Subtopic: Design and selection of machine elements – gears, pulleys, chains and sprockets and belts
Question Statement:
Which of the following statements regarding dynamic tooth loading in agricultural gear drives and the Buckingham equation is/are CORRECT?
Options:
(A) Dynamic tooth load arises from pitch line velocity, tooth spacing errors, and elastic deformation of gear teeth
(B) According to Buckingham's equation, dynamic load increases with increasing pitch line velocity up to a limiting maximum value
(C) To avoid surface fatigue failure (pitting), the wear strength ($F_w$) of gear teeth must be strictly greater than the dynamic load ($F_d$)
(D) Increasing gear face width reduces the total dynamic load experienced by the gear pair
Answer Key:
A, B, C
Step-by-Step Solution & Explanation
- **Statement A is correct:** Tooth profile errors, runout, and torsional vibrations induce inertia forces, creating dynamic load $F_d = F_t + F_i$.
- **Statement B is correct:** In Buckingham's relation $F_d = F_t + \frac{21 v (b C + F_t)}{21 v + \sqrt{b C + F_t}}$, as pitch line velocity $v$ increases, dynamic load asymptotically approaches a plateau governed by error parameter $C$.
- **Statement C is correct:** Gear wear life requires $F_w = d_p b Q K \ge F_d$ to prevent surface pitting and spalling.
- **Statement D is incorrect:** Examining Buckingham's formula, the term $b C$ increases with face width $b$, so a wider face width actually increases dynamic increment $F_i$, though it lowers stress per unit width.