Involute Spline Research Articles

Fractal theory-based contact analysis of surface microtextured involute spline coupling

Accurate estimation of the contact stress of the aviation involute spline coupling is the basis of accurate estimation of its wear. In view of this, in this work, a fractal contact coefficient for involute spline coupling with surface texture based on the gear fractal contact model and M-B fractal contact model was established. Then, the relationship between fractal dimension and actual contact area, as well as the relationship between actual contact area and load were derived. And also, a fractal contact model for involute spline coupling with surface texture was established. Finally, the influence of geometric parameter on the contact coefficient and fractal contact model was analyzed. The results indicate that: the fractal dimension (D), roughness amplitude parameter (G), and material property parameter (ϕ) have important effects on the fractal contact model of involute spline coupling on the tooth surface; There must be an appropriate fractal dimension (D) value that makes the contact state optimal; As the roughness amplitude parameter (G) value increases, the surface contact condition deteriorates and the surface contact strength decreases. Conversely, as the material property parameter (ϕ) value increases, the surface contact condition improves and the surface contact strength increases. It is a preliminary exploration for accurately calculating the contact stress of involute spline coupling, laying a solid theoretical foundation for accurately predicting the wear of involute spline coupling with surface texture.

Dynamic characteristics of rotor system with parallel and angular misaligned involute spline coupling

Dynamic characteristics of rotor system with parallel and angular misaligned involute spline coupling

Thermal characteristics analysis of hydrostatic lubrication of involute spline guideway

Thermal characteristics analysis of hydrostatic lubrication of involute spline guideway

Nonlinear dynamic meshing force analysis of PEEK-based polymer composite involute spline coupling system

The dynamic meshing force affects the stability and wear life of PEEK polymer composite involute spline couplings, but most of the dynamic meshing force is obtained by empirical formula, and there is no effective calculation method in practice. Aiming at the viscoelasticity and nonlinear behavior of PEEK material, this work established a nonlinear dynamic model of the drive system of PEEK-based polymer composite involute spline pair by using the concentrated mass method, taking into account time-varying meshing stiffness, tooth side gap, and comprehensive transmission error, and obtained a dimensionless dynamic matrix that eliminates rigid body displacement. Aiming at the thermal stability of PEEK material, the dynamic meshing stiffness and dynamic meshing force of the involute spline of PEEK-based polymer composite were calculated by considering the thermal effect of misalignment and meshing deformation. The influence of misalignment on the dynamic characteristics of the system under dynamic and static loads was studied. The results show that the dynamic meshing stiffness and dynamic meshing force of involute spline coupling of PEEK-based polymer composite materials under misalignment represent complex nonlinear characteristics; Vibration, load, and viscoelastic deformation have an impact on transmission accuracy and efficiency; And the optimal selection range for friction coefficient, Poisson's ratio, and Young's modulus were determined within the parameter range of involute spline coupling of PEEK-based polymer composite materials as the matrix. It provides a theoretical foundation for designing high-performance, high-precision, and highly reliable PEEK-based polymer composite components.

Contact stress prediction and fretting wear measurement of aeronautic crowned involute splines

Splines are widely used in aeronautic applications; however, misaligned splines often suffer contact stress concentration and fretting wear fatigue failure. Crowned modification is a useful way to relieve contact stress concentration and mitigate fretting wear for misaligned splines, but it is unclear how this method works. In this study, contact stresses for involute splines are calculated using finite elements and correlated to first-hand experimental results on fretting wear obtained using a dedicated test rig. Both contact stress distribution prediction and fretting wear measurement indicate that the crowned magnitude of splines should be selected according to the operating angular misalignment.

Nonlinear characteristics of floating involute spline coupling in a hydraulic disc brake with inner hub rim crack propagation

Spline coupling is the key component in a hydraulic disc brake (HDB) system, which has been widely used in many high power density industrial machinery. Crack failure, as one of the most widespread and dangerous spline defects, directly threatens the operating safety of HDB system. To this end, a dynamic modelling method for floating involute spline coupling system is presented to study the nonlinear characteristics caused by inner hub rim crack propagation, which can consider the varying stiffness caused by rim crack, impact forces of spline teeth pairs, and non-uniform clearances between spline teeth of floating friction plate and inner hub. Results show that both rotational speed fluctuation, impact force, acceleration and trajectory achieve nonlinear trends with crack propagation, among which the gradient of impact force outperforms other characteristics and may be suitable for crack detection. Besides, the stiffness model with rim crack fault is validated by FEM. And an impact force test bench is established to verify the correctness of the proposed dynamic model. Experimental results reveal that the proposed model is suitable for the estimation of nonlinear behaviors of floating involute spline coupling with rim crack propagation.

