orce Sensors What is a force sensor? In physics, the definition of force is any agent that causes a mass to move. When you push an object, say a toy wagon, you re applying a force to make the wagon roll. Whether the wagon actually does roll depends upon the applied force overcoming other forces that oppose the motion, such as the force from friction. A force sensor, then, is a device that measures the amount of force applied. There are many ways to measure force, and major differences among force measurement devices. actors that engineers must consider when making a force measurement decision include determining the proper output range, accuracy, price, and the ease of project integration provided by the sensor s signal conditioning electronics. orce, mass, and weight The most commonly known force is that of gravity, which continuously tries to pull objects to the earth. Holding an object stationary in your hand, say a 2-kg mass, means your hand is applying an upward force that exactly opposes the downward force of gravity. The measure of force is called a Newton (N). Gravity exerts a 9.8 N force per kilogram of mass, so a 2-kg mass exhibits a force of 19.6 N. Your hand must be exerting a 19.6 N force upward to hold the mass stationary against gravity s downward tug. Note that the previous discussion used the term mass rather than weight. In everyday use, the mass of an object is often referred to as its weight. However, this is incorrect. The physical sciences rigidly define mass and weight as separate measures. The weight of an object actually depends on several factors, most notably the force of gravity. Surprisingly, the force of gravity changes with latitude, altitude, and subsurface densities. Thus the same object can possess different weights at different points on the earth. The mass of an object, however, does not change and represents the total amount of matter in the object. or best results, the idea of weight in force sensing should be avoided. Other confusions arise with the use of the term pressure. While pressure does exert force, the amount of force is controlled by the size of the area to which the pressure is applied: orce = Pressure X Area or example, let s start with three weights, each with a mass of 2 kg. The bottom of the first weight has a surface area of 10 cm 2, the second weight 1 cm 2, and the third weight 0.1 cm 2. Holding each weight stationary in your hand means that you are applying an upward force of 19.6 N for each weight. But how the weights feel in your hand will be quite different. The first weight is easy to hold, while the second creates some discomfort. Holding the third weight becomes outright painful. In each case, the force to hold the weight stationary remained the same: 19.6 N. But the pressure changed from 1.96 N/cm 2 to 19.6 N/ cm 2 for the second, and 196 N/cm 2 for the third! Stress vs. strain An object will change its size or shape at the application of any force. A prime example of this is a diving board. As a diver walks to the end of the board, it bends downward due to the force applied to the board by the diver s weight. Once the diver leaps from the board, it snaps back to its original shape. The diving board is said to have elasticity. Material can shift many different ways in reaction to an applied force depending upon how the force is applied. Such forces typically fall into one of three classifications: tension, compression, or shear. Presented by Sponsored by 1 June 2012
A L A L A L a force of 196 N has been applied to the wire. If the wire had a cross-sectional area of 0.04 cm 2, the amount of stress applied to the wire becomes 196 N/0.04 cm 2,, or 4,900 N/cm 2 of stress. L O L O L O Tension Compression Shear Tension occurs when the force pulls on an object, increasing its length. Compression does just the opposite, pushing against an object shortening its length. In shear, the elastic object is subjected to equal but opposite forces across its opposing faces. The degree to which the object changes shape is a function of the stress and strain on the element. Strain is the relative change in the shape or size of an elastic object due to an applied force. or example, a 10-kg mass attached to a wire applies a tension force that makes the wire stretch 0.01 mm over a 20-mm length. The strain on the wire is 0.01/20 or 0.0005. The strain value thus tells us how much a particular length of wire will stretch with the same amount of force. Note that strain does not have a unit of measure. Strain = Change in Length / Original Length (for the same applied force) Because strain is typically such a small number, the value is usually measured in microstrain (µstrain). Microstrain equals the strain value times 10 6. or example, an elastic element has a strain value of 0.0000032. To convert this reading to microstrain, multiply the strain value by 10 6 : 0.0000032 10 6 = 3.2 µstrain. Stress is the measure of the internal forces acting within an object. In the wire example, the wire grew longer when attached to a 10-kg mass. We say Confusion can arise between the values of stress and pressure because this equation for stress looks similar to the equation for pressure. However, pressure is applied to the surface of an object, while stress occurs within the body of the object. or real materials, stress is proportional to strain only when strain is sufficiently small. It is possible to exceed the elastic