Design of carbon fibre composite driveshaft end fittings and adhesive joint for motorsport applications

IN

DEGREE PROJECT TECHNOLOGY, FIRST CYCLE, 15 CREDITS

STOCKHOLM SWEDEN 2016 ,

Design of carbon fibre composite driveshaft end fittings and

adhesive joint for motorsport applications

SAMAN FANNI FADI JWEDA

KTH ROYAL INSTITUTE OF TECHNOLOGY

SCHOOL OF INDUSTRIAL ENGINEERING AND MANAGEMENT

www.kth.se

Design of carbon fibre composite driveshaft end fittings and adhesive

joint for motorsport applications

Saman Fanni Fadi Jweda

SA119X Examensarbete inom materialvetenskap, grundnivå SA118X Examensarbete inom maskinteknik, grundnivå

KTH Industriell teknik och management Hållfasthetsteknik

SE-100 44 STOCKHOLM

SA119X Examensarbete inom materialvetenskap, grundnivå

SA118X Examensarbete inom maskinteknik, grundnivå

Design of carbon fibre composite driveshaft end fittings and adhesive joint for motorsport

applications

Saman Fanni Fadi Jweda

Godkänt

2016-06-17

Examinator

Jonas Neumeister

Handledare

Artem Kulachenko

Uppdragsgivare

KTH Formula Student

Kontaktperson

Saman Fanni, Patrik Ringdahl

Sammanfattning

En drivaxel i stål ersattes av en drivaxel i kolfiberkomposit med ståltappar fastlimmade på varje ände för applikationer inom motorsport. En ”Single lap” och en ”Double lap”

limfogsdesign testades experimentellt i vridning. Designparametrar såsom limtjocklek, limlängd, limbredd, limmets ändgeometri, materialstyvhet och spänningsreduktion hos limfogen undersöktes och en förbättrad limfogsdesign föreslogs.

Testproven höll designkriteriats last men gick inte till brott även under testutrustningens

maxlast. Vidare beräkningar utfördes med antaganden baserade på ideala förhållanden och

resultat från tidigare studier. Beräkningarna visade en betydlig viktminskning följande

substitutionen av stål mot kolfiberkomposit i en drivaxel. Med ökad drivaxellängd visade

substitutionen till kolfiberkomposit även mer nödvändig i motorsportsapplikationer.

SA119X Degree Project in Materials Science and Engineering, First Level

SA118X Degree Project in Mechanical Engineering, First Level

Design of carbon fibre composite driveshaft end fittings and adhesive joint for motorsport

applications

Saman Fanni Fadi Jweda

Approved

2016-06-17

Examiner

Jonas Neumeister

Supervisor

Artem Kulachenko

Commissioner

KTH Formula Student

Contact person

Saman Fanni, Patrik Ringdahl

Abstract

A carbon fibre composite drive shaft with steel end fittings coupled with an adhesive joint was designed for automotive racing applications. An experimental study was conducted to test the torque transmission strength of a single lap and a double lap joint design. Design

parameters such as adhesive thickness, lap length, lap width, adhesive fillet, adherend tapering and adhesive stress reduction on the lap strength were investigated and an improved design was proposed.

The adhesive test specimens showed strength surpassing the design criteria and appeared to be beyond the limits of the testing equipment. Further calculations were made with assumptions based on ideal conditions and results from previous studies. The calculations showed

significant weight reduction with the substitution of a conventional steel shaft with a carbon

fibre composite shaft. With increased drive shaft length, the substitution to carbon fibre

composite showed even more essential in motorsport applications.

Contents

1. Introduction ... 1

2. Literary survey ... 2

2.1. Overlap stress distribution ... 2

2.2. Overlap geometry ... 4

2.2.1. Adhesive thickness ... 4

2.2.2. Overlap length ... 5

2.2.3. Adhesive end geometry ... 8

2.3. Adherend characteristics ... 9

2.3.1. Adherend tapering and thickness ... 9

2.3.2. Adherend material and surface treatment ... 10

3. End fitting design & manufacture ... 12

3.1. Dimensions ... 15

3.2. Double lap ... 16

3.3. Pocket lap ... 17

3.4. Thin lap ... 18

3.5. FEM analysis ... 18

3.6. End fitting weight ... 21

4. Experimental methods ... 22

4.1. Adhesive bonding ... 22

4.2. Carbon fibre composite tube specifications ... 24

4.3. Testing ... 24

5. Results ... 25

6. Discussion ... 28

6.1. Evaluating the assumptions and results ... 28

6.2. Alternative end fitting materials ... 30

6.3. The Pocket lap and Thin lap ... 31

7. Conclusions ... 31

Acknowledgements ... 32

References ... 32

1

1. Introduction

In motorsport, it is essential to keep the weight of the vehicle as low as possible to increase fuel efficiency and power-to-weight ratio. It is therefore desirable to choose materials with high specific strength and few materials in that field can compete with carbon fibre composite materials. A high set of components in a car is made of metallic materials and can be

substituted for carbon fibre reinforced plastic (CFRP) materials. Carbon fibre composite’s main advantages are its low density, high relative stiffness, low rotational inertia and high vibration damping. However, carbon fibre composites are highly sensitive to machining and need to be coupled with adhesive joints to avoid damaging the fibres. The advantage with an adhesive joint is its characteristic to distribute the load on a larger area than bolts or rivets and requires no holes. Despite this, an adhesive joint produces stress concentrations at its overlap ends and needs design guidelines to minimize stresses and increase the joint strength.

Although previous studies show similar finite element (FEM) solutions and agree on several design criteria to increase joint strength, a unified design approach is not at hand.

Adams and Peppiatt [1] made finite element studies of how partial tapering of the adherends and an adhesive fillet affects the overlap shear stresses. They concluded that tapering and introducing a fillet decreases the end shear stresses of the joint. Ki Soo Kim et al. [2]

experimentally tested the fatigue and static strength of a single lap joint, single lap joint with scarf, double lap joint and double lap joint with scarf together with simulating the stresses in these joints. Figure 1 shows four of the most common adhesive joints. They concluded that the double lap has a much higher load-bearing capacity than the single lap, and that tapering the composite adherend was not beneficial. Won Tae Kim and Dai Gil Lee [3] studied the strengths of different driveshaft shapes such as a hexagonal and elliptical driveshaft and compared them to the conventional circular form with single lap or double lap joints. They concluded that the double lap joint had higher strength than the single lap because of a larger bonding area and that it’s outer adherend prevented bulging of the tube from the hoop stresses.

