mistat (version 2.0.4)

pistonSimulation: The Piston Simulator

Description

A simulator of a piston moving whithin a cylinder. The piston's performance is measured by the time it takes to complete one cycle, in seconds. Several factors can affect the piston's performance, they are listed in the arguments section.

Usage

pistonSimulation(m = 60, s = 0.02, v0 = 0.01, 
                 k = 5000, p0 = 110000, t = 296, 
                 t0 = 360, each = 50, seed = NA, 
                 check = TRUE)

Value

A data frame, a matrix-like structure, with each * n rows and with columns:

m	numeric	value of m
s	numeric	value of s
v0	numeric	value of v0
k	numeric	value of k
p0	numeric	value of p0
t	numeric	value of t
t0	numeric	value of t0
seconds	numeric	time to complete one cycle (\(s\))

Arguments

m

the impact pressure determined by the piston weight (\(kg\)). A single value or a vector of length n.

s

the piston surface area (\(m^2\)). A single value or a vector.

v0

the initial volume of the gas inside the piston (\(m^3\)). A single value or a vector of length n.

k

the spring coefficient (\(N/m^3\)). A single value or a vector of length n.

p0

the atmospheric pressure (\(N/m^2\)). A single value or a vector of length n.

t

the surrounding ambient temperature (\(K\)). A single value or a vector of length n.

t0

the filling gas temperature (\(K\)). A single value or a vector of length n.

each

non-negative integer. Each element of previous parameters is repeated each times.

seed

a single value, interpreted as an integer. If specified make the simulation replicable.

check

if TRUE (the default) then a formal check on piston parameters is perfomed

Author

Daniele Amberti

Details

Factors affect the Cycle Time \(s\) via a chain of nonlinear equations: $$s = 2\pi\sqrt{\frac{M}{k + S^2 \frac{P_0 V_0}{T_0} \frac{T}{V^2}}}$$ where $$V = \frac{S}{2k} \sqrt{A^2 + 4k \frac{P_0 V_0}{T_0} T - a}$$ and $$A = P_0 S + 19.62M - \frac{k V_0}{S}$$

References

Kenett, R., Zacks, S. with contributions by Amberti, D. Modern Industrial Statistics: with applications in R, MINITAB and JMP. Wiley.

See Also

powerCircuitSimulation, simulationGroup, LATHYPPISTON

Examples

Ps <- pistonSimulation(
  m = rep(60, 100),
  s = rep(0.02, 100),
  v0 = rep(0.01, 100),
  k = rep(5000, 100),
  p0 = rep(110000, 100),
  t = c(rep(296,35), 296*1.1^(1:65)),
  t0 = rep(360, 100),
  each = 1, 
  seed = 123,
  check = FALSE)
head(Ps)
tail(Ps)
plot(Ps$seconds)