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Advances in Mechanical Engineering

Volume 2013 (2013), Article ID 609309, 9 pages

http://dx.doi.org/10.1155/2013/609309

## Dynamic Characteristics Research of a Steel/CFRP Drive Shaft

^{1}School of Mechanical and Electronic Engineering, Wuhan University of Technology, Wuhan 430070, China^{2}Lianyungang Yingyou Carbon Plastic Material Co., Ltd., Lianyungang 222000, China

Received 14 March 2013; Revised 11 July 2013; Accepted 17 July 2013

Academic Editor: Zhongwei Jiang

Copyright © 2013 Jinguang Zhang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

The dynamic characteristics of a steel/CFRP (carbon fiber reinforced plastic) drive shaft were studied. finite element analysis (FEA) and an experiment were carried out to investigate the natural frequencies and mode shapes. The results of the experiment verified the effectiveness of the finite element model. At the same time, the FEA was used to predict the dynamic characteristics of the shaft for different stacking sequences, fiber orientation angles, and layer thicknesses. The results show that the natural frequency increases with decreasing fiber orientation angles. And the positive and negative stacking sequences are helpful to improve natural frequency. The layer thicknesses and stacking sequences will have a pronounced effect in a specific size of the shaft.

#### 1. Introduction

In recent years, CFRP has been used in many engineering fields such as mechanical, automobile, aerospace and marine. This is mainly due to its excellent mechanical properties, such as high tensile strength-to-weight ratio, high temperature resistance, and low coefficient of thermal expansion.

CFRP can improve the natural frequency and critical speed and reduce the overall weight to achieve low noise, low transmission energy loss when it is used for the shaft’s manufacture. Different from the conventional metal shaft, there are many parameters to be altered in the design of the composite drive shaft, namely, the fiber orientation angles, stacking sequences, layer thicknesses, and number of layers.

Because of its anisotropy, CFRP can provide a large number of possible designs, which could satisfy the different dynamic performance requirements. So the dynamic performance of a steel/CFRP shaft, whose external dimensions are restricted, could be achieved by changing the parameters of the CFRP laminates.

There are some studies with respect to the influences of lamination parameters on the dynamic performance.

Badie et al. [1] examined the effect of stacking sequence on the natural frequency, buckling strength, and fatigue life. The results showed that the stacking sequence has almost no effect on natural frequency but great influence on the buckling strength and fatigue life. In the dynamic study of the composite material shaft, Singh and Gupta [2] learned that the stacking sequence has no significant effect on the natural frequency, while the natural frequency decreases as the stacking angle increases.But the conclusion which scholars have drawn is inconsistent. Shokrieh et al. [3] investigated the effect of variable stacking sequences and fiber orientation angles on buckling torque and found that the natural frequency decreases with the increasing torque. Sekhar and Srinivas [4] analyzed the slotted composite drive shaft’s vibration characteristics and learned that the natural frequency rises from 316 Hz to 367 Hz for different stacking sequences. Abu Talib et al. [5] came to the conclusion that in changing carbon fibers winding angle from 0° to 90°, the loss in the natural frequency of the shaft was 44.5%, while shifting from the best to the worst stacking sequence, the drive shaft caused a loss of 46.07% in its buckling strength.

The effect of fiber orientation angle for dynamic performance has been discussed by many researchers. Badie et al. [1] used FEA to predict the bending natural frequency of a hybrid shaft and drawn that the reducing fiber orientation angle increases the natural frequency and axial elastic modulus. Gubran [6] developed a CFRP/metal hybrid shaft and carried out an analysis of natural frequencies. The conclusion drawn was that the natural frequency depends on the ratio of the elastic modulus and density while it decreases as the angle increases. However, there are some new conclusions which are different from the above studies. Kim et al. [7] examined the effect of material properties on metal/CFRP hybrid shafts and drawn the conclusions that the frequency of the 0 case is lower than those of some nonzero fiber angle cases in specific , but when shafts are very long ( = 25), this phenomenon disappears, and the lower fiber angles give the higher frequencies.

In addition, many researches have been carried out to investigate the effect of thickness on the dynamic performance. Wang and Zhou [8] found that, in certain cases, an optimum thickness of steel could maximize the frequencies of the metal/CFRP hybrid shafts. Gubran [6] found that varying the layer thickness is helpful to improve the mechanical properties, increase the natural frequency by about 12%17%, and reduce stress. Wang and Zhou [8] used the FEA and experimental analysis to study the effects of the number of layers. The natural frequency increases with the increasing number. The first frequency increases by 8% when the number rises from 1 to 3. Lee et al. [9] manufactured a composite spindle and investigated the proper design for dynamic performance. They learned that increasing thickness will improve the vibration performance.

Generally, there are sufficient studies about the lamination parameters and their effects on the performance characteristics, but the conclusions are inconsistent. The study of the mode shapes of a steel/CFRP shaft is inadequate and so is the effect of layer thickness on the dynamic characteristics. Most researchers used the control variable method to study the effect of every single factor. However, at present, all the studies did not consider the coupling effect of multiple factors.

Therefore, in this work, investigations were focused on the effect of lamination parameters on the dynamic performance. To assess the dynamic characteristics, a steel/CFRP drive shaft was fabricated. The FEA method and experimental program on fabric test piece were used to investigate the dynamic characteristics. Finally, a study of natural frequencies and mode shapes was theoretically performed by FEA under single variable and double variables in order to enable the conclusion to be accurate and comprehensive.

#### 2. Design of Test Piece

An entire carbon fiber drive shaft is easy to be destroyed in the place of holes or grooves when connected to other components such as through key, stud, and flange. So the steel/CFRP drive shaft was designed using both steel and carbon fiber-epoxy composites in which the major role is to transmit the required torque. Taking into account the requirement, the dimensions of the steel part and the parameters of the composite were calculated.

##### 2.1. Design of Steel Part

The ultimate torque is 1500 Nm. The drive shaft must be designed to meet the requirement of torque capacity according to the equation of metal shaft’s torsional shear strength in mechanics of materials: .

In the formula, , is the diameter of steel part, and the safety coefficient is 1.5 corresponding to the design torque.

The calculated result mm. The thickness of the adhesive layer between the steel part and the CFRP part is 0.15–0.20 mm. In order to avoid the decimal of the dimension for easy manufacture, the selected diameter is 50.7 mm.

##### 2.2. Calculation on Carbon Fiber Part

The finite element software SAMCEF was used to calculate and check the torsion strength. The results were shown in Figure 1.

According to the Tsai-Wu criterion, the failure index was 0.817 when the applied torque was 1500 Nm. So, the above parameters of the carbon fiber part can satisfy the torsional strength.

The composite shell is used for the type of element in SAMCEF. While the CFRP tube was treated as orthotropic material, so the material properties of three different directions should be defined according to Table 1.

The stacking sequence was [45, −45, 90, 45, −45, 90, 45, −45, 45, −45, 45, −45, 90, 45, −45, 90, 45, −45].

The number of stacking piles was 18, and the layer thickness was 6 mm.

##### 2.3. Calculation of Adhesive Layer

The thickness of adhesive layer has an effect on the bonding strength. Increasing layer thickness can reduce stress concentration and improve the bonding strength. However, too thick layers may cause bubbles and other defects, leading to the decreasing of bonding strength. Practical experience shows that the appropriate thickness was 0.1–0.15 mm; herein, the final selected thickness was 0.15 mm.

The length of the adhesive layer was calculated according to the empirical equation (from the Practical Guide to Rubber Sealing Technology of Mechanical Products, 1995): [10]. In the equation, is the diameter of the glued tube. is the yield shear strength of the glued material.

In this design, mm, and refers to 45 steel tensile yield limit; then, the calculated shear yield limit is 177 Mpa. The shear strength of the carbon fiber is relatively small, and Mpa, so select Mpa for design.

The calculated result mm. Given the present bonding technique, increasing adhesive length is helpful to improve bonding strength, so, in this research, the final manufacturing length was lengthened to 150 mm. The test piece of CFRP/steel drive shaft was shown in Figure 2.

Figure 3 is the dimensional drawing of the test piece, in which part 1 refers to steel part and part 2 refers to the carbon fiber part. The carbon fiber-epoxy prepreg is T300/5208 manufactured by Lianyungang Yingyou Carbon Plastic Material Co., Ltd. Tables 1 and 2 show the mechanical properties of carbon fiber-epoxy composites and the 45 steel.

#### 3. Finite Element Analysis

The software SAMCEF has a good performance in the finite element analysis of composite materials, so it is suitable for the simulation of the steel/CFRP shaft. In the free mode of the model, the selected element is the combination of the shell and the solid without setting any constraints.

Figure 4 showed the simplified model of the steel/CFRP shaft. In this model, two ends of the drive shaft were made of steel and defined as solid elements. Because the holes in flange would reduce the meshing quality, they were removed to simplify the model. The middle of the drive shaft was a thin-walled tube made of CFRP and defined as composite shell elements. In addition, the adhesive layer was ignored and simplified by GLUE command for difficult simulation.

