Deformation Of Shaft Research Articles

Consideration of elastic deformations of gear bodies using a reduction on a Fourier series

Elastic deformations of a gear body lead to deformations of the flank line of a gear and have therefore an impact on the load distribution on the flank. ISO 6336-1 Annex E proposes a calculation of the face load distribution factor taking into account shaft deflections, but a shaft calculation using a beam model cannot take into account additional deformations of the gear body. Additionally, elastic deformations of planetary gears have an impact on the load distribution of the supporting bearings. Gear body deformations could be considered by using a full FEA calculation of the gear-body. For repeated calculations the FEA-mesh could be statically condensed on the interface nodes to reduce the degrees of freedom of the calculation model. This has some limitations as the contact point for the gear mesh can change, for example in case of a rotating planet carrier. If the contact position changes, other nodes of the FEA-mesh would be loaded, so either the full surface mesh has to be used or the condensation is repeated on change of the contact point. For static condensation of FEA based components the MESYS shaft system calculation 10/2018 introduced a condensation to a Fourier series for gears and bearings. After condensation to the Fourier series, large rotations of the gear or changes of the contact positions can be considered without the need to redo the condensation or to include all surface nodes of the gear or bearing. The Fourier series is used in circumferential direction and an integrated Legendre polynomial is used over the face width. This approach allows the extension of a shaft system calculation for a gearbox by more accurate deformations without losing the advantages in performance compared to FEA calculations. Like the shaft deformations in ISO 6336-1 Annex E now the deformations of the flank line including gear-body deformations can be directly used to calculate the face load factor. The effect of additional gear-body deformations can then be considered in strength or life assessment according to ISO 6336 or it can be used to determine improved flank-line corrections. In case of planetary gears, the deformation can be considered in calculation of the load distribution of the bearings.

Multibody dynamic modelling of a direct wind turbine drive train

Wind turbines normally have a long operational lifetime and experience a wide range of operating conditions. A representative set of these conditions is considered as part of a design process, as codified in standards. However, operational experience shows that failures occur more frequently than expected, the costlier of these including failures in the main bearings and gearbox. As modern turbines are equipped with sophisticated online systems, an important task is to evaluate the drive train dynamics from online measurement data. In particular, internal forces leading to fatigue can only be determined indirectly from other locations’ sensors. In this contribution, a direct wind turbine drive train is modelled using the floating frame of reference formulation for a flexible multibody dynamics system. The purpose is to evaluate drive train response based on blade root forces and bedplate motions. The dynamic response is evaluated in terms of main shaft deformation and main bearing forces under different wind conditions. The model was found to correspond well to a commercial wind turbine system simulation software (ViDyn).

Analysis of the Key Structures of RV Reducer Based on Finite Element Method

In this paper, key structures of the RV reducer were calculated by finite element method respectively, including the stress and deformation of cycloidal-pin wheel and eccentric shaft. The results show that the contact stress and equivalent stress of cycloidal-pin wheel and eccentric shaft are far less than the strength of materials. It means the strength is not the main consideration of design and manufacture. The stiffness of eccentric shaft is less than the cycloidal-pin wheel, which had a great influence on the transmission accuracy of the machine. In order to improve the rigidity so as to improve the transmission accuracy of gear reducer machine, the modification methods and modification should be chosen to design by the deformation.

Effect of residual shaft bow on the dynamic analysis of a double-stage geared rotor-bearing system with translational motion due to shaft deformation

In this study, the dynamic responses of a double-stage geared rotor-bearing system with translational motion due to the effects of rotating shaft deformation were examined, which was lacking in past research. Residual shaft bow has been neglected in most geared rotor-bearing system models. In this study, the dynamic response of a double-stage geared rotor-bearing system whose gear set underwent translational motion was examined when the shaft was deformed (residual shaft bow). The proposed model considers contact ratio and pressure angle of gear pair as time-dependent variables, whereas in other models, they are constants. A finite element model of a double-stage geared rotor-bearing system with residual shaft bow was developed, and equations of motion were obtained by applying the Lagrange’s equation. System equations of motion are solved by Runge–Kutta numerical method. The dynamic response was investigated, including lateral response, contact ratio and pressure angle of gear pair with different residual shaft bow magnitudes and gear positions. The results show that residual shaft bow raises the amplitudes of lateral displacement, contact ratio and phase angle of gear pairs in the system. This study demonstrated that the residual shaft bow effect is too considerable to ignore when it becomes sufficiently large.

