辉 马 | Northeastern University (original) (raw)

Papers by 辉 马

A dynamic model of rotating shrouded blades with impacts among adjacent shrouded blades is establ... more A dynamic model of rotating shrouded blades with impacts among adjacent shrouded blades is established considering the effects of the centrifugal stiffening, spin softening and Coriolis force, and the model is validated using finite element method. In the proposed model, the shrouded blade is simplified as a cantilever Euler–Bernoulli beam with a mass point at the free end, and the flexural dynamic stiffness of shrouded blade is selected as contact stiffness during collision. Based on the developed model, the effects of symmetric and asymmetric shroud gaps, rotational speeds, and aerodynamic force amplitudes on the dynamic characteristics of shrouded blades are analyzed through Newmark-β numerical method. The results indicate that (1) the vibro-impact responses of shrouded blades under some asym-metric gaps are more complicated than that under symmetric gap. (2) With the increase of rotational speed from 6000 to 10,000 rev/min, the system vibration experiences from period-three motion, through chaotic motion, finally to period-one motion during collision process because the increasing rotational speed changes the flexural dynamic stiffness of rotating blade. (3) The vibration displacements of shrouded blades increase linearly, and impact force increases linearly with the increase of aerodynamic force amplitude.

Considering the effects of extended tooth contact (ETC), revised fillet-foundation stiffness unde... more Considering the effects of extended tooth contact (ETC), revised fillet-foundation stiffness under double-tooth engagement region, nonlinear contact stiffness and tooth spalling defect, an analytical model for time-varying mesh stiffness (TVMS) calculation of spur gears is established. In addition, the analytical model is also verified by comparing the TVMS under different spalling widths, lengths and locations with that obtained from finite element method. The results show that gear mesh stiffness decreases sharply with the increase of spalling width, especially during the single-tooth engagement; the spalling length only has an effect on the beginning and ending of gear mesh stiffness reduction; the spalling location can affect the range of gear mesh stiffness reduction, and the range will reduce when the spalling location is close to the addendum. This study can provide a theoretical basis for spalling defect diagnosis.

An improved rotor-blade dynamic model is developed based on our previous works (Ma et al. in J So... more An improved rotor-blade dynamic model is developed based on our previous works (Ma et al. in J Sound Vib, 337:301–320, 2015; J Sound Vib 357:168– 194, 2015). In the proposed model, the shaft is dis-cretized using a finite element method and the effects of the swing of the rigid disk and stagger angles of the blades are considered. Furthermore, the mode shapes of rotor-blade systems can be obtained based on the proposed model. The proposed model is more accurate than our previous model, and it is also verified by comparing the natural frequencies obtained from the proposed model with those from the finite element model and published literature. By simplifying the casing as a two degrees of freedom model, the single-and four-blade rubbings are studied using numerical simulation and experiment. Results show that for both the single-and four-blade rubbings, amplitude amplification phenomena can be observed when the multiple frequencies of the rotational frequency (f r) coincide with the conical and torsional natural frequencies of the rotor-blade system, natural frequencies of the casing and the bending natural frequencies of the blades. In addition, for the four-blade rubbing, the blade passing frequency (BPF, 4 f r) and its multiple frequency components also have larger amplitudes, especially, when they coincide with the natural frequencies of the rotor-blade system or casing; the four-blade rubbing levels are related to the rotor whirl, and the most severe rubbing happens on the blade located at the right end of the whirl orbit.

