Contents

# ## INTRODUCTION

This article presents a review of the basics of dynamic modeling so as to ascertain a base of data on which to develop the tools for the dynamic analysis of cam-follower systems.

### NEWTON’S LAWS OF MOTION

Dynamic force analysis involves the appliance of Newton’s three laws of motion .

Laws of Motion are explained in detail here:

1. The time rate of change of momentum of a body is capable of the magnitude of the applied force and acts within the direction of the force.

2. for each action force, there’s an equal and opposite reaction force. The second law is expressed in terms of the rate of change of momentum, P = mv, where m is mass and v are velocities. Mass m is assumed to be constant during this analysis. The time rate of change of mv is ma, where a is the acceleration of the mass center.

F a = m

F is the resultant of all forces on the system performing at the mass center. we will differentiate between two subclasses of dynamics problems depending upon which quantities are known and which are to be found.

The “forward dynamics problem” is that the one within which we all know everything about the external loads (forces and/or torques) being exerted on the system, and that we wish to see the accelerations, velocities, and displacements that result from the applying of these forces and torques.

This subclass is typical of problems like determining the acceleration of a block sliding down a plane, acted upon by gravity.

The second subclass of dynamics problem called the “inverse dynamics problem,” is one during which we all know the (desired) accelerations, velocities, and displacements to be imposed upon our system and need to resolve for the magnitudes and directions of the forces and torques that are necessary to produce the specified motions and which result from them.

This inverse dynamics case is usually also called kinetostatics.

Whichever subclass of problem is addressed, it’s important to understand that they’re both dynamics problems.

Each merely solves F = ma for a unique variable. So we must always first review some fundamental geometric principles and mass properties that are needed for the calculations.

DYNAMIC MODELS

It is often convenient in dynamic analysis to form a simplified model of an advanced part.

These models are sometimes considered to be a set of point masses connected by massless rods, spoken as a lumped-parameter model, or simply lumped model.

For a lumped model of a rigid body to be dynamically corresponding to the first body, three things must be true:

1. The mass of the model must equal that of the initial body.

2. the middle of gravity must be within the same location as that of the first body.

3. The mass moment of inertia must equal that of the first body.

MASS

Mass isn’t weight.

Mass is an invariant property of a rigid body.

The weight of the identical body varies betting on the gravitational system during which it sits.

We will assume the mass of our parts to be constant over time in our calculations.

When designing cam-follower systems (or any machinery), we must first do an entire kinematic analysis of our design so as to get information about the rigid body accelerations of the moving parts.

But to try and do so, we want to understand the masses of all the moving parts that have these known accelerations.

If we’ve a design of the follower train exhausted a CAD program that may calculate masses and mass moments of inertia, then we are in good condition, because the data needed for dynamic calculations are available.

Lacking that luxury, we are going to should calculate estimates of the mass properties of the follower train to try and do the dynamics calculations.

Absent a solids-modeler representation of your design, a primary estimate of your parts’ masses may be obtained by assuming some reasonable shapes and sizes for all the parts and selecting appropriate materials.

Then calculate the degree of every part and multiply its volume by the material’s mass density (not weight density) to get a primary approximation of its mass. These mass values can then be utilized in Newton’s equation to estimate the dynamic forces.

Design is, unavoidably, an iterative process.

We need the dynamic forces to try and do the strain analyses on our parts.

It is also worth noting that, unlike a static force situation within which a failed design may be fixed by adding more mass to the part to strengthen it, to try to so in a very dynamic-force situation can have a deleterious effect. More mass with the identical acceleration will generate even higher forces and thus higher stresses.

The machine designer often has to remove mass (in the correct places) from parts so as to cut back the stresses and deflections thanks to F = ma.

The designer must have a decent understanding of both material properties and stress and deflection analysis to properly shape and size parts for minimum mass while maximizing strength and stiffness to resist dynamic forces.