Sustainable Bicycle Crank Arm Selection Using Life Cycle Analysis Under Typical Cycling Pedal Forces ^†

Abstract

This research compares the performance of structural steel and general aluminum alloys in identical crank arm designs when bearing loads are applied at different stages of paddling, such as starting, climbing, and racing. Finite element analysis (FEA) was utilized to evaluate fatigue life and safety factors. A design modification strategy was proposed to reduce critical stress in failure zones, resulting in an increased fatigue life. Although steel and aluminum alloys both have significant life and nominal high fatigue life during racing and climbing, respectively, aluminum alloys are unable to withstand a 1815 N starting load, even after modification.

1. Introduction

Considering its fuel costs and human health benefits, the bicycle can be deemed a ground-breaking invention. Following its invention, cycling, which originated in Europe, became a popular, stylish sport in the 19th century and became a craze among the people of Western countries [1]. Cycling has come to receive more attention because of the alarming number of engine-propelled vehicles posing a threat to fossil fuel storage. Consequently, making the safest bicycle for risk-free movement has attained exceeding importance over time [2]. Of all the other parts of a bicycle, crank arm design and development is an exigent step in the production process and is considered to be a significant step for a new company during product launching. Furthermore, appropriate modeling and life cycle assessment of the designed crank arm before manufacturing can accelerate the production process to a remarkable stage [3,4,5]. For instance, researchers have assessed fatigue life, observing that the crank arm’s length has a positive effect on mechanical performance, reducing the stress that leads to creating structures with minimum fatigue [6,7]. Fatigue failure happens in the bicycle crank arm due to alternating stress on paddles relentlessly applied during cycling. Bicycle riders speed up the cycle’s motion in a definite direction; as a result, repeated tensile and compressive stress acts on the same point during the cycle [8,9,10]. Due to sudden failure phenomena occurring before yield stress, fatigue failure cannot be predicted using conventional failure parameters. This can be defined as an irremediable energy dissipation scheme with slow surface crack propagation without any visible defects [11]. For instance, North American bicycle supplier Shimano recalled two series of bicycles after 4519 crank arm failures were reported from 750,000 units sold [12]. In addition to structural design upgrade practices, the right material selection process must be predominant, where material should have high stiffness and strength characteristics to thwart damage under heavy loads. Where lightweight material with a high stiffness feature would result in the best feasible outcome for a racing bicycle, however, trial and error-based experimental analysis is not always acceptable due to consequences such as time-consuming attempts with significant material losses. An intelligent solution to abstain from the repercussions of material losses is to implement finite element analysis (FEA) in any material testing procedure [13,14,15]. Hence, Kenan et al. [16] scrutinized the ability of the 6061-T6 aluminum alloy as a bicycle crank to bear a 1000 N fatigue load using finite element analysis via Ansys and Solidworks simulation software and made a comparison between the results. Likewise, Shangraf Tiku et al. [17] worked on crank design optimization to improve results after obtaining the directional displacement value of carbon fiber, structural steel, and an aluminum alloy from finite element analysis. Additionally, Iain McEwen et al. [18] used additive manufacturing technology to make bicycle cranks to investigate their dynamic mechanical performance. They utilized the laser powder bed fusion process for fabrication and compared fatigue failure from experimental and numerical results.

Although researchers have shown interest in bicycle components’ life estimation in favor of reliable cycling operations, life estimation against a real load applied on crank arms has not been studied. For instance, Moizant et al. [19] validated the experimental structural integrity of a crank arm using FEA for a small range of arbitrary loads where actual pedal force was absent. A similar methodology for random load detection on crank arms was observed in [20]. Following this, our study involves life cycle analysis of the fatigue of structural steel and general aluminum-alloy-derived crank arms under the load measured by P.D. Soden et al. [21] at different stages of regular cycling. They evaluated a 310 N force applied by a driver while speeding, 750 N exerted on climbing, and 1815 N acted on starting. As a result, this study revealed the fatigue life of the crank arms, as well as the durability of both materials during the above-mentioned cycling phases. Using finite element analysis in Ansys software, comparative research was conducted to discover the best possible material for an identical crank bar.

2. Design Analysis and Material Selection

2.1. CAD Model

Autodesk Fusion 360 (student license) software was utilized to draw the required model shown in Figure 1. Appropriate measurements regarding safe driving vehicle guidelines were followed according to EN 14764:2005 of the European standard [22], which illustrates the safety, as well as performance parameters, of the design, customization, and test procedures of a bicycle. The crank bar’s circular plate connects the cycle main frame with 3 mm threaded screw holes, confirming a rigid structure. The main paddle bar is attached at the end of 170 mm of the bottom bearing hole, where human-exerted forces are applied to move the paddle. Additionally, curvature with a 2 mm depth is formed on one side of the paddle, promoting mass optimization.

2.2. Material Properties

Material selection based on physical and mechanical properties is considered a fundamental approach in any form of simulation [23]. This study chose structural steel and an aluminum alloy as the best compatible materials to investigate the performance criteria. Potential road accidents can be caused when the ideal combination of design and the best material in crank arm selection is absent. The properties of the above-mentioned materials are derived from the Ansys engineering data source listed in

Table 1. Mechanical properties of structural steel and the aluminum alloy.

