# Shaped couplings of shafts with hubs.

The calculation is designed for geometric designs and strength checks of shaped couplings of shafts with hubs. The application provides solutions for the following tasks:

1. Design of a coupling with parallel side keys.

2. Design of a coupling with Woodruff's keys.
3. Design of a coupling with straight-sided splines.

4. Design of a coupling with involute splines.

5. Strength check of designed couplings.

6. The application includes a table of keys and splines according to ISO, SAE, DIN, BS, JIS and CSN.

7. Support for 2D CAD systems.

The calculation is based on data, procedures and algorithms from specialized literature and standards ANSI, ISO, DIN and others.
List of standards: ANSI B17.1, ANSI B17.2, ANSI B92.1, ANSI B92.2M, ISO R773, ISO 14, ISO 4156, DIN 6885, DIN 6888, DIN 5464, DIN 5471, DIN 5472, DIN 5480, BS 4235, BS 6, JIS B 1301, CSN 02 2562, CSN 30 1385, CSN 01 4942, CSN 4950

## Control, structure and syntax of calculations.

Information on the syntax and control of the calculation can be found in the document "Control, structure and syntax of calculations".

## Information on the project.

Information on the purpose, use and control of the paragraph "Information on the project" can be found in the document  "Information on the project".

## Process of calculation.

The workbook with calculation of shaped couplings of shafts and hubs can be divided into two ranges. A range of common input data and results (paragraphs [1, 10, 11]) and a range of individual calculations (chapters A, B, C, D) relevant for the given type of coupling only. Two types of tasks can then be solved using the calculation:

• Design, calculation and check of the type of coupling chosen beforehand
• Design of a coupling for several different types of couplings with consequential options of the best solution

When choosing a suitable type of coupling there must also be taken into account, besides the dimensional parameters of the coupling, its use value, time demands and financial costs of production, installation and operation of the coupling. The comparative document "Choices of type of coupling of a shaft with a hub" can be helpful in selecting a suitable type of coupling.

Typical calculation / design of a coupling consists of the following steps:

1. Enter power parameters of the coupling (transferred power, speed) [1.2, 1.3].
3. Choose material of the shaft [1.21] and material of the hub [1.26].
4. Define the design of the coupling [1.14].
5. Set parameters of the coupling for the chosen type of coupling [2.1 / 4.1 / 6.1 / 8.1].
6. In case of calculations of couplings with keys, choose the material of the key [2.6 / 4.6].
7. Design dimensions of the coupling [2.11 / 4.15 / 6.5 / 8.11]. The automatic design function [4.13 / 8.9] can be used in case of couplings with Woodruff's keys and involute splines.
8. Examine results of strength checks of the designed coupling [3 / 4 / 5 / 7].
9. In case of a design for more types of couplings, compare the designed dimensions in paragraph [10].
10. Save the workbook with the suitable solution under a new name.

## Common input data. [1]

In this paragraph, enter basic input parameters, characterizing the manner, conditions and amount of loading, design of the coupling and materials of the shaft and hub.

### 1.1 Calculation units.

In the selection list, choose the desired calculation unit system. All values will be recalculated immediately after switching to other units.

### 1.2 Transferred power.

Enter the power which will be transferred by the shaft.

### 1.3 Shaft speed.

Enter the shaft speed.

### 1.4 Torque.

The transferred power and speed provide a torsional moment, which is the basic input value for the design of the coupling.

### 1.6 Power source.

Select the type of drive which best meets the requirements of the entered specifications.

1. Uniform: electric motor, steam turbine, gas turbine
2. Light shocks: hydraulic motors
3. Medium shocks: internal combustion engine

Select the loading conditions which best meet the requirements of the entered specifications.

1. Continuous: generator, conveyor (belt, plate, worm), light lift, gearing of a machine tool traverse, fan, turbocharger, turbo compressor, mixer for materials with constant density, etc.
2. Light shocks: generator, gear pump, rotary pump, etc.
3. Intermittent shocks: main drive of a machine tool, heavy forklift, crane swivel, mine fan, mixer for materials with variable density, piston pump, etc.
4. Heavy shocks: press, shears, rubber calender, rolling mill, vane excavator, heavy centrifuge, heavy feeding pump, drilling set, briquetting press, kneading machine, etc.

### 1.8 Character of operation.

Choose whether the coupling will be loaded during operation in one direction of rotation or the direction of rotation of the shaft will be changed.

### 1.9 Number of start-ups.

Choose the total number of machine start-ups during the desired service life of the coupling.

### 1.10 Desired service life of the coupling.

The parameter specifies the desired service life in hours. Orientation values in hours are given in the table.

