{"id":17274,"date":"2022-09-27T11:03:15","date_gmt":"2022-09-27T10:03:15","guid":{"rendered":"https:\/\/mollificiovalli.it\/?p=17274"},"modified":"2022-11-21T11:57:21","modified_gmt":"2022-11-21T10:57:21","slug":"fatigue-failure-of-a-spring","status":"publish","type":"post","link":"https:\/\/mollificiovalli.it\/en\/fatigue-failure-of-a-spring\/","title":{"rendered":"FATIGUE FAILURE OF A SPRING: W\u00d6HLER AND GOODMAN DIAGRAMS"},"content":{"rendered":"

We continue on the topic of spring failure<\/a>, talking about statistical tools<\/strong> (in graph \/ table form), which can be used for a preventive check of the spring geometry, to assess the risk of fatigue failure: W\u00f6hler and Goodman diagrams.<\/strong><\/p>\n

 <\/p>\n

Let’s focus on the use of springs in dynamic regime<\/em>. We can say dynamic regime<\/em> when the number of cycles of use exceeds 10,000 within the life cycle of a spring. The fatigue verification tables start at 105 cycles.<\/p>\n

At the moment there is no physical-mathematical theory that constitutes a predictive model for the fatigue verification<\/strong>. In the absence of a model, we rely on physical tests, the results of which are systematically organized with the aid of statistical tools.<\/p>\n

In other words, empirical curves<\/strong> have been obtained over the years, based on the repetition of hundreds \/ thousands of fatigue tests, on springs with known stress, varying the stroke (difference between L2<\/em> and L1<\/em>) and noting the number of cycles at which the failure occurred.<\/p>\n

 <\/p>\n

W\u00f6hler diagram<\/h2>\n

Assuming the homogeneity of the batch of tested springs, both from a dimensional point of view and the mechanical characteristics of the wire, a common trend should emerge regarding the number of cycles at which the spring breaks.<\/p>\n

The distribution of the number of cycles under the same conditions is practically normal as the mean and variance can be estimated on the basis of the sample data.<\/p>\n

Using the inferential statistic<\/strong>, we define a value which significantly (in a statistical sense) includes 95% of the detected values. That value indicates the fatigue life<\/strong> for a specific material between two defined stresses (initial at L1<\/em> and final at L2<\/em>).<\/p>\n

The tests are repeated by increasing the stress at L2<\/em> and keeping the stress fixed at L1<\/em>.<\/p>\n

It is not possible to test for all the stresses continuously. We choose an incremental interval between one test batch and the other and we linearly interpolate between the two values.<\/p>\n

Representing the information obtained in a graph with a logarithmic scale (x-axis), we obtain an S-diagram<\/strong>, the so-called W\u00f6hler diagram<\/a>.<\/p>\n

The figure below shows a W\u00f6hler diagram<\/em> for a carbon spring steel, assuming a fixed stress at L1<\/em> of 100 Mpa<\/em> and increasing the stress at L2<\/em> over 900 Mpa<\/em>.<\/p>\n

You will notice that at 700 Mpa<\/em> practically the spring has an infinite duration, the curve flattens, while as the stress at L2<\/em> increases, we observe a decrease in the cycles at which the break occurs.<\/p>\n

 <\/p>\n

\"Diagramma

 <\/p>\n

Goodman diagram<\/h2>\n

The W\u00f6hler diagram<\/em> is a less practical<\/strong> tool for the purpose of theoretical verification.<\/p>\n

By combining the results<\/strong> of multiple W\u00f6hler diagrams<\/em>, it is possible to obtain a graph that is definitively more manageable<\/strong>: we are talking about the Goodman diagram<\/em>.<\/p>\n

The Goodman diagram<\/em> has a trapezoidal shape, bounded below by the bisector of the quadrant and above by a line that defines the fatigue strength limit. The figure is defined with a horizontal line representing the yield stress limit<\/strong>.<\/p>\n

The initial stress (at L1<\/em>) is reported on the x-axis and the final stress (at L2<\/em>) on the y-axis.<\/p>\n

 <\/p>\n

 <\/p>\n

\"Diagramma

 <\/p>\n

The use of the Goodman diagram<\/em> is relatively simple, given the stresses at L1<\/em> and L2<\/em>, the point is identified on the Cartesian plane, using the stresses as coordinates.<\/p>\n

If the point falls within the trapezium area, the spring is checked under stress<\/strong>, if it is outside it is not. It is reasonable to expect fatigue failure before reaching the number of cycles indicated on the graph.<\/p>\n

In the figure shown 3 almost parallel upper straight lines are visible. These lines identify the safety area for 105 <\/sup>– 106 <\/sup>\u2013 107 <\/sup>cycles, in a decreasing sense. The top line is for 105 <\/sup> cycles and the bottom line is 107 <\/sup> cycles. It is intuitive that longer durations are obtained by decreasing the stress at L2<\/em>.<\/p>\n

For this reason, if we expect a dynamic use of the spring, a preliminary fatigue check is required<\/strong>, using the appropriate Goodman diagram<\/em>, in relation to the material with which the spring is to be produced.<\/p>\n

An unverified spring is a candidate for premature failure<\/strong> for reasons related to the phenomenon of fatigue.<\/p>\n","protected":false},"excerpt":{"rendered":"

We continue on the topic of spring failure, talking about statistical tools (in graph \/ table form), which can be used for a preventive check of the spring geometry, to assess the risk of fatigue failure: W\u00f6hler and Goodman diagrams.   Let’s focus on the use of springs in dynamic regime. We can say dynamic […]<\/p>\n","protected":false},"author":5,"featured_media":16698,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[318,332],"tags":[],"class_list":["post-17274","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-news-en","category-technical-articles"],"_links":{"self":[{"href":"https:\/\/mollificiovalli.it\/en\/wp-json\/wp\/v2\/posts\/17274","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/mollificiovalli.it\/en\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/mollificiovalli.it\/en\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/mollificiovalli.it\/en\/wp-json\/wp\/v2\/users\/5"}],"replies":[{"embeddable":true,"href":"https:\/\/mollificiovalli.it\/en\/wp-json\/wp\/v2\/comments?post=17274"}],"version-history":[{"count":0,"href":"https:\/\/mollificiovalli.it\/en\/wp-json\/wp\/v2\/posts\/17274\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/mollificiovalli.it\/en\/wp-json\/wp\/v2\/media\/16698"}],"wp:attachment":[{"href":"https:\/\/mollificiovalli.it\/en\/wp-json\/wp\/v2\/media?parent=17274"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mollificiovalli.it\/en\/wp-json\/wp\/v2\/categories?post=17274"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mollificiovalli.it\/en\/wp-json\/wp\/v2\/tags?post=17274"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}