Topic: Design of Mechanical Components

Fatigue Loading Conditions, Statics and Stress Analysis

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.

1. Fatigue Loading Conditions -

The fatigue loading conditions are based on the following loading conditions as given by the instructor. The preload static weight is set at W-min=1000 lbs.; this is taken to be the minimum static force acting on the spring during the lifetime operation of the vehicle. Dynamic loading over and above the preload static weight is determine by the use of an equivalent maximum static weight W-N-max=W-min + N*200 lbs. where N=1, 2, ... ,10. Each case N represents a separate fatigue loading condition based on the spring osculating (i.e., alternating) in compression between the W-min load static weight case and the weight W-N-max load static weight case. There is an actual vehicle loading and road surface condition that would cause the spring to osculate in deflection between the spring compression lengths equivalent to the static loadings from W-min to W-N-max. Of course, the actual vehicle loading would include both spring and damper (i.e., shocks) system to achieve the same equivalent static loadings from W-min to W-N-max that is being treated in Project 2. That is, the dynamic loading for case (W-min, W-N-max) could be simulated by vehicle hitting bumps, traveling on uneven road surfaces, and/or potholes at various speeds as well as various loading scenarios of passengers, luggage, and/or payload as well as driving behavior. In Project 2, it is unnecessary to go into the actual vehicle loading and road surface conditions that equates to the equivalent static loading condition of the case (W-min, W-N-max). Instead, for each N, we take the (W-min, W-N-max) case as a fatigue condition case. In summary, W-min is the minimum static force acting on the spring during a fatigue loading condition. W-N-max=W-min + N*200 lbs. where N=1, 2, ... ,10 is the maximum static force acting on the spring during a fatigue loading condition. We assume fatigue conditions to be at the rate of 10 (stress reversals) cycles per mile with miles traveled to be 10,000 miles per year for 10 years; that is, the spring cycles from a minimum compressed deflection caused by W-min to a maximum compressed deflection caused by W-N-max and then back again to a minimum compressed deflection caused by W-min. The spring cycles at the rate of 10 (stress reversals) cycles per mile for case N.

2. Fatigue Stresses -

For each of the spring-loaded fatigue conditions (W-min, W-N-max) where W-N-max=W-min + N*200 lbs. and where N=1, 2, ... ,10, determine max shear stress τ_W-N-max due to W-N-max.

Step 1: For the fatigue condition (W-min, W-N-max) case (for each N where N=1, 2, ... ,10) provide FBDs as needed and determine the fatigue shear stress τ_W-N-max where the shear stress τ_W-N-max is associated with a W-N-max static loading on the spring. The FBDs are for the development of the equations relating the applied force on spring to the development of the worst-case shear stresses in the spring, similar to that in Chapter 3 for the W-min case. The equation of interest here is equation #4c τ_xy-total-c as developed in Ch3 in which K_w = [4C-1]/[4C-4] +1.23/(2C) is the Wahl curvature factor: τ_xy-total-c =2C(F/A) [ (4C-1)/(4C-4) +1.23/(2C)]. Recall that this equation was used in Ch3 with F = W-min to compute τ_W-min. In Step 1 here, use this same equation with F= W-N-max to compute τ_W-N-max for each N=1, 2, ... ,10. Develop a table of the fatigue shear stresses τ_W-N-max, N=1, 2, ... ,10, showing results in both metric (MPa) units and English (ksi) units.

3. Fatigue Operating Points Plots -

Step 2: Develop a table of the N operating points (τ_W-min, τ_W-N-max), N=1, 2, ... ,10, showing results in both metric (MPa) units and English (ksi) units.

Step 3: Develop two "min-max" type plots of the N operating points (τ_W-min, τ_W-N-max), N=1, 2, ... ,10, one using ksi units; the other using MPa units.

Step 4: Determine the N operating points (for each N=1, 2, ... ,10) using the mean shear stresses τ_mean = (τ_W-N-max + τ_W-min)/2 and the alternating shear stresses τ_alt = (τ_W-N-max - τ_W-min)/2. Develop a table of the N operating points (τ_mean, τ_alt), N=1, 2, ... ,10, showing results in both metric (MPa) units and English (ksi) units.

Step 5: Develop two "mean-alt" type plots of the N operating points (τ_mean, τ_alt), N=1, 2, ... ,10, one using ksi units; the other using MPa units.

Step 6: State clearly in this chapter that the operation of fatigue condition takes place at the rate of 10 cycles per mile with miles traveled to be 10,000 miles per year for 10 years; the fatigue condition rate is for each case, N=1, 2, ... ,10.

4. References -

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

5. Level of Effort -

Document the total number of hours spent on this chapter of the project.

Attachment:- Assignment Files.rar