Interactive Jupyter Notebook
Motor Assembly textbook example, Chapter 9 through 11, Dimensioning and Tolerancing Handbook, McGraw Hill
Example (MIT Calc Demonstration Analysis)
import dimstack as ds
# ds.display.mode("text")
ds.display.mode("rich")
k = 0.25
target_process_sigma = 3
stdev = 0.036 / target_process_sigma
m1 = dim = ds.dim.Basic(
nom=208,
tol=ds.tol.SymmetricBilateral(0.036),
name="a",
desc="Shaft",
).review(
distribution=ds.dist.Normal(208 + k * target_process_sigma * stdev, stdev),
target_process_sigma=target_process_sigma,
)
m2 = dim = ds.dim.Basic(
nom=-1.75,
tol=ds.tol.UnequalBilateral(0, 0.06),
name="b",
desc="Retainer ring",
).review(
target_process_sigma=3,
)
m3 = dim = ds.dim.Basic(
nom=-23,
tol=ds.tol.UnequalBilateral(0, 0.12),
name="c",
desc="Bearing",
).review(
target_process_sigma=3,
)
m4 = dim = ds.dim.Basic(
nom=20,
tol=ds.tol.SymmetricBilateral(0.026),
name="d",
desc="Bearing Sleeve",
).review(
target_process_sigma=3,
)
m5 = dim = ds.dim.Basic(
nom=-200,
tol=ds.tol.SymmetricBilateral(0.145),
name="e",
desc="Case",
).review(
target_process_sigma=3,
)
m6 = ds.dim.Basic(
nom=20,
tol=ds.tol.SymmetricBilateral(0.026),
name="f",
desc="Bearing Sleeve",
)
m7 = dim = ds.dim.Basic(
nom=-23,
tol=ds.tol.UnequalBilateral(0, 0.12),
name="g",
desc="Bearing",
).review(
target_process_sigma=3,
)
items = [m1, m2, m3, m4, m5, m7]
stack = ds.dim.ReviewedStack(name="stacks on stacks", dims=items)
stack.to_basic_stack().show()
stack.show()
ds.calc.Closed(stack).show()
ds.calc.WC(stack).show()
ds.calc.RSS(stack).show()
ds.calc.MRSS(stack).show()
designed_for = ds.calc.SixSigma(stack, at=4.5)
designed_for.show()
spec = ds.dim.Requirement("stack spec", "", distribution=designed_for.distribution, LL=0.05, UL=0.8)
spec.show()
ds.plot.StackPlot().add(stack).add(ds.calc.RSS(stack)).show()
Returns:
WARNING:root:Assuming Normal Dist. for 1: b Retainer ring -1.75 +0.06 / +0 @ Normal Dist. μ=-1.78, σ=0.01
WARNING:root:Assuming Normal Dist. for 2: c Bearing -23 +0.12 / +0 @ Normal Dist. μ=-23.06, σ=0.02
WARNING:root:Assuming Normal Dist. for 3: d Bearing Sleeve +20 ± 0.026 @ Normal Dist. μ=20.0, σ=0.00867
WARNING:root:Assuming Normal Dist. for 4: e Case -200 ± 0.145 @ Normal Dist. μ=-200.0, σ=0.04833
WARNING:root:Assuming Normal Dist. for 6: g Bearing -23 +0.12 / +0 @ Normal Dist. μ=-23.06, σ=0.02
DIMENSION STACK: stacks on stacks
┏━━━━┳━━━━━━┳━━━━━━━━━━━━━━━━┳━━━┳━━━━━━━┳━━━━━━━━━━━━━━━━┳━━━━━━━━━━━┳━━━━━━━━━━━━━━━━━━━━━━┓
┃ ID ┃ Name ┃ Desc. ┃ ± ┃ Nom. ┃ Tol. ┃ Sens. (a) ┃ Abs. Bounds ┃
┡━━━━╇━━━━━━╇━━━━━━━━━━━━━━━━╇━━━╇━━━━━━━╇━━━━━━━━━━━━━━━━╇━━━━━━━━━━━╇━━━━━━━━━━━━━━━━━━━━━━┩
│ 0 │ a │ Shaft │ + │ 208.0 │ ± 0.036 │ 1 │ [207.964, 208.036] │
│ 1 │ b │ Retainer ring │ - │ 1.75 │ +0.06 / +0 │ 1 │ [-1.81, -1.75] │
│ 2 │ c │ Bearing │ - │ 23.0 │ +0.12 / +0 │ 1 │ [-23.12, -23] │
│ 3 │ d │ Bearing Sleeve │ + │ 20.0 │ ± 0.026 │ 1 │ [19.974, 20.026] │
│ 4 │ e │ Case │ - │ 200.0 │ ± 0.145 │ 1 │ [-200.145, -199.855] │
│ 6 │ g │ Bearing │ - │ 23.0 │ +0.12 / +0 │ 1 │ [-23.12, -23] │
└────┴──────┴────────────────┴───┴───────┴────────────────┴───────────┴──────────────────────┘