This paper aims at the blade-casing rubbing in a shaft–disk–blade (SDB) system including shaft, d... more This paper aims at the blade-casing rubbing in a shaft–disk–blade (SDB) system including shaft, disk, blade and bearing, and focuses the effects of stagger angles of blades, rotational speeds and casing stiffness on the rubbing-induced vibration responses of the SDB system and casing. Firstly, a finite element (FE) model of an SDB system is developed, and the rubbing between the blade-tip and casing is simulated using contact dynamics theory. In the proposed model, Timoshenko beam elements are adopted to simulate the shaft and the blade, and shell elements to simulate the disk, and spring-damping elements to simulate the ball bearings. A point–point contact element is adopted to simulate the blade-casing rubbing. Moreover, the augmented Lagrangian method is utilized to deal with contact constraint conditions, and the Coulomb friction model is used to simulate the friction between the blade and casing. The proposed model is also validated by comparing the natural frequencies with those obtained from the published literature. The results indicate that (1) amplitude amplification phenomena can be observed when the multiple frequency components coincide with the torsional natural frequency of the SDB system and the bending natural frequencies of the blades under rotational state; (2) the torsional vibration features of the SDB system with blade-tip rubbing are more significant than the lateral vibration features of the shaft; (3) the torsional vibration of the SDB system increases, and the blade bending vibration reduces with the increase of the stagger angle of the blade; (4) period-2 motion may appear under the large casing stiffness and high rotational speeds, and the torsional vibration of the SDB system and blade bending vibration tend to increase with the increasing casing stiffness. Blade-casing rubbing has been regarded as a significant contributor to excessive maintenance and in general to engine failure. The rubbing may result in complicated vibration of the overall unit, and may reduce the system performance and the lives of the blade and the casing. Blade-casing rubbing is essentially nonlinear, which involves contacts, large displacements and deformations of the blade. Moreover, the rubbing may be characterized by significant interactions between the global dynamics of the shaft– disk–blade (SDB) system and local vibration of the blade [1]. Many researchers studied the blade-casing rubbing mechanisms and rubbing induced complicated nonlinear dynamic behaviors using cantilever beams to simulate the blades [2–6]. Padovan and choy [2] deduced the relationship between the normal contact force and the blade radial deformation by simplifying the blade as a cantilever beam. Considering the effect of the centrifugal force of the blade, Jiang et al. [3] derived the normal blade-casing rubbing force based on Padovan's model. Based on Jiang's model [3], Ma et al. [4] developed a revised model of the rubbing between the blade and flexible casing, and verified the revised model using experimental results. Sinha [5] presented many mathematical expressions about the impulse loading, such as half-sine wave, rectangular pulse or sawtooth pulse, and analyzed the vibration responses of the rotating Timoshenko beam under the impulse loading of the half-sine wave. Simplifying the blade and casing as the straight beam and curved beam respectively, Batailly et al. [6] analyzed the rubbing between the blade tip and the casing by adopting a combination of component mode synthesis methods with a contact algorithm based on the Lagrange multiplier technique. Because cantilever beam models are difficult to describe the blade torsional vibration, many researchers adopted cantilever plate models to simulate blade-casing rubbing [7,8]. Kou and Yuan [7] simplified two types of functions (sine wave and sine pulse

In this study, the dynamic characteristics of a slant-cracked cantilever beam are studied based o... more In this study, the dynamic characteristics of a slant-cracked cantilever beam are studied based on a new finite element (FE) model where both plane and beam elements are used to reduce the computational costs. Simulation studies show that the proposed model has the same system natural frequencies and vibration responses as those in the pure plane element model but is computationally more efficient. Based on the new model, the effects of loads such as gravity F g , excitation force amplitude F 0 and direction angles of excitation force φ, and crack parameters including slant crack angle θ, dimensionless crack depth s and dimensionless crack location p, on system dynamics have been analyzed. The results indicate that (1) the gravity has a more significant effect on the sub-harmonic resonance responses than on the super-harmonic resonance and resonance responses; (2) The amplitudes of the system responses at both excitation force frequencies f e and its harmonics such as 2f e and 3f e increase almost linearly with the increase of the excitation force amplitude F 0 ; (3) Under the constant excitation force in the flexural direction, the tensile and compressive forces along the longitudinal direction can lead to opposite breathing behaviors of the crack within the super-harmonic and sub-harmonic resonance frequency regions; (4) Vibration is most severe under the straight crack angle (θ¼ 90°) and near the straight crack angle such as θ¼100° and 110°, and the vibration responses under smaller or larger crack angles such as θ¼30° and θ¼150° become weaker; (5) The resonance at 2f e is sensitive to the faint crack signals when s is small and p is large. In addition, the significant vibration responses at the multiple frequency of 3f e and the fractional frequency of 0.5f e can be regarded as a distinguishable feature of the serious crack with large s and small p.

