Group 4, Lab 6

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California State University, Northridge *

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317

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Mechanical Engineering

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Feb 20, 2024

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docx

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Fall 2023 California State University, Northridge Experiment 6 Springs in Series and Parallel Mechanics Lab AM 317 Written By:

Abstract: Understanding springs is imperative for engineers because they can release and store energy. There are three types of spring loadings that engineers must understand, those are series, parallel, and a combination of both. These different loading cases are used in different applications, so it is important that an engineer understands all of them to properly account for the situation. Springs in series store energy independently. The way that springs are loaded in series gives it an effective stiffness that is overall reduced. This configuration is useful when the goal is to produce a system that can take into account sharp movements. An example of this is the suspensions of a car. The springs in the car’s suspension act to counter the bumps in the road. Springs in parallel story energy in redundancy. The way that the springs are loaded in parallel allows each spring to bear a portion of the load. This configuration is useful when load distribution in a system is desired over the ability to account for sharp movements. An example of springs in parallel is anti-vibration mounts. The springs act in parallel in order to reduce the amount of movement that the system experiences. Some things that we expect to see in this lab is a linear relationship between deflection and load for all the singular spring loading cases. As for the more intricate loading cases we expect to see effective spring constants similar to what we calculate for them in the later theory section of the lab. For the most part we saw a perfect linear relationship for all the singular spring loading cases as well as for the series and balanced parallel loading cases. We did see different behavior

for the unbalanced parallel loading case and for the series and parallel loading which we concluded came from the springs not completely coming into contact with the bars as more and more springs were added to the system.

Introduction: The lab this week seeks to introduce us to the concept of springs, spring constants, springs in series, springs in parallel, and a combination of the two. These conditions need to be known by an engineer that is working with springs because springs behave in different ways depending on how the springs are loaded. Individual springs are the most simple type of loading condition. Individual springs only have one formula to work with and only have one spring constant to be wary of. Individual springs make up parts of other spring systems like series and parallel and bring their spring constants to the greater system. Springs in series is a slightly more complicated loading condition. Series springs store energy independently and the overall stiffness is reduced. These are good in applications where springs are used to absorb sudden forces like the suspensions on a car. The springs’ stiffness is reduced in order to reduce the bumpiness felt by the driver of the car. Springs in parallel are another loading condition. The energy stored in parallel springs is distributed amongst all the springs in the system. These are good in applications where a larger force acts on the system and the springs can more effectively reduce the force, take for example the earthquake protection you see on large buildings in California. The large springs at the base are used to counteract the motion of the earthquake. The things we are using in the lab to test spring loading conditions are a steel frame to hang the springs from, the springs, hooks, and aluminum bars in order to hold the springs to the steel frame, and a ruler to measure the displacement of the springs as loads are applied.

Theory: Springs are devices that can store and release energy. They have different behaviors depending on how the springs are arranged, their spring constants, and their positioning. Springs are used in a wide array of applications, so knowing these properties is very important for engineers. There are three types of spring loadings, series, parallel, and a combination of both. Springs connected in series share the same force or load. Effectively, the spring constant is reduced compared to an individual spring’s spring constant. Springs connected in parallel share the total force. Effectively, the springs distribute the load that is applied on them. In either case, the spring constant can be determined with the following use of Hooke’s Law, where F, the applied force, is equal to ∆ , the resulting displacement, times k, the spring constant. F = ∆ k The different arrangements of springs warrant different equations to find the equivalent spring constant, k eq . One of the cases we will be testing is of two springs attached at each other’s ends. This arrangement is a series arrangement. The k eq calculation for this arrangement is as shown, where the different k values indicate springs if different spring constants. k eq = 1 1 k 1 + 1 k 2 The next case that we wanted to test was when the springs were loaded in parallel. To do this, attached two springs of different constants to a bar and proceeded with loading weight on them. The spring constant calculation is as follows. k eq = k 1 + k 2

The next case was similar to the previous case, except the loading was unbalanced, meaning that the springs were unevenly spaced from the center. This equation has 3 new variables, L, which is the vertical length of the loading bar between the springs, a, which is the vertical distance between the left springs and the weight, and b, which is the vertical distance between the weight and the right spring. k eq = L 2 b 2 k 1 + a 2 k 2 The last case that we tested was a combination of series and parallel. It used 2 loading bars and 2 sets of 2 springs that had similar spring constants, and 1 with a different spring constant. The formula for calculating the spring constant for that case is as follows. k eq = 1 1 k 1 + k 2 + k 1 + 1 k 3 + k 3

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