 Specification Durability Household machines, seldom used devices 2000 Electric hand tools, machines for short-term runs 5000 Machines for 8-hour operation 20000 Machines for 16-hour operation 40000 Machines for continuous operation 80000 Machines for continuous operation with long service life 150000

### 1.12 Coupling design.

In the selection list, choose the design of the coupling which best meets the requirements of your specifications.

1. Fixed connection: no axial shift of the hub along the shaft occurs in the coupling; the mutual positions of the shaft and hub are fixed using a suitable bearing or constructional design (pressing-on, shaft nuts, circlips, etc.).
2. Sliding coupling without loading: mutual positions of the shaft and hub are not fixed; axial shifts of the hub along the shaft occur in unloaded couplings only.
3. Sliding coupling during loading: mutual positions of the shaft and hub are not fixed; axial shifts of the hub along the shaft occur in loaded couplings.

### 1.13 Inner diameter of the hollow shaft.

In case you use a hollow shaft in the coupling, enter here the inner diameter of the shaft. This parameter affects the size of loading of the shaft in torsion and considerably affects determination of the minimum permitted diameter of the shaft [1.20].

### 1.14 Desired safety.

With regards to accuracy and credibility of input information, importance of the coupling, quality of production and accuracy of the calculation, it is usually chosen in a range from 1.5 to 3.

##### Orientation values for choice of safety:
• 1.3 to 1.5 - Very accurate input information, perfect knowledge of material characteristics, high quality and exact following of production technology; insignificant couplings, damage to which does not cause any serious consequences.
• 1.5 to 1.8 - Less accurate calculation without any experimental verification, lower accuracy in production technology, couplings of lower importance.
• 1.8 to 2.5 - Decreased accuracy of calculations, approximate determination of material characteristics, inaccurate knowledge of actual effects of external loading; large diameters of shafts, very important couplings, damage to which could jeopardize human life or bring about high material losses.

### 1.15 Minimum diameter of the shaft.

Minimum diameter of the shaft means the diameter of a solid shaft not weakened by grooves (see the illustration). Use the designed minimum diameter of the shaft as initial information for the design of the coupling.

### 1.16 Shaft material (min. tensile strength) [hardness]

In the selection list, choose the type of material which will be used for production of the shaft. Minimum tensile strength [MPa/psi] and hardness of material are given in parenthesis. In case the checkbox to the right of the selection list is enabled, the necessary strength parameters for the chosen material are determined automatically. Otherwise, fill in the material characteristics manually. The value of the permitted pressure [1.19] is used for checks of contact surfaces of couplings for deformation. The permitted tension in shear [1.20] is used for strength checks of shafts in torsion.

### 1.21 Hub material (min. tensile strength) [hardness]

In the selection list, choose the type of material which will be used for production of the hub. Min. tensile strength [MPa/psi] and hardness of material are given in parenthesis. In case the checkbox to the right of the selection list is enabled, the necessary strength parameters for the chosen material are determined automatically. Otherwise, manually fill in the value of the permitted pressure [1.24] which is used for checks of contacts surfaces of the coupling for deformation.

### 1.27 Coupling design factor.

This coefficient reflects the effect of the coupling design on decrease of the coupling's loading capacity. It is determined according to empirical values given in the following table:

### 1.28 Application factor.

This coefficient reflects the effect of the character and type of loading on decrease of the coupling's loading capacity. It is determined according to empirical values given in the following table:

 Drive Type of loading Continuous Light shocks Cyclical shocks Heavy shocks Uniform 1.0 1.2 1.5 1.8 Light shocks 1.2 1.3 1.8 2.1 Medium shocks 2.0 2.2 2.4 2.8

### 1.29 Fatigue-life factor.

This coefficient reflects effects of the operational character and desired service life of the coupling (measured in number of start-ups) on increase of the coupling's loading capacity. It is determined according to empirical values given in the following table:

 Number of start-ups Operation Unidirectional Fully bi-directional 1000 1.8 1.8 10000 1.0 1.0 100000 0.5 0.4 1000000 0.4 0.3 10000000 0.3 0.2

### 1.30 Wear life factor.

This coefficient reflects effects of wear of contact surfaces during the desired service life of the coupling (measured in number of revolutions) on increase of the coupling's loading capacity. It is determined according to empirical values given in the following table:

 Total number of revolutions [millions] Kw 0.01 4.0 0.1 2.8 1 2.0 10 1.4 100 1.0 1000 0.7 10000 0.5

## A. Couplings with parallel side keys.

Couplings with parallel side keys are suitable for transfer of torsional moments, mostly in the same direction of rotation. These couplings are used usually for immovable couplings of cylindrical shafts with hubs. This type is less suitable for sliding couplings and tapered shafts. Typical use is with clutches, sprockets and pulleys. Faces of the keys are usually rounded.