A dynamic model of rotating shrouded blades with impacts among adjacent shrouded blades is establ... more A dynamic model of rotating shrouded blades with impacts among adjacent shrouded blades is established considering the effects of the centrifugal stiffening, spin softening and Coriolis force, and the model is validated using finite element method. In the proposed model, the shrouded blade is simplified as a cantilever Euler–Bernoulli beam with a mass point at the free end, and the flexural dynamic stiffness of shrouded blade is selected as contact stiffness during collision. Based on the developed model, the effects of symmetric and asymmetric shroud gaps, rotational speeds, and aerodynamic force amplitudes on the dynamic characteristics of shrouded blades are analyzed through Newmark-β numerical method. The results indicate that (1) the vibro-impact responses of shrouded blades under some asym-metric gaps are more complicated than that under symmetric gap. (2) With the increase of rotational speed from 6000 to 10,000 rev/min, the system vibration experiences from period-three motion, through chaotic motion, finally to period-one motion during collision process because the increasing rotational speed changes the flexural dynamic stiffness of rotating blade. (3) The vibration displacements of shrouded blades increase linearly, and impact force increases linearly with the increase of aerodynamic force amplitude.

Considering the effects of extended tooth contact (ETC), revised fillet-foundation stiffness unde... more Considering the effects of extended tooth contact (ETC), revised fillet-foundation stiffness under double-tooth engagement region, nonlinear contact stiffness and tooth spalling defect, an analytical model for time-varying mesh stiffness (TVMS) calculation of spur gears is established. In addition, the analytical model is also verified by comparing the TVMS under different spalling widths, lengths and locations with that obtained from finite element method. The results show that gear mesh stiffness decreases sharply with the increase of spalling width, especially during the single-tooth engagement; the spalling length only has an effect on the beginning and ending of gear mesh stiffness reduction; the spalling location can affect the range of gear mesh stiffness reduction, and the range will reduce when the spalling location is close to the addendum. This study can provide a theoretical basis for spalling defect diagnosis.

An improved rotor-blade dynamic model is developed based on our previous works (Ma et al. in J So... more An improved rotor-blade dynamic model is developed based on our previous works (Ma et al. in J Sound Vib, 337:301–320, 2015; J Sound Vib 357:168– 194, 2015). In the proposed model, the shaft is dis-cretized using a finite element method and the effects of the swing of the rigid disk and stagger angles of the blades are considered. Furthermore, the mode shapes of rotor-blade systems can be obtained based on the proposed model. The proposed model is more accurate than our previous model, and it is also verified by comparing the natural frequencies obtained from the proposed model with those from the finite element model and published literature. By simplifying the casing as a two degrees of freedom model, the single-and four-blade rubbings are studied using numerical simulation and experiment. Results show that for both the single-and four-blade rubbings, amplitude amplification phenomena can be observed when the multiple frequencies of the rotational frequency (f r) coincide with the conical and torsional natural frequencies of the rotor-blade system, natural frequencies of the casing and the bending natural frequencies of the blades. In addition, for the four-blade rubbing, the blade passing frequency (BPF, 4 f r) and its multiple frequency components also have larger amplitudes, especially, when they coincide with the natural frequencies of the rotor-blade system or casing; the four-blade rubbing levels are related to the rotor whirl, and the most severe rubbing happens on the blade located at the right end of the whirl orbit.