Type	Structural Steel	Aluminum Alloy
Density	7.85 × 10−6 kg/mm3	2.77 × 10−6 kg/mm3
Young’s Modulus	2 × 105 MPa	71,000 MPa
Poisson’s Ratio	0.3	0.33
Bulk Modulus	1.6667 × 105 MPa	69,608 MPa
Shear Modulus	76,923 MPa	26,692 MPa
Compressive Ultimate Strength	-	280 MPa
Compressive Yield Strength	250 MPa	-
Tensile Ultimate Strength	460 MPa	310 MPa
Tensile Yield Strength	250 MPa	280 MPa
Isotropic Thermal Conductivity	0.0605 W/mm°C	0.018 W/mm°C

.

Additionally, the SN curve fatigue data for structural steel and the aluminum alloy were acquired at zero mean stress from the 1998 ASME BPV Code [24] and MIL-HDBK-5H [25], respectively.

3. Static Structural Analysis

Finite element analysis of the bicycle paddle was carried out in Ansys 2023/R2, where the simulation process comprised material selection, geometry input, meshing, material assignment, analysis setting, boundary conditions, and solutions, in that order.

Figure 2a shows the mesh body created using user-defined requirements, where the number of tetrahedral elements after meshing was 61,202 with 108,041 nodes. The reason behind this unstructured mesh choice is geometry complexity. Multiple curvatures in the crank bar body hinder structured mesh practices. On the contrary, unstructured mesh has the freedom to form the whole body without any failed mesh. A mesh metric standard deviation of 0.18894, with an average value of 0.40093, is implied, which is close to the Ansys user guide’s recommended value of 0.5 [26]. Additionally, mesh refinement is not always effective for independent results, even after there is a possibility of wrong prediction in the life estimation process due to spurious mesh [27]. The mesh converged with 0.9 mm element sizes for both stress and fatigue life are represented in Figure 2b and Figure 2c, respectively. Figure 2d shows a fixed support acting on the lower circular disk fastened to the main frame with 3 mm screws. A mechanical analysis was created for 100 steps, with a step end time of 0.0005 s. With auto time stepping enabled, the minimum and maximum sub-steps were 30 and 100, respectively.

4. Results

4.1. Fatigue Failure Analysis at Speeding Scheme (310 N)

According to reference work, a 310 N load acts vertically on the paddle when the bicycle rider begins to accelerate. Considering this, the major goal was to determine how the selected materials behaved against the load and to compare their sustainability based on their life cycle patterns. Both materials have a high fatigue life in response to the 310 N load, as shown in Figure 3b and Figure 4b, with structural steel having a minimum fatigue life of 4.050 × ${10}^5$ cycles and the aluminum alloy having a greater value of 1.61 × ${10}^7$ cycles. According to EN 14764:2005 [22], the designed crank arms should sustain at least 100,000 cycles; the materials exhibited sustainable features over a minimum life cycle, with nominal stress measuring 100.87 MPa and 100.46 MPa, as shown in Figure 3a and Figure 4a, respectively. Safety factors for both crank arm structures are illustrated in Figure 3c and Figure 4c, where structural steel shows 1.3681 against the 1.7976 from the aluminum alloy under the same 310 N load. This figure confirms that the aluminum alloy offers a more reliable crank arm when speeding up the cycle compared with structural steel, whereas structural steel is stiffer when considering the high stress in a short period comparatively. A common phenomenon observed in both materials’ stress distribution graphs is stress intensity maintained at the circular plate, which mounts the crank arm to the bicycle main frame. Although this high-stress intensity does not lead to stress singularity, reducing sharp-edge corners may proliferate the life cycle by offering more smoother stress distribution. Consequently, we induced a fillet operation on that specific sharp edge to alleviate the effect of a sharp corner. Maintaining the same boundary conditions on modified geometry during simulation causes a rapid surge in the life cycle for both materials, with this referring to 9.69 × ${10}^5$ cycles for structural steel and 7.14 × ${10}^7$ cycles for the aluminum alloy, as listed in

Table 2. Bicycle crank bar response to different loads.

Structural Steel
Load (N)	Stress (MPa)		Life (Cycle)		SF
	Without Fillet	With Fillet	Without Fillet	With Fillet	Without Fillet	With Fillet
310	100.87	86.678	4.05 × 105	9.69 × 105	1.3681	1.5921
750	244.04	209.71	12,753	21,544	0.56547	0.65807
1815	590.59	507.49	935.77	1388.1	0.23367	0.27193
Aluminum Alloy
Load (N)	Stress (MPa)		Life (Cycle)		SF
	Without Fillet	With Fillet	Without Fillet	With Fillet	Without Fillet	With Fillet
310	100.46	86.617	1.61 × 107	7.14 × 107	1.7976	2.0848
750	243.04	209.56	4734.7	29,170	0.74299	0.86171
1815	588.17	507.13	0	0	0.30702	0.35608

. Similarly, an increasing trend appears in safety factor values, such as 1.5921 and 2.0848 for structural steel and the aluminum alloy, respectively, while stress becomes 86.678 MPa and 86.617 MPa sequentially. The same approach was seen in [28], where shape optimization with different curvatures reduced the stress concentrations at the corners, resulting in a maximum of 20% stress reduction through optimization. Additionally, Gopinath and Sushma [29] used topology optimization to reduce the weight of an engine’s connecting rods derived from different materials.