Benefits of the coupling:

• low production costs
• easy assembly and disassembly of the coupling
• centric bearing of the hub
• lower notch index compared with splined couplings

• higher pressures than with splined couplings, lower loading capacity of the coupling
• higher wear in case of sliding couplings
• more or less unusable for cyclical torsional moments; risk of loosening of the coupling after deformation of splines

Loading capacity of the coupling can be increased by using 2 keys. However, this causes a significant weakening of the shaft and thus the possible use of a shaft with a greater diameter

##### Recommended (orientation) bearing for couplings with parallel side keys
 Type of bearing Fixed couplings Sliding couplings Common bearing Tight bearing Guide key Sliding key Seating of the key in the hub groove N9 / h9 P9 / h9 N9 / h9 D10 / h9 Seating of the key in the shaft groove Js9 / h9 P9 / h9 D10 / h9 N9 / h9 Seating of the hub on the shaft H8 / h7 H8 / k7 H8 / m7 H8 / p7 H8 / f7 H8 / h7 H7 / h6

## Coupling parameters, key material, dimensional design. [2]

This paragraph can be used to choose the parameter of the given type of coupling and to design dimensions of the coupling.

### 2.2 Key type.

In the selection list, choose a type (standard) of key. Dimensions of type A keys are defined by the standard in [in], dimensions of keys of other types are defined in [mm].

### 2.3 Number of keys.

For transfer of higher torsional moments, it is possible to use two keys in the coupling. The keys are usually arranged symmetrically on the shaft (in opposite positions). A non-symmetrical arrangement is also used for transfer of cyclical moments (at 120° spacing).

###### Note: Although the loading capacity of a coupling with two keys should be theoretically doubled, it is in fact lower due to production inaccuracies. In practice, the loading capacity is usually considered 1.5-times higher than with one key.

In couplings with two keys, the loading is not distributed exactly uniformly onto the two keys due to production and assembly inaccuracies. The actual load bearing surface of the coupling is lower than the load bearing surface determined theoretically. The ratio between the theoretical and actual load bearing surface of the coupling is defined by the coefficient of distribution of the loading. With regards to the accuracy of bearing, the size of the coefficient is given in a range from 0.6 to 0.8.

### 2.5 Total service factor.

This coefficient gives the total effects of production and operational parameters on decrease of loading capacity of the coupling. Its size depends on the type of coupling, drive and loading, operational conditions and service lifespan of the coupling. With regards to the mentioned parameters, the literature gives values of the coefficient in a range from 1 to 40.

For easier choice of coefficient, the application is provided with automatic design. In case the checkbox to the right of the input field is enabled, the coefficient is determined automatically and based on parameters of the coupling defined in paragraph [1]. For a fixed coupling, the operational coefficient is calculated using the relation:

For a sliding coupling, the following relation is used:

where:

Ka - application factor

Kf - fatigue-life factor

Kd - coupling design factor

Kw - wear life factor

Meaning and size of the coefficients, see [1].

### 2.6 Key material (min. tensile strength) [hardness]

In the selection list, choose the type of the material which the key will be produced from. The min. tensile strength [MPa/psi] and hardness of material are given in parenthesis. In case the checkbox to the right of the selection list is enabled, the necessary strength parameters for the chosen material are determined automatically. Otherwise, manually fill in the value of the permitted pressure [2.9] which is used for checks of deformation of the key.

### 2.11 Design of coupling dimensions.

This paragraph can be used to design dimensions of the coupling. When designing the coupling, first choose the desired diameter of the shaft [2.14]. For the entered diameter of the shaft, the corresponding key will be chosen according to the respective standard automatically. For this chosen key, the program calculates the minimum length [2.20] which is necessary for safe transfer of the entered torsional moment. Complete the design of the coupling so that you choose the actual length of the key in row [2.22].

### 2.12 Keys for diameters.

This parameter gives standard specified diameters of the shaft for the type of key chosen in [2.2].

### 2.13 Minimum shaft diameter.

This parameter gives the minimum diameter of a solid shaft, not weakened by a key groove, which is necessary for safe transfer of the entered torsional moment.

### 2.14 Shaft diameter.

Choose a diameter of the shaft sufficient so that the diameter of a solid shaft d1, not weakened by a key groove, is larger that the minimum required diameter d1min.

### 2.20 Minimum key length.

The calculated minimum length of the chosen key, which is necessary for safe transfer of the entered torsional moment.

### 2.21 Permitted range of key lengths.

The standard specified minimum and maximum permitted length of the chosen key.

