# Tube Hole Tolerances and Clearances

The following definitions will help explain the calculation of hole clearances

Tolerance
is the amount by which the actual size of the hole or tube varies from the nominal size. This variation depends on the manufacturing process and on random errors.
Clearance
is the difference in size between the hole and the tube. Because there is a maximum and a minimum tube outside diamter and a maximum and a minimum hole diameter there will be a range of clearances.

## Tolerances

The tube OD tolerances depend on the tube manufacturer and his equipment and process. In the same way the tube sheet hole tolerances are a function of the hole making process. The best we can do is specify tolerances the manufacturer can achieve at a reasonable cost.

## Clearances

The designer of a vessel can control the clearance between tube OD and tube sheet hole diameter. But as noted above this will be a range.

The minimum clearance should be be such that the tube material once expanded into the tube undergoes plastic deformation; that is, the strain has exceeded the yield point. In most stainless steels there is no definite yield point, rather a 0.2% proof strain is regarded as the yield criterion. The criterion set for minimum clearance is thus 0.3% strain for no good reason other than it is greater than 0.2%.

The maximum clearance shall be such that the tube material is not strained more than 2.0%. See graph below (from Thum and Micleots)

It must be noted that both the minimum and maximum clearance criteria are somewhat arbitrary, but they have proved themselves in practice in a number of different types of vessels.

# Practical Application

## Kestner evaporator tube

For this example we will consider a 2 in nominal diameter tube. The tube OD tolerance is given by the manufacturer as +/- 0.23 mm.

Tube nominal diameter
Dtnom = 50.8 mm
Tube OD tolerance
told = 0.23 mm
Minimum tube diameter
Dtmin = Dtnom - told
Dtmin = 50.57 mm
Maximum tube diameter
Dtmax = Dtnom + told
Dtmax = 51.03 mm

In order to get plastic deformation of the tube as it is expanded it must be strained more than 0.2%, say 0.3%

Diametral strain
ε = 0.30%
Diametral dilation
Δd = ε Dtnom
Δd = 0.152 mm
Nominal hole diameter
Dhnom = Dtmax + Δd
Dhnom = 51.18 mm

The hole is going to be drilled and an ISO tolerance of H12 is achievable ie the tube hole diameter is 51.18H12. The H12 tolerance is +0.000 +0.300

Tube hole tolerance
tolh = 0.300 mm
Minimum hole size
Dhmin = Dhnom + 0.000 mm
Dhmin = 51.18 mm
Maximum hole size
Dhmax = Dhnom + tolh
Dhmax = 51.48 mm

## Check

We will now check that the calculated clearances meet our criteria set above

Minimum clearance
Clmin = Dhmin - Dtmax
Clmin = 0.15 mm
Minimum diametral strain
εmin = Clmin / Dtnom
εmin = 0.3% - Okay
Maximum clearance
Clmax = Dhmax - Dtmin
Clmax = 0.91 mm
Maximum diametral strain
εmax = Clmax / Dtnom
εmax = 1.796% - Okay

## Continuous vacuum pan tube

In this example we will consider a 4 in nominal diameter tube. The tube OD tolerance is given by the manufacturer as +/- 0.38 mm.

Tube nominal diameter
Dtnom = 101.6 mm
Tube OD tolerance
told = 0.38 mm
Minimum tube diameter
Dtmin = Dtnom - told
Dtmin = 101.22 mm
Maximum tube diameter
Dtmax = Dtnom + told
Dtmax = 101.98 mm

In order to get plastic deformation of the tube as it is expanded it must be strained more than 0.2%, say 0.3%

Diametral strain
ε = 0.30%
Diametral dilation
Δd = ε Dtnom
Δd = 0.305 mm
Nominal hole diameter
Dhnom = Dtmax + Δd
Dhnom = 102.28 mm

The hole is going to be drilled and an ISO tolerance of H12 is achievable ie the tube hole diameter is 102.28H12. The H12 tolerance is +0.000 +0.350

Tube hole tolerance
tolh = 0.350 mm
Minimum hole size
Dhmin = Dhnom + 0.000 mm
Dhmin = 102.28 mm
Maximum hole size
Dhmax = Dhnom + tolh
Dhmax = 102.63 mm

## Check

We will now check that the calculated clearances meet our criteria set above

Minimum clearance
Clmin = Dhmin - Dtmax
Clmin = 0.30 mm
Minimum diametral strain
εmin = Clmin / Dtnom
εmin = 0.3% - Okay
Maximum clearance
Clmax = Dhmax - Dtmin
Clmax = 1.41 mm
Maximum diametral strain
εmax = Clmax / Dtnom
εmax = 1.393% - Okay