Spline Shaft Research Articles

A measurement method for the axial bending deformation of parts with circumferential cycling element based on laser profile sensor

Abstract The cross-section of the CPP (circumferential periodic parts) is composed of fixed shaped elements regularly arranged in the circumferential direction, examples include cylinders, positive prisms, lead screws, gear shafts, and spline shafts, it has applications in many fields. Existing research has not yet proposed a universal method for measuring the axial bending of CPP. This paper presents a non-contact measurement method using a laser profile sensor that is capable of measuring axial bending of CPP. The axis of a shaft part is determined by connecting the geometric center of each cross-section. This method is suitable for measuring the bending deformation of most CPS (circumferential periodic shaft parts). To verify the validity of this method, numerical simulation calculations are conducted on cylinders, hexagonal prisms, and lead screws. Additionally, comparative experiments are performed on lead screws using self-built experimental platform and a measuring projector to investigate the effectiveness and repeatability.

The Wear Behaviour of a New Eccentric Meshing Reducer with Small Teeth Difference

Eccentric meshing reducers are widely used in agriculture, industrial robots, and other fields due to their ability to achieve a high reduction ratio within a compact volume. However, the contact wear problem seriously affects the service performance of the eccentric meshing reducer, thereby limiting their range of applications. To effectively address this issue, this study involved a stress analysis of the contact pairs and a surface wear analysis of a new eccentric meshing reducer. The wear equation for the contact pairs was derived using Archard’s wear theory, incorporating geometric and material parameters from both the reducer gear contact pair and the spline contact pair. In parallel, a wear simulation was conducted by integrating the UMESHMOTION subprogram with ALE adaptive grids. Additionally, the effects of load amplitudes on contact pair stress and surface wear were systematically investigated. It is revealed that the contact pair stress of the reducer gear was higher than that of the spline contact pair. Furthermore, the internal spline exhibited the highest wear rate, followed by the output shaft gear, external spline, and input shaft gear, in that order. This work provides a comprehensive and in-depth understanding of the wear behaviors of general reducers with small teeth differences and offers valuable scientific references for design optimization, fault diagnosis, and maintenance strategy formulation.

Manufacturing design of plain milling technology of spline shaft by formed disc-type milling cutter

Abstract The spline fittings are widely used in different mechanical constructions where high load transmission is required from a shaft to a spline plate or a tooth gear or other internal cylindrical element. In many cases a key joint connection can not bear the load that we want to transform. In this case the application of double key could give solution. But sometimes it does not give solution due to the high load that is why spline fitting should be used. This publication focuses for the manufacturing of the spline shaft with plain milling technology. The type of the tool is a formed disc type milling cutter. Since more splines are around the perimeter of the shaft the repetition of the milling process is needed in the function of the number of the splines. All of the manufacturing parameters will be determined that are needed for a complex technological analysis such as cutting forces, machining times, speeds, etc. The chip volume will be approximated by volume constancy since the separated chip volume is a quite complex geometric body. I will prescribe initial technological parameters and define existing shaft geometries for which I will determine the technological parameters to show and analyze the correlations between the technological parameters and the variable for each shaft.

Noncontact measurement of rectangular splines shaft based on line-structured light

Abstract The rectangular spline shaft, a typical type of shaft-tooth component, plays a significant role in mechanical transmissions. Existing methods for detecting size and positional tolerance in spline shafts often rely on contact-based measurement techniques, including specialized gauges and coordinate measuring machines (CMMs). To enhance the measurement efficiency, this paper proposes a method for measuring based on line-structured light. Firstly, a classification algorithm for data points on major and minor cylindrical surfaces and keyway surface of spline shaft is established, contributing to the automatic measurement. Secondly, a coaxiality error measurement model is established based on the overall least squares method, improving the measurement accuracy. Finally, a measurement model for key width and positional tolerance is established through the rotation of the spline axis. In experiments, the size and positional tolerance of the spline shaft obtained using this method are compared with measurements by CMM, meeting the general machining accuracy requirements.

