Chapter 8
Parallel key calculation according DIN 6892

    8.1   General
    8.2   The field of application of DIN 6892
    8.3   Geometry
    8.4   The loads
    8.5   Hints for method C
    8.6   Example: Parallel keys according to DIN 6892

8.1 General

A parallel key is a positive shaft-hub-connection. The torque is transmitted from the shaft to the hub via the parallel key. The main purpose of the parallel key is to transmit static and quasi-static torques. The parallel key can be used with limitations also for swelling and alternating torques. In case a good assembly and disassembly of the shaft-hub-connection are required or necessary (e.g., replacement or repair), then a parallel key may be used. A shearing off of the parallel key does not happen very often and occurs only in the event of overloading. The fretting corrosion due to rotating bending and/or torsional oscillation has been proven in numerous endurance tests and is usually the crucial factor which leads to the failure of the shaft-hub-connection. For the proof of strength of parallel keys, it is necessary to check the following factors:

In DIN 6892 a distinction is made between different methods for the proof of strength for parallel keys: method A, B and C.

The methods B and C, according to the standard, are integrated and available for the calculation.

8.2 The field of application of DIN 6892

8.3 Geometry

There is a selection of parallel key geometry according to DIN 6885-1, DIN 6885-2 and DIN 6885-3. This geometry selection includes the standard lengths of parallel keys. The supporting length is determined from the standard length and the chosen parallel key type. There are various types of parallel keys. Hence, the types A to J are available.

PIC

Figure 8.1: Types of parallel keys (A to J)

where

ltr is the supporting length

lPF  is the standard length

b is the width

For nonstandard parallel keys, it is possible to define an individual parallel key geometry and supporting lengths. The different keyway depths in shaft and hub as well as the chamfer of the parallel key are taken into consideration for the calculation. For method B, the chamfer on the shaft and hub keyway is additionally integrated into the calculation.

If the supporting length is set to the manual input, the supporting length l2tr  of the hub keyway can be smaller than ltr of the parallel key. For this case, according to DIN 6892, the length l1tr  of each extended part may be calculated as carrying up to maximum 1× b . The eAssistant uses the most conservative case as a basis for a save calculation and this exceptional case is not considered automatically by the eAssistant.

8.4 The loads

Surface pressure

The effective surface pressure between parallel key and shaft or hub keyway wall must not exceed the permissible value. The permissible values result from the material strength - for ductile materials from the yield point (Rp0,2 and/or Re  ) and for brittle materials from the tensile strength Rm  . The calculation can be accomplished by using unusual metallic materials. The following strength criteria have to be fulfilled with the appropriate safeties:

p1,2eq < fW ⋅pzul

p1,2max < fL ⋅pzul

where

fW is the changes of load direction factor

fL  is the load peak frequency factor

The calculation method applies for one-sided stress and with restriction for an alternating stress of the parallel keys. The surface pressure is determined from the torque that is transmitted.

PIC

Figure 8.2: Geometry and surface pressure on the parallel key connection

The supporting keyway depth between parallel key and shaft as well as hub keyway wall are given by the following equations. Therefore, a 45 chamfer and radius on the parallel key as well as on the shaft and hub keyway edge are considered according to the figure above:

Permitted surface pressure

where

f
S is the support factor

f
 H  is the hardness factor

The application factor

The application factor KA  is determined for the calculation of the equivalent torque Teq  similarly to the gear calculation according to DIN 3990 with the following table:






Application factors K
  A  according to DIN 3990-1: 1987-12





Working characteristics

Working characteristics of the driven machine




of the driving machine

Uniform Light shocks Moderate shocks Heavy shocks





Uniform

1,0 1,25 1,5 1,75





Light shocks

1,1 1,35 1,6 1,85





Moderate shocks

1,25 1,5 1,75 2,0





Heavy shocks

1,5 1,75 2,0 2,25 or higher







Examples for driving machines with various working characteristics
according to DIN 3990-1: 1987-12


Working characteristics

Driving machine



Uniform

Electric motor (e.g., d.c. motor), steam or gas turbine with uniform operation1 (small rarely occurring starting torques)



Light shocks

Steam turbine, gas turbine, hydraulic motor or electric motor (large, frequently occurring starting torques)



Moderate shocks

Multiple-cylinder internal combustion engines



Heavy shocks

Single-cylinder internal combustion engines



1 Based on vibration tests or on experiences gained from similar installations. 




Examples of working characteristics of driven machines
according to DIN 3990-1: 1987-12


Working characteristics

Driven machines



Uniform

Steady load current generator; uniformly loaded conveyor belt or platform conveyor; worm conveyor; light lifts; packing machinery; feed drives for machine tools; ventilators; lightweight centrifuges; centrifugal pumps; agitators and mixers for light liquids or uniform density materials; shears; presses; stamping machines1; vertical gears; running gear2.



