Shaft-hub connections

Transcription

1 Product description PG- and P4C-Polygon profile, splined shaft, muff coupling INKOMA shaft-hu connections provide for cost saving design, using assemly ready standardised components, without compromising quality. A variety of components and designs provide an effective method for the transmission of rotary motion and torque. Since the eginning of the last century patents have existed for the manufacture of near triangular profiles having a cycloid oundary. It has taken practically a century to develop the manufacture of Polygon profiles. Polygon profiles are principally for the transmission of torque. They provide an ideal alternative to other profiles, splines and knurls. The Polygon profile has no notch sensitivity, has constant inertia and transmits torque y pure torsion. In comparison with traditional profiles the Polygon has around 0% more load carrying capaility. The product range comprises Polygon shafts, Polygon hus, clamp rings and sliding naves. This product range is designed to allow the comination of a wide array of ready-toassemle options in differing materials for a range of applications. By comining flanged hus with clamp rings the quality of the required fit (low acklash, lightly sliding and fixed) can e easily adjusted. INKOMA-shafts: Supplied in up to m lengths or cut and machined to customers' requirements. INKOMA-hus: These slide on the shafts. Used in conjunction with a clamp ring the required fit condition can e adjusted etween sliding and fixed. INKOMA-clamp rings: Using a screw and lock nut every variety of fits etween sliding and fixed can e achieved. INKOMA-sliding naves: Customer's components can e machined with the required profile. 57

2 Contents list PG-, P4C-Polygon profiles, splined shafts and connections for cylindrical shafts Technical information i pre-selection and product comparison 0 Product description PG-Polygon profile 1 i Pre-selection and calculation for PG-Polygon profile strength calculation shaft and hu calculation 2 - Dimensions PG-Polygon shaft (ground) hu 4-5 Dimensions PG-Polygon clamp ring sliding nave su-contract machining - 7 Application example PG-Polygon profile Product description P4C-Polygon profile 9 i Pre-selection and calculation for P4C-Polygon profile strength calculation shaft and hu calculation Dimensions P4C-Polygon shaft (cold drawn) hu

3 Contents list PG-, P4C-Polygon profiles, splined shafts and connections for cylindrical shafts Dimensions P4C-Polygon clamp ring sliding nave Dimensions P4C-Polygon rack su-contract machining 7-77 Application example P4C-Polygon profile 7 Product description splined shafts and connecting elements for cylindrical shafts 79 i Pre-selection and calculation for spline profile strength calculation shaft and hu calculation 0-1 Dimensions splined shafts splined shaft (cold drawn) hu 2 - Dimensions splined shafts clamp ring sliding nave su-contract machining 4-5 Dimensions connections for cylindrical shafts muff coupling clamp ring - 7 Application example spline profile 59

4 D Shaft-hu connections Technical information Pre-selection and product comparison Initial selection of the size of shaft to e used should e on the asis of torsional effects. As an approximation use the internal surface area of the profile. Since the Polygon profile has no edges, fatigue effects can e ignored. Due to the favourale dimensions and since stress concentrations can e ignored in the strength calculation, a higher section modulus is achieved. Professor Dr. Ing. R Musyl of Graz Technical University conducted comparative calculations to determine the polar moment of inertia of, simple keyed connections, splines profile, and P4C-Polygon profile. All had a nominal effective diameter of 25 mm. The accompanying tale demonstrates his results. To complete this comparison the PG profile is shown. It should e noted that this profile is only for use in situations where torque is transmitted without sliding. without reference to stress concentration with reference to stress concentration Moments of inertia axial J x; J y [cm 4] polar J p [cm 4] axial β k ; J x ; J y polar β k ; J p [cm 4] [cm 4] Keyed shaft DIN 5/2 D= Ø 25 mm y D x J = 0,752 x J = 0,947 y J = 1,71525 p β kt= 1,4 J x βk= 0,5494 J y βk= 0,724 β kt= 1,4 J p βk= 1,2251 Six toothed spline DIN 541 D= Ø 25 mm y D x J = J = 1,55 x y J = 2,7170 p β kt= 1,7 βkt= 1,7 J x βk= J y βk= 0,79921 J p βk= 1,5942 Polygon profile P4C D= d = Ø 25 mm 1 e= 5 mm = 21 mm y D x J = J = 1,745 x y J = 2,74912 p β kt= 1,0 βkt= 1,0 J x= J y= 1,745 J p= 2,74912 Polygon profile PG D= D M= 25 mm = 2, mm d 2= 2,4 mm e= 0, mm y J = J = 1,5 x y J =,7 p β kt= 1,0 β kt= 1,0 J x= J y= 1,5 J p=,7 x 0

5 Shaft-hu connections Product description PG-Polygon profile INKOMA-PG-Polygon profiles have the following properties: 1. The PG-Polygon profile is designed for use where stale shaft-hu connections exist. It is unsuitale for applications having axial sliding under load. 2. Self centering. Compared with splined profiles INKOMAPG-Polygon profiles have aproximately 0% higher fatigue resistance. 4. The shaft profile is produced y grinding. 5. Both roaching and grinding are used for the manufacture of hu components.. Extremely accurate running concentricity results when the shaft and hu are produced y grinding. 1

6 Pre-selection and calculation PG-Polygon profile DIN 2711 Strength calculation: Basics for calculation PG: The formulae provide for precise calculations. Explanation: [cm] inner circle diameter D M [cm] average diameter d 2 [cm] outer circle diameter G [N/cm 2] moduls of rigidity (0 105 N/cm 2 for steel) e [cm] degree of eccentricity J P [cm 4] moment of inertia in torsion k l p s y eff y 1 [-] [cm] [N/cm 2] [cm] [µm] [µm/n] D M 5 k= 1,44 D M > 5 k= 1,20 hu length specific contact stress thinnest section of hu wall effective hu distortion specific hu distortion T t W P W x σ z perm. τ Þ [Ncm] [cm ] [cm ] [N/cm 2] [N/cm 2] [ /cm] torsional moment polar moment of resistance equatorial moment of resistance permissile tensile stress torsional strain torsional displacement A [cm 2] cross sectional area of PG profile Pre-selection of the PG profile: When the torque T t to e transmitted is known the required Polygon profile can e determined using the graph. Curves I, II and III apply to the load factor (steady, variale and reversing loading). Pre-selection of the PG profile P-5 P-55 P-45 P-40 Polygon-shaft P- P-2 P-2 P-22 P-1 P-14 III II I T [Nm] t 2

7 ( Shaft-hu connections Pre-selection and calculation PG-Polygon profile DIN 2711 Shaft and hu calculation: Shaft: Hu: Torsional strain Bending stress τ W p = T t W p 2 J p D M M σ = W x τ perm. σ perm. Specific contact stress Hu wall thickness T p = t D 2 l 0,75 π D M M e + 20 s = k ( T t σ z perm. l W x J p D M Torsional displacement 10 T l = t Þ π G J p ( π D 2 = M D 2 J M 2 p - e - π e4 4 ( Effective hu distortion y eff = T t y 1 l The graphical values y apply for steel with E= N/mm 2 1. For materials having a different modulus E 1 multiply the y 1 value with N/mm 2 E 1 Effective hu distortion µm N s= mm s= 4 mm s= 5mm s= mm s= mm s= 10 mm s= 12 mm s = 15mm y D M [mm]

8 Dimensions PG-Polygon - Welle (geschliffen) INKOMA-Polygon PG shaft profiles are produced y grinding and are to DIN Supplied in various materials, usually in C 45 and lengths up to 2 m depending on the size of the profile. 0 r R 2e Ø d 2 2e D M Ø Dimension r and R for illustration only, instead of cycloidal. Ordering example: Polygon PG - shaft Dimension D M P-14 C 45 Material Polygon PG - hu INKOMA-Polygon PG hus are prepared to DIN 2711 Supplied in: Steel C 45 St Bronze Bz 12 Bz other materials and surface treatments are supplied. Please enquire. For missing profile dimensions see Polygon-shafts. E L -1 Ordering example: Polygon PG - hu Ø D 1 - Ø C ±0,2 Ø F H7 Ø B h7 Ø a Ø d 2 D M Ø PH--14 St Dimension D M Material h 4

9 Tolerances Dimensions [mm] Section modulus D M D M g d 2 e R r W p [cm ] W x [cm ] A 2 [cm ] Mass [kg/m] P-14 P-1 P-22 P-2 P-2 P- P-40 P-45 P-55 P ,00 / -0,017-0,00 / -0,017-0,007 / -0,020-0,007 / -0,020-0,009 / -0,025-0,009 / -0,025-0,009 / -0,025-0,009 / -0,025-0,010 / -0,029-0,010 / -0,029 14, 1,12 0,44 9, 4,14 0,45 0,25 1,51 1,19 19,12 1, 0,5 12,4 5, 0,9 0,5 2,50 1,9 2,40 20,0 0,70 15,55,45 1,75 0,9,74 2,95 29,0 2,20 0,90 19,5,15,0 1,97,05 4,7 4,24 29,7 1,12 2,2,72 5,0 2,91 7,,2,50,50 1,25 2,1 9,7,90,0 9,97 7, 42,0 7,20 1,40 29,10 10,90 10,45 5,9 12,1 9,72 4,20 41,0 1,0 2,90 12,10 14,79,0 15,57 12,0 59,00 51,00 2,00 40,50 14,50 27,00 14,71 2,24 1, 9,90 0,10 2,45 4,4 1,57 44,20 24,20 2,9 25,59 Special profiles are availale. Please enquire. Dimensions [mm] Tolerances D M D M H7 d 2 B C D E F L a h Mass [kg/apiece] PH--14 PH--1 PH--22 PH--2 PH--2 PH-- PH--40 PH--45 PH--55 PH ,01 / 0 +0,01 / 0 +0,021 / 0 +0,021 / 0 14, 19,12 2,40 29,0 4,24,50 42,0 4,20 59,00 9,90 1, , 0,12 1, , 0,24 20, ,4,5 0,44 2, ,4 4 0,77 29, ,4 4 0,9, ,4 4 1,10 7, ,4 4 1,27 41, ,5 4 2,00 51, ,5 4 2,2 0, ,5 4, Special sizes according to your drawing. 5

10 Dimensions Polygon PG - clamp ring The INKOMA-Polygon PG clamp ring is made to DIN 2711 Supplied in: Steel C 45 St Bronze Bz 12 Bz other materials and surface treatments are supplied. Please enquire. e K Ø a 1 For cap head screw ISO 472 (DIN 912) For missing profile dimensions see Polygon-shafts 4. Ø D 1 - Ø C ±0,2 Ø a 2 Ø F f7 Ordering example: Polygon PG - clamp ring G Dimension D M PKR--14 St Material Polygon PG - sliding nave The INKOMA-Polygon PG sliding nave is made to DIN 2711 Supplied in: Steel C 45 St Bronze Bz 12 Bz other materials and surface treatments are supplied. Please enquire. For missing profile dimensions see Polygon-shafts 4. Ø D h9 L -1 Ordering example: Ø D M Ø d 2 Polygon PG - sliding nave Dimension D M PSH--14 St Material Polygon PG - su-contract machining In addition to our range of standard items roached with splined and Polygon profiles we offer a wide range of other internal forms. E.g. keyways, serrations to DIN 541, involutes to DIN 540 and 542, etc. Please enquire aout special internal profiles. We will e pleased to assist.

11 Dimensions [mm] PKR--14 PKR--1 PKR--22 PKR--2 PKR--2 PKR-- PKR--40 PKR--45 PKR--55 PKR--5 D M Tolerances Special sizes according to your drawing. D H7 M +0,01 / 0 +0,01 / 0 +0,021 / 0 +0,021 / 0 14, 19,12 2,40 29,0 4,24,50 42,0 4,20 59,00 9,90 d 2 1,12 1, 20,0 2,20 29,7,50 7,20 41,0 51,00 0,10 C D F G K a 1 a , 10 0, , 10 0, , , , , , , , , , , , , , , , ,97 e Mass [kg] Tolerances Dimensions [mm] D M D M H7 d 2 D L Mass [kg] PSH--14 PSH--1 PSH--22 PSH--2 PSH--2 PSH-- PSH--40 PSH--45 PSH--55 PSH Special sizes according to your drawing. +0,01 / 0 +0,01 / 0 +0,021 / 0 +0,021 / 0 14, 1,12 19,12 1, 2,40 20,0 29,0 2,20 4,24 29,7,50,50 42,0 4,20 59,00 7,20 41,0 51,00 9,90 0, ,19 0,41 0,7 1,27 1,0 2,09 2,5,02,0 5,10 P-14 P-1 P-22 P-2 P-2 P- P-40 P-45 P-55 P-5 Pilot ore [mm] 1) Ø 1,5 + 0,05 Ø 20,1 + 0,05 Ø 25, + 0,05 Ø 29,2 + 0,05 Ø 2,9 + 0,05 1) 1) 1) 1) Engaged length [mm] 1) ) 1) 1) 1) 1) These profiles can only e produced y grinding. Please enquire. 7

12 Application example PG-Polygon profile By comining Polygon-hu and Polygon-clamp ring the quality of fit can e adjusted. Polygon-clamp ring and chain sprocket. Secured using screws and dowel pins. Shaft-hu connection using a conical ground Polygon profile for acklash free torque transmission.

13 Shaft-hu connections Product description P4C-Polygon profile INKOMA-P4C-Polygon profiles have the following properties: 1. The P4C-Polygon profile is suitale for applications where axial sliding, with or without load, is a requirement for the shafthu connection, or when torque must e transmitted. 2. Self centering. Compared with splined profiles INKOMAP4C-Polygon profiles have aproximately 0% higher fatigue resistance. 4. P4C-Polygon shafts are supplied cold drawn or ground profile. 5. The internal profile is most economically produced y roaching. Grinding of ores is not possile. 9

14 Pre-selection and calculation P4C-Polygon profile DIN 2712 Strength calculation: Basics for calculation P4C: The formulae provide for precise calculations. Explanation: [cm] inner circle diameter A [cm 2] cross sectional area of P4C profile [cm] outer circle diameter G [N/cm 2] moduls of rigidity (0 105 N/cm 2 for steel) e [cm] degree of eccentricity J P [cm 4] polar moment of inertia in torsion d r [cm] calculated theoretical diameter T t [Ncm] torsional moment e r [cm] calculated degree of eccentricity W P [cm ] polar moment of resistance l [cm] hu length W x [cm ] equatorial moment of resistance p [N/cm 2] specific contact stress σ z perm. [N/cm 2] permissile tensile stress s [cm] thinnest section of hu wall τ [N/cm 2] torsional strain y eff [µm] effective hu distortion Þ [ /cm] torsional displacement y 1 [µm/n] specific hu distortion Pre-selection of the P4C profile: When the torque T t to e transmitted is known the required Polygon profile can e determined using the graph. Curves I, II and III apply to the load factor (steady, variale and reversing loading). Pre-selection of the P4C profile PW70.0 PW0.5 PW50.4 Polygon-shaft PW45.40 PW40.5 PW5.0 PW0.25 PW25.21 PW20.17 PW14.11 III II I T [Nm] t 70

15 ( Shaft-hu connections Pre-selection and calculation P4C-Polygon profile DIN 2712 Shaft and hu calculation: Shaft: Hu: Torsional strain τ W p = T t W p 0,2 τ perm. Specific contact stress p = e = r T t d 2 l π e r r d r + 20 ( (d1 - ) 4 Bending stress M σ = W x σ perm. d = r + 2 e Torsional displacement W x Þ 0,15 10 T t l = π G J p Hu wall thickness s = 0,7 T t σ z perm. l J p 0,1 4 Effective hu distortion y eff = T t y 1 l The graphical values y apply for steel with E= N/mm 2 1. For materials having a different modulus E 1 multiply the y 1 value with N/mm 2 E 1 Effective hu distortion µm N s= mm s= 4 mm s = 5mm s= mm s= mm y 1 s= 10 mm 2 s= 12 mm s= 15mm d [mm] 1 71

16 Dimensions Polygon P4C - shaft (cold drawn) INKOMA-Polygon P4C profiles are produced y cold drawing according to DIN Supplied in: Steel Ck 45 St Standard lengths of 4 to m are supplied or machined to customer requirements. When ordering a specific length please note that shafts are sawn to length and are not straightened. Should straightening e required we can carry this out at our factory. Other variants, (material, tolerances) are also availale as ground shafts. Dimension R for illustration only, instead of cycloidal. R Ordering example: Polygon P4C - shaft Dimension Dimension PW 5.0 St Material INKOMA-Polygon P4C hus are prepared to DIN Supplied in: Steel C 45 St Bronze Bz 12 Bz other materials and surface treatments are supplied. Please enquire. For missing profile dimensions see Polygon-shafts. E L -1 Ø Polygon P4C - hu Ø D 1 Ø Ø Polygon P4C - hu Ordering example: - Ø C ±0,2 Ø F H7 Ø B h7 Ø Ø a Dimension Dimension PH 5.0 St Material h R 72

17 Dimensions [mm] Tolerances Section modulus PW PW PW PW 0.25 PW 5.0 PW 40.5 PW PW 50.4 PW 0.5 PW R 14-0,01 / -0,05-0,00 / -0,122 1,1 1, 0,27 0,20 1,2 0, ,01 / -0,05-0,00 / -0,122 5,5 0,9 0,74 2,9 2, ,01 / -0,05-0,00 / -0,122 90,5 5 1,5 1,9 4,15,25 0-0,01 / -0,05-0,00 / -0,122 92,5 5,1 2,4 5,94 4, 5-0,01 / -0,0-0,00 / -0,122 95,0 5 5,40 4,05,29, ,01 / -0,0-0,00 / -0,122 11,5,5,4 11,04, 45-0,01 / -0,0-0,00 / -0,122 11,0 12,0 9,0 14,1 11,1 50-0,01 / -0,0-0,00 / -0, ,5 15,90 11,9 1,97 1, ,01 / -0,0-0,01 / -0,0-0,00 / -0,122-0,00 / -0, ,5 12,0 29,7 4,20 22, 2,40 25,0,17 19,7 2,00 e W p [cm ] W x [cm ] A 2 [cm ] Mass [kg/m] Stocked lengths 4 - m; other lengths and special profiles are availale. Dimensions [mm] Tolerances H7 H11 R B C D E F L a h Mass [kg] PH PH PH PH 0.25 PH 5.0 PH 40.5 PH PH 50.4 PH 0.5 PH ,01 / 0 +0,110 / 0 1, ,01 / 0 +0,10 / 0 5, ,021 / 0 +0,10 / 0 90,5 0 +0,021 / 0 +0,10 / 0 92,5 5 +0,021 / 0 +0,10 / 0 95, ,10 / 0 11, ,10 / 0 +0,10 / 0 11,0 117, ,190 / 0 +0,190 / 0 122,5 12, , 0, , 0, ,4,5 0, ,4 4 0, ,4 4 0, ,4 4 1, ,4 4 1, ,5 4 2, ,5 4 2, ,5 4, Special sizes according to your drawing. 7

18 Dimensions Polygon P4C - clamp ring The INKOMA-Polygon P4C clamp ring is made to DIN Supplied in: Steel C 45 St Bronze Bz other materials and surface treatments are supplied. Please enquire. e G K Ø a 1 For cap head screw ISO 472 (DIN 912) For missing profile dimensions see Polygon-shafts Ø D 1 Ø C ±0,2 Ø a 2 Ø F f7 Ordering example: Polygon P4C - clamp ring Dimension Dimension PKR 5.0 St Material Polygon P4C - sliding nave The INKOMA-Polygon P4C sliding nave is made to DIN Supplied in: Steel C 45 St Bronze Bz 12 Bz other materials and surface treatments are supplied. Please enquire. For missing profile dimensions see Polygon-shafts 72. Ø D h9 L -1 Ordering example: R Polygon P4C - sliding nave Ø Ø Dimension Dimension PSH St Material 74