REVIEWED DIMENSION STACK: stacks on stacks
┏━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┳━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┳━━━━━━━━━━━━━━┳━━━━━━━━━━┳━━━━━┳━━━━━━┳━━━━━━━━┳━━━━━━━━━┳━━━━━━━━━━━━┳━━━━━━━━━━━━━┳━━━━━━━━━━━━┓
┃ Dim. ┃ Dist. ┃ Target Sigma ┃ Skew (k) ┃ C_p ┃ C_pk ┃ μ_eff ┃ σ_eff ┃ Eff. Sigma ┃ Yield Prob. ┃ Reject PPM ┃
┡━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╇━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╇━━━━━━━━━━━━━━╇━━━━━━━━━━╇━━━━━╇━━━━━━╇━━━━━━━━╇━━━━━━━━━╇━━━━━━━━━━━━╇━━━━━━━━━━━━━╇━━━━━━━━━━━━┩
│ 0: a Shaft +208 ± 0.036 │ Normal Dist. μ=208.009, σ=0.012 │ ± 3σ │ 0.25 │ 1.0 │ 0.75 │ 208.0 │ 0.016 │ ± 2.25σ │ 98.76871101 │ 12312.89 │
│ 1: b Retainer ring -1.75 +0.06 / +0 │ Normal Dist. μ=-1.78, σ=0.01 │ ± 3σ │ 0.0 │ 1.0 │ 1.0 │ -1.78 │ 0.01 │ ± 3.0σ │ 99.73002039 │ 2699.8 │
│ 2: c Bearing -23 +0.12 / +0 │ Normal Dist. μ=-23.06, σ=0.02 │ ± 3σ │ 0.0 │ 1.0 │ 1.0 │ -23.06 │ 0.02 │ ± 3.0σ │ 99.73002039 │ 2699.8 │
│ 3: d Bearing Sleeve +20 ± 0.026 │ Normal Dist. μ=20.0, σ=0.00867 │ ± 3σ │ 0.0 │ 1.0 │ 1.0 │ 20.0 │ 0.00867 │ ± 3.0σ │ 99.73002039 │ 2699.8 │
│ 4: e Case -200 ± 0.145 │ Normal Dist. μ=-200.0, σ=0.04833 │ ± 3σ │ 0.0 │ 1.0 │ 1.0 │ -200.0 │ 0.04833 │ ± 3.0σ │ 99.73002039 │ 2699.8 │
│ 6: g Bearing -23 +0.12 / +0 │ Normal Dist. μ=-23.06, σ=0.02 │ ± 3σ │ 0.0 │ 1.0 │ 1.0 │ -23.06 │ 0.02 │ ± 3.0σ │ 99.73002039 │ 2699.8 │
└─────────────────────────────────────┴──────────────────────────────────┴──────────────┴──────────┴─────┴──────┴────────┴─────────┴────────────┴─────────────┴────────────┘
DIMENSION: 7: stacks on stacks - Closed Analysis -19.75 +0.507 / -0.207
┏━━━━┳━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┳━━━━━━━┳━━━┳━━━━━━━┳━━━━━━━━━━━━━━━━━┳━━━━━━━━━━━┳━━━━━━━━━━━━━━━━━━━━┓
┃ ID ┃ Name ┃ Desc. ┃ ± ┃ Nom. ┃ Tol. ┃ Sens. (a) ┃ Abs. Bounds ┃
┡━━━━╇━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╇━━━━━━━╇━━━╇━━━━━━━╇━━━━━━━━━━━━━━━━━╇━━━━━━━━━━━╇━━━━━━━━━━━━━━━━━━━━┩
│ 7 │ stacks on stacks - Closed Analysis │ │ - │ 19.75 │ +0.507 / -0.207 │ 1 │ [-20.257, -19.543] │
└────┴────────────────────────────────────┴───────┴───┴───────┴─────────────────┴───────────┴────────────────────┘
DIMENSION: 8: stacks on stacks - WC Analysis -19.9 ± 0.357
┏━━━━┳━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┳━━━━━━━┳━━━┳━━━━━━┳━━━━━━━━━━━━━━━━┳━━━━━━━━━━━┳━━━━━━━━━━━━━━━━━━━━┓
┃ ID ┃ Name ┃ Desc. ┃ ± ┃ Nom. ┃ Tol. ┃ Sens. (a) ┃ Abs. Bounds ┃
┡━━━━╇━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╇━━━━━━━╇━━━╇━━━━━━╇━━━━━━━━━━━━━━━━╇━━━━━━━━━━━╇━━━━━━━━━━━━━━━━━━━━┩
│ 8 │ stacks on stacks - WC Analysis │ │ - │ 19.9 │ ± 0.357 │ 1 │ [-20.257, -19.543] │
└────┴────────────────────────────────┴───────┴───┴──────┴────────────────┴───────────┴────────────────────┘
DIMENSION: 9: stacks on stacks - RSS Analysis (assuming inputs with Normal Dist. & uniform SD) -19.9 ± 0.17634
┏━━━━┳━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┳━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┳━━━┳━━━━━━┳━━━━━━━━━━━━━━━━┳━━━━━━━━━━━┳━━━━━━━━━━━━━━━━━━━━━━━━┓
