**Laboratory work**

**Measurement of linear dimensions with a caliper**

**Objective**

To master the use of calipers in measuring linear quantities.

**Tasks to be solved**

When performing laboratory work, students must solve the following tasks:

1. Study the caliper device.

2. Check the caliper.

3. Carry out the measurement of linear quantities.

**Tool to get the job done**

1. Detail to measure.

2. Caliper.

3. Guidelines and report form.

**Work order**

*1. To study the device and the principle of operation of the caliper.*

The options most commonly used in the production of designs of calipers of the ShTs type (GOST 166-89) are shown in Figures 1, 2, 3.

**Attention!** *It is forbidden to move the movable frame outside the rod to avoid losing the flat spring.*

Fig.1. ShTs-1 caliper double-sided with a depth gauge. 1 – rod; 2 – frame; 3 – clamping element; 4 – vernier; 5 – the working surface of the rod; 6 – depth gauge; 7 – sponges with edge measuring surfaces for measuring internal dimensions; 8 – sponges with flat measuring surfaces for measuring outer dimensions; 9 – rod scale

Rice. 2. Caliper ШЦ-II bilateral. 1 – rod; 2 – frame; 3 – clamping element; 4 – vernier; 5 – the working surface of the rod; 6 – fine frame setting device; 7 – sponges with edge measuring surfaces for measuring outer dimensions; 8 – sponges with flat and cylindrical measuring surfaces for measuring external and

internal dimensions, respectively; 9 – rod scale

Rice. 3. Caliper ШЦ-III one-sided (performed with or without micrometric feed). 1 – rod; 2 – frame; 3 – clamping element; 4 – vernier; 5 – the working surface of the rod; 6 – sponges with flat measuring surfaces for measuring outer dimensions; 7 – sponges with cylindrical measuring surfaces for measuring internal dimensions; 8 – rod scale

*Vernier*

The vernier scale divides an integer number of millimeters of the main scale into a certain number of parts. Figure 4 shows a vernier scale with a division value of 0.1 mm. The length of the vernier in this case is 19 mm and is divided into 10 parts. One division (length of division) of the vernier is equal to 19:10 = 1.9 mm, which is 0.1 mm less than a whole number of millimeters.

Rice. 4. Nonius scale with a reading value of 0.1 mm

On fig. 5 shows a vernier scale with a division value of 0.05 mm. The length of the cone is 39 mm divided into 20 parts. The division length is 39:20 = 1.95 mm, which is 0.05 mm less than a whole number of millimeters.

Rice. 5. Nonius scale with a reading value of 0.05 mm

*Countdown*

The order of reading the caliper readings on the scales of the rod and vernier is as follows:

read the number of whole millimeters, for this they find on the scale of the rod the stroke closest to the left of the zero stroke of the vernier, and remember its numerical value (in Fig. 6 – 25 mm);

Read fractions of a millimeter, for this, on the vernier scale, they find the stroke closest to the zero division and coinciding with the stroke of the rod scale (in Fig. 6, such a stroke of the vernier has number 3);

Calculate the full value of the reading of the caliper, for this, add the number of whole millimeters and fractions of a millimeter (in Fig. 6, the total value of the reading is 25.3 mm).

Fig.6. 25.3 mm caliper readings

For internal measurements, the size of the jaws indicated on them is added to the readings of the caliper on the main and vernier scales. An example of hole diameter measurement is shown in fig. 7.

Rice. 7. Reading of indications at internal measurements

*2. Verify the issued caliper.*

Verification, that is, the determination of the actual error of the caliper, is carried out using plane-parallel end measures of length, from which the exemplary dimensions ( *M* ) are made. Model dimensions ( *M* ) can be the size of a single measure or a block of measures made up of individual measures.

*Example.* Measures issued: 1.05; 3.5; 7.0.

It is necessary to draw up exemplary dimensions ( *M* ) for checking the measuring tool. Several options are possible: a) 1.05; 4.55(1.05+3.5); 8.05(7.0+1.05); 11.55(1.05+3.5+7.0); b) 1.05; 3.5; 7.0; 10.5(3.5+7.0) or others.

Measure plane-parallel gauge blocks with a caliper, increasing the size from the minimum to the maximum. Calculate the measurement error. The measurement error in absolute value should not exceed the tool error allowed by the technical conditions (TS), i.e. . If the tool **does not meet** specifications. The verification carried out is part of the certification process of the measuring instrument.

Fill in sections 1, 2 of the report form.

*3. Measure the linear dimensions* indicated on the sketch (Fig. 8) with a caliper.

Real values of linear quantities, i.e. obtained as a result of measurements, denote . For nominal size take the nearest integer. The size error is calculated by the formula , mm. For the validity condition, we take the inequality , where – size tolerance, determined from the tables, based on the specified quality of accuracy ( ** IT** ) and

**value.**

*Z* *Example.* Measurement result = 29.95 mm, let’s take ** Z** = 30.0 mm, then = – 0.05 mm. The degree of accuracy is set –

**, in this case**

*IT*9**= 52 microns = 0.052 mm. The validity condition is met.**

*TZ*Complete section 3 of the report form.

Fig.8. Detail sketch

*4. Analyze the measurement results of size A.*

The discrepancy in determining the size *A* according to two formulas and due to the conditions of contact between the caliper and the body. When determining the size *F* , the contact of the caliper and the body corresponds to Fig. 9a. The contact is complete (on a cylindrical surface), and the measurement error of the dimension *F* is 0.

When determining the size *G* , the contact of the caliper and the body corresponds to fig. 9b. The contact is incomplete, occurs in a straight line, and there is an error in determining the size *G.*

As follows from Fig. 9c, the theoretical size error is equal to

,

where – the thickness of the measuring sponge of the caliper ( mm).

Let’s find

,

where – radii of circles of diameters and .

.

The condition must be met

.

The difference between theoretical and experimental values arises due to a number of factors. For example, due to deviations in the shape of the hole from the ideal, due to the fact that the edge of the caliper is not perfectly sharp, etc.

Fig. 9. Contact between the caliper and the body when determining the size *A*

MGUIE | Report on the laboratory work “Measurement of angular dimensions” | FULL NAME. student |

Department of TMiM | Group | |

Option |

1. Characteristics of the caliper

Dimensions measurement limits, mm external internal | |

The division price of the main scale, mm | |

Nonius scale division price, mm | |

Interval of division of the main scale, mm | |

Nonius scale division interval, mm |

2. Checking the caliper

Size of end measure or block of measures (M), mm | Measured size (M _{r} ), mm |
Tool error , mm | Permissible error , mm | Conclusion on the results of verification (corresponds, does not correspond) |

3. Sketch of the measured part

4. Measurement results

5. Analysis of the results of measurements of size *A.*

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