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) |
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
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