The strength examination of parallel keys used in shaft-hub connections with reference to DIN 6892 - “Calculation and Design of Keys, Issue November 1998” can be executed with this program.

The examination of the required strength of a parallel key connection in decreasing, increasing and changing torques, is the determination of the effective surface pressure between the key and the respective keyway wall on the shaft. This pressure may not exceed the permissible limiting values of the respective material characteristics.

The determination of key strength for a parallel key connection is exclusively based on the dimensions and groove depths provided in DIN 6885 and DIN 6892.

The key geometries, depending on the given shaft diameter, can be retrieved by the calculation program from a technical file taken after DIN 6885.

The module “Parallel Key Connections” has altogether two selectable calculation methods on the input page.

The strength examination of the shaft for torsional and bending loads according to the nominal stress concept is not included in this calculation module.

Calculation Basis
The calculation of the key connection is based on “Calculation and Design of Keys” following DIN 6892, November 1998, Method B and Method C.
The following DIN standards were used:
-	DIN 6885 Sheet 1, Issue November 1998, Parallel keys, keyways, high type
-	DIN 6885 Sheet 2, Issue December 1967, Parallel keys, keyways, high type for machine tools
-	DIN 6885 Sheet 3, Issue February 1956, Parallel keys low type

Scope
This program “Parallel Key Connections” follows DIN 6885 Sheet 1, DIN 6885 Sheet 2, DIN 6885 Sheet 3.
Non-standardized key and keyway dimensions not following DIN 6885 can still be calculated from the key choice “Open input”. However, the strength determination then does not correspond to DIN 6892!

Input data:

Parallel Key Connections	
 	
Calculation method for strength examination	Method B	
 	
Active Torques	
Change of torque direction	No direction change	
Rated torque	Tnenn =	 80000	N*mm	
Maximum peak torque	Tmax =	 80005	N*mm	
Minimum friction moment	TRmin :	 0	N*m	
Application factor	KA =	 1	
Number of peak loads	NL :	 0	
 	
Geometry of the Parallel Key Connection	
Diameter of the shaft	d =	 35	mm	
Number of keys	i	1	
DIN Standard for parallel keys	DIN 6885 Sheet 1 Type A	
Key breadth	b =	 10	mm	
Key height	h =	 8	mm	
Keyseat depth	t1 =	 5	mm	
Chamfer or round of the key	r =	 0.6	mm	
Chamfer or round of keyseat edge	s1 :	 0	mm	
Chamfer or round of keyway edge	s2 :	 0	mm	
Key length	lpf =	 28	mm	
Load-bearing key length	ltr =	 18	mm	
Load-bearing keyway length	l2tr :	 0	mm	
 	
Loading and Unloading of forces on the Shaft and Hub	
Outer diameter of the hub	D (D2) =	 60	mm	
Diameter of the hub shoulder	D1 :	 0	mm	
Hub breadth at the outer diameter D2	c :	 0	mm	
Distance between points of force loading and unloading	a0 :	 0	mm	
 	
Shaft	
Materials (strength values) according to	Own assignment	
 	
Material designation	 C60	
Material number	 1.0037	
 	
Material group	 Unalloyed structural steel	
Heat treatment / State	 none	
 	
Standard dimension	dNm =	 40	mm	
Standard dimension	dNp =	 40	mm	
Ultimate strength for dNm	RmN =	 360	N/mm²	
Yield point for dNp	RpN =	 335	N/mm²	
Modulus of elasticity	E =	 210000	N/mm²	
Poisson's ratio	n =	 0.3	
Density	r =	 7850	kg/m³	
Elongation at break	Amin =	 12.5	%	
 	
Yield point ratio Rp/Rm	Rp/Rm <= 0.75	
 	
Material, surface hardened	no	
Loads mainly crosswise to the preferred direction of machining (rolling)	no	
 	
Supporting factor	fs =	 1.2	
Hardness factor	fH =	 1	
 	
Hub	
Materials (strength values) according to	Own assignment	
 	
Material designation	 40Cr10	
Material number	 1.0037	
 	
Material group	 Unalloyed structural steel	
Heat treatment / State	 none	
 	
Standard dimension	dNm =	 40	mm	
Standard dimension	dNp =	 40	mm	
Ultimate strength for dNm	RmN =	 360	N/mm²	
Yield point for dNp	RpN =	 335	N/mm²	
Modulus of elasticity	E =	 210000	N/mm²	
Poisson's ratio	n =	 0.3	
Density	r =	 7850	kg/m³	
Elongation at break	Amin =	 12.5	%	
 	
