Chapter 20, Problem 22P

(a)

To determine

The specification of the diameter allowed for the position tolerance zone, when the hole is produced with the diameter of $32.0$ for position tolerance specification of $\varnothing 0.3$.

The specification of the diameter allowed for the position tolerance zone, when the hole is produced with the diameter of $32.2$ for position tolerance specification of $\varnothing 0.3$.

The specification of the diameter allowed for the position tolerance zone, when the hole is produced with the diameter of $32.4$ for position tolerance specification of $\varnothing 0.3$.

Answer to Problem 22P

The specification of the diameter allowed for the position tolerance zone, when the hole is produced with the diameter of $32.0$ for position tolerance specification of $\varnothing 0.3$ is $0.3$.

The specification of the diameter allowed for the position tolerance zone, when the hole is produced with the diameter of $32.2$ for position tolerance specification of $\varnothing 0.3$ is $0.3$.

The specification of the diameter allowed for the position tolerance zone, when the hole is produced with the diameter of $32.4$ for position tolerance specification of $\varnothing 0.3$ is $0.3$.

Explanation of Solution

The maximum material condition (MMC) and the least material condition (LMC) is used as a modifier to the size of a feature in the geometric control.

The symbol $(\text{M})$ and $(\text{L})$ are included in the feature control frame.

The symbol $(\text{M})$ represents the maximum material condition modifier and the symbol $(\text{L})$ represents the least material condition modifier.

When the tolerance zone is modified with the (MMC) modifier, it means that the value applies when the feature is produced at its MMC.

The least material condition is applied, when it is too difficult to control the material at its minimum amount.

In case of MMC modification, the amount of deviation from the MMC is added to the specified geometric tolerance

In case of LMC modifier the deviation from LMC is added to the specified geometric tolerance.

For the given case, there is no modifier so the position tolerance zone is equal to the specified position tolerance and it is equal to the $0.3$.

Thus, the specification of the diameter allowed for the position tolerance zone, when the hole is produced with the diameter of $32.0$ for position tolerance specification of $\varnothing 0.3$ is $0.3$.

Thus, the specification of the diameter allowed for the position tolerance zone, when the hole is produced with the diameter of $32.2$ for position tolerance specification of $\varnothing 0.3$ is $0.3$.

Thus, the specification of the diameter allowed for the position tolerance zone, when the hole is produced with the diameter of $32.4$ for position tolerance specification of $\varnothing 0.3$ is $0.3$.

(b)

To determine

The specification of the diameter allowed for the position tolerance zone, when the hole is produced with the diameter of $32.0$ for position tolerance specification of $\varnothing 0.3\left(\text{M}\right)$.

The specification of the diameter allowed for the position tolerance zone, when the hole is produced with the diameter of $32.2$ for position tolerance specification of $\varnothing 0.3\left(\text{M}\right)$.

The specification of the diameter allowed for the position tolerance zone, when the hole is produced with the diameter of $32.4$ for position tolerance specification of $\varnothing 0.3\left(\text{M}\right)$.

Answer to Problem 22P

The specification of the diameter allowed for the position tolerance zone, when the hole is produced with the diameter of $32.0$ for position tolerance specification of $\varnothing 0.3\left(\text{M}\right)$ is $0.3$.

The specification of the diameter allowed for the position tolerance zone, when the hole is produced with the diameter of $32.2$ for position tolerance specification of $\varnothing 0.3\left(\text{M}\right)$ is $0.5$.

The specification of the diameter allowed for the position tolerance zone, when the hole is produced with the diameter of $32.4$ for position tolerance specification of $\varnothing 0.3\left(\text{M}\right)$ is $0.7$.

Explanation of Solution

To calculate the position tolerance zone, add the value of deviation from the MMC.

Write the diameter at the maximum material condition (MMC) for hole.

$\text{MMC}=D_{\text{base}\text{diameter}}+\text{LL}$ (I)

Here, the base diameter is $D_{\text{base}\text{diameter}}$, lower limit is $\text{LL}$ and the diameter at the maximum material condition is $\text{MMC}$.

Write the expression of the geometric tolerance for MMC modifier.

$\text{GT}=\left|\text{MMC}-D\right|$ (II)

Here, the geometric tolerance is $\text{GT}$, and the diameter with respect to which we have to find the geometric tolerance is $D$.

Write the expression for the position tolerance zone.

$\text{PTZ}=\text{GT}+\text{SPT}$ (III)

Here, the position tolerance zone is $\text{PTZ}$ and specified position tolerance is $\text{SPT}$.

Conclusion:

Substitute $32.0$ for $D_{\text{base}\text{diameter}}$ and $0.0$ for $\text{LL}$ in the Equation (I).

$\begin{array}{c}\text{MMC}=32.0+0.0\\ =32.0\end{array}$

Substitute $32.0$ for $\text{MMC}$ and $32.0$ for $D$ in the Equation (II).

$\begin{array}{c}\text{GT}=\left|32.0-32.0\right|\\ =0.0\end{array}$

Substitute $0$ for $\text{GT}$ and $0.3$ for $\text{SPT}$ in the Equation (III).

$\begin{array}{c}\text{PTZ}=0.0+\text{0}\text{.3}\\ \text{=0}\text{.3}\end{array}$

Thus, the specification of the diameter allowed for the position tolerance zone, when the hole is produced with the diameter of $32.0$ for position tolerance specification of $\varnothing 0.3\left(\text{M}\right)$ is $0.3$.

Substitute $32.0$ for $\text{MMC}$ and $32.2$ for $D$ in the Equation (II).