Experimental Study on the Shear Performance of Reinforced Concrete Beams Strengthened with Bolted Side-Plating

To investigate the residual shear capacity of post-fire bolted side-plated (BSP) reinforced concrete (RC) beams with different depths of steel plate and types of anchor adhesive, i.e., magnesium oxychloride cement (MOC) and HIT-RE500, a control beam and five BSP beams were fabricated, of which two were exposed to fire in accordance with ISO834 temperature curve. Four-point bending shear tests were conducted to investigate the influence of elevated temperature on the failure mode, cracking load, shear capacity, stiffness, ductility and strain development, etc. The shear capacities of RC beams were found to be improved significantly by using the BSP technique. However, the stiffness of BSP beams was seriously degraded after exposed to fire, but the reduction in shear capacity was negligible, whereas the ductility and the strain of longitudinal reinforcement were obviously increased. Thus, the failure-mode was changed from shear failure to flexural failure. Regarding the adhesive mortar used for bolt anchorage, magnesium oxychloride cement (MOC) achieved higher shear capacity and better ductility but lower stiffness for BSP beams compared with HIT-RE500. Additionally, increasing the depth of bolted steel plates effectively improved the shear performance of BSP beams. In the tests, uneven relative slips were observed on the plate-RC interface due to the shear deformation of bolt shafts and the plates’ tensile principal stress perpendicular to the main diagonal crack, which proved the deformation lag of the bolted steel plates with respect to the RC beam. The outcomes of this study provide a better understanding on the shear performance of BSP beams at room temperatures and at fire conditions.

New determination to loaded transmission error of the spiral bevel gear considering multiple elastic deformation evaluations under different bearing supports

In spiral bevel gear transmission system, the target is to get lower noise and higher strength as not only the environmental noise requirements but also customer demands must be met. The load transmission error (LTE) is the primary source of noise, and the elastic deformation is the primary source of strength. This paper proposes a new approach to computing LTE in consideration of effect of the elastic deformation under different bearing supports. Where, elastic deformation evaluation mainly includes the tooth flank contact deformation, shear deformation, especially the shaft deformation. In full consideration of above elastic deformation factors, a spiral bevel gear transmission system having the gear, web, gear shaft and bearing support structures is used as a basic design model by providing the different bearing supports. A numerical formulation of LTE considering multiple elastic deformation evaluations under different bearing supports is proposed by applying the elastic contact mechanics theory. Then, the simulated loaded tooth contact analysis (SLTCA) is used to further verify the numerical results of the formulation analysis. Finally, the given numerical instance can verify the proposed approach.

A COMPARISON OF WEAR PROPERTIES OF WATER LUBRICATED NBR AND PTFE SLIDING BEARINGS

The excessive wear of a journal shaft can be caused by many factors, for example, working conditions (e.g., temperaturę, slip speed, the type of lubricant), pressure, the type of material used on the bearings and shafts and their roughness, as well as contamination remaining in the system. This paper presents the roughness profiles co-operating with a rubber (NBR) and polytetrafluoroethylene (PTFE) bushes. The conditions of cooperation between the two materials tested in the sliding combination with the stainless steel journal were the same in each pair of bearings (PV); therefore, the comparison of their wear depends only on the material properties of the bush and the deformation of the journal shaft caused by the bending moment. To assess the size of the journal shaft, they were tested using a profilograph. In addition to the journal shaft, bearings were also evaluated, the wear level of which was noticed without the use of specialized equipment.

Forced Vibration of an Annular Cross Section in Combined Cutting and Deformation

The shaping process in the combined cutting and deformation of flexible hollow shafts is considered. Deformation of the cross section is taken into account.