19 Dimensions [mm] Tolerances H7 H11 R C D F G K a 1 a 2 e Mass [kg] PKR PKR PKR PKR 0.25 PKR 5.0 PKR 40.5 PKR PKR 50.4 PKR 0.5 PKR ,01 / 0 +0,01 / 0 +0,021 / 0 +0,021 / 0 +0,021 / 0 +0,110 / 0 +0,10 / 0 +0,10 / 0 +0,10 / 0 +0,10 / 0 +0,10 / 0 +0,10 / 0 +0,10 / 0 +0,190 / 0 +0,190 / 0 1,1 5,5 90,5 92,5 95,0 11,5 11,0 117,5 122,5 12, , 10 0, , 10 0, , , , , , , , , , , , , , , , ,97 Special sizes according to your drawing. Dimensions [mm] Tolerances H7 H11 R D L Mass [kg] PSH PSH PSH PSH 0.25 PSH 5.0 PSH 40.5 PSH PSH 50.4 PSH 0.5 PSH ,01 / 0 +0,01 / 0 +0,021 / 0 +0,021 / 0 +0,021 / 0 +0,110 / 0 +0,10 / 0 +0,10 / 0 +0,10 / 0 +0,10 / 0 +0,10 / 0 +0,10 / 0 +0,10 / 0 +0,190 / 0 +0,190 / 0 1, , , , , , , , , , ,19 0,41 0,7 1,27 1,0 2,09 2,5,02,0 5,10 Special sizes according to your drawing. 75

20 Dimensions Polygon P4C - rack By machining a gear profile into the flank of a Polygon shaft the designer has the asis of an effective, fully guided axial feeding and and positioning system. Standard Polygon racks are prepared with modern machine tools to the most exacting standards (DIN 972). The gearing quality is according to Class corresponding to DIN 92, 9 and 97. An optimal sliding quality is achieved y modifying the tooth tips. It is also possile to use the Polygon rack as an element in a measuring system. Pinions can e supplied or machined to your drawing. The INKOMA Polygon P4C rack is made to DIN Supplied in: Steel Ck 45 St Stocked length 1000 mm straight gear, lead angle 20 For missing profile dimensions see Polygon-shafts 72. Ø Ø d 0 L Ø straight gear, lead angle 20 Ordering example: Polygon P4C - rack Dimension Dimension PZ 5.0 St Material Polygon - su-contract machining In addition to our range of standard items roached with splined and Polygon profiles we offer a wide range of other internal forms. E.g. keyways, serrations to DIN 541, involutes to DIN 540 and 542, etc. Please enquire aout special internal profiles. We will e pleased to assist. 7

21 PZ PZ PZ PZ 0.25 PZ 5.0 PZ 40.5 PZ PZ 50.4 PZ 0.5 PZ Tolerances Racks having other modules and lengths are availale. Please enquire. Dimensions [mm] Gear module Mass [kg/m] 14-0,01 / -0,05-0,00 / -0,122 1,1 1,0 10,0 0, ,01 / -0,05-0,00 / -0,122 5,5 1,5 15,5 1,9 25-0,01 / -0,05-0,00 / -0,122 90,5 2,0 19,0 2,9 0-0,01 / -0,05-0,00 / -0,122 92,5 2,5 22,5 4,12 5-0,01 / -0,0-0,00 / -0,122 95,0,0 27,0 5, ,01 / -0,0-0,00 / -0,122 11,5,0 2,0 7, ,01 / -0,0-0,01 / -0,0-0,01 / -0,0-0,01 / -0,0-0,00 / -0,122-0,00 / -0,122-0,00 / -0,122-0,00 / -0,122 11,0 117,5 122,5 12,0 4,0 4,0 5,0,0,0 9,0 4,0 54,0 10,10 12,00 17,50 2,45 R d 0 P P P P 0.25 P 5.0 P 40.5 P P 50.4 P 0.5 P 70.0 Pilot ore [mm] Ø 10,7 H7 Ø 1,7 H7 Ø 20, H7 Ø 24, H7 Ø 29,7 H7 Ø 4, H7 Ø 9,7 H7 Ø 42,7 H7 Ø 52,7 H7 Ø 59,7 H7 Engaged length [mm]

22 Application example P4C-Polygon profile By comining Polygon-hu and Polygon-clamp ring the quality of fit can e adjusted. Polygon-clamp ring and chain sprocket. Secured using screws and dowel pins. Polygon-shaft with gear. Gears to customer specification can e roached with a Polygon ore. Polygon-shaft with 2 driven Polygon-hus. 7

23 Shaft-hu connections Product description Splined shafts and connecting elements for cylindrical shafts INKOMA spline connections, clamp rings and muff couplings are for use in machine uilding, process plant and tooling. 1. economical 2. simplifies the designers work A new way of saving costs without compromising quality. In 1975 this slogan announced the launch of a ready-to-assemle spline connection system. Since then we have grown to ecome the most important European manufacturer and stockist of this type of product. This success provides the stimulus for the ongoing development and improvement of the product range. In addition to the standard range we offer made-to-drawing services for splined parts as well as roaching of oth splined and Polygon profiles. 79