Light shocks

Non-uniformly (e.g., with piece or batched components) loaded conveyor belts or platform conveyors; machine tool main drives; heavy lifts; crane slewing gear; industrial and mine ventilator; heavy centrifuges; centrifugal pumps; agitators and mixers for viscous liquids or substances of non-uniform density, multi-cylinder piston pumps, distribution pumps; extruders (general); calenders; rotary kilns; rolling mill stands3 (continuous zinc and aluminium strip mills, wire and bar mills).



Moderate shocks

Rubber extruders; continuously operating mixers for rubber and plastisc; ball mills (light); woodworking machine (gang saw, lathes); billet rolling mills3,4; lifting gear; single-cylinder piston pumps.



Heavy shocks

Excavator (bucket wheel drives), bucket chain drives; sieve drives; power shovels; ball mills (heavy); rubber kneaders; crushers (stone, ore); foundry machines; heavy distribution pumps; rotary drills; brick presses; debarking mills; peeling machines; cold strip3,5; briquette presses; breaker mills.



1 Nominal torque: maximum cutting, pressing or stamping torque.  
2 Nominal torque: maximum starting torque.  
3 Nominal torque: maximum rolling torque.  
4 Torque from current limitation.  
5 KA up to 2,0 because of frequent strip cracking.  


The load factor

Due to deviation in form and position of a single parallel key, an unbalanced or uneven carrying of two parallel keys, that are arranged evenly around the circumference, occurs. Thus, the reduced load capacity of the parallel key is considered by the load factor Kv  . In practice, not more than two parallel keys are used because of the load distribution that is difficult to determine.

Kv = 1-
     iφ

Compared to the calculation of the equivalent surface pressure, a higher load part f can be estimated for the determination of the maximum surface pressure because a torque occurring in several load peaks leads to a higher load part by deformation on the parallel key and keyway ground. Using these load parts, ductile materials with pronounced yield point as well as sufficient manufacturing accuracy are required. For brittle materials (e.g., gray cast iron), there is no established knowledge about the load capacity using two parallel keys.

Load distribution factor

The load distribution factor K λ  takes an uneven load distribution into consideration along the keyway length as well as the ratio of load in and output. For using two parallel keys, the unbalanced carrying is considered by the following assumption:

The factor Kλ is dependent upon the kind of load in and output position. Regardless of the torque flow direction, three cases are distinguished. For a stepped hub, it means:

D1 Small outer diameter of stepped hub

D2  Large outer diameter of stepped hub

a0  Distance between the axial cutting planes through N and W

c Width of the hub with D2  within the carrying part of the parallel key, i.e., c ≤ ltr

D is the outer diameter of the hub or the outer diameter of the alternative cylinder with equal torsional stiffness. The alternative outer diameter is calculated as follows:

D = ∘--------D2----------
     4( D2)4(1 - c-)+  c-
        D1       ltr    ltr

Depending on a∕l
0 tr  , the factor K
 λe  is determined by using the figures 3, 4 and 5 in DIN 6892. These diagrams are integrated into the calculation module and are valid for a specific ratio a ∕l
 0  tr  (a∕l=0;0,5;1)
0tr  . For other ratios a ∕l
 0 tr  , the values are determined from two diagrams by interpolation.

Friction factor

For an interference fit, part of the torque is transmitted by friction. The friction factor KR  considers that. But it is taken into consideration only for the calculation of the maximum effective surface pressure pmax  . For a dynamic load, an interference fit stops the occurrence of fretting corrosion. A clearance fit or interference fit adversely affects the shaft strength. For the determination of the friction factor, a minimum friction torque TRmin of the interference fit is assumed. According to DIN 7190, this can be obtained for a hole without keyway. The joint pressure, that is reduced due to the parallel key in comparison to the hole without keyway, is considered by the factor q . Thus, the friction torque, effective for the power transmission, is decreased. As a first approximation, q = 0,8  can be specified for a parallel key. With the maximum load peak torque Tmax  , occurring during the entire operation time, it applies:

Tmax > q⋅TRmin

KR  = Tmax---q⋅TRmin-
           Tmax

For

Tmax ≤ q⋅TRmin

the load peak torque is transmitted by friction. In this case, the surface pressure, occurring in the parallel key, is not relevant. A check of the maximum surface pressure pmax  is not necessary according to DIN 6892. However, it is integrated into the calculation.

Please note: For brittle materials (e.g., gray cast iron), no interference fit is allowed.

