{"last_commit_sha":"070d7d5adad946a911f6c9d4f968fbfa4106e408","persisted":true,"title":"calcGeo","content":"Calculates various bearing geometry dimensions, such as contact angles, rolling radii, ellipticity parameters of the Hertzian area, angular positions of the rolling elements, etc.

Input: **`L`**,**`R`**,`T_Oil`
Output: **`G`**

|Equation|Symbol|Unit| |---|---|---| |Temperature increase of the inner ring relative to the outer ring
Default: $\Delta T_{ia}=5 K$, can be set as an option of `calcGeo`|`G.Delta_Tia`| $K$| |Temperature increase of the shaft relative to the standard temperature of 20°C (inner ring hotter than outer ring)
$\Delta T_{a,norm} = T_{Oil} - 20 K$|`G.Delta_Ta_norm`|$K$| |Temperature increase of the enclosure relative to the standard temperature of 20°C
$\Delta T_{i,norm} = \Delta T_ {a,norm} + \Delta T_{ia}$|`G.Delta_Ti_norm`|$K$| |Mean temperature
$\Delta T_{m,norm} = (\Delta T_{a,norm} + \Delta T_{i,norm})/2$|`G.Delta_Tm_norm`|$K$| |Reduced youngs modulus
$\frac{2}{(1-\nu_{RE}^2)/E_{RE} + (1-\nu_{ring}^2)/E_{ring}}$ |`G.E_red`|$Pa$| |Diameter of rolling elements after thermal expansion
$D_{RE} (1 + \alpha_{t,RE} \Delta T_{m,norm})$|`G.D_RE`|$m$| |Outer ring diameter after constriction due to housing and thermal expansion
$(D - e_{ar}) (1 + \alpha_{t,RE} \Delta T_{a,norm})$|`G.D`|$m$| |Inner ring diameter after expansion due to shaft and thermal expansion
$(d + e_{ir}) (1 + \alpha_{t,RE} \Delta T_{i,norm})$|`G.d`|$m$| |Radius of rolling elements after thermal expansion
$R_{RE}=D_{RE}/2$|`G.R_RE`|$m$| |Average diameter between outer and inner track
$d_m = (d + D)/2$|`G.d_m`|$m$| |Raceway radius of the inner ring (measured in the bearing cross-section)
$f_i D_{RE}$|`G.R_li`|$m$| |Raceway radius of the outer ring (measured in the bearing cross-section)
$f_a D_{RE}$|`G.R_la`|$m$| |Calculated width of inner/outer ring relative to diameter (without temperature influence) [not saved]
$b_{l,i} = b_{l,a} = (D-d-2 D_{RE}-c)/2$|`b_li`
`b_la`|$m$| |Calculated width of inner/outer ring relative to diameter (with temperature influence)
$b_{l,i} (1 + \alpha_{t,RE} \Delta T_{i,norm})$
$b_{l,a} (1 + \alpha_{t,RE} \Delta T_{a,norm})$|
`G.b_li`
`G.b_la`|$m$| |Radial play during operation
$P_d = D-d-2 D_{RE}-b_{l,i}-b_{l,a}$|`G.P_d`|$m$| |Inner/outer track width (with temperature influence)
$B_i (1 + \alpha_{t,RE} \Delta T_{i,norm})$
$B_a (1 + \alpha_{t,RE} \Delta T_{a,norm})$|
`G.B_i`
`G.B_a`|$m$| |Relative curvature according to Harris
$b = f_i + f_a - 1$|`G.b`|$-$| |Initial contact angle
_for $F_a = 0$ or `G.method.alphaForRaceRadius == 'zero'`_:
$\alpha_{0}=0$
_for $F_a\neq0$_:
$\alpha_{0}=\arccos \left(1-\frac{P_{d}}{2 \cdot B_{m} \cdot D_{RE}}\right)$|`G.alpha_0`|°| |Minimum inner groove radius in the rolling direction of the RE
$R_{b,i} = (d + b_{l,i}) / 2$|`G.R_bi`|$m$| |Maximum outer groove radius in the rolling direction of the RE
