Casio FX-702P, Swiss Micros DM42, HP 27S: Design of Coil Spring

Casio FX-702P, Swiss Micros DM42, HP 27S: Design of Coil Spring

Today’s blog calculates the load of a coil spring.

Variables Used

P	LOAD	Load (kg)
G	SHEAR	Shear Modulus (kg/mm^2)
A	WDIA, W.DIA	Diameter of the wire (mm)
Y	DEFL	Deflection (mm)
N, NA	#COIL	Number of Coils
D	CDIA, C.DIA	Diameter of the coil (mm)
K = (G×A^4)÷(8×N×D)		Spring Constant (kg/mm) (FX-702P only)

Casio FX-702P Code

The original BASIC programs are listed here (Casio, pg. 72, Program Library FX-702P, see sources):

5 FOR L=1 TO 5

10 INP “K,P:1,A:2,D:3,NA:4”,I

20 FOR J=1 TO 4

30 IF I=J THEN 100

40 NEXT J

50 GOTO 10

100 INP “G=”,G

110 G=G/8

120 IF I=2 THEN 150

130 INP “A=”,A:A=A↑4

140 IF I=3 THEN 170

150 INP “D=”,D:D=D↑3

160 IF I=4 THEN 180

170 INP “NA”=,N

180 INP “Y=”,Y

190 IF I=1;K=G*A/N/D:P=K*Y:PRT “K=”;K,”P=”;P:GOTO 240

200 INP “P=”,P

210 IF I=2;A=(P*D*N/G/Y)↑(1/4):PRT “A=”;A:GOTO 240

220 IF I=3;D=(A*G*Y/N/P)↑(1/3):PRT “D=”;D:GOTO 240

230 N=G*A*Y/D/R:PRT “NA=”;N

240 NEXT L

250 END

INP: input

PRT: print

Swiss Micros DM42 Solver Code: SPRING

Also for HP 42S, Free42, Plus42.

00 { 103-Byte Prgm }
01▸LBL "SPRING"
02 MVAR "LOAD"
03 MVAR "SHEAR"
04 MVAR "W.DIA"
05 MVAR "C.DIA"
06 MVAR "#COIL"
07 MVAR "DEFL"
08 RCL "SHEAR"
09 RCL "W.DIA"
10 4
11 Y↑X
12 ×
13 RCL× "DEFL"
14 8
15 RCL× "#COIL"
16 RCL "C.DIA"
17 3
18 Y↑X
19 ×
20 ÷
21 +/-
22 RCL+ "LOAD"
23 RTN
24 .END.

Run SPRING through the SOLVER.

HP 27S Equation: SPRING

Spaces added for readability.

SPRING: SHEAR × WDIA^4 × DEFL ÷ (8 ×#COIL × CDIA^3)

Example: Copper Spring Coil

Shear: G = 4558.131472 kg/mm^2

Coil Diameter: D = 10 mm

Wire Diameter: A = 0.7 mm

Deflection: Y = 5 mm

Number of Coils: N = 4

Result: Load: P: 0.17100 kg

Calculate the wire diameter if the load is 0.25 kg.

Result: Wire Diameter: A: 0.79672 mm

What if instead we have 8 coils? Wire diameter resets to 0.7 mm.

Result: Load: P: 0.08550 kg

Table of Shear Modulus Values

These are the shear modulus of various mediums. The higher the shear modulus is, the more rigid the solid is. If the solid’s modulus is smaller, it is easier to deform or change its shape. For liquids, the modulus is zero. The table below has two units, GPa (gigapascal) and kg/mm^2. The conversion rate is approximately 1 GPa = 101.9716212978 kg/mm^2.

The values in are from the “What is the Shear Modulus?” article by Dr. Helmenstine (see the Sources section) in GPa.

Shear Modulus	GPa	kg/mm^2
Rubber	0.0006	0.06118297278
Plywood	0.62	63.2224052
Nylon	4.1	418.0836473
Lead	13.1	1335.828239
Aluminum	25.5	2600.276343
Brass	40	4078.864852
Copper	44.7	4558.131472
Titanium	41.1	4191.033635

Source:

Casio. Program Library: FX-702P pp. 71-72 (English)

Helmenstine, Anne Marie, Ph.D. "What Is the Shear Modulus?" ThoughtCo, Feb. 17, 2021, thoughtco.com/shear-modulus-4176406. Retrieved January 21, 2024.

TranslatorsCafe.com “Convert gigapascal [GPa] to kilogram-force/millimeter² [kgf/mm²]”

https://www.translatorscafe.com/unit-converter/en-US/pressure/5-28/gigapascal-kilogram-force/millimeter%C2%B2/ Retrieved January 21, 2024

Eddie

All original content copyright, © 2011-2024. Edward Shore. Unauthorized use and/or unauthorized distribution for commercial purposes without express and written permission from the author is strictly prohibited. This blog entry may be distributed for noncommercial purposes, provided that full credit is given to the author.

