陕西科技大学：《包装技术基础 Fundamentals of Packaging Technology》课程PPT教学课件（英文版）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

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 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

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

Figure 13.1 Representation of mechanical shock

Figure 13.1 Representation of mechanical shock

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

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

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 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

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

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 ◼ 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:

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:

Figure 13.4 A simple product￾package system F igure 13.5 A spring-mass model for the product-package system

Figure 13.4 A simple product￾package 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: