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Research on Torsional Capacity of Composite Drive Shaft Under Clockwise and
Counter-clockwise Torque
1
1
Yefa Hu , Mo Yang , Jinguang. Zhang1,*, Chunsheng Song1 and Weiming Zhang1
1
School of Mechanical and Electronic Engineering, Wuhan University of Technology,
Wuhan, 430070, China;
*Corresponding author: Mr. Jinguang Zhang, Wuhan University of technology,
school of Mechanical and Electronic Engineering, Luoshi Road 122, Wuhan, Hubei, P.
R. China, (email) [email protected], +86 13385280905.
Abstract: The design of lay-up has a great influence on the mechanical properties of
CFRP (carbon fiber reinforced plastic) drive shaft. In this research the stress states of
each layer in the CFRP drive shaft were studied, which were different under opposite
torque direction. Tsai-Wu criteria was used to judge the torsional stability of the
composite laminates. The data from finite element analysis showed that torsional
capacities of a stacking sequence varies greatly with torque direction, and reasonable
lay-up design can reduce the difference. Torque direction should not be ignored when
design a CFRP drive shaft.
Keywords: clockwise and counter-clockwise torque; CFRP drive shaft; lay-up
design; finite element analysis;
1. Introduction
Drive shafts for power transmission are used in many applications, including
machine tool, cooling towers, pumping sets, aerospace, and automobiles. In the
metallic shaft design, the size of the shaft’s cross-section can be determined by the
value of torque and the allowable shear stress of the material [1]. Metallic
drive shafts have characteristics of weight limitations, low critical speed and vibration.
It has proved that CFRP drive shaft can solve many automotive and industrial
problems that conventional metal ones have. Aerospace development effort
demonstrates that correctly designed composite components have inherently superior
fatigue and vibration damping characteristics compared to metals [2]. CFRP is ideally
suited for long or heavy-load drive shaft. Their elastic properties can be tailored to
increase the torque and the rotational speed at which they operate [3].
In the past, many researchers have investigated the use of hybrid drive shafts. They
mainly considered the effects of fiber stacking angle, inside radius, layers thickness,
number of layers and stacking sequence on the torsional stiffness, natural frequency,
bucking strength, fatigue life and failure modes of composite tubes. In Talib and Ali’s
study, finite element analysis and experiments were used to design CFRP drive shafts
combining carbon and glass fibers within an epoxy matrix. They developed a
structure containing four layers stacked as [+45°glass/-45°glass /0°carbon/90°glass] with
high natural frequency and buckling strength, then tested the buckling torque of 14
laminates which were permutated and composed by 0°, 45°, -45° and 90°. The results
presented the effect of stacking sequence on the buckling strength and it was
concluded that the best stacking sequence is [45°/-45°/0°/90°], and sequence of
[0°/90°/-45°/45°] is the worst case [4]. According to classical lamination theory, the
in-plane shear stiffness of any laminates having the structure of [±45°]n is larger than
laminates having the structure of [90°/0°]n, therefore the specimens with 45° layers
sustain higher loads with less corresponding shear strain. Badie and Mahdi’s [5]
experiments showed that the torsional strength of the structure of [±45°]4 was two
times than [90°/0°]4. And many papers have indicated that 45° layer has a great
influence on shaft torsional performance, because the main loading of drive shaft is
torque [6, 7].
Therefore, in order to increase the shaft torsional performance, the 45° layers were
mostly designed to wind around the outermost layer of the shaft. For example, Jin
Kook Kim [8] selected a stacking sequence of [0°carbon /(±45°)N,glass] in the design of a
composite propeller shaft, it was shown that glass prepregs at least 32 plies (N=16)
were required for the static torque transmission capability of 3500Nm. With the
increase of 45° layers number, the shaft’s torsional performance increased, and when
N=31, the static torque transmission capability increased to 7380Nm. Shokrieh [9]
and Chad Keys [10] designed carbon fiber driveshaft according to shear buckling
strength. From their design, the drive shaft bears the maximum torque when the 45°
layers are winded around the outermost layer of the shaft.
In most studies of CFRP drive shaft, they always use lamination theory to design
stacking angles and number of plies, then they verified the correctness of their designs
through finite element analysis and mechanical testing. But they did not consider the
role of torque direction in their finite element analysis and mechanical testing. In fact,
the load of many machinery shafts always keeps changing, such as automotive drive
shaft, machine tool spindle, motor shaft and so on. Considering only one torque
direction, the laminated structure designed can well meet the performance
requirements under the same torque direction. But once the torque direction changes,
the stress condition of the laminated structure changes with it. Thus the design of
CFRP drive shaft without considering the changing torque direction has obvious flaw.