They also concluded that the hexagonal shape had the highest strength of all single lap joints.

Figure 1 – Different types of adhesive joints

2 In this study, a conventional steel driveshaft is substituted by a carbon fibre composite

driveshaft. Steel end fittings are mounted on each end of the carbon fibre driveshaft to be fitted into the engine and the wheel of the vehicle with tripod joints. The steel end fitting is coupled onto the driveshaft with an adhesive joint and the tripod is mechanically mounted on the end fitting with splines. A literary survey is conducted to determine the optimum design of the adhesive joint. Unlike many of the previous studies regarding adhesive joints, this study was made without any simulations for the adhesive joint because it was out of the scope of this study. Furthermore, since motorsport applications are short-term and require lightweight structures, fatigue and creep properties of the designs were not examined and only static loading was considered. The carbon fibre tubes were manufactured with 40 mm inner diameter and 2 mm wall thickness before the study was initiated. Thus, the end fittings were the only variable for designing the adhesive joint. After designing, the steel end fittings are manufactured and coupled onto the carbon fibre tube and experimentally tested in torsion loading. With the experimental results, the driveshaft can be dimensioned for a specific load and the reduction in weight from substituting a steel driveshaft with a carbon fibre driveshaft can be found. This study is developing the driveshaft of an existing race car. The race car produces a maximum torque of 400 Nm which occurs during engine braking. With a safety factor of 1.5, the torque is increased to 600 Nm which is the minimum load-bearing capacity the final designed end fittings should have.

2. Literary survey

The aim of the literary survey was to study different adhesive joint parameters that affect the joint strength and incorporating these into an optimal design for the driveshaft end fitting. The parameters reviewed are profoundly studied by several previous authors. Comprehensively, these parameters can be categorized into: overlap stress distribution, overlap geometry and adherend characteristics.

There are several different types of lap joints. Figure 1 shows the types of lap joints mentioned in this study, including a single lap, double lap, butt joint and scarf joint.

2.1. Overlap stress distribution

The overlap stress distribution is the distribution of the shear stresses along the length of the

overlap. It was known to have peaks at the overlap ends and have been verified by multiple

analytical and experimental studies. The stress peaks and the overall stress distribution are

similar for both tension and torsion load cases. Both cases produce shear stresses in the

overlap. While shear stresses are the predominant stress type in torsion, tension loading

produces peel stresses as well. This is because tension loading of a single lap joint also creates

a bending moment on the adherends, which torsion does not. Still, the features of the stress

distribution in these two cases can be compared to each because they behave the same. Figure

2 to 4 shows the finite element mesh together with the stress distribution for both tensional

and torsional load cases taken from Adams and Peppiatt’s study [1]. Except for the stress-free

3 zone in the middle of the overlap loaded in tension, both cases have the same stress

distribution form with the torsional case having higher stress eccentricity at the ends of the lap joint.

Figure 2 – Finite element mesh of overlap joint and adherends taken from Adams and Peppiatt’s study [1].

Figure 3 – Shear and normal stress distributions in tubular lap joints subjected to tension load. [1]

4

Figure 4 – Shear stress distributions in tubular and scarf joints subjected to torque. [1]

Adams and Peppiatt used the same material for both adherends but since the adherends are tubes, the outer tube has a bigger diameter than the inner tube, and therefore higher stiffness.

Hence, the graph is not completely symmetrical around its midpoint but has a higher stress peak at the end of the stiffer adherend [1] [4]. Generally, having stiff adherends benefits the joint strength but maintaining a low difference in stiffness between the adherends is even more crucial, regardless of the adherends’ stiffnesses. In other words, having two compliant adherends creates a stronger adhesive joint than having one stiff adherend and one compliant adherend bonded together. This is because in the case with two compliant adherends, both adherends will deform the same amount while in the case with one stiff and one compliant adherend, deformation is highly concentrated at the end of the stiffer adherend, increasing stress levels [5] [6].

2.2. Overlap geometry 2.2.1. Adhesive thickness

Stress gradients also occur through the adhesive thickness. These gradients are in previous

studies assumed to be uniform due to the thin adhesive thickness but have also been analysed

without this assumption [6] [7]. Hipol investigated the stress gradient through the adhesive

thickness and compared it with the uniform stress gradient assumption. He showed that the

shear stress varied with the inverse square root of the adhesive thickness and suggested that in

no circumstances should these stresses be assumed uniform and proposed using the maximum

thickness possible [6]. Other studies and sources have claimed the opposite of of this, namely,

a thinner adhesive thickness results in a stronger lap joint. The explanation for this effect is

not yet fully agreed upon [8] [9]. Some theories explain it being a result of a thicker joint

5 having less “elastic reserve” when yielding, thus yield spreads quicker in a thicker joint.

Another theory shows that the interface stresses between the adhesive and the adherend increases with joint thickness, and thus decreasing the joint strength [8]. However, a more generally accepted explanation of why thinner joints are stronger than thicker joints is that thinner ones contain less defects such as microcracks and voids [2] [9] [10]. Although, this theory has been investigated as well and shows that defects do not increase with increased adhesive thickness; additionally, the same investigation opposes Hipol’s conclusion and states that stresses through the thickness increase with increased joint thickness [11].

Overall, what differentiates these latter studies and sources with Hipol’s conclusion is that Hipol made a purely analytical analysis based on elastic conditions while the other sources are entirely experimental. It is therefore important to rely on experimental studies rather than analytical studies in the case of adhesive thickness. The experimental studies all proposed joint thicknesses in close range. Soo Kim et al. tested 14 different joint thicknesses’ fatigue life and the smallest thickness measured, 0.15 mm, sustained highest amount of cycles and was the strongest joint [2]. It was considered that using a thinner joint than 0.15 mm would create difficulties during bonding operations and so a 0.15 mm thick adhesive was considered to be optimal. da Silva et al. tested 3 different thicknesses, 0.2 mm, 0.5 mm and 1 mm, under static tension-shear loading. Their study resulted in an increase of joint strength with a decrease of adhesive thickness, the joint strength being highest with a 0.2 mm thick joint [8].

Davies et al. studied the influence of adhesive thickness on joint strength and concluded that the thickness should be kept below 0.8 mm in pure shear loading [11].

