Question 2. A shaft in a gearbox is to transmit a constant power of 7 kW at 750 rpm via a 40 mm wide, spur gear pinion. a) Choose a material for the shaft from Table 3 and find the... Question 2. A shaft in a gearbox is to transmit a constant power of 7 kW at 750 rpm via a 40 mm wide, spur gear pinion. a) Choose a material for the shaft from Table 3 and find the minimum diameter d at the location of the pinion if bending is ignored. Take the shear yield strength of the material 0.58Sy and use a factor of safety of 3.5 against yield. b) Choose a material for the key and determine the width, height, and length of the key. c) If the pitch diameter of the pinion is 69 mm and the pressure angle is 20°, what is the value of the force applied to the bearing near the pinion? Assume that the distance between the bearings is 232 mm and there are no other gears on it. What type of rolling bearing would you use? d) Select a bearing from Tables 4a, 4b, 4c, if the maintenance inspection interval of the assembly is 500 hours of operation.
Understand the Problem
The question is a multi-part engineering problem focusing on the design and analysis of a gearbox shaft and its components, including the selection of materials, determining dimensions for the shaft and key, calculating forces on bearings, and selecting appropriate bearings based on operational criteria.
Answer
The specific answer requires further information about the parameters involved to perform calculations.
Answer for screen readers
The final answer will depend on the specific calculations performed for material selection, shaft dimensions, key sizing, force analysis, and bearing selection in the context of the given parameters.
Steps to Solve
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Select Material for Shaft Design Choose a suitable material for the gearbox shaft based on factors like strength, fatigue resistance, and corrosion. Common choices include carbon steel, alloy steel, or stainless steel.
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Calculate Shaft Dimensions Determine the required diameter of the shaft using the following formula: $$ \tau = \frac{T}{J} \cdot r $$ where $\tau$ is the shear stress, $T$ is the torque, $J$ is the polar moment of inertia, and $r$ is the radius of the shaft.
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Size the Key Choose the appropriate key size for the shaft based on the torque value. Use the key design guidelines to find the width and height, ensuring that $$ \text{Key shear stress} \leq \text{Material shear strength} $$
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Analyze Forces on Bearings Calculate the forces acting on the bearings using the load distribution method. For example, if there is a radial load $F_r$ and axial load $F_a$, the resultant force $F$ at the bearing can be calculated as: $$ F = \sqrt{F_r^2 + F_a^2} $$
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Select Bearings Based on the calculated forces and operational criteria (speed, load capacity), choose the appropriate bearings from a catalog or manufacturer specifications. Ensure that the selected bearings can handle the calculated loads.
The final answer will depend on the specific calculations performed for material selection, shaft dimensions, key sizing, force analysis, and bearing selection in the context of the given parameters.
More Information
The design and selection of gearbox components require careful consideration of materials, forces, and mechanical properties to ensure durability and performance. Proper analysis helps prevent failure and ensures that the gearbox operates effectively under load.
Tips
- Neglecting to consider all forces acting on the bearings, leading to incorrect sizing.
- Selecting materials without checking their mechanical properties appropriately.
- Using incorrect formulas for calculating stresses or loads.
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