┃ ID ┃ Name ┃ Desc. ┃ ± ┃ Nom. ┃ Tol. ┃ Sens. (a) ┃ Abs. Bounds ┃
┡━━━━╇━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╇━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╇━━━╇━━━━━━╇━━━━━━━━━━━━━━━━╇━━━━━━━━━━━╇━━━━━━━━━━━━━━━━━━━━━━━━┩
│ 9 │ stacks on stacks - RSS Analysis │ (assuming inputs with Normal Dist. & uniform SD) │ - │ 19.9 │ ± 0.17634 │ 1 │ [-20.07634, -19.72366] │
└────┴─────────────────────────────────┴──────────────────────────────────────────────────┴───┴──────┴────────────────┴───────────┴────────────────────────┘
DIMENSION: 10: stacks on stacks - MRSS Analysis (assuming inputs with Normal Dist. & uniform SD) -19.9 ± 0.23866
┏━━━━┳━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┳━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┳━━━┳━━━━━━┳━━━━━━━━━━━━━━━━┳━━━━━━━━━━━┳━━━━━━━━━━━━━━━━━━━━━━━━┓
┃ ID ┃ Name ┃ Desc. ┃ ± ┃ Nom. ┃ Tol. ┃ Sens. (a) ┃ Abs. Bounds ┃
┡━━━━╇━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╇━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╇━━━╇━━━━━━╇━━━━━━━━━━━━━━━━╇━━━━━━━━━━━╇━━━━━━━━━━━━━━━━━━━━━━━━┩
│ 10 │ stacks on stacks - MRSS Analysis │ (assuming inputs with Normal Dist. & uniform SD) │ - │ 19.9 │ ± 0.23866 │ 1 │ [-20.13866, -19.66134] │
└────┴──────────────────────────────────┴──────────────────────────────────────────────────┴───┴──────┴────────────────┴───────────┴────────────────────────┘
REVIEWED DIMENSION: 11: stacks on stacks - '6 Sigma' Analysis (assuming inputs with Normal Dist.) -19.9 ± 0.26877 @ Normal Dist. μ=-19.9, σ=0.05973
┏━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┳━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┳━━━━━━━━━━━━━━┳━━━━━━━━━━┳━━━━━┳━━━━━━┳━━━━━━━┳━━━━━━━━━┳━━━━━━━━━━━━┳━━━━━━━━━━━━━┳━━━━━━━━━━━━┓
┃ Dim. ┃ Dist. ┃ Target Sigma ┃ Skew (k) ┃ C_p ┃ C_pk ┃ μ_eff ┃ σ_eff ┃ Eff. Sigma ┃ Yield Prob. ┃ Reject PPM ┃
┡━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╇━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╇━━━━━━━━━━━━━━╇━━━━━━━━━━╇━━━━━╇━━━━━━╇━━━━━━━╇━━━━━━━━━╇━━━━━━━━━━━━╇━━━━━━━━━━━━━╇━━━━━━━━━━━━┩
│ 11: stacks on stacks - '6 Sigma' Analysis (assuming inputs with Normal Dist.) -19.9 ± 0.26877 │ Normal Dist. μ=-19.9, σ=0.05973 │ ± 4.5σ │ 0.0 │ 1.5 │ 1.5 │ -19.9 │ 0.05973 │ ± 4.5σ │ 99.99932047 │ 6.8 │
└───────────────────────────────────────────────────────────────────────────────────────────────┴─────────────────────────────────┴──────────────┴──────────┴─────┴──────┴───────┴─────────┴────────────┴─────────────┴────────────┘
REQUIREMENT: stack spec
┏━━━━━━━━━━━━┳━━━━━━━┳━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┳━━━━━━━━┳━━━━━━━━━━━━━━┳━━━━━━━━━━━━━┳━━━━━━━━━━━━┓
┃ Name ┃ Desc. ┃ Distribution ┃ Median ┃ Spec. Limits ┃ Yield Prob. ┃ Reject PPM ┃
┡━━━━━━━━━━━━╇━━━━━━━╇━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╇━━━━━━━━╇━━━━━━━━━━━━━━╇━━━━━━━━━━━━━╇━━━━━━━━━━━━┩
│ stack spec │ │ Normal Dist. μ=-19.9, σ=0.05973 │ 0.425 │ [0.05, 0.8] │ 0.0 │ 1000000.0 │
└────────────┴───────┴─────────────────────────────────┴────────┴──────────────┴─────────────┴────────────┘