2.2.2. Overlap length

Increasing the width of the joint will always increase the joint strength proportionally but this is not the case for joint length. In other words, doubling the joint width will double the joint strength but increasing joint length may not necessarily have a positive effect [12]. Increasing the joint length will increase the strength up to a point, the so called “effective length”, where the strength will afterwards remain constant with increased length [13]. This phenomenon, where an increase in joint length does not increase joint strength after a certain length, is the consequence of the stress concentrations at the overlap ends. Increasing the overlap length will not spread the stress concentration over a larger area but it will instead create a stress-free zone in the middle of the overlap and the area carrying stress will be unchanged. Taken from Hosseinzadeh and Taheri’s study [14], Figure 5 shows the stress distribution for different overlap lengths. As shown, the stress curves remain in the same shape except for the growth of a stress-free zone as the overlap length increases. This means that the overlap ends carry the same stress even though the length is increased. Additionally, the outermost stress peaks remains the same as well.

These stress peaks will remain at the same level until the overlap length reaches a minimum

length, as shown in Figure 6 taken from Hosseinzadeh et al.’s study [13].

6

Figure 5 – Comparison of stress distribution for different overlap lengths. [14]

Figure 6 - Distribution of shear stress as a function of normalized overlap length. [13]

Having an adhesive joint longer than the effective length will add unnecessary weight without

increasing strength. More so, a longer overlap can create more void content during bonding

processes and thus reducing the potential strength of the joint significantly [14]. This together

with the fact that the stress peaks are at the same level slightly before and beyond the effective

length, and that additional length adds unnecessary weight to the structure makes it beneficial

to produce an overlap with or slightly below the effective length. Figure 7 shows how the

failure load of an adhesive joint changes with increased overlap length [14]. It is evident that a

value slightly below the effective length will not weaken the adhesive joint significantly.

7 Therefore, determining the exact value of the effective length is not crucial and a qualified design of the lap length can still be made without a FEM approach.

Figure 7 - Comparison of the ultimate torsional capacities of joints with different overlap lengths. [14]

In the studies reviewed, there are no established ways of calculating the effective length for a given diameter or width without a finite element analysis. Three cases with given tube diameters and corresponding effective lengths were studied as shown in Table 1.

Table 1 – Effective length of tubular adhesive joints with different diameters taken from three different studies.

Hosseinzadeh et al.

[13]

Hosseinzadeh and

Taheri [14] Hipol [6]

Adhesive diameter

[mm] 16.8 22.22 64.84

Effective length

[mm] 30 25.4 38.1

Figure 8 shows these points plotted in a graph connected with a red line and a blue line, one for each trend, together with a black line marking the present carbon fibre tube diameter of 40 mm.

The studies all show different results for how effective length and diameter of the tube correlate and cannot be plotted with a straight line, instead they show two different trends.

The red graph shows the effective length decreasing with increased diameter, and the blue

graph shows it increasing with increased diameter. Thus, a conclusion of how diameter and

effective length correlate is not possible to determine with the reviewed data. Although,

assuming each of these trends separately, two values of the effective length for the given

diameter of 40 mm can be extracted. If the trend plotted by the red graph is assumed, an

effective length of 10.3 mm is extracted for a 40 mm diameter. If the trend plotted by the blue

8 graph is assumed, an effective length of 30.2 mm is extracted. However, the values

connecting the red line are smaller and therefore it is likely that the deviations involved create a larger impact on the data. Since the dots connecting the red line are closer to each other, deviations in the values will significantly change the trend of this red line unlike the blue trend where deviations will not have a significant impact on the slope of the blue line. In other words, if the outermost dot on the red line decreases it’s value on the y-axis, the slope of the red line will change significantly, whilst a change in the y-value on the outermost dot on the blue line will not change the slope of the blue line significantly.

Conclusively, the reviewed data contains far too few data points to determine how diameter and effective length correlate, but it is still possible to make a qualified guess of which of the two extracted values are the most conservative. This would be the trend of the blue line giving an effective length of 30.2 mm for the present diameter of 40 mm.

Figure 8 – Plot of data from Table 1.

2.2.3. Adhesive end geometry

During bonding operations, the end fitting and the tube are applied with adhesive and the end fitting is pressed into the tube. Excess adhesive will automatically seep out from both ends of the applied area and create a fillet instead of a square-edged end geometry, shown in Figure 9.

There are many shapes a fillet can adopt and when applying the end fitting to the tube, the fillet created inside the tube is inaccessible and can not be observed or altered. The ultimate shape depends on different variables such as the amount of adhesive applied and the method of applying the end fitting to the tube. Since the final shape form of the fillet is unknown, it is assumed the fillet will form a triangular shape since it is the most commonly studied shape. In reality, the triangular fillet will sink when the adhesive cures and thus form a rounded

triangular shape shown in Figure 10.

9

Figure 9 – a) Overlap with square-edged end geometry. b) Overlap with fillet.

Figure 10 – a) Triangular fillet. b) Triangular fillet after curing.

Since the stress concentrations are at the overlap ends a fillet should modify the stress

distribution and have an effect on the load-bearing capacity of the adhesive joint. Adams and Peppiatt [1] showed that the maximum shear stress at the ends of the overlap are reduced with 30 % with an introduction of a fillet, yet they predict stress concentrations to occur in the adherend corner inside the fillet. It is therefore suggested by several authors that the adherend corner that resides inside the fillet is rounded [15]. In another study, Adams and Harris [16]

experimentally compared a square-edge end geometry with a triangular fillet and a triangular fillet with rounded adherend corners. The introduction of a fillet increased the load-bearing capacity of the joint with 25 % compared to a square-edged joint, close to the analytically predicted value from the previous study [1], and rounding the adherend corners increased the load-bearing capacity with 50 % compared to the square-edged joint.

2.3. Adherend characteristics

2.3.1. Adherend tapering and thickness

Tapering is done by sloping the adherends towards their ends to increase flexibility and

reduce the stress peaks in the joint ends. Figure 11 shows a tapered single lap and a scarf joint.

A tapered joint, and in some instances called a bevelled joint, is often confused with a scarf

10 joint since the adherends in both cases are tapered. In this study only tapered joints are

designed and manufactured and since the properties of a scarf joint is not comparable to that of a tapered joint, the literary review only considers tapered joints.

Figure 11 – Comparison between a tapered joint and a scarf joint.