24 Pre-selection and calculation Spline profile similar to ISO 14 (DIN 54) Strength calculation: Basics for calculation spline profile: Explanation: [mm] inner circle diameter A [mm²] cross sectional area of spline d 2 [mm] outer circle diameter D M [mm] average diameter f w h l n p [-] [mm] [mm] [-] [N/mm 2] loading factor: steady 1 variale 0,5 reversing 0,25 height of spline hu length numer of splines specific contact stress G J P T t W P τ Þ [N/cm²] [mm 4] [Nm] [mm ] [N/mm 2] [ /cm] moduls of rigidity (0 105 N/cm 2 for steel) polar moment of inertia torsional moment polar moment of resistance torsional strain torsional displacement Pre-selection of splines: When the torque T t to e transmitted is known the required spline can e determined using the graph. Curves I, II and III apply to the load factor (steady, variale and reversing loading). Pre-selection of splines Splined shaft K 2.92 K 72.2 K 2.72 K 5.5 K 52.0 K 4.54 K 42.4 K.42 K 2. K 2.4 K 2.2 K 2.2 K K 1.22 K 1.20 K 1.1 K T [Nm] t III II I 0

25 Pre-selection and calculation Spline profile similar to ISO 14 (DIN 54) Shaft and hu calculation: Shaft: Hu: Torsional strain τ = T t 10 τ W p f perm. w Specific contact stress p = T t 2000 h l n D M 0,75 p perm. W p 0,024 (d + d ) 2 1 h = 0,5 (d - d ) 2 1 Torsional displacement Þ = 10 T t 10 π G J p D = M 0,5 (d + d ) 2 1 J p = 0,00 (d + d )

26 Dimensions Splined shaft (cold drawn) The INKOMA-splined shafts are cold drawn and similar to ISO 14 (DIN 54). Supplied in: Steel Ck 45 St Standard lengths of to m are supplied or machined to customer requirements. When ordering a specific length please note that shafts are sawn to length and are not straightened. Should straightening e required we can carry this out at our factory. Other variants (material, tolerance), and sizes from K 52.0 to K 2.92, are also availale y request, as machined shafts. n= numer of splines k x 45 Ordering example: r Splined shaft Diameter Ø Ø d 2 Diameter d 2 K 2.2 St Material Splined shaft - hu The INKOMA-splined hus are made to ISO 14 (DIN 54). Supplied in: Steel C 45 St Bronze Bz 12 Bz other materials and surface treatments are supplied. Please enquire. n= numer of splines Ø a Ordering example: Ø D 1 - Ø C ±0,2 Ø F H7 h Ø B h7 Ø Ø d 2 Splined shaft - hu Diameter Diameter d 2 E Material L -1 H 2.2 St 2

27 Dimensions [mm] Tolerances K K 1.1 K 1.20 K 1.22 K K 2.2 K 2.2 K 2.4 K 2. K.42 K 42.4 K 4.54 n d 2 Mass [kg/m] / -0,0-0,01 / -0,0-0,07 / -0,20 0,2 0,2 121,9 0,95, / -0,0-0,01 / -0,0-0,07 / -0,20 0,2 0,2 14,1 1, / -0,0-0,01 / -0,0-0,07 / -0,25 0,2 0,2 24,4 1, / -0,0-0,01 / -0,0-0,07 / -0,25 0,2 0,2 12,4 2, / -0,0-0,01 / -0,0-0,07 / -0,27 0,2 0,2 99,, / -0,0-0,01 / -0,0-0,07 / -0,27 0, 0,2 505,2, / -0,0-0,01 / -0,0-0,07 / -0,27 0, 0,, 5, / -0,0-0,01 / -0,0-0,07 / -0,27 0, 0, 741,4 5, / -0,0 0 / -0,0 0 / -0,0-0,01 / -0,0-0,01 / -0,0-0,01 / -0,0-0,07 / -0,27-0,07 / -0,27-0,07 / -0,27 0, 0, 0, 0, 0, 0, 947, 115, 157,7 7,4 9,0 12, / -0,0-0,01 / -0,0-0,07 / -0,27 0, 0,4 1949,0 15,0 d 2 k r A 2 [mm ] Stocked lengths - m, other length availale. Please enquire. Special profiles are availale. Please enquire. Tolerances Dimensions [mm] H H 1.1 H 1.20 H 1.22 H H 2.2 H 2.2 H 2.4 H 2. H.42 H 42.4 H 4.54 H 52.0 H 5.5 H 2.72 H 72.2 H 2.92 n , d 2 d 2 B C D E F L a h ,045 / +0,020 +0,00 / +0,00 +0,00 / +0,00 +0,00 / +0,00 +0,00 / +0,00 +0,00 / +0,00 +0,00 / +0,00 +0,07 / +0,00 +0,00 / +0,00 +0,07 / +0,040 +0,07 / +0,040 +0,07 / +0,040 +0,07 / +0,040 +0,07 / +0,040 +0,00 / +0,040 +0,00 / +0,040 +0,00 / +0,040 +0,01 / 0 +0,11 / 0 +0,01 / 0 +0,11 / 0 +0,01 / 0 +0,1 / 0 +0,01 / 0 +0,1 / 0 +0,021 / 0 +0,1 / 0 +0,021 / 0 +0,1 / 0 +0,021 / 0 +0,1 / 0 +0,021 / 0 +0,1 / 0 +0,1 / 0 +0,05 / 0 +0,1 / 0 +0,1 / 0 +0,19 / 0 +0,19 / 0 +0,19 / 0 +0,19 / 0 +0,19 / 0 +0,22 / 0 Mass [kg] , 0, , 0, , 0, , 0, ,4,5 0, ,4,5 0, ,4,5 0, ,4 4 0, ,4 4 1, ,5 4 1, ,5 4 1, ,5 4 1, , , , , ,0 Special sizes according to your drawing.

