Select the most suitable ball screw nominal diameter (in inches) from the list below if the load on the screw is 20,000 lb and it is required to move the load up and down 14 inches in 12s and 13 times per day. The design life is 15 years.

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The question asks to select the most suitable ball screw nominal diameter (in inches) given a 20,000 lb load that must travel 14 inches up and down in 12 seconds, with 13 cycles per day, over a design life of 15 years.

First, note that the provided data allows evaluating the required dynamic capacity and service conditions for the screw because the axial load, travel speed, travel distance per cycle, and life are the key drivers for choosing a nominal diameter. In a typical design workflow, you would:
- Determine the required dynamic (Load) rating of the ball screw to safely carry 20,000 lb under the stated motion profile, including any service factor for start/stop, acceleration, reversal, and duty cycle.
- Convert the motion information into a duty cycle and calculate the equivalent dynamic load over the design life, often using a life factor (L10) and a safety factor based on standards or manufacturer guidelines.
- Compare the resulting required dynamic capacity to the available ratings for candidate diameters, while also considering efficiency, lead, and friction characteristics that affect speed and backdriving risk.

Option-related reasoning (in the absence of explicit alternative diameters):
- If the only supplied answer is 2.5 inches, you would expect a tolerance of design criteria such that a 2.5-in nominal ball screw provides sufficient dynamic load capacity for a 20,000 lb load under the given cycle rate, run time, and life expectancy (15 years). This implies the screw diameter has been selected to meet or exceed the calculated dynamic rating with an appropriate safety factor.
- In a complete multiple-choice context, the other diameters (e.g., smaller diameters) would typically fail to meet the required dynamic capacity or life requirements, while larger diameters might be acceptable but would need justification regarding weight, cost, and efficiency. Without the actual alternative options listed, we can’t assess those specific trade-offs here.

Regarding the provided data and the absence of option list: the problem would normally be solved by consulting a ball screw catalog or calculation method that provides dynamic load ratings for standard diameters at the given lead and efficiency, then selecting the smallest diameter that meets the life and duty requirements. Since the option list is empty in the prompt, we can only reason from the given correct answer value of 2.5 inches and describe the general method by which such a value would be validated in practice.

Summary of key factors that would justify a 2.5-inch nominal diameter in a fully specified design:
- Dynamic load rating is at least equal to or greater than the equivalent dynamic load derived from the 20,000 lb operating load, accounting for the cyclic dwell time and reversal during 13 daily cycles.
- The design life of 15 years is supported by a life factor applied to the dynamic rating, ensuring L10 reliability with an appropriate safety margin.
- The motion profile (14 inches per cycle, with 12 s total duration) informs the lead and efficiency considerations; the chosen diameter must maintain acceptable speed, heat generation, and backdriving resistance within allowable limits.
- Practical constraints such as weight, space, cost, and installation complexity are balanced, and 2.5 inches often represents a common nominal size that satisfies high-load scenarios while keeping the system reasonably compact.

43017 Machines and Mechanisms B - Autumn 2025 Pass-level quiz 4: Power and ball screws. Brakes and clutches. Mechanisms.

Select the most suitable ball screw nominal diameter (in inches) from the list below if the load on the screw is 20,000 lb and it is required to move the load up and down 14 inches in 12s and 13 times per day. The design life is 15 years.

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