system subjected to global bending. The stress intensity factor solutions for semi-elliptical surface cracks were obtained by finite element analyses with quadratic hexahedron elements. Solutions at the deepest and the surface points of the cracks with various aspect ratio (0.5 ≤ a/ℓ ≤ 4.0), crack depth ratio (0.01 ≤ a/t ≤ 0.8) and pipe sizes ( 1/80 ≤ t/Ri ≤ 1/2) were investigated, where t and Ri are wall thickness and inner radius of pipe, respectively. Proposed stress intensity factor solutions for cracks with a/ℓ = 0.5 are consistent with the values reported in the previous study. The solutions developed in this study are widely applicable to various engineering problems related to crack evaluation in piping systems.

Effects Of Specimen Size And Crack Depth Ratio On Calibration Curves For Modified Compact Tension Specimens

The compact tension (CT) test is frequently used to determine fracture properties of metallic materials, such as fracture energy, fracture toughness, crack propagation rate and J-R curves. In the case of cement based composites, a modified compact tension (MCT) specimen can be advantageously used due to the negligible stress concentration arising around the pulling dowel pins during the test. In this work, finite element calculations are used to determine the calibrations curves for the stress intensity factor K, COD, CMOD and CMOD(4), needed for an accurate determination of the fracture parameters, as a function of the ratio a/W. Nominal diameters are selected according to the used core bits between 50 mm and 300 mm.

Research on the Influences of Crack-Depth Ratio on Fracture Energy of Ultra-High Performance Cementitious Composites

For the study of fracture characteristics of ultra-high performance cementitious composites(ECC),16 different sizes of three-point bending beams were made and ultimate load, ultimate deflection and crack mouth opening displacement ,the curve andcurve of ECC were contructed,with the method of fracture work recommendedby RILEM , the external work was respectively calculated by the curve ofand, which determined the fracture energy of ECC.Results show that two kinds of calculation result are roughly equal;The influence of size effect on fracture character was: fracture energy increased with the increasing of the crack-depth ratio, the fracture energy of concrete specimen is the maximum when the crack-depth ratio is 0.4 ; is proportional to the initial crack-depth of the specimen, but there is no relationship betweenand crack-depth ratio. This paper would have great significance for the study of fracture characteristics of ECC.