Casio fx-CG 50: Impedance Calculations

Casio fx-CG 50:  Impedance Calculations

Introduction

The program FX61IMP contains a suite of impedance calculations.  Why the unusual name?

In the late 1980s, Casio had a fx-61F calculator.  The fx-61F is a specialized programming scientific calculator, which is the only calculator, to my knowledge, to feature an Impedance mode.  The impedance mode has specialized keys to calculate impedance of resistors, capacitors, and inductors (coils).  The calculator also featured 29 specialized electrical formulas, a 30 step programming capability, base conversions, 1 variable statistics, and complex numbers.

The main menu of FX61IMP:

1.  Impedance of a Coil (Inductor)
2.  Impedance of a Capacitor
3.  Impedance of two parallel resistors (Parallel)
4.  Impedance of a Series Resistor
5.  Analysis of total Impedance
6.  Store results in X and Y
7.  View Memory Registers
8.  Clear Variables
9.  Exit

Variables used:
Z = impedance of the current calculation
S = grand total impedance
X = user register
Y = user register

Note:  In electronics, the symbol j is used in complex numbers.  The fx-61F uses j.  However, the fx-CG50 uses i in complex numbers.  The program uses i and the user is notified of this when the program starts. 

1.  Impedance of a Coil (Inductor)
Provide the self-inductance (in H, Henrys) and frequency (in 1/s), the impedance is calculated as:
Z = 2 * π * f * L * i

The result is added to S.

2.  Impedance of a Capacitor
Provide the capacitance (in F, Farads) and frequency (in 1/s), the impedance is calculated as:
Z = 1/(2 * π * f * C * i)

The result is added to S.

3.  Impedance of two parallel resistors (Parallel)
This calculates the impedance of parallel resistors:
Z = 1/(1/a + 1/b) = (a * b) / (a + b)

The result is added to S.

4.  Impedance of a Series Resistor
The impedance of the resistor is:  R (in Ω, Ohms)

Z = R

The result is added to S.

5.  Analysis of total Impedance
Takes the total impedance (S) and returns its total, magnitude, and phase angle (in degrees).  You will have an opportunity to clear S (reset S to zero).

6.  Store results in X and Y
You can store Z or S in the variables X and Y.

7.  View Memory Registers
View the contents Z, S, X, and Y.

8.  Clear Variables
Resets Z, S, X, and Y to 0.

9.  Exit
Exits the program.

The program is listed in text form, which can be copied to the fx-CG 50.

Program Text Listing:
'ProgramMode:RUN
"2019-09-09 EWS"
Deg
a+bi
ClrText
Red Locate 1,3,"NOTICE"
Blue Locate 1,5,"J is represented"
Blue Locate 1,6,"by _Imaginary_. (_Sqrt__(-)_1)"
" "Disps0->S
0->Z
0->X
0->Y
Lbl 0
ClrText
Menu "IMPEDANCE","COIL",1,"CAPACITOR",2,"PARALLEL",3,"SERIES RESISTOR",4,"ANALYSIS",5,"STORE IN X OR Y",6,"VIEW MEMORY",7,"CLEAR VARS",8,"EXIT",E
Lbl 1
"FREQ: "?->F
"INDUCTANCE: "?->L
2piLFImaginary->ZDispsS+Z->S
Goto 0
Lbl 2
"FREQ: "?->F
"CAPACITY: "?->C
(2piFCImaginary)^<-1>->ZDispsS+Z->S
Goto 0
Lbl 3
"PARALLEL IMPEDANCE"
"A_#E6D7_B"
"A: "?->A
"B: "?->B
(AB)/(A+B)->ZDispsS+Z->S
Goto 0
Lbl 4
"RESISTANCE: "?->R
R->ZDispsS+Z->S
Goto 0
Lbl 5
"TOTAL IMPEDANCE:"
SDisps"MAGNITUDE: "
Abs SDisps"PHASE ANGLE: "
Arg SDispsMenu "CLEAR TOTAL?","YES",Y,"NO",0
Lbl Y
0->S
"CLEARED!"DispsGoto 0
Lbl 6
Menu "WHAT TO STORE?","Z_->_X",M,"Z_->_Y",N,"S_->_X",O,"S_->_Y",P
Lbl M
Z->X
"DONE!"DispsGoto 0
Lbl N
Z->Y
"DONE!"DispsGoto 0
Lbl O
S->X
"DONE!"DispsMenu "CLEAR TOTAL?","YES",Y,"NO",0
Lbl Y
0->S
"CLEARED!"DispsGoto 0
Lbl P
S->Y
"DONE!"DispsMenu "CLEAR TOTAL?","YES",Y,"NO",0
Lbl Y
0->S
"CLEARED!"DispsGoto 0
Lbl 7
ClrText
"Z: "
ZDisps"S: "
SDisps"X: "
XDisps"Y: "
YDispsGoto 0
Lbl 8
0->Z
0->S
0->X
0->Y
"DONE!"DispsGoto 0
Lbl E
ClrText
Red Locate 5,4,"FX61 IMPEDANCE"