2. Problem statement
The CFRP drive shaft is a kind of fragile shaft. When it is subjected to torsion,
failure happens along the helicoids at 45 degree, since the fragile material’s tensile
strength is inferior to its shear strength and the maximum tensile stress appears on the
oblique section at 45 degree with generatrix [11]. Y. Zhao developed an analytical
model based on the mechanics of composite materials and the maximum strain failure
criterion [12]. And A. Huille developed an analytical model of composite pipe in
torsion to calculate the buckling load [13]. Both of them have established the
kinematical equations and discussed the internal force and moment of the pipe. They
did not take the effect caused by torque direction on the stress condition of a certain
ply into consideration. With further analysis, the stress condition of a certain ply is
different under different torque direction. This difference is shown in Figure 1.
Ply 1
Ply 1
Ply 2
Ply 2
FIGURE 1: Stress condition under different torque direction
Figure 1 shows the stress condition of ±45°layers under clockwise and
counter-clockwise torque.
When the torque direction is clockwise, the maximum tensile stress direction of
ply 1 is perpendicular to the fiber direction, and the maximum tensile stress
direction of ply 2 is parallel to the fiber direction;
When the torque direction is counter-clockwise, the maximum tensile stress
direction of ply 1 is parallel to the fiber direction, and the maximum tensile stress
direction of ply 2 is perpendicular to the fiber direction.
This difference will affect the strength of CFRP drive shaft, as it is known that
the mechanical property along the fiber direction is far better than that
perpendicular to the fiber direction.
3. Scheme design
The following four kinds of ply angle are often used in composite drive shaft
design: 0° 、 90° 、 45° 、 -45°, to study the influence of clockwise and
counter-clockwise torque on the performance of drive shaft and find proper stacking
schemes to reduce such influence, six stacking schemes are made as Table 1 shows.
By applying clockwise torque and counter-clockwise torque on these six typical
schemes respectively, this influence will be discovered, and then preferable stacking
schemes can be found in such loading condition.
TABLE 1: Stacking schemes and related parameters
Stacking definition
Thickness
/mm
2.4
2.4
2.4
2.4
2.4
2.4
Length
/m
1
1
1
1
1
1
Outer
diameter/mm
100
100
100
100
100
100
Case 1
[+45/-45]4
Case 2
[+45/-45]2S
Case 3
[+45/-45/+45/-45/+45/-45/0/0]
Case 4
[0/0/+45/-45/45/-45/+45/-45]
Case 5 [+45/-45/+45/-45/+45/-45/90/90]
Case 6
[+45/-45/+45/-45/+45/-45/90/0]
4. Finite element analysis
In this research, finite element analysis is performed using ANSYS 12.0 software.
Finite element method has been widely adopted for composite design, Bauchau et al.
[14] conducted torsion tests with five different lamination schemes of transmission
shaft respectively to obtain the maximum torque, then Shokrieh et al. [9] used the
finite element method to analyzed these five schemes, the result showed a good
agreement with the results of torsion test. Mustasher et al. [6] compared the results
of composite shaft torsion test with the results of the finite element analysis, and
found the maximum torque coming from experiment was 4%~20% lower than the
results from finite element analysis, which showed the reliability of finite element
analysis result as well.
4.1. Model development
The composite drive shaft is considered as a thin-walled orthotropic tube.
Three-dimensional model of the composite drive shaft was developed and typical
meshing generated by using SHELL181 element. One end is totally fixed and the
other was applied with clockwise torque and counter-clockwise torque respectively.
The initial torque was set as 1000Nm, then increased to 2400Nm with an increment of
200Nm. Typical meshing, loading and boundary condition were shown in Figure 2.
Supporting end
Loading end
FIGURE 2: Meshing, loading and boundary condition of composite drive shaft
4.2. Material property
Material-choosing is of great importance in composite drive shaft design, since
the mechanical parameters of material will affect the performance of composite
laminate. In this paper, resin-based carbon fiber composite T300/5208 is chosen, the
mechanical properties of which are tabulated in Table2 [7].
TABLE 2: Mechanical properties of the T300/5208
Longitudinal
Transverse
Poisson’s
Shear
modulus/GPa
modulus/GPa
ratio
modulus/GPa
181
10.3
0.28
7.17
4.3. Failure analysis
The performance difference of six schemes in Table 1 under clockwise and
counter-clockwise torque can be obtained by comparing their Tsai-Wu failure
coefficients [9], this criterion considers the total strain energy(both distortion
energy and dilatation energy)for predicting failure, which is more general than the
Tsai-Hill failure criterion because it distinguishes between compressive and tensile
failure strengths.