Femoral Intramedullary Alignment in Total Knee Arthroplasty: Indications, Results, Pitfalls, Alternatives, and Controversies

While femoral intramedullary alignment has been found to be the most accurate and reproducible method for proper femoral component orientation in total knee arthroplasty, certain situations preclude the use of intramedullary alignment, such as ipsilateral long-stem total hip arthroplasty, femoral shaft deformity (congenital or post-traumatic), capacious femoral canal, and retained hardware. These cases require alternative alignment guides, that is, extramedullary alignment. The purpose of this study was to determine the accuracy of intramedullary alignment in reproducing the femoral anatomic axis. Using 35 adult cadaveric femora without obvious clinical deformity, and 7 with proximal prosthetic devices blocking the passage of an intramedullary guide, the accuracy of the guide rod was assessed both anatomically and radiographically. In the seven femora with proximal femoral devices, the guide rod could not be completely seated, resulting in a greater degree of flexion of the guide rod compared with the mechanical axis of the femur, and a greater degree of varus compared with the anatomical axis, as compared with 35 femora without obvious deformity. In cases where seating of the intramedullary guide rod is either incomplete or impossible, extramedullary femoral guides allow more accurate determination of the distal femoral cut by referencing directly from the mechanical axis, that is, the center of the femoral head. We present case studies as examples of indications for use of an extramedullary femoral guide. In addition, we demonstrate two different techniques for extramedullary femoral alignment using fluoroscopic guidance in cases incompatible with intramedullary alignment.

Elastic and Damping Properties of a Magnetorheological Coupling for Rotating Shafts

The elastic and damping properties of a magnetorheological coupling used in the diesel-generator system of portable power sources are considered. The finite-element method is used to assess the maximum shear deformation of a rotor shaft in a tractional generator.

Concave and convex modifications analysis for skewed beveloid gears considering misalignments

The mathematical models of beveloid surface with concave and convex modifications were derived. The finite element and analytical mesh models were developed considering the shaft deformation and misalignments including pinion axial position, center distance and shaft angle errors. Then, tooth contact analysis were conducted to study the impacts of loads and misalignments on contact characteristics. Results show that the higher load applied has stronger effects for enlarging contact pattern and lowering transmission error with the concave and convex modifications. Moreover, the proposed tooth modifications can decrease the sensitivity of contact characteristics to misalignments. The shaft angle error has the greatest impact on the mesh behaviors. The contact path and pattern are prone to shift the location along tooth trace direction due to shaft angle and center distance errors. The contact stress, bending stress and transmission error are seen to increase due to these two assembly errors. Pinion axial position error does not affect the location of the contact path and pattern significantly. However, it can increase the magnitude and change the location of the maximum tooth bending stress in the axis direction. Finally, it only produces minimal effect on the contact stress, contact area and transmission error.

Deformation of Compressible Layers Below Pile Foundations of a High-Speed Railway

New installation methods and techniques using single-point settlement gauges to monitor the compression deformations of pile shafts and soil layers below the pile bottom were developed. A field study was conducted at a test site of the Beijing–Shanghai high-speed railway, and a 3D finite-element analysis was performed to analyze the deformation behavior of the pile foundation. The measured compression deformations of the pile shafts from the single-point settlement gauges agreed well with the values obtained from the strain gauges, which validated the effectiveness and feasibility of the developed methods and techniques. During the construction of the high-speed railway, the pile top settlement–time curve presented a ‘ladder’ shape and then increased with time before gradually stabilizing. The compression deformations of the subsoil layers within 20–30 m below the pile bottom were not significantly different, and the average unit compression deformation under 20 m below the pile bottom remained approximately constant after construction. The axial force and tip resistance of the pile shaft increased during the consolidation of the soils surrounding the pile shaft and might result in an increase of the compressions of the pile shaft and subsoil layers. The thicknesses of compressible layers (hc) of the tested pile foundations were determined using a deformation ratio method and were approximately 15.0 m. These results demonstrate that the developed methods and techniques are useful for studying the compression deformations of subsoils below the pile bottom (especially for super-long piles).