Analysis of the approaches used for calculating involute splined couplings and the methods of considering their influence on the dynamic behavior of systems

Spline couplings, due to their high reliability and strength parameters, are widespread not only in mechanical engineering. The ability to transmit high torque with a sufficiently long service life has led to the extensive use of these couplings in the aircraft industry. Since this unit is under heavy loads in aircraft gas turbine engines, much attention is paid not only to strength characteristics, but also to the influence on the dynamic parameters of the rotor system. To mitigate the risks of destruction and the occurrence of defects, a large number of studies are carried out allowing us to evaluate the rotor system operation with splines and make a forecast of its behavior in the event of various factors leading to a change in the operation of splines. This paper provides a review of various methods, techniques and models of involute spline couplings used in the analysis of the dynamic behavior of rotor systems. The analytical models that allow us to take into account the coupling in various systems as well as finite element models that demonstrate the description of various processes in splines. The publications, devoted to the comparison of finite element models with analytical ones confirming the results associated with the dynamic characteristics of systems with an increase in radial and angular swashes, have been considered. The results of comparing the above models and their results with experimental research to verify and confirm various effects are also presented. The given research of rotor systems with swash allows for a conclusion about a significant spline influence, since they can cause a change in the coupling rigidity, redistribution of contact, increased loads in meshing, increased vibration amplitudes, change in the spectrum of excited frequencies and self-oscillatory processes due to various factors.

Design Method and Teeth Contact Simulation of PEEK Involute Spline Couplings.

In order to design an involute spline made of PEEK (polyetheretherketone)-based material with better performance and improve the design rules of involute splines, initially, an involute splines design theory for PEEK (polyetheretherketone)-based materials is presented, which combines international standards (ISO 4156, 1. 2. 3, 2005), American standards (ANSI B92.2M. 1989), and traditional empirical formulas. Second, using the involute splines calibration method in international standards as a guide, we developed the involute splines calibration method for PEEK-based materials by estimating the impact of energy consumption caused by viscoelasticity on temperature field calibration. Next, the contact characteristics of the designed spline were analyzed using ABAQUS2022 software to confirm the accuracy and reliability of the design and calibration methods. Finally, finite element simulation was used to analyze the influence of different pressure angles, moduli, combined lengths, and other parameters on the contact characteristics of the spline in order to realize the optimal design of PEEK-based material involute splines, to offer a theoretical foundation and improved design methodology for cylindrical straight-tooth involute splines.

A Study on the Influence of Nonlinear Vibration on Fretting Damage of Involute Spline Pairs in Aero-Engines

To meticulously examine the repercussions of nonlinear vibrations on fretting damage within aero-engine involute spline pairs, a dynamic model was constructed rooted in well-established theories and methodologies. MATLAB was engaged to resolve the model, where the vibration displacement function was treated under Fourier transformation. The emergent sub-model was then integrated into finite element analysis software to scrutinize the distribution curves of fretting damage over the external spline tooth surface. The analysis included a comprehensive comparison of the axial and radial distributions, in addition to scenarios with and without vibration interferences. Further, an empirical platform was devised to authenticate the outcomes harvested through finite element simulation. The results indicate that the principal mode of fretting damage failure in aero-engine involute spline pairs fundamentally comprises fretting wear. This wear occurs throughout the rotational period of the fretting cycle and reciprocally interacts with fretting fatigue phenomena. Significantly, it was ascertained that acute nonlinear vibrations escalate the magnitude of fretting damage and the quantity of worn teeth within aero-engine spline pairs. Beyond that, angular misalignment was recognized as an aggravating factor that compounds fretting damage in the secondary bond teeth of involute spline pairs. These newfound insights are of paramount significance for the strategic design of involute splines to combat wear.

