Deflection Calibration

Mechanical EngineeringSeokchang Ryu

Mi Hye Shin

Moment Diagram

: curvature at points

: position of sensors

: force point

* Beam Theory *

①

②: Moment at ① and ②

①

②

Equations for Deflection

Derive deflection equations by integration

Boundary Conditions:

Notation :

①

②

Plot for Needle Deflection

-10

0

100 50 100 150 200

-5

-4

-3

-2

-1

0

1

2

Y [mm]X [mm]

Z [

mm

]estimated shape of needle

actual shape of needle

Error at tip on x-axis: 0.09(mm)

Error at tip on z-axis: 0.07(mm)

Before : 0.7(mm) error

Assumptions

Each sensor position is the same.

The distance between two positions is constant.

There are three sensors on two positions.

If there is error at one position, then there will be almost same error at the other position.

1.

2.Constant

Constant

Applying assumptions

1st Assumption

2nd Assumption

Result_1

If we substitute in deflection equation, then we

could obtain relation between deflection error and position error.

(I consider the error in denominator has less effect than the error in numerator.)

Result_2

-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1-0.5

-0.4

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

0.4

delta y [mm]

erro

r [m

m]

error on yx

error on yz

-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 10

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

delta y [mm]

tota

l err

or [

mm

]

1. The error at tip and ∆y have linear relation.

2. Tip error has minimum value at ∆y=0.2~0.3(mm)

Appendix_1

Appendix_2