##### 3.1. Modeling, Loading, and Meshing

The steel part was considered as elastomeric material, while the CFRP tube was treated as orthotropic material, whose material properties were defined according to Tables 1 and 2. The order of stacking sequence, thickness and angle was from inside to outside. In order to make better for the continuity of the whole mesh, the tetrahedral mesh was chosen by taking into account the model transition region between the steel part and the CFRP tube, and the whole CFRP tube is meshed by mapping mesh. The ply of CFRP tube and the typical meshing were shown in Figures 5 and 6.

##### 3.2. Finite Element Results

The natural frequencies and mode shapes of the steel/CFRP shaft were shown in Table 3 and Figure 7.

In Table 3, there were two same frequencies such as 193 Hz, 672 Hz, which resulted from the symmetrical direction of the bending mode shape shown as Figure 7. Therefore, the top three natural frequencies of the test piece were 193 Hz, 513 Hz, 672 Hz, successively.

#### 4. Experiment and Conclusion

At present, excitation method is usually applied to study the structural dynamics in the field of aerospace, automotive, marine and construction engineering, and so forth. Especially after the invention of the FFT algorithm-based digital signal analyzer, the advantages of this method are more and more obvious. The basic principle of excitation method is that the excitation force is exerted on the stationary drive shaft in the frequency range of the resonant point to measure resonance frequency which is the excitation frequency corresponding to vibration peaks.

##### 4.1. Experimental Equipment

Figure 8 shows the modal testing machine which is supplied by the Danish BK Ltd. The machine consists of a power sensor, an acceleration sensor, a vibration exciter, an impulse hammer, a PULSE analyzer platform, and so on. And the modal analysis software ME’scopeVES can analyze and calculate the dynamic characteristics of the mechanical structure and, in addition, display the mode shapes and other industrial data on the three-dimensional model of the testing structure.

##### 4.2. Equipment Configuration

With two flexible strings at both ends, the test piece is suspended. It is in a free state and has a maximum degree of freedom. The free-free mode can only be obtained when the test is performed for a free-free boundary condition.

In the experiment, the exciter cannot reach the experimental requirements due to the narrow band. So the hammer is used to give excitation force, and the excited points were in the middle of the test piece’s upper surface.

Three acceleration sensors are arranged equidistantly on the upper surface of the test piece to convert the measured signal into electrical signals.

##### 4.3. Experiment Principle

Experiment modal analysis technique is the curve fitting according to measured transfer function curves to calculate the modal frequency, modal stiffness, and modal mass. The transfer function reflects the relationship between the system output and the input, that is, the complex ratio of the output and the input frequency, where, is the transfer function, is the Fourier transform transfer function of input (excitation), and is the Fourier transform transfer function of output (response). The above transfer function is not associated with the initial conditions of excitation system, and it only reflects the system’s inherent dynamic properties. So the complicated vibration system characteristics analysis can be transformed into a relatively simple analysis of the input and output signals, namely, the so-called system recognition, which provides the basis for the vibration characteristics analysis, the vibration fault analysis and diagnosis forecasting, and the optimal design for structural dynamic characteristics of the magnetic suspension rotor system.

##### 4.4. Testing Procedure

(1)Create the structure graphics of the test piece, and select hammer incentive mode as well as acceleration response measurement point.(2)Set excitation signal range, the trigger level, and time-domain window, in order to identify the appropriate frequency band.(3)Set exciting nodes, achieve 3 times valid inputs, and finally read the experiment data.

##### 4.5. Experimental Data

Figure 9 shows the frequency response function graph of test shaft. The first natural frequency of the test drive shaft is about 234 Hz, and the second natural frequency is about 596 Hz.

##### 4.6. Comparison and Discussion

The comparison was shown in Table 4. There was a different degree of deviation among the above three methods. The predicted first natural frequency agreed with experimental result with a deviation of 17.5%, while the second deviation was 13.9%. In the test, the higher the order of the natural frequency ranked, the lower the accuracy of the test results was.

The reasons for the deviation were summed up as follows.(1)There was a difference between the parameters of the test shaft and that of the ones in finite element analysis.(2)The rigid connection between the carbon fiber tube and metal was idealized to neglect the adhesive layer. In finite element analysis, the adhesive layer was replaced by GLUE command, and the hole of the flange was eliminated.(3)The arrangement of sensors was imprecise, and the intensity of each hammer excitation may not be homogeneous.

In short, the error was within the allowable range. It was proved that the finite element analysis could be used to predict the influence of various stacking parameters on the dynamic characteristics of the steel/CFRP shafts.

#### 5. Effect of Ply Stacking

Finite element models were developed to study the effects of ply stacking on the critical mechanical characteristics of the CFRP shaft.