For a 2D state plane stress, the Tsai-Wu failure criterion is expressed as:
（4）
F1σ 1 + F2σ 2 + F11σ 12 + F22σ 22 + 2 F12σ 1σ 2 + F6τ 12 + F66τ 122 =
1
The coefficients Fij of the orthotropic Tsai-Wu failure criterion are related to the
material strength parameters of the lamina and are determined by experiments. They
are calculated from these formulas:
 1
 1
 1
1 
1 
1 
=
=
F2  t − c  ，
F1  t − c  ，=
F6  t − c 
 X2 X2 
 X1 X1 
 X 12 X 12 
F11 F22
1
1
1
F22 = t c F66 = t c ，F12 = −
c
（5）
2
X X1 ，
X2 X2 ，
X 12 X 12
Table 3 shows the mechanical properties of Tsai-Wu criteria of T300/5208[6].
TABLE 3: Properties of Tsai-Wu criteria of T300/5208
Mechanical properties
Value(MPa)
t
X1 tensile strength along fiber direction
767
t
X2 tensile strength transverse to fiber direction
20
c
X1 compressive strength along fiber direction
392
c
X2 compressive strength transverse to fiber direction
70
t
X12 positive shear strength
41
c
X12 negative shear strength
41
F11 =
t
1
The stress state of the lamina calculated by the program is described by the
components: σ 1 , σ 2 and τ 12 .
σ 1 laminate stress along fiber direction
σ 2 laminate stress transverse to fiber direction
τ 12 laminate shear stress
The composite ply material directions were shown in Figure 3, direction 1 refers to
the ply fiber orientation direction; direction 2 refers to the transverse fiber direction in
the plane of the ply.
FIGURE 3: Composite ply material directions
4.4. Analysis results
Case 1 with stacking sequence [+45/-45]4 is taken as an example to show the
performance difference, the contour plot of Tsai-Wu strength index under the same
torque in opposite direction is shown in Figure 4.
(a) Clock-wise torque
(b) Counter clock-wise torque
FIGURE 4: Tsai-Wu failure contour plot
The processed analysis data of all these six cases is shown in Figure 5. Figure 5(a)
illustrates that there is an obvious difference in torsional behavior of composite drive
shaft under clockwise torque and counter-clockwise torque. The symmetric laminates
of +45°and -45° have little influence on failure coefficient under opposite torque
directions, as showed in Figure 5(b). Figure 5(c), (d), (e) and (f) show that failure
coefficients under opposite torque directions are basically the same when 0° and 90°
are the outermost layer of shaft, but they are quite different when 0° is the first layer
of shaft.
(a) Failure indices of Case 1
(b) Failure indices of Case1 and Case 2
(c) Failure indices of Case1 and Case 3
(d) Failure indices of Case 4
(e) Failure indices of Case1 and Case 5
(f) Failure indices of Case3, Case 5 and Case 6
FIGURE 5: The analysis data and comparison
5. Conclusions
In this paper, the force conditions of composite drive shaft is analyzed with
classical mechanics of materials, combining the anisotropic property of composite
material, the importance of shaft torque direction in the design of composite drive
shaft is proposed. Six stacking schemes are designed and simulated with the Finite
Element Method (FEM) in order to explore composite drive shaft's stacking schemes
under the same torque in opposite directions. The Tsai-Wu failure coefficients of shaft
under different toque direction are obtained and related data are analyzed. Major
conclusions are as follows:
1) There is an obvious difference in torsional behavior of composite drive shaft
under opposite torque direction. The most obvious one occurs in the lay-up of
[+45°/-45°] 4, where the failure coefficient of clockwise torque is 1.4-3 times larger
than the one of counter-clockwise torque.
2) The influence on failure coefficients of clockwise and counter-clockwise torque
is not obvious when the ply sequence changes from [+45°/-45°]4 to symmetric
laminates of [+45°/-45°] 2S.
3) The failure coefficients of clockwise and counter-clockwise torque are nearly
identical when 0° and 90° are the outermost layer of shaft, but the torsional behavior
of which is slightly lower than the one when 45° is the outermost layer of the shaft.
4) There is no significant difference in failure coefficients between clockwise
torque and counter-clockwise torque when 0° is the first layer of the shaft.
Conflict of Interests
The authors declare that there is no conflict of interests regarding the publication of
this paper.
Acknowledgements
This research was supported by the Significant Science and Technology Innovation
Project of Hubei Province, China (Project No. ZDG2014000290).
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