Uncertainty quantification and probabilistic reliability analysis for the self-excited vibration of a spline-shafting system

Floating involute splines are widely used in large-torque, high-speed aerospace power transmission systems. The spline rotor system may suffer from self-excited vibration due to poor lubrication. The unavoidable manufacturing tolerances, mounting errors, component deformation, and other factors make the self-excited vibration occurrence conditions have significant uncertainties. This paper provides new insights into the uncertainty quantification and reliability analysis of self-excited vibration of a spline-shafting system based on an advanced Kriging surrogate model. First, a rotor nonlinear dynamics model considering tooth surface friction is established. Then an effective Kriging surrogate model is developed to quantify the uncertainty propagation in nonlinear rotor dynamics considering the randomness of parameters such as friction coefficient, and load torque, which enables the rapid estimation of statistical information of the self-excited vibration response by the time-domain numerical integration method. The probability of instability and reliability of the system under multi-parameter uncertainty for the occurrence of self-excited vibration is also predicted. Finally, the validity of the proposed method is verified by Monte Carlo simulation. This contribution will further enrich the theory and applications of probabilistic statistical analysis and reliability assessment of complex rotating machinery.

Модель шлицевого соединения для задач роторной динамики газотурбинных двигателей

Involute spline couplings are widely used in the aircraft gas turbine engine rotors. In the rotor dynamics problems, they are usually simulated by a link connecting the shafts. Rigidity characteristics of such a connection depend on a set of factors: forces acting from the connected shafts section leading to the shafts distortion in the spline coupling; torque transmitted by the splines; gaps between the splines; friction forces in the contact pairs. Taking into account all these factors is quite labor-intensive even in the finite element formulation. In addition, spline coupling is a nonlinear element, which characteristics depend on the engine operating mode. The paper presents an analytical model making it possible to account for all operating factors of a spline coupling. The model was verified using the finite element calculations.

Nonlinear dynamic analysis of floating involute splines considering comprehensive misalignment

In this study, a bending-torsion-axial dynamic model of floating involute spline coupling was established, considering the influence of misalignment. The dynamic characteristics of the spline coupling were analyzed under a parallel misalignment of 1.0×10−4 m or 2.0×10−4 m, an angular misalignment α of 0.1° or 0.3°, and the combined misalignment. A test bench for floating involute spline couplings was constructed to verify the accuracy of the dynamic characteristics under the theory. The results revealed that misalignment had a profound impact on the dynamic characteristics of the floating spline. Under the parallel misalignment of 2.0×10−4 m and the angular misalignment α of 0.3°, the force distribution on each tooth of the spline coupling was extremely uneven, which considerably reduced its performance and service life. As the floating distance gradually increases, the stability of the system decreases dramatically. The study laid a solid numerical foundation for the design of highly reliable, precise, and durable involute spline couplings for aviation use.

Mechanism and prediction method of fretting damage in involute spline couplings of aero-engine

Aiming at the serious fretting damage and failure of aviation involute spline couplings, this work proposes the fretting damage mechanism of involute spline couplings of aero-engine based on previous theories. The optimized Archard wear volume model and Smith-Watson-Topper critical surface method are used to establish the fretting damage prediction model of involute spline couplings of aero-engine. On this basis, the law of fretting damage is analyzed and its mechanism is verified by finite element simulation and experiment. The results show that the fretting damage failure mode of involute spline couplings of aero-engine is mainly fretting wear, fretting fatigue and fretting wear compete and influence each other. With the increase of contact stress and sliding distance, the fretting damage degree increases, but when it reaches a certain critical value, the fretting damage degree decreases. The fretting damage degree increases with the increase of angle mismatch and friction coefficient. The theory is in good agreement with the actual results, which provides a feasible way to study the fretting damage mechanism of other spline couplings.

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 and Verification of Involute Spline Tooth Surface Wear before and after Carburizing Based on Energy Dissipation Method

This work studies the tooth surface wear of floating involute spline couplings. Based on the energy dissipation method, this study takes the floating involute spline couplings as the research object, divides the whole wear cycle into three wear stages and analyzes its wear mechanism, and proposes a wear prediction model suitable for floating involute spline couplings. By using Abaqus, the simulation of the involute spline couplings before and after carburizing was carried out when the floating distance was 0 mm, 0.3 mm and 0.6 mm, respectively. The wear depth of each tooth was compared and analyzed, and the axial and radial distributions of the wear on the tooth surface of the involute spline couplings were explored. Finally, the floating involute spline couplings test bench was used to verify the spline wear before and after carburizing. The results show that with the increase in floating distance, the wear of the tooth surface also increases, and the upper edge of the tooth surface is seriously worn. Through the comparative analysis of the spline tooth surface wear before and after carburizing treatment, it can be seen that carburizing treatment can effectively reduce the wear degree of the spline couplings tooth surface and improve the service life of the spline couplings, but at a high floating distance, carburizing treatment has no significant effect on improving the performance of the tooth surface.