Hipol [6] studied the effect of tapering the steel adherend with a 45° and a 75° angle in finite element analysis and showed that tapering reduced stress peaks and that a 75° angle reduced the stresses more than a 45° angle. He concluded that it is not feasible to reduce stress levels by tapering the steel adherend since it only marginally increases joint strength and that it would require large taper angles, which may have manufacturing constraints. In contrast, it is believed that the constraints Hipol referred to were present at the time of the report’s release in 1984, since large taper angles create no constraints in manufacturing today. Soo Kim et al.

[2] studied how tapering affects the joint strength both analytically and experimentally. They used a carbon fibre composite adherend and a steel adherend, tapered both and compared their results to the non-tapered one. The finite element results showed that the tapered overlap had a higher load-bearing capacity than the non-tapered one but the experimental results showed the contrary, tapering reduced the joint strength. They concluded that it was a result of tapering the composite and that it is not beneficial to taper the fibre composite adherend.

By only tapering the steel adherend the stress peaks will decrease but simultaneously the stiffness imbalance will be reduced. The stiffnesses of each adherend should be as close to each other as possible and can also be calculated. However, in this study the steel adherends are the heaviest parts of the driveshaft and should be designed as light as possible which includes making the adherend as thin as possible regardless of stiffness imbalance. Hipol [6]

concluded that the stiffest possible composite adherend should be chosen together with the most compliant metallic adherend to decrease stiffness imbalance. Simultaneously, in his report a 2.54 mm thick carbon fibre tube was coupled in FEM with steel adherends with three different thicknesses where the thinnest one, 0.635 mm, produced lowest stress levels.

Making the steel adherend even thinner will render it impossible to make a fillet with rounded corners. Since including a fillet with rounded corners showed much greater increase in load- bearing capacity, the inclusion of a fillet is prioritized over reducing the adherend stiffness imbalance further.

2.3.2. Adherend material and surface treatment

The carbon fibre composite tubes were manufactured before the study and it was decided

beforehand that steel would be the material for the end fitting. It is still interesting to evaluate

11 different possible materials with respect to adhesion properties, mechanical properties,

manufacturing ease, cost and environmental effect, in search for better solutions and lightweight designs.

Steel is in motorsport preferred to be substituted with lighter materials when possible due to the large amount of weight steel adds to the car. Steel is on the other hand inexpensive, have good mechanical properties, have low environmental impact and is easy to process. But if all other variables can be sacrificed to benefit performance, lighter materials with higher specific strength are desired. In the metallic range, aluminium, magnesium and titanium are commonly used in motorsport. Table 2 compares steel with these metals with regards to their typical values of density, specific strength and their highest potential values for adhesive bonding.

Table 2 – Comparison of density, specific strength and adhesive bonding strength for 4 different metals.

Density [g/cm

] Specific strength [kN*m/kg]

Bonding strength [MPa], [ref.]

Steel 8 151 37, [17]

Aluminium 2.8 204 26, [17]

Titanium 4.5 288 15, [18]

Magnesium 1.7 158 20, [19]

Comparing these materials it is evident that substituting steel with any of the other three metals is going to reduce the bonding strength and therefore a larger bonding area is needed.

As shown in section 2.2.2. (Overlap length), to increase joint strength by increasing area, the width or the diameter should be increased and not the overlap length. Thus, the dimension of the driveshaft is increased. This will counteract the weight reduction from using light metals and it is therefore unclear if the substitution of steel with a lighter metal would be beneficial in terms of weight reduction and should be studied experimentally.

The bonding operations are done by an adhesive specialist company. The surface treatment, bonding process and curing are all done within the company and with the company

technology [20]. This is to ensure the maximum potential strength of the joint is reached.

Hence, the effect of surface treatment on the strength of the adhesive joint was not studied in this review.

In summary, the literary study found several key points that can be integrated in the design of an overlap joint to increase its strength. The key points include the adhesive thickness, length, end geometry, stress reduction and lastly adherend tapering. These key points can be

incorporated together in an improved overlap design. The manual work regarding the joint

strength, such as surface treatment and bonding operations were handed over to an adhesive

specialist company.

12

3. End fitting design & manufacture

The literary study reviewed different design parameters each with potential of increasing joint strength and an optimized design was made.

Figure 12 – Improved design of adhesive overlap joint for end fitting.

Figure 12 shows the design of the adhesive joint. The applied design parameters are noted in Figure 12 and explained as follows:

1) Adhesive is applied on the rim of the carbon fibre tube forming a butt joint. This is to utilize the contact area on the rim of the tube as well and not solely the overlap.

2) A “joggle” or “step” is included for the purpose of aligning the geometrical center of the end fitting with the tube. This is manufactured with a 0.1 mm larger radius than the inner radius of the tube to create a tight fit between the tube and the end fitting.

3) The adhesive thickness is 0.3 mm. This is to keep the thickness as low as possible and maintain a margin of safety by having a thickness that will ensure a smooth bonding process. Simultaneously, the adhesive specialist company advised to have a thickness of or above 0.3 mm to prevent the cured adhesive joint from becoming too brittle.

4) The taper angle of the steel adherend, marked θ in Figure 12, is 2°. An angle of 2°

would correspond to an angle of 88° in Hipol’s study [6].

5) At the overlap end the adhesive thickness is increased to 0.6 mm to reduce strain. If deformation is assumed constant over the overlap length, doubling the adhesive over a small length will decrease the strain there with 50 % and therefore also the stress, as illustrated in Figure 13. For a given deformation Δ, the shear strain α for the smaller thickness is larger than the shear strain β for the larger thickness.

6) The rounded edge inside the fillet has a radius of 0.6 mm which is the biggest possible radius at that edge. All other rounded edges in the adhesive joint have 0.2 mm radius.

These are not as big as possible since there could occur problems during milling if rounded edges were too close to each other.

7) Triangular fillet.

13

Figure 13 – Illustration of strain difference for different adhesive thicknesses. a) Shear strain α for a deformation Δ with an adhesive thickness of 0.3 mm. b) Shear strain β for a same deformation Δ with a thickness of 0.6 mm,

where α > β.

4 different end fittings were designed with a total of 3 different adhesive joints as shown in Figure 14. The Double lap joint has the same lap joint design as the Single lap joint but

utilizes the outside area of the composite tube as well as the inside area. For the sake of clarity, the 4 different end fittings will hereafter be called: a) Single lap, b) Double lap, c) Pocket lap, d) Thin lap. The Single lap and the Double lap were the designs that were manufactured, totalling to three parts including the Double lap sleeve. The pocket lap was not manufactured with advice from the adhesive specialist company [20] on that the bonding process would be timeconsuming. The thin lap was not manufactured mainly due to budget, material and time restrictions, but also because the adherend failed in FEM under the the testing equipment’s maximum torque of 1000 Nm.