limit of the material. The elastic limit is defined as the maximum force that can be applied to a material without permanently changing its shape. orces kept below the elastic limit let the material snap back to its original shape when the force is removed. However, if the elastic limit is exceeded, the material s shape is permanently changed, destroying its calibration to measure the applied force. As even more weight is added, the wire eventually breaks. This is the breaking stress of the wire. Every material has its own elastic modulus, elastic limit, and breaking stress. Hooke s Law states that stress is directly proportional to strain as long as the load does not exceed the elastic limit of the material being stretched. That means if the weight attached to the wire should double, the wire should stretch to 0.02 mm, twice the amount. By measuring the amount the wire stretches, it should be possible to calculate the amount of force applied to the wire, and thus the amount of mass attached to the wire. If the wire stretched 0.005 mm, then the mass is 5 kg. However, if the wire stretched 0.015 mm, the mass equals 15 kg. Measuring strain Now that it has been demonstrated that the elastic element changes its shape when a force is applied, a way to measure that change is needed. The most common method uses an electrical resistance strain gauge. (Note that Stress = orce / Cross-sectional Area 2 June 2012
orce, Elastic region Elastic limit Plastic region Change in length, L Load cells The most common means for measuring force is the load cell. The geometric shape and modulus of elasticity of the elastic element within the load cell determines the range of force that can be measured, the dimensional limits of the cell, its final perforsome texts refer to these devices as strain gages. This is an accepted alternate spelling.) Electrical resistance strain gauges work under a simple principle: All conductors exhibit some degree of resistance that is directly proportional to the conductor s length, and inversely proportional to its cross-sectional area. Make the conductor longer, and its resistance goes up. Conductors with large diameters have lower resistance than those with small diameters. If a predetermined length of wire with a specific resistance is bonded to an elastic element, its size and shape will change with changes in the size and shape of the element. By measuring this change in resistance, the change in size of the elastic element can be determined, and the force applied to the elastic element calculated. The two most common strain gauges use either a metallic foil or wire, or a semiconductor material. Each has a specific gauge factor, the measure of the output for a given strain. Semiconductor gauges typically have a 100 to 150 gauge factor while metallic wire and foil gauges typically only have a 2 to 4 gauge factor. The output of semiconductor gauges is non-linear with strain, and so they usually need special linearization circuitry. They are sensitive to temperature changes, especially high temperatures, thus need careful matching of the gauges within any given load cell. Even so, they may still need a high degree of temperature compensation. The high gauge factor of semiconductors leads them to be the element of choice for small transducers. Typical uses are as force transducers, accelerometers, and pressure sensors whose sensing element may be Breaking point micro-machined out of a single piece of silicon. Wire strain gauges were the original resistancetype strain gauge. Even though they are more expensive to produce than semiconductor or thin-film gauges, they are still the gauge of choice for high temperatures and stress analysis. A 20-to-30-µm diameter wire is bonded to a substrate material that is in turn bonded to the elastic element. To improve sensitivity, the wire makes several back-and-forth paths to extend its length along the force axis. A relative newcomer to the force sensing arena is made of piezoresistive material sandwiched between two conductive plates. Piezoresistive material differs from other strain gage material in that its resistance depends upon the amount of force applied to the material rather than change in overall length or volume. With no force applied, piezoresistive material offers an electrical resistance of several megohms (MΩ) almost an open circuit. However, as force is applied its resistance drops to the low kilo-ohm (kω) range. The large swing in resistance with changes in force helps simplify the sensing electronics as well. Contact Silicon Contact 3 June 2012
+Exc +Exc +Exc R 1 R 2 R 1 Sig +Sig Sig +Sig Sig +Sig R 3 R 3 Exc Exc Quarter-bridge Half-bridge ull-bridge Exc mance, and its production costs. Each load cell contains an elastic element to which the force is applied. It is the change in shape of this elastic element that measures the overall force applied to the load cell. The load cell housing merely protects the elastic element and the sensing gauges attached to it. The elastic element can take on many different shapes. Some shapes the elastic element may assume include that of a simple solid cylinder, a hollow cylinder, a bending beam, a shear beam, an S-beam, a double-ended shear beam, a ring, or a toroidal ring. The material used for the elastic element is usually tool steel, stainless steel, aluminum, or beryllium copper. The best materials exhibit a large linear relationship between stress and strain with no noticeable change over time. There must also be a high level of Load Spherical load button Diaphragm-1 Diaphragm-2 Housing (enclosed inert gas) Elastic body repeatability between applications of force to ensure that the load cell is a reliable measuring device. To achieve these characteristics it is usual to subject the material to a special heat treatment. This may include a sub-zero heat treatment cycle to get maximum stability. Circuits to Measure Change Because of the extremely small resistance changes that occur with both semiconductor and metallic wire and film load cells, the most common measuring circuits for those devices use a Wheatstone Bridge. The load cell makes up one or more legs of the bridge. A sensitive voltmeter or other electronic circuit monitors the amount of imbalance in the bridge, and thus the level of applied force. Bridge circuits are classified as quarter, half, and full bridge depending upon how many load sensing elements are used and how they wire into the bridge. Less than full bridges need completion resistors to complete the other legs of the bridge circuit. An excitation voltage is applied to the bridge (+Exc, -Exc) to create voltage drops across the four resistive elements. The output signal (+Sig, -Sig) measures the difference in voltage drops from one side of the bridge to the other. When +Sig and Sig are equal, the bridge is said to be balanced. Any force applied to a strain gauge changes the gauge s resistance, producing a change in the signal voltage. or half and fullbridge circuits, the strain gauges are arranged in such a way that as one gauge rises in resistance, the other drops. This enhances the measured 4 June 2012
100lb Sensor Ressitance (K-Ohms) 1200 1000 800 600 400 200 0 0 10 20 30 40 50 60 70 80 90 100 110 120 orce (lbs) signal over the smaller bridge types. A piezoresistive force sensor has a much larger range of resistance output which lends itself to a simpler electronics implementation. In addition, the drop in resistance is inversely proportional to the force applied to the material. The inverse resistance effect means that the conductance of the sensor becomes directly proportional to the force applied. There are a variety of circuit options available to measure this relationship. A simple voltage divider configuration is easily integrated into a small portable device where overall packaging size is of critical importance. However, as shown earlier, it is conductance that responds in a linear fashion with force. As current flow maintains a linear relationship with conductance, a standard I-V op-amp circuit is recommended for applications that need optimal linearity. This simpler sensing arrangement is easily adapted to microprocessorbased operation such as the type used for embedded control systems. Surface force distribution All of the prior force measurement systems have one common limitation: They can only measure the force applied to one point. However, there are times when it s desired to look at the distribution of force applied Conductance: 1/R Resistance 0.020 0.018 0.016 0.014 0.012 0.010 0.008 0.006 0.004 0.002 0.000 over a larger surface area. Measuring the different forces applied over a large area can be daunting, in that it needs an individual force sensor for each measurement point. This can easily reach into the hundreds, if not thousands, of force sensors distributed over the surface of an object. However, thin-film piezoresistive force sensors simplify that task. The piezoresistive material of the sensor is crossed with two sets of parallel lines set in a crosshatch pattern. A simple scanning multiplexer checks the resistance at each point where the lines cross. If there are 10 horizontal and 10 vertical lines, sensing for 100 points is possible. A 20 by 20 line matrix produces 400 sensing points. Dynamic pressure distribution systems currently available can contain as many as 1,600 sensing points per square inch. By analyzing the reading at each point, an overall distribution of the forces applied to the surface area of the sensor can be displayed. Summary orce sensors can measure any push from a feather landing on a brick to the thrust of the space shuttle s rocket engines. It s adaptable for many other types of measurements, such as pressure, Piezoresistive element VT= 5V R LEXORCE V IN = 5V C1 REEDBACK VEE = Ground + _ R1 VCC= +5V V OUT V OUT = V IN * R LEXIORCE / (R 1 + R LEXORCE ) MCP6002 VOUT 5 June2012
mass, weight, and torque. When used with proper temperature compensation, it s capable of operating over a wide temperature range from numbing Antarctic cold to blistering desert heat. While load cells offer the greatest sensitivities to force measurements, their bulk and operational needs place definite limitations on their use in areas where weight and size are at a premium. Thin-film piezoresistive sensors built on flex- ible circuit materials typically less than 0.01-in. thick overcome many of these size limitations. In addition, their simpler interface and low-power operation makes them an ideal candidate for portable, lowcost force measuring systems. Though force sensors can only detect the force applied to a single point, surface force distribution measurement designs using thin-film piezoresistive materials can incorporate thousands of test points permitting display of the distribution of forces across the entire surface. 6 June 2012