Topic: Design of Mechanical Components

Part A - Fatigue Tests/Models, Failure Criteria and Fatigue Failure Mechanisms

Note: All calculations made with equations must be shown in text along with equations. Make calculations using excel. Provide all references used in this section and document.

Background: In Project 1, we understood the difference between Stress Endurance Limits Se and Se'? We understood where they appeared on a fatigue plot. Se' was the (normal) stress endurance limit before fatigue factors are account for. For example, for normal stresses, Se'=0.5*Su for infinite life for steel. Se accounted for the addition of fatigue factors that reduce the stress endurance limit Se'. For example, Se was equal to (Factors)*Se' where (Factors) = (C_LC_GC_SC_TC_R); or (Factors) = (C_LC_GC_SC_TC_R)/K_f; or (Factors) = (C_LC_GC_SC_TC_R)/K_t; where C_L, C_G, C_S, C_T, and C_R are fatigue strength reduction factors; K_f is fatigue stress concentration factor; and K_t is theoretical or geometric (stress concentration) factor. In Project 2, in conducting fatigue analysis, we work directly with shear stresses (and not normal stresses). As a result, we are working with Shear Stress Endurance Limits Ses and Ses' in which Ses=(Shear Stress Factors)*Ses' where (Shear Stress Factors)= C_LsC_GsC_SsC_TsC_Rs. Since curvature effects are directly accounted for in the shear stress correction equation, we essentially take K_t = 1; q = 0; and K_f = 1 in the (Shear Stress Factors) equation. Recall the shear strength properties of our spring material: Sus=1280 MPa=185.65 ksi and Sys=831.38 MPa=120.58 ksi. Also, recall the shear stress fatigue strength life properties of our spring material: S3s=1152 MPa=167.08 ksi; S4s=896 MPa=129.95 ksi; S5s=640 MPa=92.82 ksi; and S6s=464 MPa=67.31 ksi. For these life cases, Se3s'= S3s for L3s; Se4s'= S4s for L4s; Se5s'= S5s for L5s; and Se6s'= S6s for L6s. And, furthermore, Se3s, Se4s, Se5s, and Se6s account for any shear stress factors C_Ls, C_Gs, C_Ss, C_Ts, and C_Rs. Since we work directly with Sus and Sys (without making use of Su and Sy) in computing Ses and Ses', it follows that C_Ls=1.0. Since our Sus and Sys values already account for the wire diameter of the spring, the gradient factor C_Gs =1. Since our spring application avoids high-temperature effects, we have C_Ts =1. We assume the best production wire surface finish that includes "shot peening"; we assume C_Ss = 1. In Project 2 we take CRs = 1. The bottom line is that all fatigue factors are unity for Project 2. The conclusion is that Ses = Ses' for Project 2.

1. Fatigue Factors

Step 1: Construct a table for all shear strength properties and shear stress fatigue strength life properties of the material of Project 2's helical coil compression spring; use both metric and English units.

Step 2: Surface Effects: What is shot peening? How does "surface roughness" affect the "fatigue stress endurance limit?

Step 3: Effects Due to Presetting: What is pre-setting? What is the effect of pre-setting on stresses during loading of helical compression springs?

Step 4: Elevated Temperature Effects: Discuss elevated temperature effects on loading of helical compression springs.

Step 5: Selected Fatigue Factors: Based on the background notes, the instructor requires that all students use the following fatigue factors for all fatigue analysis in Project 2: C_Ls =1; C_Gs =1; C_Ss =1; C_Ts =1; and C_Rs =1 (also, K_t = 1; q = 0; and K_f =1). Of course, with all fatigue factors having unity values, (Shear-Stress-Factors)= C_LsC_GsC_SsC_TsC_Rs = 1 and as a result, Ses=Ses'; Se3s= Se3s'; Se4s= Se4s'; Se5s= Se5s'; and Se6s= Se6s'. Construct a table of the selected fatigue factors.

2. Modified Goodman Fatigue Model

Describe the Modified Goodman fatigue model. [How does it compare with the Goodman fatigue model?] Describe all parameters needed in performing fatigue life analysis for the helical compression spring that uses the Modified Goodman fatigue model. Write an equation for Modified Goodman fatigue model for each life case: L3s; L4s; L5s; and L6s. List all Modified Goodman fatigue model parameters in a table.