##### 5.1. Fiber Orientation Angles

The FEA is used in this type of problems, and there is no need to apply a load because the natural frequency is the only function of mass and stiffness. The ends of the drive shaft are both simply supported. The fiber orientation angle is taken as one variation of the test piece. Some specific angles were in the test, such as 0°, 15°, 30°, 45°, 60°, 75°, −75°, and 90°.

The results are as follows in Table 5.

The results showed that the natural frequency increased as the angle decreased in the same condition. Sometimes it was not consistent, as the first natural frequency of stacking with the angle of 10° was greater than that with angles of 5° and 0°. The relationship of the fiber orientation angle and natural frequency is nonlinear because of the orthotropic material properties of CFRP. So, in practical design, under the premise of enough strength, it is useful to appropriately increase some ply angles to improve the natural frequency and stay away from the resonant frequency to achieve high stability, longer life.

##### 5.2. Monolayer Thickness

The monolayer thickness is taken as the variable, and the other parameters are invariant. The selected monolayer thickness is 0.11 mm, 0.22 mm, 0.33 mm, 0.66 mm, 0.99 mm, and 0.39 mm.

The results were shown in Table 6.

It can be found that monolayer thickness had little influence on the natural frequency. Compared with Table 6, for the stacking with an angle of 45°, the top three natural frequencies were 140 Hz, 390 Hz, and 521 Hz, whereas the angle 45° was replaced by alternately 45°/−45°; the top three natural frequencies changed into 173 Hz, 559 Hz, and 655 Hz. The same phenomenon occurred in cases that positive and negative angles were used alternatively. Therefore, maximization of the positive and negative fiber angles is to achieve not only convenient processing but also improve dynamic characteristics.

##### 5.3. Stacking Sequence

As an another variable of the stacking, some classical sequences were arranged as Table 7.

As was shown in Table 8, the stacking sequence had little effects on the first natural frequency but had a certain degree of impact on the second and third natural frequencies under specific conditions.

##### 5.4. Variable Thickness of Monolayer

Under the premise of the same fiber angles and entire thickness, the monolayer thickness was varied in the following cases as shown in Tables 9 and 10.

The above variable configurations had the same proportion of each angle. It is unnecessary to consider the influence of different angles. The comparison in Table 11 presented that natural frequencies would change apparently when the layers oriented at , and constant thickness of monolayer contributed to greater natural frequencies. But due to the limited size, the change of first natural frequency was not particularly remarkable. The change would be more apparent if the shaft size increased.

##### 5.5. Multiple Factors

It is known that most scholars focused on the effect of every single factor, leaving a blank for the research of multiple factors. The configurations of the test piece were taken as an example, and five cases were discussed in Table 12.

In Table 13, the top three configurations showed that the natural frequencies changed a lot because of varying fiber angles. Comparison between case 2 and case 4, as well as case 3 and case 5, different thicknesses, and number of layers contributed to the change of natural frequencies. In conclusion, the natural frequency was mainly determined by the selected angles, whereas the various thickness and number of layers just had a little effect on it.

#### 6. Conclusions

From the previously presented results, the conclusions are drawn as follows.(1)The natural frequency of the steel/CFRP drive shaft increases along with the decreasing of fiber orientation angle.(2)The stacking sequence has a little effect on the natural frequency.(3)Varying layer thickness can change the natural frequency of the steel/CFRP shaft, only if the shaft size is big enough.(4)The predicted natural frequency agrees with the analytical solution with a deviation of 7.8%.

And there are some new conclusions that can be drawn to guide future design.(1)When positive and negative angles are used for layers at the same time, the natural frequency of the steel/CFRP drive shaft is higher than that of a shaft with only positive or negative angles.(2)When multiple factors work together, the trend of the effect of every single factor on natural frequency is hardly affected by other factors. The natural frequency is mainly determined by the fiber orientation angle and slightly affected by the stacking sequence and layer thickness.

#### 7. Recommendations for Further Work

There are many deficiencies and unresolved issues in this study. Suggestions for further work are listed as follows.(1)The reason for the deviation between experiment and finite element analysis. Modeling defects and the simulation of the adhesive layer need to be solved for the better prediction in future designs.(2)The effects of stacking sequence, layer thickness, and other factors on natural frequency in all cases.(3)Optimal design of lamination parameters for the best dynamic performance.(4)The damping characteristic and dynamic natural frequency for further research.

#### Conflict of Interests

The authors declare that they have no financial and personal relationships with other people or organizations that can inappropriately influence their work, and there is no professional or other personal interest of any nature or kind in any product, service, and/or company that could be construed as influencing the position presented in our paper.

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