Load direction change factor

Parallel key connections are only conditionally usable during changing the direction of torque. However, the rating life is limited if it comes to constant slipping between shaft and hub and thus to a deflection of the parallel key connection. There are two different cases:

In case 2, the changes of load direction factor fW  is dependent upon the frequency NW  of changes of load direction for the parallel key. It can be determined according to DIN 6892, figure 6. Two cases are differentiated:

Load direction changes, that occur due to special cases, have to be considered as well.

Load peak frequency factor

Load peaks occur when the torque clearly exceeds the equivalent torque Teq  . Special cases may occur due to starting impacts, short-circuit torques, emergency breaking torques, abrupt blockings etc. The frequency NL  of the load peaks has to be estimated during the entire operating time. For a single load peak, depending on the ductility of the material, the 1,3 to 1,5 times the permanent surface pressure is allowed. The progress of fL for ductile and brittle materials over the frequency is shown in figure 5 according to DIN 6892.

PIC

Figure 8.3: Load peak frequency factor fL

The support factor

Using the support factor fS  , a supporting effect can be considered that occurs for compressive stress components. From experience, the supporting effect for hubs is larger due to the higher stressed material volume than for shafts and parallel keys (see table: support and hardness factors for different materials).

The hardness influence factor

The hardness influence factor fH  is determined from the ratio of surface strength to core strength for case-hardened components. By the hardness influence factor, an increasing of the permissible surface pressure is considered (see table: support and hardness factors for different materials).





Support and hardness influence factors for different materials




Component Material fs  fH




Parallel key Structural steel according to DIN EN 10 025 1,0 1,0
Bright steel according to DIN 1652-4 1,0 1,0
Heat-treated steel according to DIN EN 10 083-1 and DIN EN 10 083-2 1,0 1,0
Case-hardened steel according to DIN 17210 1,0 1,15




Shaft Structural steel according to DIN EN 10 025 1,2 1,0
Heat-treated steel according to DIN EN 10 083-1 and DIN EN 10 083-2 1,2 1,0
Case-hardened steel according to DIN 17 210 1,2 1,15
Gray cast iron with lamellar graphite according to DIN 1693-1 and DIN 1693-2 1,2 1,0
Steel casting according to DIN 1681 1,2 1,0



Gray cast iron with lamellar graphite according to DIN 1691 1,0 -




Hub Structural steel according to DIN EN 10 025 1,5 1,0
Heat-treated steel according to DIN EN 10 083-1 and DIN EN 10 083-2 1,5 1,0
Case-hardened steel according to DIN EN 17 210 1,5 1,15
Gray cast iron with spheroidal graphite according to DIN 1693-1 and DIN 1693-2 1,5 1,0
Steel casting according to DIN 1681 1,5 1,0



Gray cast iron with lamellar graphite according to DIN 1691 2,0 -




8.5 Hints for method C

The calculation method C according to DIN 6892 is suitable only for a rough calculation of parallel keys. The method is based on the following simplifications:

Limitations:

8.6 Example: Parallel keys according to DIN 6892

The calculation example shall support you with a fast start into the parallel key calculation module with its numerous possibilities. We prepared the following example for an introduction to this calculation module (see DIN 6892, Example E.2).

8.6.1 Start the calculation example

Please login with your user name and your password. Select the module ‘Parallel key’ through the tree structure of the Project Manager by double-clicking on the module or clicking on the button ‘New calculation’.

The calculation module is opened in a new window.

PIC

Figure 8.4: A general overview

8.6.2 The input values

A strength calculation for the following shaft-hub-connection has to be accomplished. Please enter the following values into the input fields:

Diameter of shaft = 60 mm

Application factor = 1.75

Outer diameter hub D
 2  = 120 mm

Calculation method = B

Input data method B:

Kind of load = Alternating torque with a slow torque increase

Changes of load direction = 106

Max. reverse torque T
  maxRev  = 3900 Nm

Small outer diameter of stepped hub D
  1  = 120 mm

Big outer diameter of stepped hub D
  2  = 120 mm

Width of hub with D
  2  internal l
 tr  (c ) = 91 mm

Axial distance between load in and output position a
 0  = 45.5 mm

Chamfer or radius on the shaft keyway edge s
 1  = 1.0 mm

Chamfer or radius on the hub keyway edge s
 2  = 1.0 mm

Operation nominal torque T
 nom  = 1.950 Nm

Min. frictional torque T
 Rmin  = 1.250 Nm

Max. load peak torque T
 max  = 3.900 Nm

Load peaks N
 L  = 500

Material shaft = C45 hardened and tempered

Material hub = 34CrNiMo6 hardened and tempered

Parallel key = DIN 6885.1 AB 18 x 11 x 100

Material parallel key = 34CrNiMo6 hardened and tempered

Standard length parallel key = 100 mm

Number of parallel keys = 1

8.6.3 The calculation

Please note: While you enter the data into the input fields, the calculations are accomplished. Thereby it can happen that the input fields are marked in red. Nevertheless, continue to enter the complete input data.

