General shell model for a rotating pretwisted blade

TLDR: In this article, a novel dynamic model for a pretwisted rotating compressor blade mounted at an arbitrary stagger angle using general shell theory and including the rotational velocity is developed to study the eigenfrequencies and damping properties of the pre-strained rotating blade.

About: This article is published in Journal of Sound and Vibration.The article was published on 2013-10-28 and is currently open access. It has received 67 citations till now. The article focuses on the topics: Angular velocity.

Figures

Figure 1: The scheme of the rotating blade model.

Figure 5: The influence of the radius of the disk (r̄ = 0, 0.5, 1, 1.5, 2, 5) on the predicted eigenfrequencies; q = 0.8, l̄ = 2, t̄ = 40, ϕ = 30◦ and θ = 60◦.

Figure 2: Convergence study of a rotating pretwisted blade; q = 1, l̄ = 2, t̄ = 40, r̄ = 1, ϕ = 30◦ and θ = 60◦.

Figure 6: Modal damping ratios at the first 10 eigenfrequencies; q = 0.5 v 6.5, l̄ = 2, t̄ = 40, r̄ = 1, ϕ = 30◦ and θ = 60◦.

Figure 7: Exponential damping factors at the first 10 eigenfrequencies; q = 0.5 v 6.5, l̄ = 2, t̄ = 40, r̄ = 1, ϕ = 30◦ and θ = 60◦.

Table 5: Comparisons of the non-dimensional eigenfrequencies p, θ = 60◦, l̄ = 2, t̄ = 40 and r̄ = 0.

Frequently asked questions

Q1. What are the future works mentioned in the paper "General shell model for a rotating pretwisted blade" ?

This model allows to study the dynamic behavior of a rotating pretwisted blade of arbitrary thickness, stagger angle and pretwist. If the modal damping ratio exchanges due to frequency loci veering are kept in mind, it can be concluded that for the lower part of the rotational velocity range considered, the modal loss factors decrease as the rotational velocity increases. 

Q2. What are the contributions in "General shell model for a rotating pretwisted blade" ?

A novel dynamic model for a pretwisted rotating compressor blade mounted at an arbitrary stagger angle using general shell theory and including the rotational velocity is developed to study the eigenfrequencies and damping properties of the pretwisted rotating blade. Furthermore, frequency loci veering as a result of the rotation velocity is observed. The proposed model is an efficient and accurate tool for predicting the dynamic behavior of compressor blades of arbitrary thickness, stagger angle and pretwist, potentially during the early designing stage of turbomachinery. 

Q3. What is the eigenvalue analysis for the free vibration case?

In the eigenvalue analyses for the free vibration case the external forcing term is set to zero, but the Coriolis terms are included, leading to complex eigenvalues. 

Q4. What is the modal damping factor for the first two modes?

For higher rotational velocities the exponential damping factor increases for the first two modes as the rotational velocity increases and continues to decrease for the higher order modes. 

Q5. What is the advantage of the proposed general shell model?

The advantage of the proposed general shell model is that it is fast and easy to vary parameters, which is quite useful to investigate a number of possible blade configurations in the beginning design phase. 

Q6. What is the simplest way to describe the dynamic behavior of a rotating blade?

The parameters of the twisted blade, of rectangular cross-section, are: the length of the blade along xaxis L; the width b ; the thickness h; the density ρ; the Young’s modulus E; Poisson’s ratio µ and the rotation velocity Ω.Several coordinate systems are defined in this paper for dynamic modeling. 

Q7. What is the effect of the thick shell theory on the damping value of a rotating blade?

It is shown that, due to inertial and Coriolis effects, damping decreases as the rotation velocity increases for the lower part of the velocity range considered and either decreases or increases depending on the mode order for higher velocities. 

Q8. What is the effect of frequency loci veering on the modal damping ratio?

If the modal damping ratio exchanges due to frequency loci veering are kept in mind, it can be concluded that for the lower part of the rotational velocity range considered, the modal loss factors decrease as the rotational velocity increases. 

Q9. Why have beam models been used extensively in the literature?

Due to their simplicity, beam models have extensively been applied in the literature [3, 4, 5, 6, 7, 8, 9] to study the dynamic response of a single rotor blade. 

Q10. What is the thick shell theory used to describe the deformation of a rotating blade?

According to the thick shell assumption, three displacement and two rotation angle variables are used to describe the deformation of the blade in a rotating reference system, including the effect of the rotational stiffening and Coriolis acceleration. 

Q11. What is the rotation velocity of a damped blade?

A damped pretwisted blade (pretwist angle θ = 60◦) mounted at a 30◦ stagger angle is studied with the rotation velocity q = 0.5 − 6.5. 

Q12. Why is the 2D shell model stiffer than the general shell model?

This is expected, since the 2D shell model is stiffer than the general shell model because the ζ coordinate is not considered in the 2D shell model. 

Q13. What is the difference between the 2D and the general shell theory?

In other words, with respect to the thin shell theory, the thick shell theory has more degrees of freedom to describe the structure, which leads to a relatively flexible structure, finally resulting in decreasing the eigenfrequencies. 

Q14. What is the description of the two-dimensional shell theory?

While in [23, 24], the vibration of the non-rotating twisted composite blade is investigated, where a detailed description about the two-dimensional shell theory is given. 

Q15. What is the simplest way to describe the deformation field on the blade?

 k. (4)This coordinate system can be used in thin shell theory to describe the deformation field on the blade, assuming small blade thickness [10].