All designs have two holes in the protruding end of the end fitting, marked a) and b) in Figure 15. Hole a) is made so that a steel rod can be inserted in it for the testing equipment to apply a force couple on, which in turn induces torque on the end fitting. Hole b) is designed to let air out from inside the tube during the bonding process. When inserting the second and last end fitting on the tube, air is compressed into the tube where it might disturb the adhesive and create voids, especially in the interface between the adhesive and the air which is where the fillet is located. To eliminate this problem, hole b) lets air escape through the middle of the end fitting. The hole is placed so it makes little impact on the strength of the structure.

The protruding end is designed differently for the study than it would be for the real

application. Since a large hole is drilled in the protruding end, it was dimensioned with a

larger diameter to not fail during testing. Therefore, the weight of the test specimens are

higher than what it would be in the real application.

14

Figure 14 – The 4 end fitting designs.

Figure 15 – Shows the two holes in the protruding end. a) Hole for a steel rod. b) Air outlet.

15

3.1. Dimensions

Table 3 shows the data for the end fitting materials. Both end fittings were made in Uddeholm Nimax

steel except for the Double lap sleeve which was made in EN 1.4301 (SS 2333) conventional stainless steel. This was due to the diameter of the sleeve being larger than the diameter the Uddeholm Nimax

steel rod was available in.

Table 3 – Properties of the two steel alloys used to make the end fittings.

Density [g/cm

] Rp

[MPa], [ref.] Hardness [HB]

Uddeholm Nimax

7.9 785 360-400

EN 1.4301 (SS 2333) 7.9 340, [21] 215

The dimensions for the Single lap, the Double lap and the Double lap sleeve are shown in Figures 16 to 18.

Figure 16 – Dimensions for the Single lap end fitting.

Figure 17 – Dimensions for the Double lap end fitting.

16

Figure 18 – Dimensions of the Double lap sleeve.

3.2. Double lap

The Single lap joint is designed according to the previously listed design parameters. The Double lap joint is identical to that of the Single lap joint but the end fitting is designed in two pieces due to manufacturing restraints, as shown in Figure 19. The Double lap sleeve was made into a separate part since the available milling tools could not mill a 30 mm deep axial pattern. Instead a V-joint was introduced between the Double lap and the sleeve where a weld joint couples the pieces together, as shown in Figure 20. Since welding can create

deformations, the thickness around the V-joint was made thicker to minimize the

deformations the sudden difference in temperature can cause. The weld joint was TIG-welded with the additive Elgatig 100.

Figure 19 – The Double lap consisting of two parts, it’s inner adherend and it’s sleeve.

17

Figure 20 – The two parts of the Double lap are welded together with a V-joint.

3.3. Pocket lap

The Pocket lap is designed for a different bonding process in an attempt to minimize adhesive void content. Instead of applying adhesive onto both adherends and inserting the end fitting into the tube, the Pocket lap is inserted into the tube and adhesive is injected through a hole connecting to the adhesive pocket. Figure 21 shows the modified design parameters of the Pocket lap. Adhesive is injected through a hole, a), into a pocket, b). The air located inside the pocket is pushed out by the adhesive through a hole, c), located 180° on the opposite side of a). Since the pocket is flat and enclosed, no previous design parameters are applied except the thickness of the adhesive and the tapering of the adherend.

Figure 21 – The Pocket lap with it’s design parameters. a) Adhesive inlet. b) Adhesive pocket. c) Air outlet hole.

18

3.4. Thin lap

The Thin lap, shown in Figure 22, is the lightest design and is designed with two motives. If a simple overlap without any design parameters is stronger than the adherends, it will be the lightest possible end fitting which would be the best solution in this application. In other words, if both the Single lap and the Thin lap are stronger than the adherends, the Thin lap would suffice and be the best solution since it is the lightest, even if the Single lap has a stronger joint. This is because the joint of the Single lap is too strong and the added weight of making it stronger is therefore excessive. The reason why the Thin lap can not include any design parameters such as a fillet is because the adherend is too thin. It is also interesting to evaluate the differences in load-bearing capacity between the Single lap and the Thin lap to investigate if the design parameters of the Single lap add any strength compared to an end fitting with no design parameters. The thickness of the Thin lap adherend is chosen to be 0.5 mm to give a significant weight difference between the Thin lap and the Single lap,

thicknesses well above 0.5 mm will not make a sufficient impact on the weight.

Figure 22 – The Thin lap.

3.5. FEM analysis

All 4 designs were studied in FEM before manufacturing to assure the end fitting would not

fail during testing. The testing equipment loads a maximum of 1000 Nm in torque which was

applied in FEM. Figure 23 and 24 shows the boundary conditions. The stress behaviour of all

4 end fittings are visualized in Figure 25 to 28. The end fittings for the real application were

also analysed in FEM but with a load of 600 Nm and all designs passed.

19

Figure 23 – Application of torque on the driveshaft in FEM.

Figure 24 – Application of fixed support on the driveshaft in FEM.

Figure 25 – Single lap under a torque load of 1000 Nm in FEM.

20

Figure 26 – Double lap under a torque load of 1000 Nm in FEM.

Figure 27 – Pocket lap under a torque load of 1000 Nm in FEM.

Figure 28 – Thin lap under a torque load of 1000 Nm in FEM.

21 In the FEM analysis, neither the Single lap or the Double lap reached the proof strength of 785 MPa or 340 MPa for the Double lap sleeve. The Thin lap reached a maximum of 772 MPa on a large area on the adherend and 868 MPa at the sharp edge between the joggle and the adherend. The Pocket lap reached 600 MPa on the outer rim and 2350 MPa in a small singularity at the sharp edges of the air outlet hole, shown in Figure 29. This is believed to be a boundary condition error in FEM and not a risk in reality. This is because the area where this stress concentration is located is not bonded to the tube and should therefore not

experience high stresses, and this large stress is located at the corner which indicates that it is a simulation error. This high-stress singularity is also the reason why the Pocket lap is so differently colored than the other end fittings. Due to the large hole in the protruding end, stress concentrations occur near the hole at the rounded edge, as can be seen in Figure 25 and 26.