This paper aims at the blade-casing rubbing in a shaft–disk–blade (SDB) system including shaft, d... more This paper aims at the blade-casing rubbing in a shaft–disk–blade (SDB) system including shaft, disk, blade and bearing, and focuses the effects of stagger angles of blades, rotational speeds and casing stiffness on the rubbing-induced vibration responses of the SDB system and casing. Firstly, a finite element (FE) model of an SDB system is developed, and the rubbing between the blade-tip and casing is simulated using contact dynamics theory. In the proposed model, Timoshenko beam elements are adopted to simulate the shaft and the blade, and shell elements to simulate the disk, and spring-damping elements to simulate the ball bearings. A point–point contact element is adopted to simulate the blade-casing rubbing. Moreover, the augmented Lagrangian method is utilized to deal with contact constraint conditions, and the Coulomb friction model is used to simulate the friction between the blade and casing. The proposed model is also validated by comparing the natural frequencies with those obtained from the published literature. The results indicate that (1) amplitude amplification phenomena can be observed when the multiple frequency components coincide with the torsional natural frequency of the SDB system and the bending natural frequencies of the blades under rotational state; (2) the torsional vibration features of the SDB system with blade-tip rubbing are more significant than the lateral vibration features of the shaft; (3) the torsional vibration of the SDB system increases, and the blade bending vibration reduces with the increase of the stagger angle of the blade; (4) period-2 motion may appear under the large casing stiffness and high rotational speeds, and the torsional vibration of the SDB system and blade bending vibration tend to increase with the increasing casing stiffness. Blade-casing rubbing has been regarded as a significant contributor to excessive maintenance and in general to engine failure. The rubbing may result in complicated vibration of the overall unit, and may reduce the system performance and the lives of the blade and the casing. Blade-casing rubbing is essentially nonlinear, which involves contacts, large displacements and deformations of the blade. Moreover, the rubbing may be characterized by significant interactions between the global dynamics of the shaft– disk–blade (SDB) system and local vibration of the blade [1]. Many researchers studied the blade-casing rubbing mechanisms and rubbing induced complicated nonlinear dynamic behaviors using cantilever beams to simulate the blades [2–6]. Padovan and choy [2] deduced the relationship between the normal contact force and the blade radial deformation by simplifying the blade as a cantilever beam. Considering the effect of the centrifugal force of the blade, Jiang et al. [3] derived the normal blade-casing rubbing force based on Padovan's model. Based on Jiang's model [3], Ma et al. [4] developed a revised model of the rubbing between the blade and flexible casing, and verified the revised model using experimental results. Sinha [5] presented many mathematical expressions about the impulse loading, such as half-sine wave, rectangular pulse or sawtooth pulse, and analyzed the vibration responses of the rotating Timoshenko beam under the impulse loading of the half-sine wave. Simplifying the blade and casing as the straight beam and curved beam respectively, Batailly et al. [6] analyzed the rubbing between the blade tip and the casing by adopting a combination of component mode synthesis methods with a contact algorithm based on the Lagrange multiplier technique. Because cantilever beam models are difficult to describe the blade torsional vibration, many researchers adopted cantilever plate models to simulate blade-casing rubbing [7,8]. Kou and Yuan [7] simplified two types of functions (sine wave and sine pulse

In this study, the dynamic characteristics of a slant-cracked cantilever beam are studied based o... more In this study, the dynamic characteristics of a slant-cracked cantilever beam are studied based on a new finite element (FE) model where both plane and beam elements are used to reduce the computational costs. Simulation studies show that the proposed model has the same system natural frequencies and vibration responses as those in the pure plane element model but is computationally more efficient. Based on the new model, the effects of loads such as gravity F g , excitation force amplitude F 0 and direction angles of excitation force φ, and crack parameters including slant crack angle θ, dimensionless crack depth s and dimensionless crack location p, on system dynamics have been analyzed. The results indicate that (1) the gravity has a more significant effect on the sub-harmonic resonance responses than on the super-harmonic resonance and resonance responses; (2) The amplitudes of the system responses at both excitation force frequencies f e and its harmonics such as 2f e and 3f e increase almost linearly with the increase of the excitation force amplitude F 0 ; (3) Under the constant excitation force in the flexural direction, the tensile and compressive forces along the longitudinal direction can lead to opposite breathing behaviors of the crack within the super-harmonic and sub-harmonic resonance frequency regions; (4) Vibration is most severe under the straight crack angle (θ¼ 90°) and near the straight crack angle such as θ¼100° and 110°, and the vibration responses under smaller or larger crack angles such as θ¼30° and θ¼150° become weaker; (5) The resonance at 2f e is sensitive to the faint crack signals when s is small and p is large. In addition, the significant vibration responses at the multiple frequency of 3f e and the fractional frequency of 0.5f e can be regarded as a distinguishable feature of the serious crack with large s and small p.