The effect of floating spline parameter on the dynamic characteristic of encased differential planetary gear train

The load sharing performance of encased differential planetary system has a great impact on the operating performance and service life of the transmission system of the coaxial high speed helicopter. In order to improve the load-sharing performance of the gear pair, the influence of different floating spline structural parameters on the load sharing characteristics of the system was studied. Considering the manufacturing error, installation error, time varying meshing stiffness and other factors, the Lagrange equation is used to construct the dynamic model of encased differential planetary gear train with floating spline structure. The effects of input torque, spline clearance, spline shaft stiffness and spline friction coefficient on the load sharing performance of gear pairs were analyzed. The results show that the differential stage system has a better load sharing performance than the encased stage system. The increase of input torque helps to improve the load sharing performance of the system, and the improvement of the encased stage system is more obvious. The floating spline of sun gear of the encased stage has a greater impact on the load sharing performance of the system. Furthermore, increasing the floating spline clearance, reducing spline shaft stiffness or increasing the friction coefficient of the spline can improve the load sharing performance of the system overall.

Study on bending fretting fatigue behaviour of 15-5PH stainless steel with different fretting regimes

The failure of the aircraft spline shaft was attributed to overstressing, cyclic bending loads, and other complex conditions. This study investigates the bending fretting fatigue behaviours and failure mechanisms of 15–5PH stainless steel. The study analysed the residual stress, microstructure, morphology, and chemical state of the worn surface and the fatigue failure mechanisms. The results showed that fretting wear significantly reduces the bending fatigue life. The surface residual stress transitions from compressive to tensile stress states. The value of residual stress increased, and the oxygen content of the worn surface was higher in the mixed fretting regime. Fatigue fractures occur at a depth of 50–100 µm below the surface in the present experiment.

Effects of Material Properties on the Teeth Accuracy of Spline Shafts in Cold Form Rolling

Effects of Material Properties on the Teeth Accuracy of Spline Shafts in Cold Form Rolling

FIELD EXPERIENCE OF DOWNHOLE EQUIPMENT OPERATION IN HYDROGEN SULFIDE-CONTAINING ENVIRONMENTS

The article describes the results of operation of downhole equipment in hydrogen sulfide-containing media in relation to local and corrosion-mechanical failures. Useful life (without anti-corrosion protection) for most common manganese steel tubing before the appearance of through fracture was shown. The minimum concentrations of H2S and CO2 in the water phase for wellhead sample are shown when determining the degree of corrosivity of well media and types of corrosion depending on their concentration, in relation to carbon and low-alloy steels. The corrosion-mechanical destructions the downhole equipment were visualized according to GOST 53679. The necessity of taking into account the tendency of stainless steel grade 40Х13 (foreign analogue in the USA is AISI 420) of intersection splined couplings and shafts of an electric centrifugal pump unit made of steel grade 05Х16Н4Д2Б (foreign analogue is not defined) to hydrogen embrittlement as a result of exposure to acidic compositions (12–15 % HCl), used in technological operations, is shown. Practical solutions are proposed for tubing resistant to local and corrosion-mechanical failures (by steel grades and strength groups) based on the proposals of a domestic manufacturer. Two main factors are shown that reduce the service life of tubing and couplings to them to one year. Four polymorphic forms of iron sulfide (the main products of hydrogen sulfide (H2S-) and mixed (CO2 + H2S) corrosion), the conditions for their formation and the maximum rate of local corrosion, up to a through ulcer, under sulfide deposits, were identified. The statistics of tubing by steel grades and the percentage of their use in the fields operated by the Company are shown.

An Analysis of Stress Distribution in a Spline Shaft Subjected to Cycilc Impulsive Load

In this paper the effect of engagement length, number of teeth, amount of applied load, wave propagation time, number of cycles, and initial crack length on the principal stress distribution, velocity of crack propagation, and cyclic crack growth rate in a spline coupling subjected to cyclic torsional impact have been investigated analytically and experimentally. It was found that the stresses induced due to cyclic impact loading are higher than the stresses induced due to impact loading with high percentage depends on the number of cycles and total loading time. Also increasing the engagement length and the number of teeth reduces the principal stresses (40%) and(25%) respectively for increasing the engagement length from (0.15 to 0.23) and the number of teeth from (8 to 10). while increasing the other parameters (amount of applied load, wave propagation time, number of cycles, and initial crack length) increase the principal stresses at the root of the tooth (37% when the applied load rises from (8 KN to 11KN) and (62% when the wavepropagation time rises from (0.5 to 1).