### 2.22 Chosen key length.

Choose a length of key within the standard specified range [2.21] so that it is larger than the minimum length [2.20]. When determining the length, keep in mind that the chosen length of the key influences the length of the hub. Recommended lengths of hubs can be found in the document "Guiding values for choices of dimensions of hubs".

## Strength checks of the coupling. [3]

In case of couplings with keys, there are usually performed only two types of strength checks. A check of loading of the shaft for torsion and a check of deformation of contact surfaces of the coupling. The check for loading of the key for shear is usually not performed. Standardized keys are dimensioned so that in case the requirements of the check for deformation are met, requirements of the check for shear stress are also met.

### 3.1 Check of shaft for torsion.

The check is performed for a diameter of a solid shaft d1 [2.18], not weakened by the key groove. The resulting safety of the coupling [3.4] is given by the ratio of the permitted shear stress of the shaft material to the calculated comparative stress. If the coupling is to be sufficient, the calculated safety must be higher than the required one [1.19].

### 3.5, 3.9, 3.13 Check for deformation of contact surfaces.

The check for deformation is performed independently for each part of the coupling. Individual levels of safety [3.8, 3.12, 3.16] are given by the ratio of the permitted pressure of the respective material to the calculated comparative pressure acting on the given part of the coupling. In case the coupling is to be sufficient, the value of the lowest safety must be higher than the value of the required safety [1.19].

## B. Couplings with Woodruff's keys.

Couplings with Woodruff's (disk) keys are suitable for transfers of smaller torsional moments with shafts of smaller diameters mostly with the same direction of rotation. These couplings are used for fixed couplings of cylindrical or tapered shafts with short hubs. This type is usually not used for sliding couplings.

Benefits of the coupling:

• low production costs
• easy assembly and disassembly of the coupling
• centrical bearing of the hub
• suitable for tapered ends of shafts

• higher pressures than with splined couplings, lower loading capacity of the coupling
• unsuitable for sliding couplings
• greater weakening of the shaft due to splines than with parallel side keys
• unsuitable for cyclical torsional moments, risk of release of the coupling after deformation of the groove

The loading capacity of the coupling can be increased using two keys. However, this causes a more significant weakening of the shaft and thus a possible need to use a shaft with a greater diameter.

##### Recommended (orientation) bearing for couplings with Woodruff's keys
 Type of bearing Common bearing Tight bearing Bearing of the key in the groove of the hub N9 / h9 P9 / h9 Bearing of the key in the groove of the shaft Js9 / h9 Js9 / h9 Bearing of the hub on the shaft H8 / h7 H8 / k7 H8 / m7 H8 / p7

## Coupling parameters, key material, dimensional design. [4]

This paragraph can be used for choices of parameters of the given type of coupling and for a design of dimensions of the coupling.

### 4.2 Key type.

In the selection list, choose a type (standard) of key. Dimensions of the key are defined in the standard for types A, B, E, F v [in], in case of other types, the dimensions are defined in [mm]. Keys are produced in two basic designs (see the illustration):

1. Design with full rounding
2. Flat design

Both types can be further designed with chamfered tops.

### 4.3 Number of keys.

For transfer of higher torsional moments, it is possible to use two keys in the coupling. The keys are usually arranged symmetrically on the shaft (in opposite positions). A non-symmetrical arrangement is also used for transfer of cyclical moments (at 120° spacing).

###### Note: Although the loading capacity of a coupling with two keys should be theoretically doubled, it is in fact lower due to production inaccuracies. In practice, the loading capacity is usually considered 1.5-times higher than with one key.

In couplings with two keys, the loading is not distributed exactly uniformly onto the two keys due to production and assembly inaccuracies. The actual load bearing surface of the coupling is lower than the load bearing surface determined theoretically. The ratio between the theoretical and actual load bearing surface of the coupling is defined by the coefficient of distribution of the loading. With regards to the accuracy of bearing, the size of the coefficient is given in a range from 0.6 to 0.8.

### 4.5 Total service factor.

This coefficient gives the total effects of production and operational parameters on decrease of loading capacity of the coupling. Its size depends on the type of coupling, drive and loading, operational conditions and service lifespan of the coupling. With regards to the mentioned parameters, the literature gives values of the coefficient in a range from 1 to 40.

For easier choice of coefficient, the application is provided with automatic design. In case the checkbox to the right of the input field is enabled, the coefficient is determined automatically and based on parameters of the coupling defined in paragraph [1]. For a fixed coupling, the operational coefficient is calculated using the relation:

For a sliding coupling, the following relation is used:

where:

Ka - application factor

Kf - fatigue-life factor

Kd - coupling design factor

Kw - wear life factor

Meaning and size of the coefficients, see [1].

