Maximum Tension in the Bicycle Chain

In summary: The links and pins are both made from the same steel material with a tensile yield strength of kt and a shear yield strength of ks = 0.5kt. To calculate the allowed stress for each component, we use the given safety factor of SF = 3 and the equation σ_design = (1/SF) x σ_fail, where σ_fail = kt for tensile strength and σ_fail = ks for shear strength. Using this equation, we can calculate the allowed stress for the pin and link as follows: For the pin: σ_design_pin = (1/3) x kt For the link: σ_design_link = (1/3) x 0.5kt = (1/6) x kt Therefore, the
  • #1
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Figure 1 below shows drawings of a typical bicycle chain. Consider two components of the
chain:
(i) the pin, and (ii) the link.
The chain is under tension caused by a load applied by a person pushing on one of the
pedals. Calculate the maximum tension in the chain.
Calculate the stresses in the two components, i.e., the pin, and the link. First,
derive symbolically the relationship for stresses for the two components.
Next, make numerical calculations and indicate which is the most critical part
of the chain in terms of the applied load.
The links and pins are made from the same steel material. The tensile yields strength, [tex]\sigma[/tex]y,
is denoted kt. The shear yield strength is denoted ks. Assume ks = 0.5kt.
Let the safety factor be SF = 3. Then we can write for each component,
[tex]\sigma[/tex]design = [tex]\frac{1}{SF}[/tex][tex]\times[/tex][tex]\sigma[/tex]fail (1)
where: [tex]\sigma[/tex]design is the allowed stress, [tex]\sigma[/tex]fail = kt for tensile strength, and [tex]\sigma[/tex]fail = ks for shear strength.

Given data:
The maximum load applied by a person to the pedal is Pmax.
The length of the pedal is L.
The diameter of the main sprocket is D.
The diameter of the minor sprocket is d.

The pin is 2.5 mm diameter. The distance between the inner links is 4.6 mm. The link
is 5.8 mm at its widest part (where the pin hole is), and 3.5 mm at its narrowest part
(between the chain holes). The thickness of the link is 1.2 mm.

image002.gif


image004.gif


Figure 1: Construction and components of a bicycle chain

Could anyone give me a clue to figure out this question?
I have no idea how and where to start...
 
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  • #2
Solution: The maximum tension in the chain is equal to Pmax, the maximum load applied by the person to the pedal. The stresses in the two components can be calculated using the following equations: For the pin: σ_des_pin = SF x kt x (D-d)/2d For the link: σ_des_link = SF x kt x (L-D)/2d where kt is the tensile yield strength, D is the diameter of the main sprocket, d is the diameter of the minor sprocket, and L is the length of the pedal. Since the stresses in the pin and link are proportional to the tensile and shear yield strengths, respectively, the most critical part of the chain is determined by the component with the higher stress. Thus, in this case, the most critical part of the chain is the pin.
 
  • #3


I can provide some guidance on how to approach this problem. First, we need to understand the concept of tension and how it affects different components of the bicycle chain. Tension is the force that is transmitted through the chain when a load is applied to the pedals. This tension is distributed throughout the chain, causing stress on different components such as the pins and links.

To calculate the maximum tension in the chain, we need to consider the maximum load applied by a person to the pedal (Pmax). This load is transmitted through the chain and can be calculated using the equation Pmax = F x L, where F is the force applied by the person and L is the length of the pedal.

Next, we need to calculate the stresses in the pin and link components. To do this, we can use the equations for tensile and shear stresses, given by:

Tensile stress (\sigma) = F/A, where F is the applied load and A is the cross-sectional area of the component.

Shear stress (\tau) = F/A, where F is the applied load and A is the cross-sectional area of the component.

For the pin, we can use the given diameter of 2.5 mm to calculate its cross-sectional area. For the link, we need to consider the varying thickness and width of the component at different points. We can use the given dimensions to calculate the cross-sectional area at the widest and narrowest points, and then take an average to get an approximate value for A.

Once we have calculated the stresses in the pin and link, we can use the equations given in the problem to determine the allowed stress for each component. We can then compare the calculated stresses to the allowed stresses to determine which component is the most critical in terms of the applied load.

It is important to note that the safety factor of 3 should also be taken into consideration when calculating the allowed stress. This means that the actual allowed stress for each component should be divided by 3 to ensure a safe design.

In conclusion, to solve this problem, we need to first understand the concept of tension and its effects on different components of the bicycle chain. We then need to use the given equations and dimensions to calculate the maximum tension, stresses, and allowed stresses for the pin and link components. Finally, we can compare these values to determine the most critical component in terms of the applied load.
 

What is maximum tension in the bicycle chain?

The maximum tension in the bicycle chain refers to the amount of force or stress that the chain can withstand before breaking or becoming damaged. This tension is caused by the weight of the rider and the power generated by pedaling.

Why is maximum tension important in a bicycle chain?

Maximum tension is important because if the tension in the chain exceeds its limit, it can cause the chain to break or skip off the gears, leading to potential accidents or damage to the bicycle.

How is maximum tension in the bicycle chain calculated?

Maximum tension in the bicycle chain is calculated by multiplying the rider's weight by a factor of 2.5. This takes into account the additional force generated by pedaling and the weight distribution on the chain.

What happens if the maximum tension in the bicycle chain is exceeded?

If the maximum tension in the bicycle chain is exceeded, it can cause the chain to stretch or even break, leading to potential accidents or damage to the bicycle. It can also put additional strain on the gears and other components of the bike.

How can the maximum tension in the bicycle chain be adjusted?

The maximum tension in the bicycle chain can be adjusted by changing the gear ratio, which determines how much force is required to turn the pedals. Lower gear ratios require less force, while higher gear ratios require more force. Adjusting the gear ratio can help distribute the tension more evenly on the chain.

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