Note:  Disps:  ◢, ⊿
Imaginary:  i  [SHIFT] [ 0 ]

Program Calculator Listing:
"2019-09-09 EWS"
Deg
a+bi
ClrText
Red Locate 1,3,"NOTICE"
Blue Locate 1,5,"J is represented"
Blue Locate 1,6,"by i. (√-1)"
" "⊿
0->S
0->Z
0->X
0->Y
Lbl 0
ClrText
Menu "IMPEDANCE","COIL",1,"CAPACITOR",2,"PARALLEL",3,"SERIES RESISTOR",4,"ANALYSIS",5,"STORE IN X OR Y",6,"VIEW MEMORY",7,"CLEAR VARS",8,"EXIT",E
Lbl 1
"FREQ: "?->F
"INDUCTANCE: "?->L
2πLFi->Z⊿
S+Z->S
Goto 0
Lbl 2
"FREQ: "?->F
"CAPACITY: "?->C
(2πFCi)⁻¹->Z⊿
S+Z->S
Goto 0
Lbl 3
"PARALLEL IMPEDANCE"
"A||B"
"A: "?->A
"B: "?->B
(AB)÷(A+B)->Z⊿
S+Z->S
Goto 0
Lbl 4
"RESISTANCE: "?->R
R->Z⊿
S+Z->S
Goto 0
Lbl 5
"TOTAL IMPEDANCE:"
S⊿
"MAGNITUDE: "
Abs S⊿
"PHASE ANGLE: "
Arg S⊿
Menu "CLEAR TOTAL?","YES",Y,"NO",0
Lbl Y
0->S
"CLEARED!"⊿
Goto 0
Lbl 6
Menu "WHAT TO STORE?","Z->X",M,"Z->Y",N,"S->X",O,"S->Y",P
Lbl M
Z->X
"DONE!"⊿
Goto 0
Lbl N
Z->Y
"DONE!"⊿
Goto 0
Lbl O
S->X
"DONE!"⊿
Menu "CLEAR TOTAL?","YES",Y,"NO",0
Lbl Y
0->S
"CLEARED!"⊿
Goto 0
Lbl P
S->Y
"DONE!"⊿
Menu "CLEAR TOTAL?","YES",Y,"NO",0
Lbl Y
0->S
"CLEARED!"⊿
Goto 0
Lbl 7
ClrText
"Z: "
Z⊿
"S: "
S⊿
"X: "
X⊿
"Y: "
Y⊿
Goto 0
Lbl 8
0->Z
0->S
0->X
0->Y
"DONE!"⊿
Goto 0
Lbl E
ClrText
Red Locate 5,4,"FX61 IMPEDANCE"

The || is found in (CHAR), (MATH).

Examples:

Example 1:
Two coils in a series with inductance of 0.1 H and 0.2 H, respectively.  The frequency is 50 Hz. 

Sequence:
Option 1:  Enter 50 for frequency, 0.1 for inductance.
Option 1:  Enter 50 for frequency, 0.2 for inductance.
Option 5:  For analysis.

Total Impedance:  94.24777961i
Magnitude:  94.24777961
Phase Angle:  90°
(Clear the total)

Example 2:
A capacitor of 30 μF, a resistor of 10 Ω, and coil of 0.3 H are in a series.  Find the total impedance of the circuit if the frequency is 65 Hz.

Sequence:
Option 2:  Enter 65 for frequency, 30E-6 for capacity
Option 4:  Enter 10 for resistance
Option 1:  Enter 65 for frequency, 0.3 for inductance
Option 5:  For analysis

Total Impedance:  10 + 40.90419396i
Magnitude: 42.10882429
Phase Angle:  76.26214952°
(Clear the total)

Example 3:
Three resistors in parallel with 100 Ω, 200 Ω, and 400 Ω, respectively.  Find the total impedance.

Sequence:
Option 3:  Enter 100 for A and 200 for B.
Option 6:  Store S in X.  Clear the total.
Option 3:  Enter X for A and 400 for B.
Option 5:  For analysis

Total Impedance: 57.14285714
Magnitude: 57.14285714
Phase Angle: 0°

Eddie

All original content copyright, © 2011-2019.  Edward Shore.   Unauthorized use and/or unauthorized distribution for commercial purposes without express and written permission from the author is strictly prohibited.  This blog entry may be distributed for noncommercial purposes, provided that full credit is given to the author.