PIC

Figure 8.5: Input value

PIC

Please note: If you right-click into an input field, you can change the unit of measurement. A context menu is opened. The both arrows mark the current setting. The current field value will be converted automatically into the selected unit.


Calculation method B

Because of the reversal of the direction, a rough calculation according to method C is not possible. Select the calculation method B.

PIC

Figure 8.6: Calculation method B

When selecting the calculation method for the first time, the window ‘Input data method B’ opens immediately.

Enter the further values here and confirm your inputs with ‘OK’. If you would like to change your input values later, please click on the button ‘Input values method B’ and the input mask appears again.

PIC

Figure 8.7: Values for the calculation method B

Input of load peaks

The number of load peaks is ‘500’. Select ‘User defined input’ from the listbox and enter the value ‘500’.

PIC

Figure 8.8: Specification of load peaks

Inputs for the shaft

Define a material for the shaft. For our example the material ‘C45 hardened and tempered’ is required.

PIC

Figure 8.9: Shaft

The calculation module offers an easy possibility to choose the material directly from the listbox. But if you click on the button ’Material’, you will get to the material database. Here you will receive further information about the material source, kind of material, yield point, hardness factor f
 H  as well as the support factor f
 H  . After you have selected the material ‘C45 hardened and tempered’, please confirm with the button ‘OK’. Then you will get to the main mask.

PIC

Figure 8.10: Material database

User defined material

Use the possibility to specify your own defined material. Select the entry ’User defined’ from the listbox. You can add a comment or change the kind of material. Enter your own input values for the hardness factor f
 H  or for the support factor f
 S  .

PIC

Figure 8.11: User defined inputs

Inputs for the hub

Determine the material of the hub. The required material is here ‘34CrNiMo6 hardened and tempered’. You can select the material directly from listbox. In case you need further information, please click on the button ‘Material’. Then you get to the material database of the hub. Select the material ‘34CrNiMo6 hardened and tempered’ and confirm with the button ‘OK’.

The material is taken over to the main mask.

PIC

Figure 8.12: Hub

The button ‘Material’ allows you to define your own material.

Input data for the parallel key

For a comfortable working, a parallel key selection according to DIN 6885 sheet 1 to 3 is available. Here you can choose the parallel key geometry as well as the size. Find all appropriate standardized lengths for the parallel keys. The dimensions of the parallel key are as follows:

Parallel key: DIN 6885.1 AB 18 x 11 x 100

Standard length

To determine the standard length of the parallel key, select the value ‘100’ from the listbox.

PIC

Figure 8.13: Standard length

The length is taken over to the geometry of the parallel key.

PIC

Figure 8.14: Geometry

Selection of the parallel key geometry

Click on the button ‘Parallel key’ to select the shape of the parallel key.

PIC

Figure 8.15: Button ‘Parallel key’

A new window is opened. The appropriate parallel key will be displayed immediately.

PIC

Figure 8.16: Selection dialog for the parallel key

Select the parallel key geometry ‘DIN 6885 sheet 1-8/1968’ as well the shape ‘AB’ from the appropriate listbox.

PIC

Figure 8.17: Selection of the parallel key

Confirm with the button ‘OK’ to take over the values into the main mask.

PIC

Figure 8.18: Dimensions of the parallel key

Please note: The input of non-standard parallel keys

You have got the possibility to calculate non-standard parallel keys. You can define parallel keys different from the standard. The parallel keys A to J are also available here. In case you would like to define a non-standard parallel key, click on the button ‘Parallel key’ and you will get to the selection dialog again. Now activate the option ‘Own input’ and choose the appropriate dimension from the list or enter the dimensions directly.

PIC

Figure 8.19: Option ‘Own input’

Selection of a material

Select the material ‘34CrNiMo6 hardened and tempered’ directly from the listbox.

PIC

Figure 8.20: Material for the parallel key

If you need further information on the material, click on the button ‘Material’ and you will get to the material database.

PIC

Figure 8.21: Button ‘Material’

The supporting length l
tr  is calculated automatically from the already specified standard length.
You can use the listbox to select the number of parallel keys. For our calculation example we specify one parallel key.

