Paper Feeding Example

Chapter 30: Paper Feeding Example

30

Paper Feeding Example



Summary



Introduction



Requested Solutions



FEM Solution



Results



Input File(s)

498 499

499

503 503

499

498 MD Demonstration Problems CHAPTER 30

Summary Title

Chapter 30: Paper Feeding Example

Geometry

Material properties

See Summary of Materials

Analysis type

Transient explicit dynamic analysis

Boundary conditions

• Fixed at each pinch and drive. • Fixed at the center point of each guide.

Applied loads

1. Angular velocity to each pinch. 2. Translational force to each pinch for deleting a gap between a pinch and driver. 3. Gravitational acceleration.

Element type

0-D 1-D 2-D 3-D

concentrated mass element spring and damper element shell element solid element

Contact properties FE results t = 0 sec

t = 0.1 sec

t = 0.2 sec

t = 0.3 sec

t = 0.4 sec

CHAPTER 30 499 Paper Feeding Example

Introduction The paper feeding analysis is done to predict the paper jamming and capacity of the printer. In this example, angular velocities are applied on five rollers to feed the paper in the printer. There are 31 contact body definitions to simulate the paper feeding process. Total time of simulation is 0.4 seconds.

Requested Solutions A numerical analysis will be performed to find the printer behavior. The angular velocity of each drive and pinch is defined such that a 1500 mm/s circumferential velocity is created. The rotational velocities are applied sequentially at center node of the drive starting from drive 1 through drive 5 by defining Tables and SPCD. Gravity is also taken into account. To push a drive to the paper, a load is applied at the center of each driver.

FEM Solution The printer consists of 21 parts as shown in Figure 30-1. entrance

drive_1 paper

upper guide_1 upper guide_5

upper guide_4 pinch_5

pinch_4 upper guide_3

pinch_1 lower guide_1

pinch_3

lower guide_5 drive_5 lower guide_4

pinch_2 drive_2

drive_4

guide_2 drive_3

Figure 30-1

lower guide_3

Analysis Model

Using the BCTABLE and several CBODY and BCSUFT entries, the following 31 contacts are defined. Contact Number

Slave

Master

Contact Number

Slave

Master

1 (self contact)

paper

paper

17

paper

entrance

2

paper

drive_1

18

paper

lower guide_1

3

drive_1

pinch_1

19

paper

upper guide_1

500 MD Demonstration Problems CHAPTER 30

Contact Number

Slave

Contact Number

Slave

4

pinch_1

drive_1

20

paper

guide_2

5

paper

drive_2

21

paper

lower guide_3

6

drive_2

pinch_2

22

paper

upper guide_3

7

pinch_2

drive_2

23

paper

lower guide_4

8

paper

drive_3

24

paper

upper guide_4

9

drive_3

pinch_3

25

paper

lower guide_5

10

pinch_3

drive_3

26

paper

upper guide_5

11

paper

drive_4

27

paper

pinch_1

12

drive_4

pinch_4

28

paper

pinch_2

13

pinch_4

drive_4

29

paper

pinch_3

14

paper

drive_5

30

paper

pinch_4

15

drive_5

pinch_5

31

paper

pinch_5

16

pinch_5

drive_5

Master

Master

TSTEPNL describes the number of Time Steps (100) and Time Increment (0.004 sec.) of the simulation. End time is

the product of the two entries. Notice here the Time Increment is only for the first step. The actual number of Time Increments and the exact value of the Time Steps are determined by SOL 700 during the analysis. The step size of the output files is determined by the Time Increment as well. TSTEPNL

1

100

.004

1

ADAPT

2

10

The enforced angular velocities are applied to all pinches and drivers. The nodes, located on the circumference of each drive and pinch, are rigidly connected to the center node using RBE2 entry. Each enforced angular velocity is defined to have the same circumferential velocity (1500 mm/sec.) at the tip of drivers and pinches using SPCD2. The angular velocities vary depending on the diameter of drivers and pinches. The boundary conditions are applied only to pinches. A combination of spring and damper elements, CDAMP1D and CELAS1D, connect the fixed node and the center node of pinches. To close the gap between all the drives and the pinches, two vertical forces are applied, in opposite directions by using a combination of FORCE and Table entries. The magnitude of the load is predefined at each drive location. The boundary condition and enforced motion at each pinch are shown as Figure 30-2. In the cases of the drive_1 and dirver_5, their diameters are 25 and 15 mm, respectively. The angular velocity of drive_1 is applied as 120 radian/sec. (25/2×120 = 1500 mm/sec.). And 225 radian/sec. is applied to driver_5. The example below shows how to define the boundary conditions and the enforced angular velocity of pinch_1.

CHAPTER 30 501 Paper Feeding Example

Various angular velocities are applied to get 1500 mm/sec circumferential velocity.

RBE2 Translational force is applied

Damper

Figure 30-2

Spring

Boundary Condition And Enforced Angular Velocity At Pinch

Node 21002 is fully fixed and connected to the center node 21001 using CELAS1D and CDAMP1D. The coefficients of the spring and damper are 4.9 N/mm and 196 N·sec /mm, respectively. Node 21001, the center node of the pinch_1, is fixed except in the y-direction to which a spring and a damper are connected. PELAS CELAS1D PDAMP CDAMP1D $ SPC1 SPC1

18 21001 19 21002 8 1

4.9 18 196. 19 13456 123456

21001

2

21002

2

21001

2

21002

2

21001 21002

The circumference nodes are connected to the center node 21001 rigidly using RBE2. RBE2

55003 1006

21001 1007

123456 1008

1001 1009

1002 1010

1003 1011

1004 1012

1005 1013

... At the center node, angular velocity 120 is applied to negative z angular direction. And, at the same node, translational force is applied as well. TLOAD1 LSEQ SPCD FORCE

19 1 21 4

20 20 21001 21001

VELO 21 6 0

Summary of Materials Paper - Linear elastic material: E

(Young’s Modulus) = 3e+6 N/mm2



(Poisson’s ratio) = .3

 density=

8.4e-7 kg/m3

-120. 9800.

1 0.

1.

0.

502 MD Demonstration Problems CHAPTER 30

Rubber 1 - Linear elastic material: E

(Young’s Modulus) = 1e+4. N/mm2



(Poisson’s ratio) = .49

 density=

1.5e-6 kg/m3

Rubber 2 - Linear elastic material: E

(Young’s Modulus) = 3e+4. N/mm2



(Poisson’s ratio) = .49

 density=

1.5e-6 kg/m3

Pinch and driver - Linear elastic material: E

(Young’s Modulus) = 7e+5. N/mm2



(Poisson’s ratio) = .3

 density=

2.7e-6 kg/m3

Entrance and guide - Linear elastic material: E

(Young’s Modulus) = 3.e+5. N/mm2



(Poisson’s ratio) = .3

 density=

7.86e-6 kg/m3

CHAPTER 30 503 Paper Feeding Example

Results t = 0 sec

t = 0.1 sec

t = 0.2 sec

t = 0.3 sec

t = 0.4 sec

Figure 30-3

Paper at Various Positions

Input File(s) File nug_30.dat

Description MD Nastran input file for printer feeding example