DeepHardness 1.0

DEEPHARDNESS 1.0 ESTABLISHES THE MICRO HARDNESS GRADIENT HV1 NECESSARY TO THE CONTACT FATIGUE RESISTANCE FOR MECHANICAL ELEMENTS MADE OF STEEL LIKE: PLANAR CAMS, BEARING RACES WITH ROLLER ROLLING AND ROLLS, CYLINDRICAL COGWHEELS WITH RIGHT AND HELICAL FRIPS

DESCRIPTION:
DEEPHARDNESS 1.0 calculates the micro hardness gradient HV1 necessary to the contact fatigue resistance, on assuming discontinuities like not metallic inclusions as nucleation sources for subsurface fatigue cracks, according to the Murakami-Endo theory. DEEPHARDNESS 1.0 uses the Hertz theory for the calculation of the contact pressure, then it is valid for cylindrical bodies (absence of convexities).
In case of coupling of materials with different Poisson coefficient, the micro hardness gradient HV1 in calculated referred to the body with subscript 2.
CONDITIONS:

1. The tool does not consider the chemical nature of the inclusion (sulphide or oxide), its degree of adhesion to the metallic matrix and the distribution inside it. The presetted maximum dimension d relative to the bigger inclusion, equal to 50 µm, is considered properly precautionary with respect to the manufacturing methodologies of the modern special structural steels destined to the realization of components subjected to contact fatigue (steels for surface hardening, quench and tempering steels, case hardening steels, nitriding steels with the exception of the RE-SULPHURIZED and ADDED-Pb types. To obtaining a further refining of the calculation it is suggested to follow the DH1 procedure for the determination of d. Only in the case of use of specific steels for bearings it is advised to put d=30 µm avoiding to perform the inquiry defined by the DH1 procedure.
2. It is not considered the micro structural variation that is highlighted from the core surface consequent to the specific surface hardness treatment (for example white layers during nitriding, retained austenite during carbonitriding)
3. Convexities are not considered

USEFULNESS:

1. Optimization of the surface hardness treatment (costs reductions, reduction of the heat treatment deformations, reduction of stocks from grinding)
   
2. Reduction of the costs derived from prototype and trial

CAUTION:

1. DEEPHARDNESS 1.0 calculates the micro hardness gradient HV1 as a function of the z depth normal to the contact surface. This gradient will give an indication about the surface hardness treatment to choose regarding surface hardness and effective hardening thickness. The micro hardness gradient HV1 vanishes asymptotically, then it is necessary to evaluate what core hardness prescribe as a function of the hardness treatment it will be chosen. For small loads it is possible the tool will return values of hardness simply obtainable with massive treatments, like for example quenching and tempering. THE MICROHARDNESS GRADIENT HV1 ALWAYS MUST BE INTERPRETED BEFORE THE PRESCRIPTION OF A SURFACE HARDNESS TREATMENT
2. For planar cams and bearing races it must be considered, along the whole profile, the heaviest condition in terms of F, D₁ and D₂

USE:

1. Introduce the demanded parameters in the entry mask
   1. D₁ e D₂ : diameters of the osculating circles of the bodies in the contact point respecting the convention of signs of the Hertz theory. For internal surfaces, the diameter is negative. For the cogwheels these diameters are calculated by the suitable routine putting in the number of frips, the modulus, pressure angle and helix angle of the gear. It is considered the pitch contact point between the frips
      
   2. F : contact force between the bodies
      For the cogwheels the force is calculated introducing the couple that acts on the pinion (wheel 1), besides the dates indispensable to calculate D₁ and D₂. It is necessary to introduce even the overloading factor ( K ), utilised in the measuring of the gear, obtained as a product of the overloading factors relative to each contribution, that is: application load factor ( K_a ), dynamical factor ( K_v ), longitudinal distribution of the load factor ( K_hβ ), transversal distribution of the load factor ( K_hα ), according to UNI 8862-1/2 : 1987
      
   3. l : contact width, that is band width of the cam or rolling race. For the cogwheels it is calculated putting in the width b of the gear (it is always intended the overlap width)
      
   4. E₁ ; E₂ ; ν₁ ; ν₂ : characteristics of the material of the bodies in contact: Young modulus, Poisson coefficients of the bodies 1 e 2
      
   5. η : safety factor towards the yielding due to contact fatigue
      
   6. μ : friction coefficient between the bodies in contact
      
   7. d : maximum dimension of the bigger not metallic inclusion
      
   The prefixed parameters are useful as a guide and example for the user
2. Start the calculation
3. Extract the gradient HV1 as a tabulation, define the surface hardness ( HV1 for z=0 ) and the hardness thickness
4. Choose the treatment that assure the safety characteristics obtained. The choice is a function of the material, of the geometry and of the dimensions of the component. For the manner of indication in the drawings cfr DRAWINGSPECIFICATIONS 1.0. In case of difficulty in the choise of the treatment or presence of convexities info@graniteng.com.

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