28 Dimensions Splined shafts - clamp ring The INKOMA-splined clamp rings are made to ISO 14 (DIN 54). Supplied in: Steel C 45 St Bronze Bz 12 Bz other materials and surface treatments are supplied. Please enquire. Ø a 2 Ø a 1 n= numer of splines Ø D 1 - Ø C ±0,2 Ø F f7 Ø Ø d 2 Ordering example: e G K For cap head screw ISO 472 (DIN 912) Splined shafts - clamp ring Diameter Diameter d 2 KR 2.2 St Material Splined shafts - sliding nave The INKOMA-splined sliding naves are made to ISO 14 (DIN 54). Supplied in: Steel C 45 St Bronze Bz 12 Bz other materials and surface treatments are supplied. Please enquire. n= numer of splines Ordering example: Splined shafts - sliding nave Ø d 2 Ø r Diameter Diameter d 2 k x 45 Material Ø D h9 L -1 SH St Splined shafts - su-contract machining In addition to our range of standard items roached with splined and Polygon profiles we offer a wide range of other internal forms. E.g. keyways, serrations to DIN 541, involutes to DIN 540 and 542, etc. Please enquire aout special internal profiles. We will e pleased to assist. 4

29 Dimensions [mm] Tolerances n d 2 d 2 C D F G K a 1 a 2 e Mass [kg/m] KR KR 1.1 KR 1.20 KR 1.22 KR KR 2.2 KR 2.2 KR 2.4 KR 2. KR.42 KR 42.4 KR 4.54 KR 52.0 KR 5.5 KR 2.72 KR 72.2 KR , ,045 / +0,020 +0,00 / +0,00 +0,00 / +0,00 +0,00 / +0,00 +0,00 / +0,00 +0,00 / +0,00 +0,00 / +0,00 +0,07 / +0,00 +0,00 / +0,00 +0,07 / +0,040 +0,07 / +0,040 +0,07 / +0,040 +0,07 / +0,040 +0,07 / +0,040 +0,00 / +0,040 +0,00 / +0,040 +0,00 / +0,040 +0,01 / 0 +0,11 / 0 +0,01 / 0 +0,11 / 0 +0,01 / 0 +0,1 / 0 +0,01 / 0 +0,1 / 0 +0,021 / 0 +0,1 / 0 +0,021 / 0 +0,1 / 0 +0,021 / 0 +0,1 / 0 +0,021 / 0 +0,1 / 0 +0,1 / 0 +0,05 / 0 +0,1 / 0 +0,1 / 0 +0,19 / 0 +0,19 / 0 +0,19 / 0 +0,19 / 0 +0,19 / 0 +0,22 / , 5 0, , 5 0, , 10 0, , 10 0, , , , , ,4,4,4 10,5 10,5 10,5 1,0 1,0 1, ,5 1,5 1, ,55 0,5 1,05 1,20 1,0 1,45 1,70 2,20 2, ,5 17, ,00 4,90 Special sizes according to your drawing. SH SH 1.1 SH 1.20 SH 1.22 SH SH 2.2 SH 2.2 SH 2.4 SH 2. SH.42 SH 42.4 SH 4.54 SH 52.0 SH 5.5 SH 2.72 SH 72.2 SH 2.92 n Special sizes according to your drawing. d 2 Dimensions [mm] Tolerances D L k r ,045 / +0,020 +0,01 / 0 +0,11 / , 0,2 0,11, ,00 / +0,00 +0,01 / 0 +0,11 / , 0,2 0, ,00 / +0,00 +0,01 / 0 +0,1 / , 0,2 0, ,00 / +0,00 +0,01 / 0 +0,1 / , 0,2 0, ,00 / +0,00 +0,021 / 0 +0,1 / , 0,2 0, ,00 / +0,00 +0,021 / 0 +0,1 / , 0,2 0, ,00 / +0,00 +0,07 / +0,00 +0,00 / +0,00 +0,07 / +0,040 +0,07 / +0,040 +0,07 / +0,040 +0,07 / +0,040 +0,07 / +0,040 +0,00 / +0,040 +0,021 / 0 +0,021 / 0 +0,1 / 0 +0,1 / 0 +0,1 / 0 +0,1 / 0 +0,1 / 0 +0,19 / 0 +0,19 / 0 +0,19 / 0 +0,19 / ,4 0,4 0,4 0,4 0,4 0,5 0,5 0,5 0,5 0, 0, 0, 0, 0, 0,5 0,5 0,5 0,5 0,5 0,95 1,25 1,2 2,15 2,45,10 5,00, ,00 / +0,040 +0,00 / +0,040 +0,05 / 0 +0,19 / 0 +0,22 / , 0, 0, 0, 10,10 11,90 d 2 Mass [kg] Pilot ore [mm] Engaged length [mm] Pilot ore [mm] Engaged length [mm] K K 1.1 K 1.20 K 1.22 K K 2.2 K 2.2 K 2.4 K 2. Ø 11 H7 Ø 1 H7 Ø 1 H7 Ø 1 H7 Ø 21 H7 Ø 2 H7 Ø 2 H7 Ø 2 H7 Ø 2 H K.42 K 42.4 K 4.54 K 52.0 K 5.5 K 2.72 K 72.2 K 2.92 Ø H7 Ø 42 H7 Ø 4 H7 Ø 52 H7 Ø 5 H7 Ø 2 H7 Ø 72 H7 Ø 2 H

