{"id":557425,"date":"2024-11-05T18:17:59","date_gmt":"2024-11-05T18:17:59","guid":{"rendered":"https:\/\/pdfstandards.shop\/product\/uncategorized\/esdu-080152009\/"},"modified":"2024-11-05T18:17:59","modified_gmt":"2024-11-05T18:17:59","slug":"esdu-080152009","status":"publish","type":"product","link":"https:\/\/pdfstandards.shop\/product\/publishers\/esdu\/esdu-080152009\/","title":{"rendered":"ESDU 08015:2009"},"content":{"rendered":"<p><strong>INTRODUCTION<\/strong><\/p>\n<p>The dynamic behaviour of cylindrical helical springs, comprising<br \/>\nboth tension\/compression and torsion springs, is extremely<br \/>\ndifficult to calculate since its geometrical shape is a curve in<br \/>\nthree-dimensional space. To make the calculations manageable,<br \/>\nsimple but representative mathematical models are required. The<br \/>\nsimplest of such models is the straight elastic rod, the so called<br \/>\n\u2018equivalent rod&#039; which clearly must have the same elastic<br \/>\nproperties as the helical spring it represents. It is rather<br \/>\nsurprising, but fortunate, that the use of this very simple<br \/>\nmathematical model should yield such reasonable results, certainly<br \/>\naccurate enough for most practical purposes<\/p>\n<p>An earlier Data Item No. 06024<sup>[2]<\/sup> defined the<br \/>\nassumptions and limitations that apply to the calculation procedure<br \/>\nfor estimating the dynamic characteristics of springs, together<br \/>\nwith the prescribed loading conditions assumed to apply to the<br \/>\nspring. The Item also provided derivation of the deformation,<br \/>\nstresses and transverse loading on the spring and the form design<br \/>\nof the spring ends which will affect the loading characteristics.<br \/>\nThe elastic stability of compression and torsion springs are<br \/>\ndiscussed and formulae given for ensuring stability.<\/p>\n<p>The present Item extends the scope of the earlier Item,<br \/>\npresenting the vibration characteristics of cylindrical helical<br \/>\nsprings.<\/p>\n<p>Section 3 discusses the axial vibration of compression\/tension<br \/>\nhelical springs on the basis of the \u2018equivalent rod&#039; approximation,<br \/>\ndealing with both free and forced axial vibration. For free<br \/>\nvibration, cases when both ends of the rod are free, one end of the<br \/>\nrod is clamped and the other end is free and both ends of the rod<br \/>\nare clamped, are considered. For forced vibration, the case when<br \/>\none end of the spring is forced to follow a cyclic motion and the<br \/>\nstresses induced by the cyclic motion is discussed .<\/p>\n<p>Section 4, considers the free and forced vibrations of a<br \/>\nspring-mass system in reasonable detail, dealing with the cases<br \/>\nwhen the system mass is large compared to the mass of the spring<br \/>\nand of comparable size. The influence of various kinds of damping,<br \/>\nCoulomb and viscous friction, material hysteresis, etc. are also<br \/>\ndiscussed. In conjunction with forced vibration, the resonance<br \/>\nphenomenon is dealt with in a number of sections. Although it is an<br \/>\nimportant design principle to avoid resonance whenever possible, in<br \/>\nhigh speed applications it is sometimes inevitable that the elastic<br \/>\nsystem during its normal operation must pass through the resonance<br \/>\ndomain. In such cases the only practical possibility is to try to<br \/>\navoid sustained resonance. Recognising the engineering importance<br \/>\nof this problem a separate section is devoted to the discussion of<br \/>\nthe transition through resonance.<\/p>\n<p>A further Data Item in this series on springs, No.<br \/>\n09003<sup>[3]<\/sup>, considers the dynamic characteristics of<br \/>\ncylindrical helical springs due to impact loading, which is an<br \/>\nintegral part of the normal operation of the majority of machines<br \/>\nthat execute rapid alternating motion. The Item also provides<br \/>\nworked examples that estimate spring dynamic performance.<\/p>\n","protected":false},"excerpt":{"rendered":"<p><b>Dynamic Characteristics of Cylindrical Helical Springs &#8211; Part 2: Vibration<\/b><\/p>\n<table style=\"width: 100%\" border=\"0\" cellspacing=\"0\" cellpadding=\"0\">\n<tbody>\n<tr>\n<td>Published By<\/td>\n<td>Publication Date<\/td>\n<td>Number of Pages<\/td>\n<\/tr>\n<tr>\n<td><a href=\"https:\/\/pdfstandards.shop\/product-category\/publishers\/esdu\/\"><b>ESDU<\/b><\/a><\/td>\n<td>2009-08<\/td>\n<td>64<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n","protected":false},"featured_media":557435,"template":"","meta":{"rank_math_lock_modified_date":false,"ep_exclude_from_search":false},"product_cat":[2675],"product_tag":[],"class_list":{"0":"post-557425","1":"product","2":"type-product","3":"status-publish","4":"has-post-thumbnail","6":"product_cat-esdu","8":"first","9":"instock","10":"sold-individually","11":"shipping-taxable","12":"purchasable","13":"product-type-simple"},"_links":{"self":[{"href":"https:\/\/pdfstandards.shop\/wp-json\/wp\/v2\/product\/557425","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/pdfstandards.shop\/wp-json\/wp\/v2\/product"}],"about":[{"href":"https:\/\/pdfstandards.shop\/wp-json\/wp\/v2\/types\/product"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/pdfstandards.shop\/wp-json\/wp\/v2\/media\/557435"}],"wp:attachment":[{"href":"https:\/\/pdfstandards.shop\/wp-json\/wp\/v2\/media?parent=557425"}],"wp:term":[{"taxonomy":"product_cat","embeddable":true,"href":"https:\/\/pdfstandards.shop\/wp-json\/wp\/v2\/product_cat?post=557425"},{"taxonomy":"product_tag","embeddable":true,"href":"https:\/\/pdfstandards.shop\/wp-json\/wp\/v2\/product_tag?post=557425"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}