### 4.6 Key material (min. tensile strength) [hardness]

In the selection list, choose the type of the material which the key will be produced from. The min. tensile strength [MPa/psi] and hardness of material are given in parenthesis. In case the checkbox to the right of the selection list is enabled, the necessary strength parameters for the chosen material are determined automatically. Otherwise, manually fill in the value of the permitted pressure [4.9] which is used for checks of deformation of the key.

### 4.11 Automatic design of the coupling.

The automatic design chooses all suitable keys for the chosen type [4.2] and additionally calculates the minimum sufficient diameter of the shaft for the keys. The design calculation is started by clicking the button in row [4.13]. After completion of the calculation, the table of designed solutions [4.14] is filled in and sorted and the values of the chosen solution are transferred automatically to paragraph [4.15]. The table is sorted according to the criterion set out in row [4.12] and can be re-sorted whenever using another chosen criterion.

If the design calculation was unsuccessful and no suitable solution was found, this fact is indicated by a warning message and the table of solutions is deleted. In such cases, repeat the design for a coupling with more keys or materials of a higher quality.

### 4.14 Table of designed solutions

Meaning of parameters in the table:

 d Diameter of the shaft d1 Diameter of a solid shaft not weakened by a key groove L Length of the key sT Safety of the strength check of a shaft for torsion sp Safety of the strength check for deformation Key Marking of the key (see [4.19])

### 4.15 Coupling dimensions.

This paragraph can be used to determine dimensions of the coupling. The dimensions can be chosen manually or the values of the designed solution can be transferred using a selection from table [4.14]. In case of values entered manually, first choose the desired diameter of the shaft [4.18]. After entering the shaft diameter the list of keys [4.19] assigned to the given diameter according to the respective standard is automatically filled in. Complete the design of the coupling by selecting a suitable key.

### 4.16 Keys for diameters.

This parameter gives standard specified diameters of the shaft for the type of key chosen in [4.2].

### 4.17 Minimum shaft diameter.

This parameter gives the minimum diameter of a solid shaft, not weakened by a key groove, which is necessary for safe transfer of the entered torsional moment.

### 4.18 Shaft diameter.

Choose a diameter of the shaft sufficient so that the diameter of a solid shaft d1, not weakened by a key groove, is larger that the minimum required diameter d1min. After entering the shaft diameter, a list of keys [4.19] assigned to the given diameter according to the respective standard is automatically filled in.

### 4.19 Key.

In the selection list, choose a suitable key. The list includes all keys assigned to the chosen diameter of the shaft [4.18] according to the respective standard. Marking of the keys in the list is given by the chosen type (standard) of key. The convention of marking for individual types of keys is given in the following table.

 Type of key [4.2] Standard Marking A, B, E, F ANSI B17.2, BS 6 No. (b x D) C, D, I, J DIN 6888, CSN 30 1385 b x h G, H JIS B 1301 b x D

where:

b - width of the key

h - height of the key

D - diameter of the key

## Strength checks of the coupling. [5]

In case of couplings with keys, there are usually performed only two types of strength checks. A check of loading of the shaft for torsion and a check of deformation of contact surfaces of the coupling. The check for loading of the key for shear is usually not performed. Standardized keys are dimensioned so that in case the requirements of the check for deformation are met, requirements of the check for shear stress are also met.

### 5.1 Check of shaft for torsion.

The check is performed for a diameter of a solid shaft d1 [4.22], not weakened by the key groove. The resulting safety of the coupling [5.4] is given by the ratio of the permitted shear stress of the shaft material to the calculated comparative stress. If the coupling is to be sufficient, the calculated safety must be higher than the required one [1.19].

### 5.5, 5.9, 5.13 Check for deformation of contact surfaces.

The check for deformation is performed independently for each part of the coupling. Individual levels of safety [5.8, 5.12, 5.16] are given by the ratio of the permitted pressure of the respective material to the calculated comparative pressure acting on the given part of the coupling. In case the coupling is to be sufficient, the value of the lowest safety must be higher than the value of the required safety [1.19].

## C. Couplings with straight-sided splines.

Couplings with straight-sided splines are suitable for transfer of great, cyclical and shock torsional moments. These couplings represent in practice the most common type of splines (approx. 80%). This type is used both for fixed and for sliding couplings of cylindrical shafts with hubs. These couplings are used typically in case of sliding gears in manual gearboxes.

Benefits of the coupling:

• lower pressures than in couplings with keys, higher loading capacity of the coupling
• smaller wear with sliding couplings
• suitable for cyclical torsional moments
• easy assembly and disassembly of the coupling

• higher production costs than in the case of couplings with keys
• higher notch coefficient than in the case of couplings with keys

The method of centering is chosen according to technological and operational requirements and demands for accuracy. Centering is possible on the inner diameter (used rarely) or on sides of teeth. Centering on diameters is used in case of a need for higher accuracy of the bearing. Couplings centered on the sides show higher loading capacity and are suitable for loading with variable moments and shocks.

