The Sugar Engineers

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

D_tnom = 50.8 mm

Tube OD tolerance

tol_d = 0.23 mm

Minimum tube diameter

D_tmin = D_tnom - tol_d
D_tmin = 50.57 mm

Maximum tube diameter

D_tmax = D_tnom + tol_d
D_tmax = 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 D_tnom
Δd = 0.152 mm

Nominal hole diameter

D_hnom = D_tmax + Δd
D_hnom = 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

tol_h = 0.300 mm

Minimum hole size

D_hmin = D_hnom + 0.000 mm
D_hmin = 51.18 mm

Maximum hole size

D_hmax = D_hnom + tol_h
D_hmax = 51.48 mm

Check

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

Minimum clearance

Cl_min = D_hmin - D_tmax
Cl_min = 0.15 mm

Minimum diametral strain

ε_min = Cl_min / D_tnom
ε_min = 0.3% - Okay

Maximum clearance

Cl_max = D_hmax - D_tmin
Cl_max = 0.91 mm

Maximum diametral strain

ε_max = Cl_max / D_tnom
ε_max = 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

D_tnom = 101.6 mm

Tube OD tolerance

tol_d = 0.38 mm

Minimum tube diameter

D_tmin = D_tnom - tol_d
D_tmin = 101.22 mm

Maximum tube diameter

D_tmax = D_tnom + tol_d
D_tmax = 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 D_tnom
Δd = 0.305 mm

Nominal hole diameter

D_hnom = D_tmax + Δd
D_hnom = 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

tol_h = 0.350 mm

Minimum hole size

D_hmin = D_hnom + 0.000 mm
D_hmin = 102.28 mm

Maximum hole size

D_hmax = D_hnom + tol_h
D_hmax = 102.63 mm

Check

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

Minimum clearance

Cl_min = D_hmin - D_tmax
Cl_min = 0.30 mm

Minimum diametral strain

ε_min = Cl_min / D_tnom
ε_min = 0.3% - Okay

Maximum clearance

Cl_max = D_hmax - D_tmin
Cl_max = 1.41 mm

Maximum diametral strain

ε_max = Cl_max / D_tnom
ε_max = 1.393% - Okay