Contact analysis and strength calculations of involute spline couplings

A finite element method (FEM) is presented to conduct loaded tooth contact analysis and strength calculations of involute spline couplings. Special FEM software has been developed. Contact, bending and shear stresses of the spline couplings are analyzed by the developed software and they are compared with results obtained by an approximation method. It is found that “Edge loads” exist at tooth tip and root contacts and also exist at two sides of the face width when the pair of teeth has different face widths. Effects of tooth profile deviations and pitch errors on tooth contacts are also investigated by the developed software respectively. It is found that tooth contact and stresses are affected by the tooth profile deviations and pitch errors greatly. Finally, reliability of the presented method and software are discussed.

Prediction and Experimental Validation of Aviation Floating Involute Spline

Based on the research on the wear mechanism of floating involute spline coupling, combined with the traditional Archard wear equation, a wear prediction model of aviation floating involute spline coupling was established. The transient simulation of spline coupling with floating distances of 0 mm, 0.3 mm, and 0.6 mm was carried out using Abaqus, and the accuracy of the theoretical model was verified by analyzing the wear and failure parts of the spline coupling. The analysis results show that there is oxidation wear, adhesive wear, abrasive wear, and other wear forms on the tooth surface of the aviation floating involute spline coupling. Under the influence of the floating distance of the spline coupling, the calculation results are closer to the actual working situations. In addition, with increasing floating distance, the wear depth of the tooth surface increases significantly, and the wear depth becomes larger and larger along the floating end. The above study provides a theoretical basis for designing and maintaining aerospace involute spline couplings.

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.

Prediction of fretting damage and wear fatigue of floating involute spline couplings

In this paper, a finite element model of the floating spline pair is first established, and the distribution of the contact pressure on the tooth surface of the spline with the axis and angular misalignment is analyzed. Then, the effects of axial misalignment and angular eccentricity on tooth fretting damage were evaluated, based on Ruiz fretting damage parameters. Finally, a floating spline wear fatigue damage model considering the wear effect is established based on the energy dissipation and critical plane SWT model, and the fretting fatigue cumulative damage distribution and life of the tooth surface under axial and angular misalignment are analyzed and evaluated. The results show that the misalignment of the axis makes the contact pressure distribution of each tooth uneven, and the RFFDP value of the most dangerous tooth is parabolic along the x direction, that is, serious fretting damage may occur at both ends of the tooth surface, and the crack initiation position on the tooth occurs near x/L=0. The angular misalignment makes the tooth contact only at one end edge, and the RFFDP value of the most dangerous tooth increases along the x direction, showing an exponential growth trend, reaching the maximum at x/L=1, and the crack initiation position occurs at near x/L=1. With the increase of axis or angular misalignment, the damage phenomenon of the floating spline tooth surface becomes more obvious, and the wear-fatigue life decreases sharply.

Optimal shaft-hub connections

In all power transmitting machines the shaft-hub connection has a large impact on the overall machine size, if the strength can be increased we can reduce the size. The connection between shaft and hub is a machine element with many possible designs available and described in standards. The connection can be either permanent or changeable, the goal is in all cases to have as high a strength for the connection as possible. Focus is in the present paper on the connections with easy assembly and disassembly, that is, on positive connections (geometrically locked). The designs specified in standards are traditionally made with straight lines and circular arches. Alternatively the involute spline can be used. For this case the cutting tool shape is made with straight lines and circular arches. Present standard designs are not made with minimum stress concentrations as the main objective, other features as for example, easy manufacturing has the primary importance. In the present paper we show how the involute spline design can be significantly improved in relation to strength maximization by reducing the maximum stress. The maximum stress can in many cases be reduced by more than [Formula: see text] relative to standard design.