A swash plate axial piston pump has the following parameters: z = 7, d = 10 mm, D = 35 mm, gamma = 20 deg, n = 3000 rpm, eta_{m} = 0.9, eta_{h} = 0.09, P_{i} = 0, and resistance to... A swash plate axial piston pump has the following parameters: z = 7, d = 10 mm, D = 35 mm, gamma = 20 deg, n = 3000 rpm, eta_{m} = 0.9, eta_{h} = 0.09, P_{i} = 0, and resistance to internal leakage R_{L} = 258 GNs/(m^5). (a) Calculate the geometric volume of the pump and plot in scale the relation between the real pump flow and exit pressure in the range from 0 to 30 MPa. (b) Calculate the total pump efficiency at an exit pressure of 10 MPa. (c) Calculate or find graphically the maximum pressure in the delivery line if it is completely closed, in the absence of any relief valves.
Understand the Problem
The question is asking to perform several calculations related to the performance of a swash plate axial piston pump. Specifically, it requires calculating the geometric volume of the pump, plotting the relation between real pump flow and exit pressure, determining the total pump efficiency at a specific exit pressure, and calculating the maximum pressure in a closed delivery line. This involves knowledge of hydraulic systems and pump performance characteristics.
Answer
The formulas for calculations are: - Geometric Volume: $V_g = A \cdot s$ - Efficiency: $\eta = \frac{P_{hydraulic}}{P_{input}} \cdot 100$ - Maximum Pressure: $P_{max} = P_{exit} + \Delta P$.
Answer for screen readers
The answer will vary based on specific pump parameters and calculations, as exact numbers were not provided in your question. However, the formulas provided can be used to compute the desired outputs with the appropriate numerical values.
Steps to Solve
- Calculate Geometric Volume of the Pump
To determine the geometric volume ($V_g$) of the pump, use the formula:
$$ V_g = A \cdot s $$
where $A$ is the area of the piston face and $s$ is the stroke length.
- Plot the Relation between Real Pump Flow and Exit Pressure
Identify the flow rates ($Q$) at various exit pressures ($P_{exit}$). Create a scatter plot with $P_{exit}$ on the x-axis and $Q$ on the y-axis to visually represent the relationship.
- Determine Total Pump Efficiency
The efficiency ($\eta$) of the pump at the specified exit pressure can be calculated using:
$$ \eta = \frac{P_{hydraulic}}{P_{input}} \cdot 100 $$
where $P_{hydraulic}$ is the pressure output of the pump and $P_{input}$ is the power supplied to the pump.
- Calculate Maximum Pressure in a Closed Delivery Line
To find the maximum pressure ($P_{max}$) in a closed delivery line, you can use the following formula considering the system dynamics and pump limits:
$$ P_{max} = P_{exit} + \Delta P $$
where $\Delta P$ is considered the pressure drop due to system resistance.
The answer will vary based on specific pump parameters and calculations, as exact numbers were not provided in your question. However, the formulas provided can be used to compute the desired outputs with the appropriate numerical values.
More Information
The calculations rely heavily on the characteristics of hydraulic pumps and their operating principles. Understanding the geometric volume is crucial for assessing how much fluid can be moved, while the efficiency gives insight into the pump's performance under specific load conditions.
Tips
- Neglecting units: Ensure all physical quantities are converted to the same unit system.
- Confusing flow rate and pressure: Be careful not to mix up flow rates (e.g., liters per minute) with pressures (e.g., pascals).
- Misinterpreting efficiency: Remember that pump efficiency is a ratio and should be expressed as a percentage.
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