##### Recommended (orientation) bearing for straight-sided splines
 Centering dimension Bearing of the dimension Note: d b D Fixed couplings at high loading with shocks, without frequent disassembly b - F8 / js7 - Fixed couplings at medium loading and with frequent disassembly d H7 / g6 D9 / js7 D9 / k7 F10 / js7 F10 / f9 - Medium speeds b - F8 / js7 - Low speeds D - F8 / js7 H7 / js6 High speeds For movable couplings under loading d H7 / f7 H7 / g6 D9 / h9 D9 / js7 F10 / f9 - Hardened surfaces For movable couplings without loading d H7 / f7 H7 / g6 D9 / h9 F10 / f9 - Low and medium speeds D - F8 / f7 F8 / f8 H7 / f7 High speeds

where:
d - spline inner diameter
D - spline outer diameter
b - width of the teeth

## Coupling parameters, dimensional design. [6]

This paragraph can be used to choose parameters of the given type of coupling and to design dimensions of the coupling.

### 6.2 Splines type.

In the selection list choose a type (standard) of splines. Spline dimensions are defined in the standard for types A, B, C in [in], in case of other types, the dimensions are defined in [mm].

##### Recommended use of spline:
 Type Standard Series Use A SAE A Fixed couplings with low or medium loading B SAE B Sliding couplings without loading, couplings for transfer of large and cyclical moments C SAE C Sliding couplings under loading for transfers of large, cyclical and shock moments. D ISO 14 Low Fixed couplings with low or medium loading E ISO 14 Medium Sliding couplings, couplings for transfers of large and cyclical moments F, I DIN 5464 CSN 014942 Heavy Sliding couplings under loading, couplings for transfers of large, cyclical and shock moments, automotive industry G, H DIN 5471 DIN 5472 Couplings for machine tools

Due to production and assembly inaccuracies, the loading is not distributed uniformly onto all teeth of the spline. The actual load bearing surface of the coupling is smaller than the load bearing surface determined theoretically. The ratio between the theoretical and actual load bearing surface of the coupling is defined by the coefficient of distribution of the loading. With regards to accuracy of the bearing, the size of the coefficient is given in a range from 0.6 to 0.8.

### 6.4 Total service factor.

This coefficient gives the total effects of production and operational parameters on decrease of loading capacity of the coupling. Its size depends on the type of coupling, drive and loading, operational conditions and service lifespan of the coupling. With regards to the mentioned parameters, the literature gives values of the coefficient in a range from 1 to 40.

For easier choice of coefficient, the application is provided with automatic design. In case the checkbox to the right of the input field is enabled, the coefficient is determined automatically and based on parameters of the coupling defined in paragraph [1]. For a fixed coupling, the operational coefficient is calculated using the relation:

For a sliding coupling, the following relation is used:

where:

Ka - application factor

Kf - fatigue-life factor

Kd - coupling design factor

Kw - wear life factor

Meaning and size of the coefficients, see [1].

### 6.5 Design of coupling dimensions.

This paragraph can be used to design dimensions of the coupling. When designing a coupling, first choose dimensions of the spline [6.8]. For the chosen spline, the program calculates its minimum functional length [6.14], which is necessary for safe transfer of the entered torsional moment. Complete the design of the coupling by choosing the actual length of the spline in row [6.15].

### 6.6 Splines for diameters.

This parameter gives a standard given range of outer diameters of spline for the chosen series of splines [6.2].

### 6.7 Minimum shaft diameter.

This parameter gives the minimum diameter of a solid shaft, not weakened by splines, which is necessary for safe transfer of the entered torsional moment.

### 6.8 Spline.

In the selection list, choose a spline of suitable dimensions. Choose the spline so that the inner diameter of spline d is greater than the minimum diameter dmin. Dimensions of spline are given in the list in the following form: "Outer diameter" - "Prescribed marking". The convention of marking for individual types of splines is given in the following table.

 Type of splines [6.2] Marking A, B, C D x n D - I n x d x D

where:

n - number of grooves

d - spline inner diameter

D - spline outer diameter

### 6.14 Minimum functional length of spline.

The parameter gives the minimum functional length of the chosen spline, which is necessary for safe transfer of the entered torsional moment.

### 6.15 Chosen spline length.

Choose a length of spline greater than the calculated minimum length [6.14]. When determining the length, keep in mind that the chosen length of the spline is at the same time the minimum permissible length of the hub. Recommended lengths of hubs can be found in the document "Guiding values for choices of dimensions of hubs".

