The Dynamic Simulation Environment

Simulation overview

During a typical design process, designers go through a series of typical questions, such as: do the parts fit together? Do the parts move well together? Is there interference? Do the parts follow the right path? Even though most of these questions can be catered for by 3D CAD and rendering software, there may be other questions that cannot. For example, designers may want to know the machinery time cycle. Is the actuator powerful enough? Is the link robust enough? Can we reduce weight? All these questions can only be answered by building a working prototype or a series of prototypes. The major issues with this method are that it is timely and costly. An alternative cost-effective method is to create a working virtual prototype by using the Inventor simulation suite. The Inventor simulation suite allows the designer to convert assembly constraints automatically to mechanical joints, provides the capability to apply external forces including gravity, and allows the effects of contact friction, damping, and inertia to be taken into account. As a result of this, the simulation suite provides reaction forces, velocities, acceleration, and much more. With this information, the designer can reuse reaction forces automatically to perform finite element analysis, hence reducing risks and assumptions. Ultimately all this information helps the designers to build an optimum product, as illustrated by the following example.

Simulation – Basic Theory

Simulation enables understanding of the kinematic and dynamic behavior of mechanisms. 'Kinematics' simply refers to the motion of the mechanism, including determining position, velocity, and acceleration, whereas 'dynamics' is the study of masses and inertial forces acting on the mechanism.

=M×a

where

F = external force

M = mass

a = acceleration

This is Newton's Law of Motion, which can also be expressed as

=M×dvdt

From both equations we can determine acceleration as a function of velocity

=dvdt=FM

By integrating acceleration we can determine velocity

=dxdt=FMt2

By integrating velocity we can determine position

=12×FMt2

Inventor Simulation 2011 calculates acceleration, velocity, and the position of the component/assemblies at each time step, referred to as image frames within the user interface.

Open-and Closed-Loop Mechanisms

A mechanism can, furthermore, be conceptually viewed as a set of rigid bodies interconnected to each other by joints that constrain, but not restrict, relative motion between any two bodies. Common joints used in mechanisms include revolution, cylindrical, prismatic, and spherical; a complete list of joints is given on page 17. The slider mechanism below comprises three revolutions, one prismatic, and one fixed (grounded) joint.

In addition, mechanisms can be generally categorized into open-loop mechanisms and closed-loop mechanisms. The difference is that the joint degrees of freedom (DOF) in open-loop mechanisms are independent of one another whereas in closed-loop mechanisms they are not independent. Extensive information on open- and closed-loop mechanisms is available from standard engineering books; theoretical technical information is beyond the scope of this book. The above slider mechanism is an example of closed loop; another example would be a Whitworth Return Mechanism. On the other hand, the following robot manipulator is an example of an open-loop mechanism, with one spherical, two revolution, and one fixed joint.

Redundant Mechanisms

Key pieces of information required from a mechanism analysis are the reaction forces and moments, due to acceleration, and inertial and external forces. These reaction forces are unique for a non-redundant model, whereas for a redundant model the reaction forces will not be unique, as explained by the simple shaft bearing example below.

For equilibrium, applied force (F) should be equal to the sum of all reactions at the bearings (RL)

=R1+R2

Also, for equilibrium, the sum of all moments should be equal to zero

1L3=2R2L3

For a 1 m shaft this becomes

13=2R23orR1=2R2

Substituting the value of R1 into the force equation gives us

=2R2+R2=3R2orR2=F3

Now substituting R2 into the force equation gives us

=R1+F3orR1=2F3

For a shaft with two bearings we have two unknowns and two equations, giving us one unique result, as

1=2F3andR2=F3

Now let us consider the same shaft with another bearing in the middle.

Again, for equilibrium, ∑F = 0 and ∑M = 0.

=R1+R2+R3

1L3=R3L3+R2L3

This creates three unknowns and two equations. To determine the reactions, we need to make some assumptions.

Solution 1 – Let's assume R2 equals 0; then we get

1=F2andR3=F2

Solution 2 – Let's assume R3 equals 0; then we get

1=2F3andR2=F3

We can continue to carry on making more assumptions but here it is important to note that adding a third bearing has resulted in there being more than one possible solution.

The reason for this is that, to maintain equilibrium of the shaft, two bearings are sufficient. Adding a third bearing has resulted in over-constraining the shaft mechanism. In reality this may not necessarily happen as the shaft can bend, whereas in the simulation we treat the shaft as rigid, resulting in a redundant model.

The redundancy process is further explained using a door and hinge example later in this chapter.

Contact Properties

To simulate reality as closely as possible, contact properties, including friction and restitution, need to be defined as accurately as possible. In Simulation there are two types of contact, which can be specified as two-dimensional (2D) and three-dimensional (3D). If the contact between two components remains planar before and after contact, and is not normal to the component, then 2D contact should be used. On the other hand, a 3D contact should only be used if the contact between two components does not remain in one 2D plane before and after contact. A contact is defined by two key material properties: restitution and friction.

It is easier to control restitution properties of 2D contact when compared to 3D contact.

In 3D contact, you cannot define restitution by specifying a value between 0 and 1, as it uses elastic stiffness and damping properties to simulate impact and bounce. This means that when two components come into contact there will always be vibration, and thus bounce, meaning that a restitution value of 0 is difficult, if not impossible, to simulate with a 3D contact.

Friction properties can be easily specified in both contacts.

Two-dimensional projected geometry can be used to define a 2D contact.

Restitution

Restitution indicates how the normal velocity between the two components changes during a shock.

=Normal velocity after contactNormal velocity before contact

For example, if we drop a ball, with a restitution value set to 1, the ball will bounce back to its original position and will keep bouncing; in other words, the ball is completely elastic – perhaps made from plastic. On the other hand, if we drop the ball with the restitution value set to 0, the ball will drop without any bounce; in this case, the ball is inelastic – perhaps made out of a lead-like material. The default is set to 0.8 when a contact is created for the first time.

Friction

The coefficient of friction (μ) is the ratio defining the force that resists the motion of one body in relation to another body in contact with it. This ratio is dependent on material properties and most materials have a value between 0 and 1. In...