$R_{b,a} = (D - b_{l,a}) / 2$|`G.R_ba`|$m$| |Inner race radius at point of contact
$R_{r,i} = R_{b,i} + R_{RE}(1-cos(\alpha))$|`G.R_ri`|$m$| |Outer race radius at point of contact
$R_{r,a} = R_{b,a} - R_{RE}(1-cos(\alpha))$|`G.R_ra`|$m$| |Other temperature corrected dimensions
$d_{bL,i} (1 + \alpha_{t,RE} \Delta T_{i,norm})$
$d_{bR,i} (1 + \alpha_{t,RE} \Delta T_{i,norm})$
$D_{bL,a} (1 + \alpha_{t,RE} \Delta T_{a,norm})$
$D_{bR,a} (1 + \alpha_{t,RE} \Delta T_{a,norm})$
|
`G.d_bLi`
`G.d_bRi`
`G.D_bLa`
`G.D_bRa`
|$m$ |Curvature sum
$\sigma_{\varrho,i} = (2/R_{RE} + 1/R_{r,i} - 1/R_{l,i})$
$\sigma_{\varrho,a} = (2/R_{RE} - 1/R_{r,a} - 1/R_{l,a})$|`G.Sigmarho_i`
`G.Sigmarho_a`|$\frac{1}{m}$| |$R_{s,i} = 1 / \sigma_{\varrho,i}$
$R_{s,a} = 1 / \sigma_{\varrho,a}$|`G.R_si`
`G.R_sa`|$m$| |Reduced radii in rolling direction
$R_{x,i} = \frac{1}{1/R_{RE} + 1/R_{r,i}}$
$R_{x,a} = \frac{1}{1/R_{RE} - 1/R_{r,a}}$|`G.R_xi`
`G.R_xa`|$m$| |Reduced radii perpendicular to rolling direction
$R_{y,i} = \frac{1}{1/R_{RE} - 1/R_{l,i}}$
$R_{y,a} = \frac{1}{1/R_{RE} - 1/R_{l,a}}$|
`G.R_yi`
`G.R_ya`|$m$| |$\gamma = D_{RE} cos(\alpha) / d_m$|`G.gamma`|-| |Herzian parameters
$\mathfrak{F}(k) = \int_0^{\pi/2}\left(1 - (1-1/k^2)sin^2(\varphi) \right)^{-1/2} \; d\varphi$
$\mathfrak{E}(k) = \int_0^{\pi/2}\left(1 - (1-1/k^2)sin^2(\varphi)\right)^{1/2} \; d\varphi$|
`fraktF`
`fraktE`|$-$| |$F_i = \frac{( \gamma/(1-\gamma)+D_{RE}/(2 R_{l,i})}{2+\gamma/(1-\gamma)-D_{RE}/(2 R_{l,i}))}$
$F_a = \frac{(-\gamma/(1+\gamma)+D_{RE}/(2 R_{l,a})}{2-\gamma/(1+\gamma)-D_{RE}/(2 R_{l,a}))}$|
`G.F_i`
`G.F_a`|$-$| |_Solve for k:_
$1-\frac{2}{k_i^2-1} \left(\frac{\mathfrak{F}(k_i)}{\mathfrak{E}(k_i)}-1\right)-F_i = 0$
$1-\frac{2}{k_a^2-1} \left(\frac{\mathfrak{F}(k_a)}{\mathfrak{E}(k_a)}-1\right)-F_a = 0$|
`k_i`
`k_a`|$-$| |Deflection constant of the inner contact
$K_{p,i} = \pi k_i E_{red} \left(\mathfrak{E}_i/(4.5 \sigma_{\varrho,i} \mathfrak{F}_i^3)\right)^{1/2}$|`G.K_pi`|$\frac{N}{m}$| |Deflection constant of the inner contact
$K_{p,a} = \pi k_a E_{red} \left(\mathfrak{E}_a/(4.5 \sigma_{\varrho,a} \mathfrak{F}_a^3)\right)^{1/2}$|`G.K_pa`|$\frac{N}{m}$| |Deflection constant of whole rolling element
$K_p= 1/\left(1/K_{p,i}^{2/3}+1/GK_{p,a}^{2/3}\right)^{3/2}$|`G.K_p`|$\frac{N}{m}$| |Angle difference between two neighbouring rolling elements
$\Delta_\psi = 2 \pi/Z$|`G.Deltapsi`|$rad$| |Vector of all rolling element angles
`G.psi_ = (0:L.Z-1) .* G.Deltapsi`|`G.psi_`|$rad$|","front_matter":{},"format":"markdown","uploads_path":"https://git-ce.rwth-aachen.de/api/v4/projects/25517/wikis/attachments","slug":"calcGeo","path":"/pmd_etribosystems/bear-imp-public/-/wikis/calcGeo","wiki_path":"/pmd_etribosystems/bear-imp-public/-/wikis/home","help_path":"/help/user/project/wiki/_index.md","markdown_help_path":"/help/user/markdown.md","markdown_preview_path":"/pmd_etribosystems/bear-imp-public/-/wikis/calcGeo/preview_markdown","create_path":"/pmd_etribosystems/bear-imp-public/-/wikis"}