mech engg paraphrasing

Executive Summary

A Phosphor-bronze (B159) helical compression spring will be designed with infinite life that could sustain a fluctuating dynamic load that varies from 4 to 18 lbf at a frequency of 6.5 Hz [1]. The deflection of the spring varies from 0.5 to 2 inches [1]. Due to an assembly considerations, the solid height must not exceed 1.0 inches and the free length cannot be more than 4.0 inches [1]. The spring-maker has certain sizes of wires in stock: 0.075, 0.078, 0.080, 0.085, 0.090, 0.095, 0.105, and 0.112 inches [1]. The spring is required to be an as wound, un-peened spring that has been squared and ground. Calculations were performed for all available wire sizes in this material using equations, tables, figures, and examples provided in the 10th edition of Shigley’s Mechanical Engineering Design textbook [2]. The calculation outcomes were then compared to the failure criteria that could be shown in Table 1. Red highlighted values in Table 2 represents the failure spots where the outcomes have not met the design criteria.

Table 1: Table of failure criteria

The calculation outcomes verified the size of the wire that should be used, which is 0.095 inches as shown in Table 2. The calculated index of the designed spring (C) was 10.46 which lied under the given range between 4 and 12. The number of active coils (Na) for the wire size of 0.095 was calculated to be 6.9 turns, which is within the acceptable range of 3 to 15 turns. The solid length of the spring (Ls) was founded to be 0.85 inches and is under the required 1 inch maximum. The free length (Lo) was to be 3.15 inches which is under the 4 inches maximum of free length. The critical free length (Lo)crwas larger than the calculated free length with a value of 5.23 inches. The factor safety for both fatigue (nf) and solid height (ns) were 1.5 or larger as indicated. The designed spring has a natural frequency of 133.3 which is significantly greater in comparison to the operating of 6.5 Hz and is larger than the required criteria of 130 Hz. The wire of 0.095 only failed in the natural frequency unlike the others where they failed in more than one criteria. The calculation concluded that the wire size of 0.095 is the optimal one for this material and the design constraints. Sample of a hand calculations will be attached in Appendix A

Table 2: Table shows the wire sizes along with the optimal and the failure spots.

References:

[1]Mindek, Richard B., ME 425 Design of Machine Elements –Final Design Project, Western New England University, 2015

[2] Budynas, Richard G., Nisbett, J. Keith, Shigley’s Mechanical Engineering Design, 10th ed., McGraw-Hill, New York, 2015

Appendix A

Wire Size0.0750.0780.0800.0850.0900.0950.1050.112

Mean Coil DiameterD (in)0.440.510.560.690.830.991.381.69

Inner DiameterID (in)0.370.430.480.600.740.901.271.58

Outer DiameterOD (in)0.520.590.640.770.921.091.481.80

Spring IndexC5.936.556.988.089.2410.4713.1115.10

Number of Active CoilsNa (turns)29.9423.1119.6313.439.506.903.892.71

Solid LengthLs (in)2.401.961.731.311.030.850.620.53

Free LengthLo (in)4.704.264.033.613.333.152.922.83

Critical Length(Lo)cr (in)2.342.692.943.614.385.237.248.90

Fatigue Factor of Safetynf1.501.501.501.501.501.501.501.50

Solid Height Factor of Safetyns1.601.601.591.591.581.581.571.56

Natural Frequencyfn121.16123.73125.25128.48131.09133.25136.57138.34

fom-1.58-1.54-1.53-1.51-1.53-1.58-1.76-1.97

d (in)