PIC

Figure 8.22: The supporting length and number of parallel key

Please note: The supporting length for non-standard parallel keys

It is possible to define a supporting length for non-standard parallel keys. Select the option ‘User defined input’ from the listbox for the standard length. Now you can enter your own value into the input field for the supporting length.

PIC

Figure 8.23: User defined input

It is possible to specify different supporting lengths for the shaft and for the hub. Activate the input field for the supporting length for shaft and hub.

PIC

Figure 8.24: The supporting length for shaft and hub

8.6.4 The calculation results

The safeties of the operation load and at the maximum load for all three components (shaft, hub, and parallel key) are determined and displayed immediately in the result panel during the input. Which means that after every input of data, the results are calculated again. You will get the results for the equivalent pressure and for the pressure at load peak as well as the safety at operation load and the safety at peak load.

PIC

Figure 8.25: The calculation results

You can find also some additional information about your results in the message window.

PIC

Figure 8.26: The message window

In our calculation example the safeties for the shaft, the hub and the parallel key are marked in red. This means that the minimum safeties are not fulfilled. In addition, you get also an appropriate message in the message window. The parallel key is not suitable for our calculation example.

8.6.5 The documentation: The calculation report

Use the button ‘Report’ to generate the calculation report very fast. This report contains the calculation method, all input values as well as the detailed results.

PIC

Figure 8.27: The button ‘Report’

The calculation report contains a table of contents. You can navigate through the report via the table of contents that provides links to the input values, results and figures. The report is available in HTML and PDF format. Calculation reports, saved in HTML format, can be opened in a web browser or in Word for Windows.

PIC

Figure 8.28: The calculation report for the parallel key

8.6.6 How to save the calculation

After the accomplishment of your calculation, save the calculation either on the eAssistant server or on your own workstation locally. Click on the button ‘Save’.

PIC

Figure 8.29: The button ‘Save’

If you have activated the option ‘Enable file save local’ in the Project Manager and the option ‘Local’ in the calculation module, a standard Windows dialog for saving the file on your workstation appears.

Please note: You must not forget that the calculation module has to be closed to activate the option ‘Enable file save local.’

PIC

Figure 8.30: Windows dialog to save the file

In case you have not activated this option, a new window is opened and you can save the calculation on the eAssistant server (find further information in the chapter ‘The general functions’).

PIC

Figure 8.31: Save the calculation

Please enter a name into the input field ‘Filename’ and click on the button ‘Save’. Then click on the button ‘Refresh’ in the Project Manager. Your saved calculation file is displayed in the window ‘File’.

8.6.7 The dimensioning functions

The button for the dimensioning functions is marked by a calculator symbol and is located next to the input fields. If you click on the dimensioning buttons, you get a suggestion for an appropriate input value. There the calculation of the value takes place that the given minimum safety is just fulfilled.

By the following dimensioning buttons you are optimally supported:

PIC

Dimensioning of the shaft diameter


PIC

Dimensioning of the operation nominal torque


PIC

Dimensioning of the maximum load peak torque


PIC

Dimensioning of the standard length


PIC

Dimensioning of the supporting length

Minimum safety: The dimensioning of the shaft diameter

The shaft diameter has to be determined so that the given safety of ‘1.2’ for the parallel key connection is achieved. Click on the dimensioning button (calculator) for the shaft diameter.

PIC

Figure 8.32: The dimensioning button for the shaft diameter

Now the new shaft diameter is determined.

PIC

Figure 8.33: New shaft diameter

The shaft diameter is now d = 111.88 mm. With it the minimum saftey of ‘1.2’ is achieved and the parallel key is suitable for this application.

PIC

Figure 8.34: The result

Because of its larger diameter, a new parallel key size is determined automatically.

PIC

Figure 8.35: Parallel key

In case you click on the button ‘Parallel key’, the larger parallel key is displayed automatically.

PIC

Figure 8.36: New parallel key

8.6.8 The button ‘Redo’ and ‘Undo’

The button ‘Undo’ allows you to reset your input to an older state. The button ‘Redo’ reverses the undo.

PIC

Figure 8.37: The ‘Redo’ and ‘Undo’ button

8.6.9 The button ‘Options’

Click on the button ‘Options’.

PIC

Figure 8.38: The ‘Options’ button

The ‘Options’ button allows you to change some general settings such as the minimum safety as well as the number of decimal places.

PIC

Figure 8.39: Options

Our manual is improved continually. Of course we are always interested in your opinion, so we would like to know what you think. We appreciate your feedback and we are looking for ideas, suggestions or criticism. If you have anything to say or if you have any questions, please let us know via telephone +49 (0) 531 129 399-0 or email eAssistant@gwj.de.