Study of volute cutwater diameter on the structural strength of pump rotor

Based on the Workbench platform, temperature and pressure loads are applied to the rotor system (impeller, pump shaft and impeller nut) in high temperature hot water circulating pump when the medium temperature is 150 ° C. The corresponding boundary conditions are defined, and steady-state thermal analysis and static analysis are carried out. The temperature distribution, the equivalent stress and the total deformation of the rotor system is discussed in detail when the volute cutwater diameter is 214mm, 216mm and 218mm. The results show that the deformation of impeller, pump shaft and impeller nut has the maximum value when cutwater diameter is 216mm. With the increasing of cutwater diameter, the minimum temperature and maximum equivalent stress of the impeller decreases gradually. There is an obvious stress concentration in the shaft shoulder which is from bearing fitting section to the maximum shaft diameter.

Physical modeling of the controlled shaft deformation law during the solid backfill mining of ultra-close coal seams

Solid backfill mining has gradually become the key technology to control shaft deformation during industrial square coal pillar recovery. The industrial square area of the Nantun coal mine was studied in this paper. Based on similarity criteria of the physical modeling, an experimental model was designed to study the shaft deformation law under caving mining and backfill mining. A non-contact full-field strain measurement system and a resistance strain gauge were adopted to monitor the model. The mining-induced deformations, failures and stress distributions of shaft-surrounding rock masses during the recovery of industrial square coal pillars by caving mining and backfill mining were explicitly compared and analyzed. The results showed that the deformation and failure of shafts was caused by strata movements during the mining of the coal seams. Different lithology, stiffnesses, and thicknesses of adjacent rock strata result in asynchronous stratum movements, which thus cause shaft failure. The key to controlling mining-induced deformation of shafts during solid backfill mining is to control strata movement as follows: solid backfilling → control of the strata movement → control of the shaft deformation → decrease of the tension and shear force experienced by the shaft → decrease of shaft damage. Finally, the design method of the backfill body’s compression ratio based on shaft deformation control during the solid backfill mining process is proposed, thus laying the foundation for the safe recovery of an unexploited coal industrial square in resource-exhausted coal mines.

Shaft failure characteristics and the control effects of backfill body compression ratio at ultra-contiguous coal seams mining

Solid backfill coal mining is a mainstream method in green coal mining, which has gradually become a key technology to control shaft deformation when recovering industrial square pillars during mining of ultra-contiguous coal seams. On the basis of the engineering background of Nantun Coal Mine, this paper combined physical simulation, numerical simulation, and theoretical analysis for studying shaft deformation, failure characteristics, and stress variation rules during the mining of ultra-contiguous coal seams. The results revealed that shaft deformation and failure were the results of the movement of strata caused by coal mining; in addition, the backfill body compression ratios in two adjacent coal seams were the key factors in shaft deformation control during the mining of ultra-contiguous coal seams. Moreover, the effects of the backfill body compression ratios on shaft deformation in ultra-contiguous coal seam mining were simulated by ABAQUS, and the optimal compression ratios of backfill body in two coal seams were determined. Finally, based on the probability-integral method, the vertical compressive deformation and the inclined deformation of shaft were estimated and the results showed that the shaft safety and stability at ultra-contiguous coal seam mining can be provided when the backfill body compression ratios of 3upper and 3lower coal seams were set at 85%.

The influence of golf shaft torque on clubhead kinematics and ball flight

ABSTRACTThe purpose of this study was to investigate the influence of shaft torque (torsional rigidity) on clubhead kinematics and the resulting flight of the ball. Two driver shafts with disparate levels of torque, but otherwise very similar properties, were tested by 40 right-handed golfers representing a range of abilities. Shaft deflection data as well as grip and clubhead kinematics were collected from 14 swings, with each shaft, for each golfer using an optical motion capture system. Ball flight and additional clubhead kinematics were collected using a Doppler radar launch monitor. At impact, the high torque shaft (HT) was associated with increased delivered loft (P = .028) and a more open face (P < .001) relative to the low torque shaft (LT). This resulted in the HT shaft being associated with a ball finishing position that was further right (P = .002). At the individual level, the change in face angle due solely to shaft deformation was significantly higher for the HT shaft for 25/40 participants. Although shaft twist was not directly measured, it was logically deduced using the collected data that these outcomes were the result of the HT being twisted more open relative to the LT shaft at impact.

