Stress Analysis of Screw Threads

Structural Design and Analysis
Engineering Analysis

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Stress Analysis of Screw Threads

During the past several years of production at Rock Island Arsenal, approximately 10% of all submitted material nonconformances have directly involved thread forms. Variations in minor, pitch, and major diameters along with other geometry considerations in V, Acme, Buttress, and special thread forms; may adversely affect the assembly, life, and strength of a given thread joint. Nonconforming parts have ranged from common fasteners under static loading to recoil yokes and piston adapters subjected to enormous weapon firing loads. The cost/scheduling impact and critical function requirements have established a crucial need for a rapid and reliable thread joint evaluation method.

Thread analysis procedures to date include (1) Precedent Method, (2) Thread Class Substitution, (3) Routine Stress Analysis, and (4) Testing. The Precedent Method, as the name implies, bases a thread nonconformance evaluation on previous evaluations of similar types under similar loading and environmental conditions, where these results may be derived from calculations, experiments, or experience. This method is practical and effective, being employed whenever a reasonable and verifiable precedent case can be found. The quantitative "how much" or "how bad" answers, however, must be obtained by other means.

The Class Substitution Method, somewhat similar in philosophy to the Precedent Method, uses the tolerance variations within thread class specifications as a criterion for acceptance. The method is primarily a "rule-of-thumb" approach and also lacks quantitative accessment of thread joint performance. The Class Substitution Method, used only occasionally for critical fit applications, does have the distinct advantage of providing distinct documented limits, but is generally so conservative as to disqualify thread conditions that still possess adaquate strength.

Routine Stress Analysis, using the more readily available textbook references, serve to provide quantitative analysis of limited accuracy, being based on several simplifying and gross assumptions. Highly detailed stress results, leading to more accurate analysis, is not a simple exercise and must generally be conducted by persons having that specialized discipline. Usually, evaluation response time for a given occurance precludes this type of in-depth analysis.

The testing approach, used sparingly due to cost and time constraints, offers perhaps the most accurate and verifiable means of analyzing thread nonconformances. Testing as a sole means of evaluation, however, would require experimental recreation of exact geometry and loading conditions per given nonconformance. More general experiments designed to evaluate"trends" due to certain geometry and load conditions can provide useful and interesting results, but seldom provide the required degree of accuracy.

An alternative evaluative method, which is being documented in this report, involves development of three-dimensional state-of-stress equations using specific thread geometry relati )nships and Heywood's formula. Thorough literature research on thread analysis, both domestic and foreign, have confirmed and further refined this analytical approach to solve joint strength of nonconforming threads. However, as with any analytical solution, several key assumptions were required to simplify complicated geometries and loading conditions. Some experimental data adopted from literatures and mathematical model were integrated into an interactive computer program for solution of user supplied thread geometry, applied loads and material property parameters. In this report, both static analysis and fatigue analysis were provided under assumption of elasticity.

Table of Content

List of Tables
List of Figures
1. Introduction
2. Thread Geometry
3. Theoretical Background
3.1 Failure Modes
3.2- Load Distribution along Threaded Connection
3.3 Axial Load
3.4 Shear Failure
3.5 Preload
3.6 Thread Load and Heywood's Formula
3.7 Pressure Flank Load Distribution
3.8 Combined Loading
3.9 Fatigue
4. Interactive Computer Program on Thread Stress Analysis
5. Discussion
6. References
7. Appendices
A.1 Program Variable List
A.2 Common BLOCKS
A.3 Compile and Load Instructions
A.4 Main Program and Subroutines
A.5 Example 1: V Thread
A.6 Example 2: Acme Thread
A-7 Example 3: Stub Acme Thread
A.8 Example 4: Buttress Thread
A.9 Example 5: PF20 Waterviet Special Thread

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