Figure 29 – Singularity showing 2350 MPa at the air outlet hole on the Pocket lap.

3.6. End fitting weight

The difference in the protruding end of the end fitting is shown in Figure 30 where the test specimen requires a large hole to go through the end and therefore requires a larger diameter, increasing weight. The real application end fitting requires no such hole and can be

dimensioned smaller and weighs less. The weights of the end fitting designs, shown in Table

4, are for the real application end fittings and not the test specimens.

22

Figure 30 – The protruding ends of the test specimen end fittings (left) and the real application end fitting (right).

Table 4 – Weights of the test specimen and real application end fittings.

Single lap Double lap Pocket lap Thin lap

Weight [g] 173 295 165 133

Weight (test

specimens) [g] 235 337 - -

4. Experimental methods

4.1. Adhesive bonding

The adhesive and bonding operation process was recommended and conducted by the adhesive specialist company [20]. The adhesive used was LOCTITE® EA 9466™ or LOCTITE® Hysol® 9466™, a toughened high shear strength epoxy adhesive manufactured by Henkel Corporation. Table 5 shows the properties of the adhesive. The adhesive data sheet specifies that bonding with grit blasted steel following the ISO 4587 standard has a strength of 37 MPa and that special curing can increase the joint strength with 25 % [17]. This method was applied in the manufacturing of the test specimens.

The end fittings were bonded on each side of a 15 cm long carbon fibre tube with inner

diameter of 40 mm and wall thickness of 2 mm. Figure 31 shows the final test specimens after curing.

The bonding process steps were as follows:

1) Washing of the steel adherend.

23 2) Abrasion of steel adherend with Scotch-Brite brown surface conditioning disc.

3) Blowing with compressed air.

4) Application of primer 3901.

5) Abrasion of composite adherend.

6) Adhesive application process.

7) Curing.

The excess adhesive on the outside of the Double lap was manually shaped into a triangular fillet. The Double lap is also expected to have less void content than the Single lap. This is because the Double lap is partly filled with adhesive and then pressed onto the tube where the adhesive will slowly be pushed up by the tube and push the air out of it’s way.

Figure 31 – The two test specimens: Single lap (top) and Double lap (bottom)

24

Table 5 – Properties of the epoxy adhesive.

4.2. Carbon fibre composite tube specifications

The composite tube has an inner diameter of 40 mm, a wall thickness of 2 mm and is made of 5 layers of carbon fibre tow. It is dimensioned for a torque of ~1000 Nm. The layers

thicknesses and fiber orientations are:

1) 0.15 mm, 90° layer 2) 0.7 mm, ±45° layer 3) 0.3 mm, 0° layer 4) 0.7 mm, ±45° layer 5) 0.15 mm, 90° layer

4.3. Testing

Torque testing was conducted at the Solid Mechanics Laboratory in KTH Royal Institute of Science and Technology, Sweden, on an MTS 160 kN/1100 Nm torsional and axial tester at room temperature (22 °C). The testing equipment loads a maximum of 1000 Nm in torsion.

Special steel grips were produced to hold the test specimens in place, as seen in Figure 32.

Since the torque is transferred through a small steel rod with a diameter of 12 mm it is of importance the steel grips grip the steel rod as close to the end fitting as possible to not induce large bending moments on the steel rod.

LOCTITE® EA 9466™

Shear strength (Grit blasted steel, ISO 4587)

37 MPa

Mix ratio by volume 2:1

Viscosity

Medium

Curing time

5 days, 22° (1 hour, 80°/100° gives 125 %

strength)

25

Figure 32 – Single lap test specimen with steel rods inserted and attached into the steel grip.

5. Results

Since a driveshaft will be loaded rapidly and abruptly during acceleration and engine braking, the test specimens were intended to be loaded with the highest velocity the testing equipment were capable of outputting, but for precautionary reasons they were loaded slowly to give the opportunity of aborting the experiment if something faulted. The test specimens were

therefore initially loaded with a velocity of 0.1°/s up to 1080 Nm where they did not break or give any indication on crack or failure. They were then loaded again with a velocity of 10°/s where they again did not fail at the maximum load of 1080 Nm.

The aim of the experiment was to determine the strength of both adhesive joints and then with that data dimension the end fittings load bearing capacity to 600 Nm without altering the design parameters, to then calculate the driveshaft weight reduction. However, assumptions must be made in order to advance with the calculations since it is only known that the test specimens have a load-bearing capacity of more than 1080 Nm.

Notation:

D = Refers to the inner diameter of the composite tube. = 0.04 [m]

r = D/2 = Refers to the inner radius of the composite tube. = 0.02 [m]

L = Overlap length = 0.75*D = 0.03 [m]

A

= Refers to the adhesive area on the Single lap = 0.00377 [m

] A

= Refers to the adhesive area on the Double lap = 0.0079 [m

] M = Applied torque

F = Applied force = M/r

σ = Applied stress on the adhesive joint = F/A

26 A

= Joint area for the new driveshaft dimension.

W = Weight of current steel driveshaft without tripod joints = 506 [grams]

Subscripts:

new = Refers to the new dimension of the driveshaft.

SL = Refers to the Single lap.

DL = Refers to the Double lap.

tube = Refers to the carbon fibre composite tube.

f = refers to failure.

The Double lap should produce the highest possible weight reduction since it is 2.1 wider and therefore 2.1 times stronger than the Single lap since joint strength is proportional to joint width. The Double lap has therefore more joint strength-per-weight than the Single lap. The calculations were therefore focused on the weight reduction of the Double lap only.

Simultaneously, the area of the adhesive joints are calculated without void content since the two adhesive joints are expected to contain different amount of voids and no qualified guess can be made for each amount of void content.

Assumption 1:

Assuming the failure of the Single lap occurs at 1100 Nm, exactly above the tested and proved value of 1080 Nm, we can dimension the Double lap design down to a new diameter that fails at 600 Nm and then calculate the resulting weight reduction.

⁽¹⁾

(2)

⁽³⁾

With a failure load of 2310 Nm for the Double lap, it results in an ideal adhesive failure stress of 14.6 MPa. With this information, the Double lap can be dimensioned to fail at 14.6 MPa for a failure load of 600 Nm instead.

₍₄₎

⁽⁵⁾

27

⁽⁶⁾

extracting D

will give the new diameter of the driveshaft: D

= 2.47 [cm]

Weight reduction:

The Double lap was designed with this diameter in CAD and its weight was calculated to 120 grams. It was then analysed in FEM to assure it does not fail under a load of 600 Nm. To calculate the new weight of the carbon fibre composite tube, the current driveshaft length of 30 cm was used together with the material density of 1.6 g/cm

. Simultaneously, reducing the diameter of the composite tube required thicker walls to resist buckling. It was therefore assumed that the new driveshafts with smaller dimensions required a wall thickness of 4 mm instead of 2 mm. For this new diameter, it would give an inner diameter of 2.47 cm and an outer diameter of 3.27 cm, resulting in a new weight of 173 grams where the steel driveshaft weighs 506 grams. With the end fittings, this would result in a weight reduction of:

Weight reduction:

(7)

Assumption 2:

Assuming ideal conditions, the shear stress being constant over the overlap and no stress concentrations occur at the overlap ends, the adhesive should then fail at a shear stress of 37 MPa. Assuming this would mean that the whole adhesive area distributes the stresses evenly when in reality the middle section of the adhesive layer is less stressed than the boundary layers.

The new dimensions can be calculated as previously:

⁽⁸⁾

extracting D

will give the new diameter of the driveshaft: D

= 1.77 [cm]

Weight reduction:

⁽⁹⁾

Assuming failure at 37 MPa, the failure load for the Double lap would equal to 5850 Nm and

2790 Nm for the Single lap.

28 Table 6 shows the weight reduction for each assumed failure load for both the Single lap and the Double lap. The weight reductions were calculated by calculating the adhesive area required to fail at 600 Nm of torque. Thereafter, the diameter of the shaft can be extracted by knowing the correlation between area and tube diameter. Then this smaller end fitting is designed in CAD and the weight is extracted through the software. The weight of the composite tube is then calculated using the new diameter and a 4 mm wall thickness.

Table 6 – Failure load and resulting weight reduction for each assumption.

Assumed failure load for both designs

Single lap: 1100 Nm Double lap: 2310 Nm

Single lap: 2790 Nm Double lap: 5850 Nm

Weight reduction 18.4 % 42.5 %

6. Discussion

6.1. Evaluating the assumptions and results

The assumptions made in the results are difficult to perceive realistically since there are no methods of predicting the adhesive joint strength without knowing the properties of the glue at the interface. Instead, we can compare our two assumptions with values from previous studies where the specimens failed. Further discussion can then be made regarding the legitimacy of the assumptions. We can compare our study with the study of Won Tae Kim &

Dai Gil Lee’s study [3] since they use similar specimens and bonding processes as in our study, although they do not include any design parameters in their lap joints. They use a carbon fibre composite tube with 60 mm inner diameter, 3 mm wall thickness and ±45° fibre stacking sequence and tested a single lap and a double lap joint with steel adherends. Their circular single lap joint had a failure load of 3200 Nm where the adhesive failed. Their

identical double lap joint had a failure load of 3626 Nm where the composite adherend failed.

Knowing their joint area and failure load, we can compare the stresses of their single lap at failure to our two assumptions and find which of our two assumptions fit their case best. Their overlap length was 60 mm, with an inner radius of 30 mm and an adhesive shear strength of 13.7 MPa:

⁽¹⁰⁾

⁽¹¹⁾

Thus, at failure, Won Tae Kim & Dai Gil Lee’s [3] single lap experiences a calculated stress

of 9.4 MPa when the adhesive intrinsically experiences a shear stress of 13.7 MPa. The

calculated stress assumes the stresses being equally distributed over the area but since this is

29 not the case, the stresses being higher in the boundaries, the calculated stress at failure will be lower than the data sheet values. Knowing that the adhesive fails when it experiences a stress of 13.7 MPa and that the experiments showed a calculated stress of 9.4 MPa, a stress

concentration factor can be extracted by dividing the two and used in our test results to make a better prediction of the failure load for our test specimens. The stress concentration factor would convey how much higher the stress concentrations are above the ideal level. In their study, the stress concentration factor is:

⁽¹²⁾

Dividing the shear strength of our adhesive with this factor will show at what ideal stress level our adhesive joint would fail and this enables us to calculate the failure torque. The calculated stress level would be:

⁽¹³⁾

This stress level gives a failure load of 1900 Nm for our Single lap which would result in a weight reduction of 36 %, a failure load almost precisely between the values obtained from assumptions 1 and 2. This value is extracted relying on values from the study of Won Tae Kim & Dai Gil Lee’s [3]. A significant difference between the present study and theirs is that Won Tae Kim & Dai Gil Lee did not include any design parameters for their single lap and double lap joint design. The design parameters, as reviewed, strengthen the joint with a great amount. Yet, these are being overlooked in our calculations since they can not be accurately incorporated. The design parameters’ effect on joint strength can be listed to clarify the extent of their effects that are being overlooked. Listing these would give an idea of how much stronger our lap joints are than those of Won Tae Kim & Dai Gil Lee:

- The Butt joint: has an area of 2.64 cm

, increasing the Single lap joint area with 7 %, therefore theoretically increasing strength with 7 %.

- Fillet with rounded adherend corners: joint strength increases with 50 % compared to a square edged one.

- Double adhesive thickness at the overlap end: strain decreases with 50 %.

- Tapering: joint strength increases marginally.

Simultaneously, the 25 % increase in strength that the special curing of the adhesive brings with is also overlooked. This would increase the lap shear strength from 37 MPa to 46 MPa.

Albeit, it is not proved that these listed positive effects can be summed together. In previous experimental studies, the design parameters have been studied separately by their authors.

However, when incorporating all these design parameters at once it is not established that their effects can be added together or that they will not interfere with each other.

Meanwhile, in both the present study and the study of Won Tae Kim & Dai Gil Lee the

Double lap is 2.1 times as wide as the Single lap and therefore 2.1 times as strong. This joint

30 strength surpassed the strength of the composite adherend in their study and it was the

composite adherend that failed for all double lap tests. This will most likely be the case as well for the Double lap in the present study, regardless of the driveshaft diameter. When dimensioning the driveshaft for 600 Nm, the driveshaft diameter will be decreased and so the carbon fibre tube wall thickness must be increased to avoid buckling. Increasing wall

thickness will simultaneously increase the Double lap joint area meaning it will still be stronger than the adherends no matter how the tube is dimensioned. This means that the Double lap joint is probably always stronger than the adherends and the Single lap is not.