Dynamic modelling of gear–spline system with nonuniform spline clearance and wear evolution of spline

The gear–spline system consisting of the internal spline of gears and the external spline of shafts is widely used in mechanical transmission systems. However, considering the nonuniform spline clearance caused by the assembly and manufacturing errors, the vibration characteristics of the system and the spline wear mechanism are still unclear. This article proposed a dynamic model of the gear–spline system with nonuniform spline clearance and wear evolution of spline. Compared with the existing models, the new contribution of this article is to reveal the coupling vibration mechanism of the gear–spline system under the condition of nonuniform spline clearance through the dynamic model. On this basis, the support stiffness characteristics and wear evolution law of the spline pair under the dynamic gear meshing force are studied. The results show that under the condition of nonuniform clearance, the displacement response of the system is modulated by the rotation frequency, and the motion trajectory tends to be chaotic. The load distribution of spline teeth and the equivalent stiffness of the spline depends on the number of loaded spline teeth, which in turn depends on the input torque and clearance distribution. In addition, the spline teeth with smaller clearance bear more loads and wear faster, and the wear causes the nonuniform clearance to gradually increase and become uniform. This study can provide theoretical guidance for revealing the vibration mechanism of the gear–spline system and calculating the support stiffness of the spline shaft.

Analysis of factors affecting the wear failure of an aeroengine spline pair and evolution mechanism of the tribolayer

Involute spline shafts are widely used in aerospace applications. Splines often undergo severe failure due to wear under complex operating conditions, and their life expectancy often falls short of expectations. We simulated and characterized an aero-engine involute spline that failed after 1000 h of actual flight in an aero-engine. The results showed that the local stress concentration area analyzed in the simulation matched the actual area that underwent severe wear in the spline pair. The microstructure and misalignment of the involute spline subsets affected the wear and loss of efficiency. The fretting tribolayer was analyzed using ion beam in situ cutting and high-resolution transmission characterization techniques. High-density dislocation lamellar structures and oxide nanoparticles formed by martensite that underwent strong plastic deformation in the tribolayer were present, and microcracks were found in both the nanosized lamellar structure and oxide particles. Based on combining the above characterization results, the microscopic mechanism and a model of drive shaft failure were proposed. Cracks that formed inside brittle oxides and the nano-scale lamellae were the main causes of the eventual failure due to fretting wear. The above mechanism provides a theoretical basis for deepening the understanding of the process and essential reasons for spline pair failure as well as improving the production process and increasing the service life of spline pairs.

Simulation of the distribution of temperature, stresses and deformations during splined shafts hardfacing

This article describes the process of modeling the restoration operations of the destroyed segment of the spline and its complete restoration using modern methods, such as hardfacing in a protective gas environment with a consumable electrode. The ANSYS Workbench 19.2 software with an additional Welding Distortion and Moving Heat Source extension was used to simulate the process of hardfacing a damaged surface. The thermomechanical behavior of the deposited layer on the outer surface of the splined shaft is analysed. Dependences of the value of temperature fields on the parameters of the hardfacing mode in one and two passes depending on time are established. Dependences of residual stresses (0.413-239 MPa) and deformations (0.02-0.23 mm) in the process of semi-automatic hardfacing are determined. Experimental studies of samples during hardfacing were carried out for comparison with the geometry of the weld during modeling. The simulation results are in good agreement with the experimental data.