Yield point ratio Rp/Rm	Rp/Rm <= 0.75	
 	
Material, surface hardened	no	
Loads mainly crosswise to the preferred direction of machining (rolling)	no	
 	
Supporting factor	fs =	 1.2	
Hardness factor	fH =	 1	
 	
Key	
Materials (strength values) according to	Own assignment	
 	
Material designation	 E335	
Material number	 1.0037	
 	
Material group	 Unalloyed structural steel	
Heat treatment / State	 none	
 	
Standard dimension	dNm =	 40	mm	
Standard dimension	dNp =	 40	mm	
Ultimate strength for dNm	RmN =	 360	N/mm²	
Yield point for dNp	RpN =	 335	N/mm²	
Modulus of elasticity	E =	 210000	N/mm²	
Poisson's ratio	n =	 0.3	
Density	r =	 7850	kg/m³	
Elongation at break	Amin =	 12.5	%	
 	
Yield point ratio Rp/Rm	Rp/Rm <= 0.75	
 	
Material, surface hardened	no	
Loads mainly crosswise to the preferred direction of machining (rolling)	no	
 	
Supporting factor	fs =	 1.2	
Hardness factor	fH =	 1	

Results:	

Equivalent torque	Teq	=	     80.00	 N*m	
Equivalent force	Feq	=	   4571.43	 N	
Maximum force	Fmax	=	   4571.71	 N	
Load-bearing keyseat depth	t1tr	=	      3.67	 mm	
Load-bearing keyway depth	t2tr	=	      3.13	 mm	
Load-bearing key length	ltr	=	     18.00	 mm	
Load-bearing keyway length	l2tr	=	     18.00	 mm	

Key name	 A 10x 8x 28 DIN 6885 Blatt 1 Form A	

Effective surface pressure	
Load distr. factor (equiv. surf. pres.)	Kveq	=	      1.00	
Load distr. factor (max. surf. pres.)	Kvmax	=	      1.00	
Load sharing factor	Kl	=	      1.09	
Friction factor	KR	=	      1.00	

Equivalent surface pressure keyseat	p1eq	=	     75.48	 N/mm²	
Equivalent surface pressure keyway	p2eq	=	     88.53	 N/mm²	
Maximum surface pressure keyseat	p1max	=	     75.49	 N/mm²	
Maximum surface pressure keyway	p2max	=	     88.54	 N/mm²	

Allowable surface pressure	
Load direction change factor	fw	=	      1.00	

Load peak frequency factor	fl	=	      1.50	

Material Data	
Tensile strength of shaft	Rm	=	    360.00	 N/mm²	
     for deff		=	     35.00	 mm	
Yield strength of shaft	Re	=	    335.00	 N/mm²	
     for deff		=	     35.00	 mm	

Tensile strength of hub	Rm	=	    352.02	 N/mm²	
     for deff		=	     60.00	 mm	
Yield strength of hub	Re	=	    318.66	 N/mm²	
     for deff		=	     60.00	 mm	

Tensile strength of key	Rm	=	    360.00	 N/mm²	
     for deff		=	      8.00	 mm	
Yield strength of key	Re	=	    335.00	 N/mm²	
     for deff		=	      8.00	 mm	

Allowable surface pressure of shaft	pzul	=	    402.00	 N/mm²	
Allowable surface pressure of hub	pzul	=	    382.39	 N/mm²	
Allowable surface pressure of key	pzul	=	    402.00	 N/mm²	

Strength Check of the Effective Surface Pressure		

Shaft		
p1eq =   75.48 < fw*pzul =  402.00 N/mm²	
p1max =   75.49 < fL*pzul =  603.00 N/mm²	
Safety for equivalent surface pressure	Seq	=	       5.3	
Safety for maximum surface pressure	Smax	=	       8.0	

Hub		
p2eq =   88.53 < fw*pzul =  382.39 N/mm²	
p2max =   88.54 < fL*pzul =  573.59 N/mm²	
Safety for equivalent surface pressure	Seq	=	       4.3	
Safety for maximum surface pressure	Smax	=	       6.5	

Key		
p2eq =   88.53 < fw*pzul =  402.00 N/mm²	
p2max =   88.54 < fL*pzul =  603.00 N/mm²	
Safety for equivalent surface pressure	Seq	=	       4.5	
Safety for maximum surface pressure	Smax	=	       6.8