Some studies on mathematical modeling and dynamic stress analysis of a variable compression ratio diesel engine crankshaft

The objective of the present work is to investigate the induced stress and deformation of a crank shaft. For this purpose, Variable Compression Ratio (VCR) engine is tested at 16.5 compression ratio. Peak pressures were recorded at various crank angles. A Matlab code is generated for dynamic analysis. For structural analysis and factor of safety, a three dimensional model crank shaft was developed using solid works. Finite element analysis of AISI E4340 Forged steel and Aluminum alloy 7076-T6 materials are carried by using analysis software ANSYS. The obtained results are equivalent Von-Mises stress, total deformation and factor of safety at different crank angles for the two materials are analyzed. It is concluded that Aluminum alloy exhibits better results than forged steel.

Optimal Analysis of Tunnel Construction Methods through Cross Passage from Subway Shaft

The conversion section of the cross passage and shaft is a priority concern in the stress transformation of a tunnel structure during subway underground excavation. In the construction of Subway Line 5 in Xi'an, China, the main line in the loess layer was constructed through the cross passage from the subway shaft of the Yue Deng Pavilion–San Dian Village Station tunnel section. Numerical simulation and field measurement were adopted to study the construction stability of the cross passage and shaft under two possible construction methods: the “shaft followed by cross passage construction” method and the “cross passage parallel shaft construction” method. The results showed that the surface deformation and plastic zone of the surrounding rock are similar under the two construction methods. However, of the two, the “cross passage parallel shaft construction” method was more advantageous in controlling the structural deformation of the original shaft and the stress distribution of the horsehead structure. The field monitoring data showed that the surface settlements and the deformation of the original shaft structures meet the requirement of control standards under the “cross passage parallel shaft construction” method.

Probabilistic void detection using FEA

Shaft is the important mechanical component used to transmit power and torque. Manufacturing of shafts by various manufacturing processes specially casting may induce imperfections like voids or porosity in the shaft. Detection of such imperfections becomes necessary in crucial components like shaft to avoid its adverse effects. The voids can vary in size and shape and could be present at various locations.The imperfections can be compensated in condition where shaft is not exposed to extremity. However voids can have adverse effect on shaft being exposed to operating conditions or environment of vibrations. This can also occur when a shaft is exposed to environment for longer duration of time. This condition also fosters the growth of voids. Ultimately the crack is formed being followed by void nucleation, void growth and void coalescence. If this condition continues the crack propagation accelerate resulting in failure of shaft. Therefore, it is necessary to address the problem of voids. The presence of void, size and location of void affects the natural frequency or total deformation of shaft.By using concept of natural frequency or total deformation presence of void can be detected. This can be done by comparing the natural frequency or total deformation of shaft without void with that having voids. The same study can be done to know the size and location of void for shaft geometries with different diameters. It has been found that the presence of voids gives a significant change on the natural frequency and the total deformation of the shaft.

The rigid–flexible coupling dynamic model and response analysis of bearing–wheel–rail system under track irregularity

As the main bearing components of vehicle wheel/rail systems, railway bearings take on the main load of wheel/rail system. These bearings can be easily damaged after a long-term load, which causes vibrations and significant deterioration of force distribution and directly affects the driving stability of the locomotive. Current systems available for modeling the dynamics of wheel/rail systems rarely consider nonlinear contact load bearing, which causes errors in the calculation of wheel/rail system dynamics. According to the bearing structure characteristics and working features of a specific system, this paper thoroughly evaluates the flexible deformation of shaft and bearing, time-varying nonlinear contact load, track irregularity, and bearing to establish a wheel/rail system coupling dynamics model. Then, based on the coupling dynamics theoretical model, the wheel/rail system’s coupling nonlinear dynamic characteristics are studied under random load. Then, this theoretical model of the wheel–bearing–rail system dynamics is verified using the railway bearing as an example. Finally, the model is applied to the process of rail/wheel low force design. Results show that under irregular stimulation, the maximum contact load increased by 71.2% and the maximum contact stress increased by 19.6%. After moderate wear, the wheel/rail system vibration and loading condition deteriorate rapidly. Under the low rail/wheel force, the wheel tread and diameter had significant effects on wheel/rail contact force distribution. The rail specifications are found to affect the wheel/rail system’s vibration significantly. This paper has important theoretical value and practical significance for developing reliable railway bearings and wheel/rail systems with good static/dynamic characteristics that can withstand dynamic impact load.