NUMERICAL SIMULATION OF ELASTIC-PLASTIC DEFORMATION OF TORSION SHAFTS OF VEHICLE SPRING SYSTEMS, TAKING INTO ACCOUNT CONTACT INTERACTION

The paper develops a model of stress-strain state of torsion shafts. A variable formulation of the problem on the basis of the theory of variational inequalities was made. Numerical modeling of the stress-head-deformed state was made with the involvement of the finite element method. In the model of the stress-head-deformed state of torsion shafts, its generalized parametric description is integrated. It contains both varied significant design and technological indicators, in particular, the structural design of the torsion head, the galley transition and the diameter of the stem torsion shaft stem, and the parameters of the technological process of double winding: twist angles and features of the shaft material. It is established that the stresses that occur in the torsion shaft are mainly concentrated in the contact interaction zone of the spline shaft head with the spline coupling. The parametric dependencies of the level of equivalent stresses by Mises on the level of double windings and on the ratio of the head diameter and the stem of the torsion shaft stem have been determined. Recommendations have been developed regarding the improvement of strength characteristics of torsion shafts. Contact pressure distribution on the slots of the torsion bar head is also determined. Its characteristic features depend on the type of boundary conditions. If bilateral interaction is enabled on the boundary, the contact pressure may become negative. Furthermore, the contact pressure gets a sharp spike. This non-physical feature disappears if unilateral contact conditions are imposed. Therefore, this version of the boundary conditions is more adequate. It was used to compute the stress-strain state of a torsion bar, taking into account the plastic deformation of the material and the contact interaction with conjugate bodes. Keywords: torsional shaft; stress-strain state; finite element method; theory of variational inequalities; contact interaction

Fracture analysis on involute spline of large tunnel boring machine

The main drive spline shafts of two large tunnel boring machines were broken after service of less than 150 h. The failure located at the section flush with the end of the spline sleeve. Different from the gear fracture occurred at the tooth roots of the working side, the spline fracture started from the tooth roots of the non-working side. The non-working side cracks were wider and longer than these of working side, and their damage were more serious. At the failed roots, there were obvious fan-shaped shellfish lines which these were significant fatigue characteristics. Through chemical composition test and metallographic analysis, the spline shaft material was speculated to be 17CrNiMo6, and quenched and tempered heat treatment. The microstructure was mainly bainite with tempered martensite and retained austenite. The micro-hardness was uneven and fluctuated between 31 and 43HRC. Sulfide inclusion was grade 2 and alumina inclusion was 2.5. The calculation by finite element method (FEM) showed that the maximum stress was located at the tooth root of the non-working side. The safety factors calculated by three methods were less than 1.0. Therefore, the root cause of spline failure is improper design and heat treatment. Failure analysis, theoretical calculation and simulation test show that the failure mode was torsion fracture.

Multiple Drive Shaft Fractures in Lift Oil Pumps

Abstract Several high-pressure lift oil pump failures were reported from the field. These assemblies are used to inject lubrication oil into the sliding bearings of heavy rotating turbomachinery equipment, such as steam and gas turbine rotors, often weighing in excess of a hundred tons. This ensures that the rotor shaft “floats” on a lube oil film even at low rotational speeds, when hydro-dynamic lubrication conditions have not yet been fully established. A fractured spline shaft, which was the driven shaft of one of the failed pumps, was received from the client for the determination of the metallurgical root cause of failure. The subject spline shaft failed due to torsional overload. This cracked the hardened case and initiated high cycle fatigue (HCF) cracking as secondary damage. The main fatigue cracks were nucleated at overload fractures in the hardened case, in the fillet radii at the base of the teeth of the spline shaft. No evidence of any material defects that could have contributed to the failure or could even have been causative for it was found.

In situ ground settlement sensor for oil-tank monitoring by combining a fiber-optic low-coherent interferometry with a fine mechanical design.

An in situ robust ground settlement (IR-GS) sensor was designed to meet the requirements for oil-tank health monitoring by combining a low-coherent fiber-optic interferometry with a fine mechanical spline shaft. A floating mirror was mounted on the shaft and moved up and down along with the liquid surface. The liquid-contained chambers were hydraulically connected at the bottom by using a liquid-filled tube. The liquid level inside each chamber was initially at equal level. One of the chambers was fixed on a steady ground point, which was chosen in a surveying point of view and served as a reference. The others were distributed around an oil tank and separated the tank's perimeter into eight equal spans. Thereby, the health states of the oil tank were able to be evaluated based on these sensing results. Interrogation of the sensor was employed via a low-coherent fiber-optic Michelson interferometer. One path of the interferometer was composed by the floating mirror, whereupon a light was reflected. The other path was projected to a mirror that was fixed on a stepping motor. Therefore, the corresponding liquid level could be optically surveyed. Differential settlements between each chamber and the reference served as a measure of how much the liquid level was changed from its initials. Experimental tests demonstrated that this IR-GS design, with the optimized shape and weights of the spline shaft, could overcome the error caused by dust, hysteresis, temperature, etc. and meet the practical requirement in the accuracy of ±0.5mm. A practical application was carried out, and its long-term stability has been proved.

