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Nächste Überarbeitung		Vorhergehende Überarbeitung
en:eingabe_der_schneckendaten:schneckenzonen [2025/02/27 20:08] – neelesten:eingabe_der_schneckendaten:schneckenzonen [2025/07/16 14:51] (aktuell) – cschall
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 ======General notes on defining the screw geometry====== ======General notes on defining the screw geometry======
  
-The following paragraphs serve for the specification of the geometrical values, which are needed in the input mask.  \\+The following paragraphs serve for the specification of the geometrical values, which are needed in the input masks.  \\
  
 ===== Input of values ===== ===== Input of values =====
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 Some values, such as the length $L$ or the pitch $t$, can be specified either as absolute values or as dimensionless values in relation to the diameter $D$. Some values, such as the length $L$ or the pitch $t$, can be specified either as absolute values or as dimensionless values in relation to the diameter $D$.
  
-As the leakage current is taken into account in the calculations, the following definitions must be observed:+As the leakage is taken into account in the calculations, the following definitions must be observed:
   * The inner cylinder diameter (the ‘nominal diameter’) must be entered as the diameter $D$. This can only be set in the feed zone.   * The inner cylinder diameter (the ‘nominal diameter’) must be entered as the diameter $D$. This can only be set in the feed zone.
   * The screw clearance $δ$ (delta) describes the radial clearance between the screw and the barrel.   * The screw clearance $δ$ (delta) describes the radial clearance between the screw and the barrel.
-  * All other geometry variables of the screw are independent of the barrel diameter. 
   * A distinction is made between the worm clearance $δ$ (delta) and the flight depth $h$.   * A distinction is made between the worm clearance $δ$ (delta) and the flight depth $h$.
  
-The only exceptions here are the cylindrical and the conical shear part. For these two shear sections, the shear gap height from the base of the shear section to the cylinder surface must be entered.+The only exceptions here are the cylindrical and the conical shearing sections. For these two shear sections, the shear gap height from the base of the shear section to the cylinder surface must be entered.
  
 {{ :eingabe_der_schneckendaten:abb_kanalgeometrie_uebersicht_en.svg?nolink&800 |}}  {{ :eingabe_der_schneckendaten:abb_kanalgeometrie_uebersicht_en.svg?nolink&800 |}} 
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 Basically, the width of the channel results in Basically, the width of the channel results in
-$$b=t \cdot cos(\varphi) - e$$+$$b=\frac{t \cdot cos(\varphi) - i  \cdot e}{i}$$
 $$\text{with}$$ $$\text{with}$$
-$$tan(\varphi)=\frac{t}{\pi \cdot (D-h)}$$ +$$tan(\varphi)=\frac{t}{\pi \cdot \overline{D}}$$ 
-with the pitch $t$, the pitch angle $\varphi$, the flight width $e$ and the nominal screw diameter $D$. \\ +$$\text{and}$$ 
-In the figure above, however, areas that reduce the channel cross-section are marked in red. As REX/PSI always calculates with a simplified rectangular duct, the reduction of the duct cross-section is taken into account by a reduced duct width:+$$\overline{D} = D-h$$ 
 +with the pitch $t$, the pitch angle $\varphi$, the flight width $e$, the nominal screw diameter $D$, the channel depth $h$ ,the number of channels $i$ and the effective diameter $\overline{D}$. \\ 
 +In the figure above, however, areas that reduce the channel cross-section are marked in red. As REX/PSI always calculates with a simplified rectangular channel, the reduction of the channel cross-section is taken into account by a reduced channel width:
 $$b_{effective}=\frac{b \cdot h-A_{radii,\gamma}}{h}$$ $$b_{effective}=\frac{b \cdot h-A_{radii,\gamma}}{h}$$
-Dividing the actual duct cross-section by the duct height $h$ results in the effective duct width.+Dividing the actual channel cross-section by the channel height $h$ results in the effective channel width.
  
-The duct cross-section $A_{radii,\gamma}$ is calculated as follows:+The channel cross-section $A_{radii,\gamma}$ is calculated as follows:
 $$A_{r<h,\gamma=90°} = \frac{r^2}{4} (4 - \pi)$$ $$A_{r<h,\gamma=90°} = \frac{r^2}{4} (4 - \pi)$$
  
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 ===== Notes on calculating the duct cross-section and volume =====  ===== Notes on calculating the duct cross-section and volume ===== 
  
-The calculation of the duct cross-section takes into account the actual duct width $b$, the effective duct width $b_{effective}$, the duct height $h$, the web width $e$ and the screw clearance $\delta$. The channel volume is made up of 2 areas:+The calculation of the channel cross-section takes into account the actual channel width $b$, the effective channel width $b_{effective}$, the channel height $h$, the flight width $e$ and the screw clearance $\delta$. The channel volume is made up of 2 areas:
  
-$$A_{ges.}=A_{Kanal}+A_\delta$$+$$A_{total}=A_{channel}+A_\delta$$
 $$\text{with}$$ $$\text{with}$$
 $$A_{channel} = b_{effective} \cdot h$$ $$A_{channel} = b_{effective} \cdot h$$
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 {{ :eingabe_der_schneckendaten:abb_kanalvolumen_en.svg?nolink&800 |}} {{ :eingabe_der_schneckendaten:abb_kanalvolumen_en.svg?nolink&800 |}}
  
-The duct volume is calculated by multiplying the duct cross-section by the unwound duct length $L_{duct}$:+The channel volume is calculated by multiplying the channel cross-section by the unwound channel length $L_{channel}$:
  
-$$V_{channel} = A_{ges} \cdot L_{channel}$$+$$V_{channel} = A_{total} \cdot L_{channel}$$
 $$\text{with}$$ $$\text{with}$$
 $$L_{channel} = \frac{L_{zone}}{sin(\varphi)}$$ $$L_{channel} = \frac{L_{zone}}{sin(\varphi)}$$