Analysis of newly designed wheel is carried out by considering the following effects;
· Effect of Driving Force and Torque,
· Effect of Braking Torque,
· Effect of Weight of Rider on the Wheel
· Effect of Driving Torque and Total Combined Weight (Dynamic Driving Loads).
· Effect of Braking Torque and Total Combined Weight (Dynamic Braking Loads).
Different Mass of the rider are assumed to be m1 = 70 kg, m2 = 85 kg, m3 = 100 kg and mass of the bicycle is assumed to be 15 kg for the analysis of the wheel. The Total Combined Mass is taken into consideration for analysis i.e. M1 = 85 kg, M2 = 100 kg,M3 = 115 kg.
As the bicycle is in motion, the spring steel strips are the members that constantly deflect due to shocks and loads. So, failure may occur at spring steel strips. Thus, assuming Factor of Safety for spring steel as 2 (Fs = 2) 1
Sut = 331 N/mm2 2 Syt = 285 N/mm2 2
The Stresses generated on the wheel should be less than the Safe Design Stress. For Stationary Condition (i.e. Rider on the bicycle and no motion of bicycle), the designing is done considering Syt. Therefore, Safe Design Stress for the stationary condition is 142.5 N/mm2.
For Dynamic Condition (i.e. Rider on the bicycle and bicycle in motion), the designing is done considering Sut. Therefore, Safe Design Stress for the dynamic condition is 165 N/mm2.
For analysis, the Elemental Nodal Stress generated should be less than the Safe Design Stress.
Effect of Driving Torque
Assuming that the bicycle is moving with constant velocity on a road, then the pedal force on the rear wheel should be more than the resisting force opposing the bicycle motion. These resisting forces opposing the bicycle motion are Gravity, Rolling Resistance, Aerodynamic Drag and internal bicycle friction. Here Total Combined Mass (M) is taken into consideration
The Driving/Pedaling force produced by the rider through pedaling is obtained by the given equation (1) consider the resisting forces on bicycle and rider.
F = Mg* sinØ + Crr * Mg + 0.5 Cd ?Av2 3 (1)
This above equation is taken into consideration when Angle of Inclination (Ø) is to be considered. So when no inclination is considered the equation (2) is as follows:
F = Crr * Mg + 0.5 Cd ?Av2 3 (2)
This above equation gives pedaling force required to get the cycle in motion. The torque produced at the wheels can be determined from the given equation (3):
T = F * R (3)
The torque generated on the rear wheel of the bicycle is equal to the torque obtained on the front wheel of the bicycle. These values of pedaling torque that produce stress in the wheel as shown in the Figure 4.
Elemental Nodal Stress are taken into consideration to know whether the stresses generated in the elements due to pedaling torque are under the Safe Design Stress Limit. The values of Elemental Nodal Stress Due to Pedaling Torque is shown in Table 1.
Effect of Braking Torque
The braking torque is the torque produced at the wheels while braking. The effect of the braking torque is higher than the effect of the pedaling torque. So it is necessary to consider Effect of Braking Torque for safe design of the wheel. Here Total Combined Mass (M) is taken into consideration for Calculations.
The Braking Torque (Tb) can be determined by the following equation (3):
E = Tb * ? (3)
Here, it is assumed that the bicycle is in motion on the road at a constant velocity of 5.56 m/s (20 km/h). Assuming 8 seconds as the time taken by the bicycle to stop. For calculation of braking torque, total energy of the wheel is calculated by the following expression:
E = Kinetic Energy (K.E.) + Energy of rotating body
= 0.5mv2 + 0.5I ?2
Moment of Inertia (I) = Mb * R
Angular velocity of wheel (?) = V/R = 19.04 rad/s
Now, consider the kinematic equations of motion of linear form and converting them to polar form to determine the Angular Acceleration of wheel (?).
Angular Acceleration (?) = ? / t = 2.38 rad/s2
The angular distance (?) traveled by the wheel during braking is given by solving the polar form of kinematic equation (4) given below:
? = ?0t + 0.5?t2 ? (4)
? = 76.16 radians
The Braking Torque on the wheel can be determined by the following equation (5):
Tb = E / ? (5)
The braking torque generated due to braking of the bicycle and their values of braking torque are shown in Figure 4.
Elemental Nodal Stress is taken into consideration to know whether the stresses generated in the elements due to braking torque are under the Safe Design Stress Limit. The values of Elemental Nodal Stress Due to Braking Torque is shown in Table 2.
The values of stress generated in the wheel due to Pedaling torque and Braking Torque.
Nodal stress generated in the wheel due to pedaling as well as braking should be less than the Safe Design Stress i.e. 165 N/mm2. Thus, the design is safe when driving torque acts on the wheel.