VM-EXD-MECH-010

VM-EXD-MECH-010
Calculation of Velocity of Slider and Force by Collar

Overview

Reference:	Beer-Johnston ‘Vector Mechanics for Engineers’ Statics & Dynamics (In SI Units), 7th Edition, TATA McGRAW HILL Edition 2004, Problem 13.73, Page No: 793
Analysis Type(s):	Explicit Dynamics 3-D (Fully Rigid)
Elements:	Rigid Body Elements and Spring Element
Boundary Conditions:	Remote Displacement (fixed DOFs), Standard Earth Gravity
Structural Interactions:	No
Fluid-Structure Interactions:	No
Connections:	Cylindrical
Materials:	Steel

Test Case

A 1.2 Kg collar is attached to a spring and slides without friction along a circular rod in a vertical plane:

Figure 247: Slider and Collar Schematic

The spring has a nondeformed length of 105 mm and a constant K = 300 N/m. Knowing that the collar is at rest at C, it is given a slight push to get it moving.

Length OP = 75 mm

Length OB = 180 mm

Determine the force exerted by the rod on the collar as it passes through points A and B.

Material Properties

Geometric Properties

E = 2E11 Pa

ν = 0.3

Spring:

Undeformed length = 105 mm

Stiffness K = 300 N/m

Gravitational acceleration = -9.8066 m/s² (Y direction)

Results Comparison

Results	Target	Explicit Dynamics [1]	Error (%)
At point A (N)	15.345	15.346	.0065
At point B (N)	-24.017	-24.017	0

To compare these results to those obtained using rigid body dynamics, see VM-WB-MECH-057.