Frame deflection is the amount of bending or deformation that a frame experiences when subjected to external loads. A frame's deflection is determined by a number of parameters, including material qualities, cross-sectional shape, boundary conditions, and the type and magnitude of loads applied. Deflection can make the frame unstable, lower its stiffness and strength, and damage the structure's performance and safety.
To determine the deflection of a frame, we must first identify the loads operating on the frame, then analyse the frame using structural mechanics, define the material and cross-sectional properties of the frame, then compute the maximum deflection. The maximum deflection is calculated using calculations based on the type of load and the boundary conditions. Once the maximum deflection has been determined, it is compared to the frame's permitted deflection limit to guarantee safe and efficient functioning.
Deflection in a machine frame is calculated by estimating
how much the frame will bend or deformed under stress. This is a major problem
in machine frame design since excessive deflection can cause machine problems
and breakdowns. To calculate deflection in a machine frame, perform these
steps:
1. Determine the load: The first step in determining deflection is to determine the load that will be applied to the machine frame. Static loads, dynamic loads, and impact loads are all examples of this.
2. Determine the material qualities: The machine frame's material properties are crucial in determining its deflection. The modulus of elasticity (E) and Poisson's ratio (v) of the frame's material should be calculated. The modulus of elasticity measures the stiffness of a material, whereas Poisson's ratio measures how much a material shrinks or expands in the perpendicular direction when subjected to a stress.
3. Determine the cross-sectional area and moment of inertia: The machine frame's cross-sectional area and moment of inertia are critical quantities in calculating deflection. The cross-sectional area is defined by the shape and dimensions of the frame. The moment of inertia measures how well a frame segment resists bending. The shape and dimensions of the frame define it, and it may be computed using the formula
I = (1/12)bh3
for a rectangular cross-section.
4. Determine the maximum permissible deflection: The maximum allowed deflection is defined by the machine's individual application and specifications. In general, the maximum permissible deflection should not be greater than one thousandth of the span length.
5. Determine the deflection: The machine frame's deflection can be determined using one of several approaches. Among these methods are:
We need to know the load, the length of the machine frame, the material qualities, and the cross-sectional properties to compute the maximum deflection.
Consider a rectangular steel frame having a length of 2 metres and a width of 0.1 metres. The steel frame has a modulus of elasticity of 200 GPa and a Poisson's ratio of 0.3. A uniformly distributed load of 500 N/m is applied to the frame.
To calculate the maximum deflection, we must first find the rectangular frame's area moment of inertia.
For a rectangular shape, the area moment of inertia (I) is given by
I = (b * h3) / 12,
where
b is the width of the frame = b
= 0.1 metre
h is the height of the frame. = h = 2 metre
As a result,
I = 0.00167 m4.
The maximum deflection due to an evenly distributed load can therefore be calculated using the following formula:
maximum
deflection = (5wL4)/(384EI).
Where
w =denotes
the load per unit length,
L =the frame length,
E =the modulus of elasticity,
I =the area moment of inertia.
With the data entered,
we get
max def= (550024)/(384200e90.00167) =
0.00029 metres.
Under a uniformly distributed load of
500 N/m, the maximum deflection of the rectangular steel frame is 0.00029 metres or 0.29 mm. It is
critical to compare this figure to the machine frame's permitted deflection
limit and make any necessary adjustments to guarantee safe and efficient
operation.
Numerical takes on involve modelling the machine frame with computer software and determining its deflection. A common numerical method used in engineering design is finite element analysis (FEA). FEA entails breaking down the machine frame into individual parts and analysing each one with mathematical calculations.
The machine frame is physically tested to evaluate its deflection using experimental methods. Strain gauges, deflectometers, and other measuring instruments can be used to do this.
6. Assess the outcomes: After calculating the deflection, it should be compared to the maximum permissible deflection to see if the design is acceptable. If the deflection exceeds the maximum permitted deflection, the design should be modified to stiffen the frame or lessen the load.
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