Since the weight of the driveshaft comes from the adherends, it is sought to have the

adherends as the weakest point since they can easily be dimensioned and the minimum weight can be reached. It is therefore a matter of finding adherend materials with higher specific strength which there are none in the case of carbon fibre.

6.2. Alternative end fitting materials

Alternatively, to further reduce weight, the materials listed in Table 2 can be used instead of the steel. Aluminium is cheap, 3 times lighter than steel and is easily machinable. Although, aluminium has weaker adhesive bonds compared to steel and requires a larger bonding area, which in turn requires a larger and heavier composite tube. But the larger aluminium end fitting may be significantly lighter than the steel end fitting and still result in a lighter

driveshaft. For example, if the driveshaft in Assumption 1 had aluminium end fittings instead of steel end fittings, the weight reduction would be increased from 18.4 % to 49 %. This applies to all the exemplary materials in Table 2 and remains to be experimentally tested in order to be further discussed.

When substituting a steel driveshaft with a carbon fibre composite driveshaft, the length of the steel driveshaft will not be fully substituted with carbon fibre composite since a length on each end will be comprised by the end fittings. Since a carbon fibre composite driveshaft consists of two components, a shaft and two end fittings, it is desired that the carbon fibre tube make up as much percentage of the whole driveshaft length as possible. This is so that the high specific strength and thus weight reduction the carbon fibre composite material brings with can be utilized as effectively as possible. It is proven that even for a short

driveshaft of 30 cm, it is possible to reduce the weight by substituting a steel driveshaft with a

carbon fibre composite one. It is therefore essential to replace a 30 cm long driveshaft for a

carbon fibre composite driveshaft in motorsport applications and even more important when

the driveshaft is longer than this since the weight would be reduced further. With a steel

driveshaft much longer than 30 cm, a substitution to carbon fibre material can increase the

performance of a race vehicle significantly.

31

6.3. The Pocket lap and Thin lap

Two end fitting designs were discarded before manufacturing, the Pocket lap and the Thin lap.

These designs serve different purposes. The Pocket lap is designed for a different bonding operation to minimize the void content in the adhesive joint since the void percentage equally reduces joint strength by minimizing area and inducing cracks. However, the pocket makes it impossible to include a fillet in the design. Simultaneously, making the joint thickness thicker in the overlap end in the Pocket lap can create machining difficulties which can be overcome by adding material to the adherend, increasing weight significantly. Two design parameters that greatly increase the joint strength, namely the fillet and the increase in thickness, are sacrificed in the Pocket lap design in an attempt to reduce void content. If the Pocket lap joint should be comparative to the Single lap joint, the increase in bonding area and strength that the void reduction leads to should be equal to the strength increase the fillet and the increase in thickness at the overlap end lead to. This is unlikely since these two design parameters are expected to greatly increase joint strength, where only the fillet increases strength with up to 50 % [16]. It is interesting to experimentally compare the torque failure strength of the Pocket lap and the Single lap but it is also necessary to verify the effect on void content the Pocket lap has. This can be performed by bonding the Single lap and the Pocket lap on clear

transparent tubes, enabling the researcher to directly see the voids through the tube assuming no voids are enclosed in the adhesive thickness since the adhesive thickness is thin.

Furthermore, tapering the inside of the adherend on the Pocket lap to increase the adhesive thickness towards the end can have the same effect as doubling the adhesive thickness on a short length like in the Single lap design.

The second discarded design, the Thin lap, served another purpose. The Thin lap is the lightest design where the adherend thickness is made as small as possible with no design parameters included. This means that the Thin lap is expected to be weaker than the Single lap.

But if the Thin lap can be made stronger than the adherends, thus making the adherends the weakest point in the driveshaft and not the adhesive joint, it is unnecessary to include design parameters since they only add weight. The strength of the Thin lap can easily and reliably be predicted using FEM, unlike an overlap including a lot of design parameters, and doesn’t necessitate an experimental study. Simulating the strength of the Thin lap in FEM should give a reliable prediction of its strength and convey whether the sacrifice of the design parameters for lower end fitting weight is worthwhile. Furthermore, the Thin lap can be made as a double lap joint as well.

7. Conclusions

A conventional steel driveshaft was substituted by a carbon fibre composite driveshaft with

steel end fittings for motorsport applications. A single lap and a double lap joint were

designed and manufactured with several joint design parameters aimed to increase the load-

bearing capacity of the adhesive joints and reduce the driveshaft weight. The adherends

composed of a carbon fibre composite shaft and steel end fittings bonded together with a

32 toughened epoxy adhesive. The torque bearing capacity of the joints were experimentally tested in torsion where both test specimens showed strength surpassing the design criteria and the maximum load capacity of the testing equipment. Further calculations were based on two different assumptions and their reliability were later discussed. From the results and

discussion, the following conclusions were made:

- Substituting a 30 cm long conventional steel driveshaft with a driveshaft including a carbon fibre composite shaft and steel end fittings can reduce the weight of the driveshaft.

- With a conventional steel driveshaft longer than 30 cm, the substitution to a carbon fibre composite driveshaft increases the weight reduction further and can greatly increase the performance of motorsport vehicles.

- The possibility of reducing the end fitting weight by substituting the steel material with lightweight metals such as aluminium, titanium and magnesium has potential of further reducing the driveshaft weight. It is therefore interesting to study and should be tested experimentally.

- The Pocket lap sacrifices some design parameters when introducing the adhesive pocket and should therefore be designed further to minimize the negative effect these sacrifices have on the joint strength. Furthermore, the Pocket lap should be

experimentally tested and visually studied and compared to the Single lap joint to verify if the different bonding operation increases the joint strength. Finite element simulation can predict the joint strength of the Thin lap and testing it experimentally is unnecessary.

Acknowledgements

The authors wishes to acknowledge Stefan Grönqvist at Aros Polymerteknik AB, Västerås for his contribution to this study by performing the bonding operations of the test specimens quickly, professionally and free of charge. To Patrik Ringdahl at KTH Formula Student for his technical expertise and for introducing us to the thesis. Our supervisor Artem Kulachenko for his all-round general help and supervision regarding the study and presentation. Anton Kviberg at the IIP workshop at KTH for welding the Double lap joint, and Kavithasan Patkunam at KTH Formula Student for rendering final images of the carbon fibre driveshaft.

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