3. Fatigue Safety Factor

Describe how the fatigue safety factor is computed when using the Modified Goodman fatigue model (and/or the Goodman fatigue model). Write out an equation for the fatigue safety factor. List all parameters in a table that are needed in the equation for computing the fatigue safety factor for each life case: L3s; L4s; L5s; and L6s.

4. References

List all appropriate references/resources (literature, handouts, PowerPoint slides, papers, web resources) used in your chapter.

Part B - Fatigue Failure Analysis and Life Expectancy

Note: All calculations made with equations must be shown in text along with equations. Make calculations using excel. Provide all references used in this section and document them in this chapter.

[Using modified Goodman fatigue models, conduct fatigue analysis for the ten operating points due to fatigue loading conditions (W-min, W-N-max) where W-N-max=W-min + N*200 lbs. and where N=1, 2, ... ,10. Recall the four fatigue plots that were developed in Ch4 containing the ten operating points; two were "min-max" type plots (one using ksi units; the other using MPa units); and the other two were "mean-alt" type plots (one using ksi units; the other using MPa units). On each of the four fatigue plots include the fatigue model lines for each of the four life conditions L3s, L4s, L5s, and L6s. Determine the life expectancy of the spring for each of the N fatigue loading conditions. Determine fatigue safety factors for each of the ten operating points with respect to the four life conditions L3s, L4s, L5s, and L6s. Provide tables of all results.]

1. Modified Goodman Fatigue Model and Equations

Determine and write-up the equations of the modified Goodman fatigue model that applies for each of the life conditions L3s, L4s, L5s, and L6s. Provide a table of all values (metric and English) that are used in the equations.

2. Min-Max Fatigue Plots (ksi units and MPa units)

Using modified Goodman fatigue model and equations for life conditions L3s, L4s, L5s, and L6s, plot the four (4) modified Goodman fatigue lines on each of the two "min-max" fatigue plots that were developed in Ch4 containing the ten operating points. Provide a table of all values (metric and English) that are used in making the two plots (include the values of the ten operating points).

3. Mean-Alt Fatigue Plots (ksi units and MPa units)

Using modified Goodman fatigue model and equations for life conditions L3s, L4s, L5s, and L6s, plot the four (4) modified Goodman fatigue lines on each of the two "mean-alt" fatigue plots that were developed in Ch4 containing the ten operating points. Provide a table of all values (metric and English) that are used in the two plots (include the values of the ten operating points).

4. Life Expectancy

Conduct fatigue analysis (i.e., determine life expectancy and fatigue safety factors) for the ten operating points due to fatigue loading conditions (W-min, W-N-max) where W-N-max=W-min + N*200 lbs. and where N=1, 2, ... ,10.

Step 1: Determine which of the N fatigue loading conditions provide L3s life expectancy for the spring.

Step 2: Determine which of the N fatigue loading conditions provide L4s life expectancy for the spring.

Step 3: Determine which of the N fatigue loading conditions provide L5s life expectancy for the spring.

Step 4: Determine which of the N fatigue loading conditions provide L6s life expectancy for the spring.

Provide a table of the results coming from Steps 1-4.

5. Fatigue Safety Factors for L3s Life

Determine the fatigue safety factor respect to L3s life for each of the ten operating points due to the N=1, 2, ... ,10 fatigue loading conditions (W-min, W-N-max), W-N-max=W-min + N*200 lbs. Provide a table of all fatigue safety factors respect to L3s life.

6. Fatigue Safety Factors for L4s Life

Determine the fatigue safety factor respect to L4s life for each of the ten operating points due to the N=1, 2, ... ,10 fatigue loading conditions (W-min, W-N-max), W-N-max=W-min + N*200 lbs. Provide a table of all fatigue safety factors respect to L4s life.

7. Fatigue Safety Factors for L5s Life

Determine the fatigue safety factor respect to L5s life for each of the ten operating points due to the N=1, 2, ... ,10 fatigue loading conditions (W-min, W-N-max), W-N-max=W-min + N*200 lbs. Provide a table of all fatigue safety factors respect to L5s life

8. Fatigue Safety Factors for L6s Life

Determine the fatigue safety factor respect to L6s life for each of the ten operating points due to the N=1, 2, ... ,10 fatigue loading conditions (W-min, W-N-max), W-N-max=W-min + N*200 lbs. Provide a table of all fatigue safety factors respect to L6s life.

9. References

List all appropriate references/resources (literature, handouts, PowerPoint slides, papers, web resources) used in your chapter.

Attachment:- Assignment Files.rar