## Strength checks of the coupling. [7]

In case of splined couplings, only two types of strength checks are usually carried out. A check of loading of the shaft for torsion and a check of deformation of contact surfaces of the coupling.

### 7.1 Check of shaft for torsion.

The check is carried out for the diameter of a solid shaft d, not weakened by splinines [6.10]. The resulting safety of the coupling [7.4] is given by the ratio of the permitted shear stress of the shaft material to the calculated comparative stress. If the coupling is to be sufficient, the calculated safety must be higher than the required one [1.19].

### 7.5 Check of deformation of grooving sides.

The check for deformation is carried out by comparison of the permitted pressure of a material of lower quality with the calculated comparative pressure acting on the sides of the groove. If the coupling is to be sufficient, the calculated safety must be higher than the required one [1.19].

## D. Couplings with involute splines.

Couplings with involute splines are suitable for transfers of great, cyclical and shock torsional moments. This type is used both for fixed and for sliding couplings of cylindrical shafts with hubs. The use is similar as with straight-sided splines.

General benefits of the coupling:

• lower pressures than couplings with keys, higher loading capacity of the coupling
• lower wear of sliding couplings
• suitable also for cyclical torsional moments
• easy assembly and disassembly of the coupling

Benefits of the coupling compared with Straight-sided spline:

• higher number of teeth (lower pressures, higher loading capacity of the coupling, more uniform distribution of forces along the perimeter, option of fine adjustment of the hub on the shaft)
• lower weakening of the shaft, lower notch coefficient
• economical lot production using a hobbing method
• high accuracy of production similarly as with accurate gears

• higher production costs than couplings with keys
• higher notch coefficient than couplings with keys
• difficult execution of alignment and perpendicularity of the coupling
• non-parallelism of sides of the teeth causes additional radial forces in the coupling; these forces then try to open the hub

The splined profile is shaped as involute toothing in the cross section, with basic angles of the profile 30°, 37.5° or 45°. It is centered to the outer diameter or sides of the teeth. Centring to the diameter is more accurate, centring to sides is more economical and is used much more frequently in practice The groove bottom can be flat or rounded.

##### Recommended (orientation) bearings for involute splines
 Centering dimension Bearing of the dimension Note t Do Immovable couplings at high loading with shocks, without frequent disassembly t 7H / 9r 7H / 8p 7H / 7n H11 / h11 Immovable couplings at medium loading, disassembled frequently t 7H / 8k 7H / 9h H11 / h12 Low speeds Do 9H / 9h 9H / 9g 9H / 9d H7 / n6 H7 / js6 High speeds For movable couplings Do - H7 / h6 H7 / g6 H7 / f7 Hardened surfaces

where:
Do - outer diameter of external spline
t - width of the teeth

## Coupling parameters, dimensional design. [8]

This paragraph can be used for options of parameters of the given type of coupling and to design dimensions of the coupling. As marking of individual dimensions of spline is different in various standards, the calculation uses marking according to ANSI B92.1 and the differences in marking are given in the following table:

 ANSI B92.1 ANSI B92.2M ISO 4156 DIN 5480 CSN 4950 Diametral pitch P - - Module - m m Number of teeth N Z z Pitch diameter D D d Base diameter Db DB db Reference diameter - - D Shift of basic profile - - xm Major diameter of external spline Do DEE da Minor diameter of external spline Dre DIE df Minor diameter of internal spline Di DII Da Major diameter of internal spline Dri DEI Df Tooth thickness tv SV s Groove width sv EV e

### 8.2 Splines type.

In the selection list, choose a standard and a type of spline. Dimensions of spline are defined for types A to E by the standard in v [in], in case of other types the dimensions are defined in [mm]. Individual types of spline are described in the list as follows: "Standard of spline" - "Angle of the profile", "Design of the spline", "Centering method".

Due to production and assembly inaccuracies, the loading is not distributed uniformly onto all teeth of the spline. The actual load bearing surface of the coupling is smaller than the load bearing surface determined theoretically. The ratio between the theoretical and actual load bearing surface of the coupling is defined by the coefficient of distribution of the loading. With regards to accuracy of the bearing, the size of the coefficient is given in a range from 0.4 to 0.8.

##### Recommended values for options of the coefficient of distribution of the loading:
 KL Design of spline 0.75 Fixed couplings with short lengths and high accuracy of bearing 0.6 - 0.7 Couplings with normal accuracy of bearing 0.5 Sliding couplings with great lengths of contact surfaces and great non-alignment of the coupling

### 8.4 Total service factor.

This coefficient gives the total effects of production and operational parameters on decrease of loading capacity of the coupling. Its size depends on the type of coupling, drive and loading, operational conditions and service lifespan of the coupling. With regards to the mentioned parameters, the literature gives values of the coefficient in a range from 1 to 40.