30 Dimensions Muff couplings The INKOMA-muff coupling is similar to DIN 115. Supplied in: Steel C 45 St Stainless steel (1.405) VA other materials are supplied. Please enquire. SKA: for same shaft diameter d= 55 mm muff coupling: SKA 55 SKB: for different shaft diameters d=55 mm and 0 mm muff coupling: SKB 0/55 Should the diameters of the connected shafts differ widely the selection must e ased on the larger shaft. Keyway to BS 425 Pt. 1 (DIN 5) When enquiring or ordering state clearly whether or not a keyway is required. S Ø D Ordering example: SKA 55 St Muff coupling Bore d Material L Keyway to customer requirements Ø d N7 Clamp ring for cylindrical shafts The INKOMA-clamp ring for cylindrical shafts: Supplied in: Steel C 45 St Stainless steel (1.405) VA other materials are supplied. Please enquire. Ordering example: 0 Ø F Ø D 1 - Ø C ±0,2 Ø F f7 Ø a 1 Ø a 2 Gr 10 St Clamp ring (for cylindrical shafts) Preferred ore Material Keyway to customer requirements also recessed ore for screw k B e

31 Dimensions [mm] Operational data Bore Torque with keyway Torque without keyway Mass moment of inertia Clamp screw Mass d D L T [Nm] T [Nm] J [kg m 2] S [kg] SKA 20 SKA 25 SKA 0 SKA 5 SKA 40 SKA 45 SKA 50 SKA 55 SKA 0 SKA 70 SKA 0 SKA 90 SKA 100 SKA 110 SKA 120 SKA 140 SKA 10 SKA 10 SKA 200 SKA 220 SKA 240 SKA 20 SKA , , , , , , ,01 0, , ,0 0,12 0, , ,27 1,150 2, , ,00 12, , , ,00 71,00 xm 2,20 xm10 4,40 xm10 4,20 xm10 4,0 xm10 4,50 xm10,90 xm10,5 xm10 14, xm10 1,90 10xM12 10xM12 12xM1 21,50 1,50 44,10 12xM1 1,50 12xM1 14xM1 14xM20 2,90 11,00 1,70 14xM24 251,00 14xM24 14xM27 59,00 492,00 1xM0 92,00 1xM0 50,00 1xM 1xM42 100, ,00 Dimensions [mm] Preferred ore max. possile ore max. possile spigot diameter max. possile ore diameter at Ø F Mass F 1) B C D a a 2 e k 1) 1 [kg] GR 10 GR 15 GR 20 GR 25 GR 0 GR 5 GR 40 GR 45 GR 50 GR 55 GR 0 GR 70 GR 0 GR 90 GR 100 GR 110 GR , 14, , , 14, , , 14, , , 14, , , 14, , , 14,5 9,5 0, , 14,5 9,5 0, , 14,5 9,5 0, , 14,5 9,5 1, , 14,5 9,5 1, , 14,5 9,5 1, ,4 17,5 11,5 1, ,4 17,5 11,5 1, ,4 17,5 11,5 1, ,4 17,5 11,5 1, ,2 19,5 14,5 2, ,2 19,5 14,5,0 1) Spigot according to customer requirement Please state when ordering whether keyway or spigot is required. Ø d also availae threaded 1 7

32 Application example Spline profile similar to ISO 14 (DIN 54) The comination of splined hu and clamp ring allows adjustment of the quality of fit. Splined clamp ring and sprocket. Secured using screws and dowels. Doule clamping for long components. INKOMA-clamp ring GR: for positioning components on cylindrical shafts. These clamp rings are extremely versatile: 1. as delivered 2. the ore a can e enlarged to suit the next size of 1 socket head cap screw. the ore a can e threaded. a is then equivalent 1 1 to the reference location diameter 4. in addition a locating spigot can e machined 5. d can e ored larger or threaded for use as a clamping nut 1. the clamp ring can e supplied with or without a keyway INKOMA muff couplings SKA/ SKB: provide a rigid connection etween two shafts having the same or different diameters. Supplied in two versions: 1. SKA for same shaft diameter, with keyway if required. 2. SKB for different shaft diameter, with keyway if required.