$\begin{array}{c}\text{GT}=\left|32.0-32.2\right|\\ =0.2\end{array}$

Substitute $0.2$ for $\text{GT}$ and $0.3$ for $\text{SPT}$ in the Equation (III).

$\begin{array}{c}\text{PTZ}=0.2+\text{0}\text{.3}\\ \text{=0}\text{.5}\end{array}$

Thus, the specification of the diameter allowed for the position tolerance zone, when the hole is produced with the diameter of $32.2$ for position tolerance specification of $\varnothing 0.3\left(\text{M}\right)$ is $0.5$.

Substitute $32.0$ for $\text{MMC}$ and $32.4$ for $D$ in the Equation (II).

$\begin{array}{c}\text{GT}=\left|32.0-32.4\right|\\ =0.4\end{array}$

Substitute $0.4$ for $\text{GT}$ and $0.3$ for $\text{SPT}$ in the Equation (III).

$\begin{array}{c}\text{PTZ}=0.4+\text{0}\text{.3}\\ \text{=0}\text{.7}\end{array}$

Thus, the specification of the diameter allowed for the position tolerance zone, when the hole is produced with the diameter of $32.4$ for position tolerance specification of $\varnothing 0.3\left(\text{M}\right)$ is $0.7$.

(c)

To determine

The specification of the diameter allowed for the position tolerance zone, when the hole is produced with the diameter of $32.0$ for position tolerance specification of $\varnothing 0.3\left(\text{L}\right)$.

The specification of the diameter allowed for the position tolerance zone, when the hole is produced with the diameter of $32.2$ for position tolerance specification of $\varnothing 0.3\left(\text{L}\right)$.

The specification of the diameter allowed for the position tolerance zone, when the hole is produced with the diameter of $32.4$ for position tolerance specification of $\varnothing 0.3\left(\text{L}\right)$.

Answer to Problem 22P

The specification of the diameter allowed for the position tolerance zone, when the hole is produced with the diameter of $32.0$ for position tolerance specification of $\varnothing 0.3\left(\text{L}\right)$ is $0.7$.

The specification of the diameter allowed for the position tolerance zone, when the hole is produced with the diameter of $32.2$ for position tolerance specification of $\varnothing 0.3\left(\text{L}\right)$ is $0.5$.

The specification of the diameter allowed for the position tolerance zone, when the hole is produced with the diameter of $32.4$ for position tolerance specification of $\varnothing 0.3\left(\text{L}\right)$ is $0.3$.

Explanation of Solution

Write the diameter at the least material condition (LMC) for hole.

$\text{LMC}=D_{\text{base}\text{diameter}}+\text{UL}$ (IV)

Here, the base diameter is $D_{\text{base}\text{diameter}}$, upper limit is $\text{UL}$ and the diameter at the least material condition is $\text{LMC}$.

Write the expression of the geometric tolerance for MMC modifier.

$\text{GT}=\left|\text{LMC}-D\right|$ (V)

Here, the geometric tolerance is $\text{GT}$, and the diameter with respect to which we have to find the geometric tolerance is $D$.

Write the expression for the position tolerance zone.

$\text{PTZ}=\text{GT}+\text{SPT}$ (VI)

Here, the position tolerance zone is $\text{PTZ}$ and specified position tolerance is $\text{SPT}$.

Conclusion:

Substitute $32.0$ for $D_{\text{base}\text{diameter}}$ and $0.4$ for $\text{UL}$ in the Equation (I).

$\begin{array}{c}\text{LMC}=32.0+0.4\\ =32.4\end{array}$

Substitute $32.4$ for $\text{LMC}$ and $32.0$ for $D$ in the Equation (II).

$\begin{array}{c}\text{GT}=\left|32.4-32.0\right|\\ =0.4\end{array}$

Substitute $0.4$ for $\text{GT}$ and $0.3$ for $\text{SPT}$ in the Equation (III).

$\begin{array}{c}\text{PTZ}=0.4+\text{0}\text{.3}\\ \text{=}0.7\end{array}$

Thus, the specification of the diameter allowed for the position tolerance zone, when the hole is produced with the diameter of $32.0$ for position tolerance specification of $\varnothing 0.3\left(\text{M}\right)$ is $0.7$.

Substitute $32.4$ for $\text{LMC}$ and $32.2$ for $D$ in the Equation (II).

$\begin{array}{c}\text{GT}=\left|32.4-32.2\right|\\ =0.2\end{array}$

Substitute $0.2$ for $\text{GT}$ and $0.3$ for $\text{SPT}$ in the Equation (III).

$\begin{array}{c}\text{PTZ}=0.2+\text{0}\text{.3}\\ \text{=0}\text{.5}\end{array}$

Thus, the specification of the diameter allowed for the position tolerance zone, when the hole is produced with the diameter of $32.2$ for position tolerance specification of $\varnothing 0.3\left(\text{L}\right)$ is $0.5$.

Substitute $32.4$ for $\text{LMC}$ and $32.4$ for $D$ in the Equation (II).

$\begin{array}{c}\text{GT}=\left|32.4-32.4\right|\\ =0.0\end{array}$

Substitute $0.0$ for $\text{GT}$ and $0.3$ for $\text{SPT}$ in the Equation (III).

$\begin{array}{c}\text{PTZ}=0.0+\text{0}\text{.3}\\ \text{=0}\text{.3}\end{array}$

Thus, the specification of the diameter allowed for the position tolerance zone, when the hole is produced with the diameter of $32.4$ for position tolerance specification of $\varnothing 0.3\left(\text{L}\right)$ is $0.3$.