For easier choice of coefficient, the application is provided with automatic design. In case the checkbox to the right of the input field is enabled, the coefficient is determined automatically and based on parameters of the coupling defined in paragraph [1]. For a fixed coupling, the operational coefficient is calculated using the relation:

For a sliding coupling, the following relation is used:

where:

Ka - application factor

Kf - fatigue-life factor

Kd - coupling design factor

Kw - wear life factor

Meaning and size of the coefficients, see [1].

### 8.5 Automatic design of the coupling.

The automatic design selects the 20 best solutions for the chosen type and series of spline in view of the requirement for the minimum diameter of the shaft. The length of spline is chosen with regards to the recommended dimensions of the hub. The design eliminates all solutions where the length of the hub results in more than a doubling of the outer diameter of spline.

The design calculation is started by clicking the button in row [8.9]. After completion of the calculation, the table of designed solutions [8.10] is filled in and sorted and the values of the chosen solution are transferred automatically to paragraph [8.11]. The table is sorted according to the criterion set out in row [8.7] and can be re-sorted whenever using another chosen criterion.

In case the design calculation was unsuccessful and no suitable solution was found for the entered values, this fact is indicated by a warning message and the table is deleted. In such cases, repeat the design for a coupling with materials of a higher quality.

### 8.6 Filter of the design.

In the list, choose a range of input data (spline dimensions) used by the automatic design for selection of a suitable solution.

### 8.8 Maximum length of the hub.

When enabling the checkbox, the design eliminates all solutions where the length of the hub results in a higher value than the entered value Lmax.

### 8.10 Table of designed solutions.

Meaning of parameters in the table:

 m/P Module or pitch of the spline resp. (according to the splines type) n Number of teeth Do Major diameter of external spline Dre Minor diameter of external spline Lmin The minimum functional length of spline which is necessary for safe transfer of the entered torsional moment. L The chosen length of spline sT Safety of the strength check of the shaft for torsion sp Safety of the strength check for deformation

### 8.11 Coupling dimensions.

This paragraph can be used to determine dimensions of the coupling. The dimensions can be chosen manually or the values of the designed solution can be transferred using a selection from table [8.10]. When entering the values manually, first choose a suitable dimension of spline [8.13].

For the chosen spline, the program calculates its minimum functional length [8.21], which is necessary for safe transfer of the entered torsional moment. Complete the design of the coupling by choosing the actual length of the spline in row [8.22].

### 8.12 Minimum shaft diameter.

This parameter gives the minimum diameter of a solid shaft, not weakened by splines, which is necessary for safe transfer of the entered torsional moment.

### 8.13 Spline.

In the selection list, choose a spline of suitable dimensions. Choose the spline so that the inner diameter of spline Dre is greater than the minimum diameter Dremin. Spline dimensions are given in the list as follows: "Outer diameter" - "Module / Pitch" x "Number of teeth". Preferred (recommended) dimensions of spline are marked in the list using the symbol "*".

### 8.21 Minimum functional length of spline.

The parameter gives the minimum functional length of the chosen spline, which is necessary for safe transfer of the entered torsional moment.

### 8.22 Chosen spline length.

Choose a length of spline greater than the calculated minimum length [8.21]. When determining the length, keep in mind that the chosen length of the spline is at the same time the minimum permissible length of the hub. Recommended lengths of hubs can be found in the document "Guiding values for choices of dimensions of hubs".

## Strength checks of the coupling. [9]

In case of splined couplings, only two types of strength checks are usually carried out. A check of loading of the shaft for torsion and a check of deformation of contact surfaces of the coupling.

### 9.1 Check of shaft for torsion.

The check is carried out for the diameter of a solid shaft Dre, not weakened by splines [8.17]. The resulting safety of the coupling [9.4] is given by the ratio of the permitted shear stress of the shaft material to the calculated comparative stress. If the coupling is to be sufficient, the calculated safety must be higher than the required one [1.19].

### 9.5 Check of deformation of grooving sides.

The check for deformation is carried out by comparison of the permitted pressure of a material of lower quality with the calculated comparative pressure acting on the sides of the groove. If the coupling is to be sufficient, the calculated safety must be higher than the required one [1.19].

## Comparative table. [10]

This paragraph can be used for a fast comparison of designed solutions of couplings of shafts with hubs. Only basic dimensions are given here for individual types of couplings. Complete dimensions of the coupling can be found in the independent chapter (section) of the respective calculation.