{"id":557434,"date":"2024-11-05T18:18:00","date_gmt":"2024-11-05T18:18:00","guid":{"rendered":"https:\/\/pdfstandards.shop\/product\/uncategorized\/esdu-090032009\/"},"modified":"2024-11-05T18:18:00","modified_gmt":"2024-11-05T18:18:00","slug":"esdu-090032009","status":"publish","type":"product","link":"https:\/\/pdfstandards.shop\/product\/publishers\/esdu\/esdu-090032009\/","title":{"rendered":"ESDU 09003:2009"},"content":{"rendered":"

INTRODUCTION<\/strong><\/p>\n

The dynamic behaviour of cylindrical helical springs, comprising
\nboth tension\/compression and torsion springs, is extremely
\ndifficult to calculate since its geometrical shape is a curve in
\nthree-dimensional space. To make the calculations manageable,
\nsimple but representative mathematical models are required. The
\nsimplest of such models is the straight elastic rod, the so called
\n\u2018equivalent rod' which clearly must have the same elastic
\nproperties as the helical spring it represents. It is rather
\nsurprising, but fortunate, that the use of this very simple
\nmathematical model should yield such reasonable results, certainly
\naccurate enough for most practical purposes.<\/p>\n

The first Data Item in this series on springs, No. 06024,
\ndefines the assumptions and limitations that apply to the
\ncalculation procedure for estimating the dynamic characteristics of
\nsprings, together with the prescribed loading conditions assumed to
\napply to the spring. The Item also provides derivation of the
\ndeformation, stresses and transverse loading on the spring and the
\nform design of the spring ends which will affect the loading
\ncharacteristics. The elastic stability of compression and torsion
\nsprings is discussed and formulae given for ensuring stability.<\/p>\n

The second Data Item, No. 08015, extends the scope of the
\nearlier Item, presenting the vibration characteristics of
\ncylindrical helical springs. The Item discusses the axial vibration
\nof compression\/tension helical springs on the basis of the
\n\u2018equivalent rod' approximation, dealing with both free and forced
\naxial vibration. For free vibration, cases when both ends of the
\nrod are free, one end of the rod is clamped and the other end is
\nfree and both ends of the rod are clamped, are considered. For
\nforced vibration, the case when one end of the spring is forced to
\nfollow a cyclic motion and the stresses induced by the cyclic
\nmotion is also discussed.<\/p>\n

ESDU 08015 further considers free and forced vibrations of a
\nspring mass system, dealing with the two cases when the system mass
\nis large compared to the mass of the spring and when it is of
\ncomparable size. The influence of various kinds of damping, Coulomb
\nand viscous friction, material hysteresis, etc. is also discussed.
\nIn conjunction with forced vibration, the resonance phenomenon is
\ndealt with in a number of sections. Although it is an important
\ndesign principle to avoid resonance whenever possible, in high
\nspeed applications it is sometimes inevitable that the elastic
\nsystem during its normal operation must pass through the resonance
\ndomain. In such cases the only practical possibility is to try to
\navoid sustained resonance. Recognising the engineering importance
\nof this problem a separate section is devoted to the discussion of
\nthe transition through resonance.<\/p>\n

The present Item extends the scope of the earlier Items to
\nimpact loading.<\/p>\n

In the majority of machines, particularly those which execute
\nalternating motion, impacts occur during their normal operation.
\nOften displacement impacts are small, such as clearances in
\nbearings or joints, in other cases the impacts are an integral part
\nof the normal functioning of the machines or mechanisms, for
\nexample in vehicle suspensions systems, valves of internal
\ncombustion engines, forging hammers, firearms, etc. In these latter
\ncases springs are normally employed to absorb or store the energy
\nof the impact. When designing machine components for impact
\nloading, the stresses and deformations in the components must be
\nconsidered. It is also necessary to find out what effects these
\nstresses and deformations have on the materials involved.<\/p>\n

The classical theory of impact regards the bodies involved as
\nrigid and the impact as being instantaneous and so it is suitable
\nonly for determining the kinetic consequences of the impact. When
\nthe impact process itself is to be investigated, i.e.<\/i> its
\nduration and the deformations, forces and stresses involved, much
\nmore advanced theories must be used. However, when the dynamic
\nbehaviour of only a spring mass system after impact is the subject
\nof the investigation, and not that of the spring itself, the
\nclassical theory of impact proves to be very useful.<\/p>\n

As far as the impact process is concerned, there are two extreme
\nidealised cases, the perfectly non elastic impact and the perfectly
\nelastic impact. The reality lies somewhere in between these two
\nextremes. Accordingly, in practical calculations a so-called
\n"impact coefficient", designated k, is introduced which has the
\nvalues in the range 0\u00a0lessthan or equal to\u00a0k lessthan or
\nequal to 1. The value of must be determined by experiment. In the
\ncase of a perfectly non elastic impact its value is zero,
\ni.e.<\/i> k = 0\u00a0, and in the case of a perfectly elastic
\nimpact, k = 1.<\/p>\n

In the first part of this Item, the impact on spring mass
\nsystems is investigated using the classical theory of impact. In
\nthe latter part of the Item, the problem of an impact on an elastic
\nrod is considered. This latter problem has a special practical
\nsignificance, since an elastic rod can be used as an "equivalent
\nrod" representing a helical spring.<\/p>\n","protected":false},"excerpt":{"rendered":"

Dynamic Characteristics of Cylindrical Helical Springs – Part 3: Impact Loading on Compression Springs<\/b><\/p>\n\n\n\n\n
Published By<\/td>\nPublication Date<\/td>\nNumber of Pages<\/td>\n<\/tr>\n
ESDU<\/b><\/a><\/td>\n2009-11<\/td>\n43<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n","protected":false},"featured_media":557441,"template":"","meta":{"rank_math_lock_modified_date":false,"ep_exclude_from_search":false},"product_cat":[2675],"product_tag":[],"class_list":{"0":"post-557434","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\/557434","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\/557441"}],"wp:attachment":[{"href":"https:\/\/pdfstandards.shop\/wp-json\/wp\/v2\/media?parent=557434"}],"wp:term":[{"taxonomy":"product_cat","embeddable":true,"href":"https:\/\/pdfstandards.shop\/wp-json\/wp\/v2\/product_cat?post=557434"},{"taxonomy":"product_tag","embeddable":true,"href":"https:\/\/pdfstandards.shop\/wp-json\/wp\/v2\/product_tag?post=557434"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}