Reliability Analysis of Critical Systems in A Fuel Booster Pump Using Advanced Simulation Techniques.

The fuel booster pump is one of the most vulnerable physical assets in an operating engine due to the harsh environmental and operational conditions. However, because of its high structural complexity and extreme operational conditions, the reliability design of the fuel booster pump becomes especially difficult, particularly by means of experiments. Thus, to overcome such a problem, advanced simulation techniques have become adequate solutions for the reliability assessment and analysis of a fuel booster pump at the design stage. In this paper, by considering the effects of the uncertainties of multiple design parameters, fatigue life distributions of the four key components (which are the sealing bolt, spline shaft, graphite ring, and inducer, respectively) in a fuel booster pump were first predicted by PoF-based reliability simulations. Then, through further sensitivity analysis on each key component, the design parameters most sensitive to the component mean fatigue life were detected from a total of 25 candidate parameters. These parameters include the “nominal diameter” and “preload” for the sealing bolt, “major and minor diameters of the small spline” for the spline shaft, “inside diameter” for the graphite ring, and “fuel pressure on the blade front surface” for the inducer, respectively. These sensitivity results were found to be in good agreement with the results from the qualitative cause analysis on each key component.

Experimental investigation and numerical analysis of axle spline shaft analysis for different materials

This paper presentsan investigation of numerical analysis of splined shafts made of various materials. These axle spline shafts are subjected to torsional stress to determine if they can withstand the load without failing. The investigation aims to identify the best material type that can withstand high torsional stress levels. Additionally, a Calyx simulation has been used to examine the effects of tooth error. The experiment was conducted to determine the effect of the spline axle shaft's mechanical and chemical endurance strength. The troptometer is used to determine the angular distortion of a bar or piece that has been subjected to torsion. Torsion tests are conducted using a torsion testing machine, and numerical simulation is performed using Ansys software. The result indicates that AISI 1040 torqued between 2800 and 3000 lb-in until it reached a breaking point. AISI 1050 produced between 5700 and 6000 lb-in of torque until it reached its limit. AISI 1340 reached a maximum torque of approximately 8000–8500 until it reached a breaking point.

Analysis of the Spline Shafts Reliability by Machine-Building enterprises

Analysis of the Spline Shafts Reliability by Machine-Building enterprises

Improving the productivity of Pini-Kay fuel briquettes by modernizing the working part of the PSH-250 press

The research related to the productivity of production of fuel briquettes of the "Pini-Kay" type, due to the modernization of the working part of the press line for the production of fuel briquettes with a capacity of 250 kg / h (LVB - 250) was carried out. It is known that the press used on this line is PSH-250, it is the main working equipment of this line, as it serves to press the briquette under temperature and is the closing link in the whole briquette process. In the presented study, the main criterion of productivity was considered to be the number of manufactured products before the break of the splined auger, because the breakdown forces to stop the equipment and replace it. This in turn reduces the number of manufactured products. The paper states that the modernization was carried out as follows: the slot screw, which is the main working body of the press PSH - 250, made of structural steel (steel 45) by casting, was replaced by a slotted screw made by machining on CNC machines, high-quality structural alloy steel 40HMFA. This steel is used to make splined shafts, connecting rods and rods, and is best suited for making a splined auger. In addition, to increase the structural strength, the workpiece of the auger, was made heat treatment - normalization. The proposed technological solution allowed to increase the productivity of fuel briquettes, by reducing the downtime of equipment for repair and replacement of working parts of the press PSH-250. This in turn reduced the company's financial costs for spare parts and affected the cost of finished products. The obtained results show that the slotted augers proposed by the authors allowed to increase the productivity of fuel briquettes production almost 10 times in comparison with the previous results.