4.2. Fatigue Failure Analysis at Speeding Scheme (750 N)

In comparison to the aluminum alloy, structural steel had a longer fatigue life at a 750 N bearing load, as evaluated by life cycle analysis. Figure 3e and Figure 4e show that life estimation for both materials plummeted drastically with the increase in load to 750 N during climbing. For instance, the aluminum-alloy-made crank arm sustained up to 4734.7 repetitive cycles, which is 3400 times lower than its value estimated at a 310 N load during regular cycling. Surprisingly, the structural-steel-fabricated crank arm showed better life estimation at 12,753 cycles, which is almost threefold that of the aluminum-alloy-exerted life, albeit both showed a similar decreasing trend with increasing load. A similar observation referring to fillets on sharp-edge corners saw life estimation significantly improved at 21,544 cycles from 12,753 cycles for the structural steel crank arm, whereas the aluminum-alloy-derived crank arm showed 29,170 cycles, while initial values were counted from 4734.7 cycles without any modifications. A similar trend was observed in stress distribution and safety factors, such as 244.04 MPa stressed structural steel offering only 209.71 MPa after modification and the 0.56547 safety factor becoming 0.65807.

Likewise, the aluminum-alloy-based crank arm offered 209.56 MPa stress from 243.04 MPa after modification under the 750 N load listed in Table 2. Although the aluminum alloy crank arm showed a lower life estimation compared with structural steel designed for 100,000 cycles, it offered 0.74299 safety factors, which is greater than the 0.56547 exerted by the structural steel crank arm. Following this, both types exhibited increased factors of safety with the addition of fillets, measuring 0.86171 and 0.65807 for the aluminum alloy and structural steel, respectively.

4.3. Fatigue Failure Analysis at Speeding Scheme (1815 N)

At the start of cycling, a high torque is needed to accelerate; as a result, a high load consisting of 1815 N is applied by the passenger, as determined in our reference paper. Conspicuously, our designed model should have the ability to resist loads over 1815 N in order to be investigated as an integrated model. Following this, Figure 3h and Figure 4h compare structural steel and aluminum alloy life patterns against the 1815 N load. Where the aluminum alloy completely failed to bear any load, like 0 cycles indicated at the fatigue region, structural steel has a low fatigue life of 935.77 cycles. The same fillet addition approaches were considered to increase fatigue life for both materials, but the aluminum alloy remained the same, whereas structural steel showed a positive response, reaching a high fatigue life with a value of 1388.1 cycles. One interesting phenomenon that happened during the 1815 N load scheme instead of the 310 N and 750 N schemes is that a fracture zone on the main crank arm and fixed end fracture occurred, which was completely absent up to 750 N. Likewise, structural steel provided 590.19 MPa initially and exhibited 507.49 MPa after modification; those were close to aluminum-alloy-generated stress, but structural steel was firm enough to withstand the 1815 N load. At the 1815 N load, both types of crank arms showed a lower safety factor of less than 0.5, as illustrated in Figure 3i and Figure 4i consecutively.

5. Conclusions

In this study, a computer-aided model was created according to safety regulations to avoid mistakes that lead to fatal accidents. The designed paddle structure was carefully studied in order to ascertain whether it could be sustained against the load applied during different stages of bicycle paddling. Previous works were taken into account for exact load consideration during the cycle’s starting, speeding, and climbing schemes. An aluminum alloy and structural steel were selected for finite element analysis following their comparison for the determination of the best material. During the speeding of the cycle, the passenger exerts a pedal force of 310 N. At a 310 N bearing load, structures show a high fatigue life; structural steel and the aluminum alloy showed a minimum life estimation of ${4.05\times 10}^5$ and ${1.61\times 10}^7$, respectively, whereas the designed life was set to 100,000 cycles. Nevertheless, factors of safety were satisfactory during speeding. Structural-steel and aluminum-alloy-assigned structures showed high cycle fatigue during climbing operations, but these were not sustained after 12,753 and 4734.7 cycles, respectively. Furthermore, at the start of the cycle, permanent failure happened after 935.77 cycles in structural steel, but the aluminum alloy failed without any cycle operation, as it was unable to bear the 1815 N load. Shape optimization by incorporating fillets on critical stressed zones improved fatigue life significantly, resulting in an approximate two- and seven-fold increment in structural steel and the aluminum alloy for both speeding and climbing schemes. The structural steel crank arm life shifted to one having high fatigue life estimation with the new design, but the aluminum alloy failed even after modification.

Eventually, the designed structure should be modified to make a better load-carrying, capable paddle that could bear more than a 1815 N load in order to obtain high fatigue life estimation, where altering the paddle structure, along with high-strength material selection, would be another means of addressing the issue of developing a sustainable paddle.