Lesson 13 Mechanical Shock Theory 第13课机械冲击理论
Lesson 13 Mechanical Shock Theory 第13课 机械冲击理论
Introduction Throughout the distribution system, packages are manhandled and mishandled in various ways dropped, thrown, kicked and otherwise roughly abused fall from conveyors or forklifts and crash to the floor subjected to a variety of vehicle impacts; trucks starting, stopping, hitting chuckhole and railroad crossings, railcar humping, jolting and other moderately violent actions suffers an impact with another object: floor, truck bed, pallet, bulkhead or another package. A mechanical shock occurs when an object's position, velocity or acceleration suddenly changes. Such a shock may be characterized by a rapid increase in acceleration followed by a rapid decrease over a very short period of time. Figure 13.1: the acceleration versus time plot for most shocks
Introduction ◼ Throughout the distribution system, packages are manhandled and mishandled in various ways: dropped, thrown, kicked and otherwise roughly abused; fall from conveyors or forklifts and crash to the floor; subjected to a variety of vehicle impacts; trucks starting, stopping, hitting chuckholes and railroad crossings, railcar humping, jolting and other moderately violent actions; suffers an impact with another object：floor, truck bed, pallet, bulkhead or another package. ◼ A mechanical shock occurs when an object's position, velocity or acceleration suddenly changes. Such a shock may be characterized by a rapid increase in acceleration followed by a rapid decrease over a very short period of time. ◼ Figure 13.1: the acceleration versus time plot for most shocks
ACCELERATION ACCELERATION gs time(milliseconds) time(mIlliseconds) a Figure 13.1 Representation of mechanicalshock
Figure 13.1 Representation of mechanical shock
边sh a package shock may typically be 20 milliseconds(. 020 seconds)long and have a magnitude or height"of 150 gs. need to know both the magnitude of the acceleration and the duration of the shock The Free Falling Package the length of time it takes a package to fall from a drop height, h the downward velocity at which it will be traveling a moment before impact;, the impact velocity ugh As is shown in Figure 13.2. a package will rebound a little or a lot depending on the nature of the package and the surface it hits
A package shock may typically be 20 milliseconds (0.020 seconds) long and have a magnitude or "height" of 150 g's. need to know both the magnitude of the acceleration and the duration of the shock. The Free Falling Package ◼ the length of time it takes a package to fall from a drop height, h ◼ the downward velocity at which it will be traveling a moment before impact; , the impact velocity: ◼ As is shown in Figure 13.2. A package will rebound a little or a lot depending on the nature of the package and the surface it hits. g h t 2 = g h t 2 = g h t 2 = g h t 2 = v gh I = 2 vI = 2gh
V=0 V=V V=VI IMPACT REBOUND Total velocity change =I VII+I VR Figure 13.2 A falling package
Figure 13.2 A falling package
coefficient of restitution, e, describes the rebound velocity as a function of the impact velocity 13.1 total velocity changeR evr 13.2 △v=vr+vR (1+e)1=(1+e)2gh 13.3 Becauseo 1(typical values falling in the 0.3 to 0.5 range) 2gh≤A≤2√gh 13,4 velocity change is also numerically equal to the area beneath the shock pulse as shown in Figure 13.3
coefficient of restitution, e, describes the rebound velocity as a function of the impact velocity 13.1 total velocity change: 13.2 13.3 Because 0 1(typical values falling in the 0.3 to 0.5 range): 13.4 velocity change is also numerically equal to the area beneath the shock pulse as shown in Figure 13.3. vR = evI I R v = v + v v = (1+ e)vI = (1+ e) 2gh 2gh v 2 2gh
Area Veloci ty Change 山uOxu DURATIO MILLISECONDS Figure 13. 3 The relationship among shock parameters
Figure 13.3 The relationship among shock parameters
Package damage is related to the three factors involved in mechanical shock: Peak Acceleration ■ Duration a Velocity Change Mechanical Shock Theory Shown in Figure 13. 4, the product-package system consists of four basic components: the outer container, the cushion, the product, and a critical element a shown in Figure 13. 5: the product-package model:
Package damage is related to the three factors involved in mechanical shock: ◼ Peak Acceleration ◼ Duration ◼ Velocity Change Mechanical Shock Theory ◼ Shown in Figure 13.4, the product-package system consists of four basic components: the outer container, the cushion, the product, and a critical element. ◼ shown in Figure 13.5: the product-package model:
M1, CRITICAL ELEMENT M2, PRODUCT CONTAINER M CUSHION Figure 13. 4 A simple product- package system igure 13.5 A spring-mass model for the product-package system
Figure 13.4 A simple productpackage system F igure 13.5 A spring-mass model for the product-package system
M2-the mass of the product M1-represents the mass of the critical element or CE M3-represents the mass of the outer container Kl- the linear spring constant of the sprint-mass system representing the critical element k2 -the linear spring constant of the cushion system Assumptions for simplicity: a. ignore the mass of the outer container and assume that it provides no spring action b the cushion has no mass or damping and suffers no permanent deflection from a shock; C the product-package system impacts a perfectly rigid floor; d. the mass of the critical element is negligible compared to the mass of the product In Figure 13.6, the impact of a product-package:
◼ M2 - the mass of the product ◼ M1- represents the mass of the critical element or CE ◼ M3 - represents the mass of the outer container ◼ kl - the linear spring constant of the sprint-mass system representing the critical element ◼ k2 - the linear spring constant of the cushion system Assumptions for simplicity: a. ignore the mass of the outer container and assume that it provides no spring action; b. the cushion has no mass or damping and suffers no permanent deflection from a shock; c. the product-package system impacts a perfectly rigid floor; d., the mass of the critical element is negligible compared to the mass of the product. In Figure 13.6, the impact of a product-package: