Chapter 4 collision

Chapter 4 collision

Teaching Purpose

1. Define the characteristics of the collision phenomenon and the basic assumptions of the collision. Have a clear understanding of the concept of instantaneous force, recovery coefficient and impact center.
   
2. Skillfully use the momentum theorem and the moving moment Theorem in integral form to solve the problems of the two objects under the normal collision of the heart and the impact of the Rotating Rigid Body of the Rao definite axis. Ability to calculate the loss of dynamic energy in the Process of two objects colliding with the center
   

Highlights and difficulties of this chapter:

This chapter focuses on collision characteristics, physical meaning of sparse restoration, basic theorem of collision and its application. Impact center.

I. Collision Overview

1. Collision Motion Features and basic assumptions

Feature: the object's velocity changes in a very short period of time.

Fig 17.1

Fig 17.2

 

Feature Analysis: Huge

Extremely small

Basic assumption: in the collision process, the normal force is ignored and only the collision force is considered.

B's displacement is negligible during the collision process.

2. Restoration coefficient of a Rigid-Body Model with local contact deformation

Fig 17.3

The restoration coefficient (experimental law) indicates the degree of deformation recovery of an object.

Full elastic collision (Object Deformation completely restored)

Elastic collision (Object Deformation cannot be completely restored. (Retain partial deformation)

Plastic collision (Object Deformation cannot be restored, that is, all deformation is retained)

3. Study the universal theorem of Collision Motion

1. Momentum Theorem for collision process ----- impulse Theorem
   

Or

2) momentum moment theorem used in the collision process -- impulse moment Theorem

Particle:

Quality System

-The impulse moment of the "O" point.

Note: "O" is any point.

4. Induction: the main theoretical basis for studying Collision Motion

1) Basic Assumptions

2) recovery coefficient

3) general theorem used in the collision process: impulse theorem and impulse moment Theorem

2. collision between two balls

The collision between two balls refers to the collision of two translation objects. It mainly studies the changes of collision speed, collision impulse and Engineering Application Problems.

1. Positive collision between two balls

If the two-ball center velocity vector and the two-ball center line overlap, it is called a positive collision.

Fig 17.3

Let's set the quality of the two balls to sum, the speed before the collision is, and the recovery coefficient is, the speed of the two balls after the collision is analyzed as, the collision impulse, and a simple determination of the recovery coefficient, loss of kinetic energy and its application.

1) analyze the speed of the last two balls ,.

Study the collision process between two balls

()

Recovery Coefficient

(B)

Simultaneous (a) (B ):

Fig 17.4

2) Analysis of collision impulse and another meaning ""

Study the collision process of ball 1 (or ball 2) (Figure 17.4)

Impulse in deformation phase (d)

Impulse in the recovery phase (e)

Where u is the common velocity at the end of the deformation phase of the two balls, which is obtained by the momentum conservation of the two balls.

(F)

(D), (e), and

(G)

(H)

Derived from formula (g) and (h)

That is

3) "" Determination

Use the material of the coefficient to be tested to make a small ball and a large tablet, and fix the tablet (Figure 17.5)

Fig 17.5

 

Where

4) analyze the loss of kinetic energy and Its Application

Pre-touch kinetic energy, post-touch kinetic energy, and Kinetic Energy Loss

Substituted, obtained

Discussion :,

Forging application (Figure 17.6) The efficiency of forging is to make the forging deformation as big as possible.

Fig 17.6

Fetch

Yes,

Forging Efficiency should be enabled to improve efficiency

Piling application (Fig. 17.7)

 

 

 

Fig 17.7

The piling efficiency is to maximize the kinetic energy obtained by the piling. The efficiency is

To improve efficiency

Example 17.1: As shown in 17.8a, an object falls freely from its height and collides with the block mounted on the spring. Set weight, weight, stiffness factor of spring. After the collision, the two objects move together.

Figure 17.8a

The maximum deformation of the spring.

Solution: 1 before the study starts to fall

2. Study the collision process between two things (Figure 17.8b)

Figure 17.8b

 

()

3. Move down after the collision ends until the speed is zero.

(B)

(C)

(A) and (c) are substituted into (B), and simplified.

Substitute the data to obtain

The maximum deformation is

2. oblique collision between two balls

If the center velocity vector of the two balls before and after the collision is not in line with the two balls, it is called oblique collision. If the collision contact surface is smooth, the collision impulse along the public line of the contact surface (Figure 17.9 ()),

Fig. 17.9 ()

In this case, the oblique collision of the two balls has the following features:

1. Because (Fig. 17.9 (B ))
   

Fig. 17.9 (B)

Yes,

(2) The two balls are composed of vertices.

()

(3) recovery coefficient

(B)

Simultaneous (a) and (B) can be obtained, and thus can be obtained ,.

Example 17.2 known: the US "Apollo" ship A and the Soviet Union"

Ship B was connected after the rendezvous in December July 15, 1975 (Figure 17.10 ). The quality of Ship B is respectively. Ship B is at rest in the inertial reference system. The velocity of ship A is omitted from the rotation of ship A and ship B.

Fig 17.10

1. If the first connection is successful, try to find the center speed of the consortium;

2. If the first collision fails, the collision recovery coefficient is generated. Try to find the speed after the collision between the two ships.

Solution: 1. the first connection is successful and is a plastic collision.

Study A and B because. Yes

Where

2. The first connection was unsuccessful. If the friction between the two ships is not considered, the speed components of the two ships in the direction remain unchanged before and after the collision.

Study ships A and B Because (in the direction of the Public normal) has

()

Recovery Coefficient

(B)

The two types of simultaneous (a) and (B) are obtained.

Iii. Impact of collision impulse on the rotating rigid body around the fixed axis impact center

1. Changes in the velocity of the Rigid Body

Set the rotation of the rigid body around the fixed axis to be affected by the impulse of the outer collision, as shown in Figure 17.11.

Fig 17.11

2. Bearing constraints collision impulse impact center

:

:

Resolution

Ling

Impact center: When the bearing collision constraint impulse is zero, the intersection of the outer collision punch and the shaft (OC line) "K" is called the impact center.

4. Rigid Body collision example

For example, 17.3 it is known that the OA rod of homogeneous rod is long and the quality is as follows: the OA rod starts to lead straight, and then falls right after disturbance, and a smooth collision occurs between A and B. (Figure 17.12), set the recovery coefficient.

Fig. 17.12 ()

Evaluate: 1 OA rod rebound angle; 2 A end and bearing o collision impulse.

Solution: 1. Study rod from before touch

Fig. 17.12 (B)

2 study the collision process

Set the collision angular velocity

Where

:

:

:

3. After study collision, the rod returns to zero velocity.

For example, 17.4 it is known that the quality is, the length is a homogeneous fine rod, and the horizontal position does not fall freely at the initial speed. When the falling height is reached, the A-side collision with the fixed rigid hook E (Figure 17.13), and the collision impulse of hook e acting on the straight rod during the collision process.

Fig. 17.13 ()

Solution: After the-end and rigid hook e are combined, it is no longer separated and forces the AB rod to change from ing to rotation. This is known as the "highlight constraint" problem and belongs to the collision movement.

Fig. 17.13 (B)

1. Study the AB rod from the beginning to before the touch
   

1. Research on the collision process, the AB rod changes from ing to rotation
   

That is

:

: