Shock Absorber Dynamometer

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  • Shock Absorber DynamometerDesign Group B

    Shock Absorber Dynamometer http://poisson.me.dal.ca/~dp_98_7/report/firstreport.htm

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  • Date: Team Members

    December 4, 1998 Daren MacDonald

    Matthew Glaze

    Submitted to: Steven Lee

    Dr. A. Warkentin Todd Nauss

    Aaron Shepherd

    Abstract

    The purpose of this project is to design and build a machine that will test the characteristics of various shocks. The technical name of this machine is a Shock Absorber Dynamometer. This progress report will discuss our currentstatus, the problems encountered and the project projections.The project was requested by Mike MacKenzies MASCAR team, who wish to get the edge on their competition by analyzing and tuning their shocks. The team would test each shock on the dyno and generate graphs for the shockcharacteristics. These graphs could be printed for each of the shocks or stored so the team could develop a database of how each shock performed under the test conditions. When the team is preparing for races on a certain trackthey could refer to their catalog of shock settings and their journal of their performances to determine which shock they should run on the car.The machine will be variable speed and allow the user to cycle his shock speeds from 0ips up to 15ips at variable stroke lengths. It will be simple to use and the computer will display and graph the force versus velocity and theforce versus displacement. It will be built in a modular style that will allow future modifications to the machine if the client wishes to make his better.

    Currently, we have completed the basic math modeling of the system, the stress analysis of the structure and the analysis of the limiting factors of our design. We are planning to order our electrical components to allow forsufficient time for arrival early next term. The construction of the main structure will begin during the start of the Christmas break. The completion of the construction depends of the date of arrival of our desired parts.

    Table of Contents

    Pages

    1.0 Introduction

    2.0 Terminology

    3.0 Client Requests

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  • 4.0 Shocks

    4.1 What is a Shock?

    4.2 How Does a Shock Work?

    4.3 Shock Models and Geometry

    5.0 What is a Shock Dynamometer

    5.1 Current Models

    5.2 Why are they used?

    5.3 How are they used?

    6.0 Requirements

    6.1 Performance

    6.1.1 Speed

    6.1.2 Force

    6.1.3 Vibration

    6.2 Structure

    Safety3.

    Enviroment4.

    7.0 Mechanism Designs

    7.1 Piston Crank Linkage

    7.2 Scotch Yoke Slider

    8.0 Electrical Components

    8.1 Electric Motor

    8.2 Load Cell

    Sensors and Wiring3.

    Data Acquisition4.

    Computer5.

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  • 9.0 Cost Projections10.0 Plans for Next Term

    Appendix A Calculations

    Appendix B Drawings

    Appendix C Sample Graphs

    Appendix D Load Cell

    Introduction1.

    The purpose of our design project is to design and build a testing device for shocks. The technical name for our machine is a shock absorber dynamometer, but for brevity, we will referto it from now on as a dyno from now on. The shock dyno project was requested by Mike MacKenzies MASCAR team, who wish to get the edge on their competition by creating adatabase of their shock performances with their choice of shocks. By correlating their performances with their setups and their knowledge of shock adjustments, they will be able to setup the car better for their next race. When the client is using rebuildable shocks he to reach certain benchmarks that are currently used to fine tune his suspension.

    The dyno will cycle and record the shock forces through a range of speeds. A computer will graph the force versus velocity and force versus displacement curves for the shock. Thegraph can be used to create a calibrated set of shocks and correlated with the drivers "feel" of the car to give teams the competitive edge. This is of interest to a race team where thesuspension setup can mean the difference between going home with the big win, or going home with your tail between your legs.

    The dyno will consist of a structure that will cycle the shock, a motor to drive it and a computer to log and display the data in either a graphical or tabular format. The structures beingconsidered are a scotch yoke and a piston-crank slider mechanism. The motor will be variable speed and allow the user to cycle his shock at speeds from zero inch per second (ips)up to fifteen ips at variable stroke lengths. The computer will log data and display tables and graphs of the data. It will also save individual test results and allow the operator to overlaya test on a previous tests results to compare the two performances.

    The construction of the main structure and mechanism will start during the Christmas break and will continue into the second term. The connection of the computer components, loadcell, DAQ and the motor will depend on the satisfactory completion of the mechanism. It is projected that the dyno will be assembled by March 1 to undergo testing and refinement.2.0 Terminology

    Blowoff - The performance characteristic of the shock when the shaft speed is very high. This usually occurs when the vehicle encounters a large bump and the tire is forced upwardin rapid response. The blowoff occurs at these shock speeds by valves opening and releasing some of the pressure in the shock to allow the shock to travel at a fast speed to maintaincontrol of the vehicle.

    Compression - When the shock is being compressed the shaft of the shock is moving into the casing. This damping is usually lower because the shock is only slowing the unsprungweight of the vehicle.

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  • Orfice - Small holes in the piston of the shock that allow the working fluid to pass through them to a different chamber. The resistance caused by the size of these holes and theviscosity of the fluid creates the damping force.

    Oversteer - The condition of a car that is unable to turn any harder because the rear wheels are swinging out from behind the front; often called sliding. This iscommon for cars that are set-up too loose. This is usually remedied by stiffening the front shocks and softening the rear shocks depending on other settings of camber, caster, springrates and tire pressures.

    Figure 1. Oversteer

    Rebound or Extension - The cycle where the shock is undergoing extension. The shaft of the shock is moving out of the casing towards the ground. Damping in this direction isusually required to be a maximum because the shock is slowing the travel of the weight of the vehicle.

    Unsprung Weight - The weight of the components of the vehicle that are not supported by the spring but by the tire. These are usually steering, suspension, braking components andthe wheel; much smaller than the weight of the vehicle.

    Understeer - The condition of a car that is unable to turn any harder because the front wheels of the car push towards the outside of the turn and the rear endfollows. Usually a race car driver prefers this condition because they can ease up on the throttle to shift more weight to the front tires. This condition is remedied through shocks bysoftening front shocks and stiffening the rear shocks depending on Figure 2. Understeer1

    settings of camber, caster, spring rates and tire pressures.

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  • 3.0 Client Requirements

    The client requires the machine to output force versus velocity and force versus displacement graphs. These graphs will be put into a database for comparing the characteristics ofdifferent shocks.

    Cost is the main design criteria for this machine. This type of machine would normally cost $20,000-$40,000 on the current market, but this is out of the reach of many small teams.The cost of our machine will be less than $4000 which ignores the cost of engineering and manufacturing. The client will provide the resources necessary to obtain the materials.

    The client has no major concerns over the size and weight of the machine. It will consist of:a structure to hold and cycle the shock,

    a load cell to measure the forces on the shock,

    a velocity sensor to measure the velocity of the shock,

    a computer to process the data and output it to the user.

    The client requests the computer display a graph of the processed data and a table of the raw data. This will be available through a display screen as well as a hard copy from aprinter. The client would also like the software to be able to save and overlay various shock tests on the screen to be analyzed by the operator.

    Other requirements are:

    resistant to dust, oil, and moisture

    infinite life

    easy to use (no special training or computer skills required)instruction and maintenance manuals

    .

    4.0 Shocks

    A shock controls the dynamic response of the suspension; every car that is on the road today has them. This well-engineered tool, is required to maintain the wheels of any automobileon the road and to ease the comfort of a bumpy ride. Despite what many people think, conventional shock absorbers do not support vehicle weight. When the wheel encounters abruptbumps or potholes, the damping force falls to a reduced level called blowoff, enabling the wheel to follow the terrain without transmitting jolts to the automobile. This allows for asmoother ride and increased traction for the tires because they remain in contact with the road. Also, when the chassis tries to lean forward during braking or side to side during turns,the shocks in your car limit the speed of weight transfer. This will make the car more stable.

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  • 4.1 What is a Shock?

    Shock absorbers are basically oil pumps. As shown in Fig. 1, a piston is attached to the end of a piston rod and works against hydraulic fluid in the pressure tube. Asthe suspension travels through compression and rebound, the hydraulic fluid is forced through tiny holes called orifices inside the piston. These orifices let only a small amount of fluidthrough the piston. This slows down the piston, which in turn slows down spring and suspension movement. (See figure 3)

    Figure 3.

    The amount of resistance a shock absorber develops depends on the speed of the suspension components and the number and size of the orifices in the piston. Shock absorbers arevelocity sensitive hydraulic damping devices, meaning the faster the suspension moves, the more resistance the shock absorbers provide. Because of this feature, shock absorbersadjust to road conditions. As a result, shock absorbers reduce:

    Bounce

    Roll or sway during turns

    Forward momentum during braking

    Backward momentum during acceleration

    Shock absorbers work on the principal of fluid displacement on both the compression and extension cycle. A typical car or light truck will have more resistance during its extensioncycle than its compression cycle. This is because the extension cycle controls the motions of the vehicle sprung weight. The compression cycle controls the motions of the lighterunsprung weight. (Ref. Munroe, 1998)

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  • 4.2 How does a shock work?

    There are two stages during a complete cycle of a shock, a compression cycle and then the extension cycle. During the compression stroke which is a downward motion, some fluidflows through the piston from Chamber B to Chamber A, and some through the compression valve into a reservoir, Chamber C. Three valving stages in the piston and in thecompression valves controls the flow. At slow speeds, the first stage opens and oil flows through the oil ports from Chamber B to Chamber A. When the car is suddenly jolted and theshock experiences a sudden compression, the second stage valve below the piston opens. At the bottom of Chamber B, oil that is displaced by the piston rod is passed through thethree stage compression valve into Chamber C. (Ref. Munroe, 1998)As the piston and rod move upward toward the top of the pressure tube, the volume of Chamber A is reduced, and thus is at a higher pressure than Chamber B. Because of this higherpressure, fluid flows down through the pistons three stage extension valve into Chamber B. The volume of the piston rod is withdrawn from Chamber B. This increases the volume andthe volume of the fluid from Chamber A is insufficient to fill Chamber B. The pressure in Chamber C is now greater than that of Chamber B, forcing fluids to

    flow to the lower pressure chamber. This keeps the pressure tube full and then the cycle is repeated.

    Figure 4. Shock Cycles

    4.3 Shock Models and Geometry

    Shocks are available in a variety of shapes, sizes and configurations from many manufacturers around the world. This dyno will be used to test shocks built for automotive racing. Theshocks are usually available in 15 and 19 inch variations for our application.

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  • The suspension of the race car is what is known as a coil-over suspension. The suspension has the shocks mounted inside the coil springs. The shocks have a threaded body so thecoil spring mount can be threaded on the shock. On shocks without a threaded body; a threaded sleeve is mounted over them. Most shocks have rubber or polyurethane bushings forthe mounts, however, racing shocks contain a rotational eyelet that allows for shock travel and misalignment.

    Shocks are usually mounted in a specific direction, with the cased end up because of the fluid in the shock and the valves, however, this is not always the case. Some racingmanufacturers build shocks that can be mounted either way.

    5.0 What is a Shock Dynamometer?

    A dynamometer is an apparatus for measuring force, speed, or power. Thus a shock dynamometer is a device that measures those entities on a car shockabsorber. The shock dynamometer is a precision testing instrument, which takes the mystery out of shock damper tuning and development. This machine replaces the trial and errorapproach or "seat of the pants engineering" into a reliable and efficient method to determine the shocks used during a race. The required outputs are plots of force versus velocity andforce versus displacement.

    Figure 5. A shock dyno.

    5.1 Current Models

    Today, there are many manufacturers of shock dynamometers. Each company has designed their own model and each has its own advantages. The one thing common to thesemodels is the price. Most of the machines cost from $20,000 to about $40,000 USD, depending of the options you chose. Most are powered by a 5hp electric motor and have suchoptions as variable stroke, temperature sensors, load cells of 2000-5000 lbs capacity and Pentium computers. The market for this expensive equipment is the larger race teams, suchas NASCAR. Unfortunately, for the smaller and lower budget teams, the price is simply too much.

    5.2 Why are they used?

    A shock dyno can give a complete force versus velocity or displacement curve for the shock over a variety of strokes and speeds. The advantage of having these charts is realized bypeople who know how to properly adjust their shocks for specific race tracks. The graph will show how the shock responds at low or high speeds so that the operator can judge if theshock is going to cause the car to over-steer or under-steer. Over-steer is when the rear wheel lose traction and the back end slides sideways. This characteristic is common withrear-wheel drive cars with poor traction. Under-steer is when the front tires slide before the rear tires. The driver turns the wheel but the car continues to go strait or doesnt turn

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  • enough. The ideal situation is when all four tires begin to slide at the same time. This is what is referred to as neutral handling and generally is the best way to have a car perform.

    How are they used?3.

    Shocks are bolted into the dyno unit on the provided mounting locations. The stroke is set to a chosen length and the speed range is chosen. The computer is set up to receive thedata and the initial temperature is taken. The machine is then started and the shock is cycled into the chosen velocity range where the data is sent to the computer. The computer canthen display the data in a graphical method that will allow the operator to adjust the shocks accordingly. For example, if a car is coming out of the turns too tight the operator will runthe shock on the dyno to check the setting. The shock is then rebuilt to loosen up the shock and ran on the dyno again. With the proper expertise, the shock can be reinstalled on thecar with the desired characteristics to help speed up the drivers times by making the turn as desired.

    6.0 Requirements

    6.1 Performance

    6.1.1 Speed

    The shocks will be tested from a range of zero to fifteen inches per second (ips). This is in accordance with data from industry sources such as Penske Race Shocks and DynamicSuspension. They informed us that race shocks withstand a maximum of 200 (ips). Penske Race Shocks also stated that before a speed of 15 (ips), their shocks encounter "blow-off".This means that the shock is compressing or rebounding at a greater rate than the damper was designed for and a relief (blow-off) valve releases the pressure so the shock is notdamaged. This area reveals a linear force versus velocity curve. Therefore, the only range where shock performance can be modified to provide an on-track performance gain is up tothe blow-off velocity. Blow-off will not affect the testing of the shock. In the event the shock encounters blow-off during the test on the compression stroke, it will recover in time to giveusable data on the rebound stroke and vice-versa. A typical force versus velocity curve and force versus displacement curve for a shock can be seen in Appendix B, figure ***.

    6.1.2 Force

    The loads this machine will encounter are in the range of five hundred to seven hundred pounds as found from sources within the industry. A safety factor of two will be used to ensurethat there are no situations where the load cell would be exposed to a load greater than its design load and subsequently not be damaged. Thus, the design load of the dyno will beapproximately 1500lbs.

    6.1.3 Vibration

    The natural frequency of the dyno structure will be well above the 4hz frequency at which we will be testing. This is because the dyno structure has a heavy and rigid base; comparedto the rest of the structure. A vibration analysis will be completed during the second term. In the unlikely event excessive vibration occurs, rubber mounts can be added to the base.The mass of the base can be increased or the dyno can be bolted to either a wall or the floor.

    6.2 Structure

    The structure will consist of a flat bottom plate with two vertical cylindrical beams. The two cylindrical beams will be tied together with a strong top beam, to which the load cell will bebolted. The load cell will have an adapter for bolting the shock to it. The flat bottom plate will act as a mount for the pillow block bearings and the two cylindrical shafts.

    The structure will be made of steel since it is the most economical choice and will stand up well in a garage environment. Geometrically, the structure will be approximately two to threefeet tall for the scotch yoke design and approximately four feet tall for the piston crank design. The weight of the structure, including all sensors and motor should weigh approximatelytwo hundred pounds.

    6.3 Safety

    The motor on the shock dyno will be operating at 1750 rpm. There will be many moving parts included in the reduction of this rotational speed to obtain the test rate of 180 rpm at theshock. The following methods will ensure safety:

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  • A metal cover will cover the base of the shock dyno structure and will enclose the motor, gear reducer and mechanism.

    A lock-out switch will be placed on the shock dyno. This switch will disconnect the motor from the power supply. This will be used during mounting of the shock to ensure the dynoisnt turned on accidently.

    These safety measures should be sufficient to allow the dyno to be operated safely. Any other safety issues that arise during the building of the dyno structure will be addressed at thattime.

    6.4 Environment

    The shock dyno will be set up in a garage, so it will experience dust, grease and moisture. The covers will prevent dust buildup around the motor and gear reducer and will also preventvarious fluids, such as grease, oil and paint over-spray from accumulating on the working parts of the dyno. A standard set of plastic covers will prevent these from accumulating on thecomputer hardware. An operations and maintenance manual will be provided with the dyno to ensure its correct use and care.

    7.0 Mechanism Designs

    The purpose of the mechanism is to translate rotational motion into linear motion. The two main designs being considered were the piston-crankmechanism and the scotch yoke slider (See figure 6 and 7). The major consideration for the mechanical design was durability. These mechanisms see forces that cycle from -1500lbsto +1500lbs at rates up to 180 rpm. This is being built on a budget so the machine should be cost effective.

    figure 6. Piston-crank linkage figure 7. Scotch yoke slider

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  • 7.1 Piston - Crank Mechanism

    This mechanism consists of a flywheel (crank), connecting rod, and piston similar to the piston-crank mechanism in an internal combustion engine. The flywheel will have holes drilledto achieve different stroke lengths. The disadvantage of using this mechanism is that it does not produce perfect sinusoidal motion in the piston, but having a longer connecting rod cancompensate for this. To achieve close enough to sinusoidal motion the connecting rod should be 5 times the stroke length. Although it is not necessary to have sinusoidal motion, itdoes help reduce vibration. For a maximum stroke length of 4" the connecting rod would be 20" long. The advantage to this mechanism is its cost effectiveness because there is lesshigh tolerance machining. It is simple to build and it is possible to buy it pre-built.

    Scotch Yoke Slider2.

    The scotch yoke has three advantages over the piston-crank mechanism. The first is space. The scotch yoke is considerably shorter in height then the piston-crank. The secondadvantage is that it produces perfectly sinusoidal motion and therefore will have less vibration. The third advantage is that there is very little side loading on the support structure.

    The scotch yoke has two major disadvantages. It is expensive. The fine tolerance that would be required for the slider wouldincrease machining costs. There is also more maintenance required with a slider joint. With the loads that a slider joint will experience the wear on the mechanism would be high. Thescotch yoke was not considered to have enough advantages to offset the high cost and lack of durability to make this the design of choice. The piston-crank mechanism was chosenbecause of its cost effectiveness and ease of construction.

    Table 1. Selection Criteria Matrix

    8.0 Electrical Components

    8.1 Electric Motors

    The dyno requires a variable speed drive to change our shaft speeds for different stroke lengths. According to the analysis, the dyno requires a minimum of 5hp (see Appendix A). Thispower can be obtained from either AC or DC electric motors; each offer good and bad characteristics.

    The DC motor was considered because of its relatively simple velocity control and small size to weight ratio. The maximum and minimum speeds, the acceleration/deceleration andbrake speed has to be set using a potentiometer (PID control). After tuning, the motor speed can controlled very accurately by voltage regulation. The primary problems with the DCmotor are the cost of the AC/DC inverter and the need for qualified personal to operate and care for it.

    The AC motor was considered because of its large range of customization and availability. The motors size and power is limited to its supply voltage. For applications up to 2hp, themotor can be powered by the usual 110v domestic power source. Larger motors in the 2hp to 10hp range can be powered by the 220v power source which is regularly found in mostgarages which contain air compressors or arc welders.

    AC motors are not usually adjustable speed however the speed can be controlled by PWM (Pulse Width Modulation) or variable speed drives. The speed controller can be purchasedwith a motor or as an addition to another motor but may void the warranty of the motor. The speed is not as linearly adjustable as the DC motor is the problem encountered with PWM.

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  • Most of the variable speed drives are completely adjustable with a LCD display and menu. This is better than a DC motor where you have to adjust everything with potentiometer.Another requirement is the motor needs good ventilation to keep the motor cool (a 5hp motor dissipates around 200 W). This problem could be solved with a simple vent in the rear ofthe casing.

    The decision was made to work with the AC motor. While the variable speed drive would increase the cost and the added control of speed could allow for testing the shock throughdifferent cycle speeds.

    8.2 Load Cell

    A load cell is a transducer that converts load acting on it into analog electrical signals. This conversion is achieved by the physical deformation of strain gages. Weight applied to theload cell either through compression or tension produces a deflection of the beam, which introduces strain to the gages. The strain will produce an electrical resistance changeproportional to the load. The change in resistance will be recorded and translated into a force measurement.

    A load cell attached to the crossbeam will measure the force placed on the shock. The load cell is required to have a sampling frequency of 1 kHz and able to withstand cyclic forcesup to 1500 lbs. The sample frequency of 1 kHz allows for approximately 100 measurements per cycle. This would allow for a clear force graph with many points. Research on shockabsorbers revealed that shocks rarely exceed 700lbs under normal loading conditions and should not exceed 1500lbs at rapid velocity testing.

    8.3 Sensors and Wiring

    There are two different ways to measure temperature of our shocks. The simplest method would be to have the operator take the temperature of the shock periodically to discover ifthere is a serious change over testing periods. A simple surface thermometer could do this adequately. If the temperature appeared to be a factor, the second method could be usedfor more accurate and convenient results.

    In the second method, temperature would be measured using a thermocouple attached to the casing of the shock with a Velcro strap. The thermocouple data could then be input intothe computer through the DAQ to provide an interface for correlating results.

    All wiring will have a degree of toughness to endure the harsh environment of the race car garage. The connection from the sensors to the computer would be shielded to ensureaccurate readings with little interference and also add a degree of protection to the wiring.

    8.4 Data Acquisition

    After searching various data acquisition catalogs, a simple 4 channel 1000 Hz per channel, Data Acquisition (DAQ) board was decided on. The actual system only needs 3 channels orinputs but industry only sells DAQs with inputs of a factor of four. The three inputs would be temperature, force, and velocity.

    The sampling frequency of 1 kHz per channel was decided upon because of the shocks maximum speed of a 180 RPM. It was thought that 100 points would clearly show the path.With multiple cycles the average of the points would give a definite path without any outliners.

    8.5 Computer

    A 486 DX computer has sufficient computing power; the math coprocessor could speed up the computations without affecting the other processes. A graphical user interface (GUI)would allow for easier use for those who are not familiar to the use of a computer.

    9.0 Cost ProjectionOur client, Mike MacKenzie has agreed to fund the whole project. As mentioned, the cost of constructing this shock dyno will be under $4000. Our major expense lies in the electroniccomponents. From various sources, we are able to estimate the cost of each section of the mechanism. This is shown below:

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  • Steel- from ' Metal's R Us', our projected cost is $100. The steel column cost $6.67/ft and flat steel is about $.80/lb.Load Cell- From 'Amcell' , the projected cost of the load cell is $800CDNDAQ- Our source is 'Omega' and we are estimating $1200CDN

    Electric Motor- 'Princess Auto' - $500

    Bearings- 'NTN' - $200

    Miscellaneous- which includes welding, nuts and bolts- $200

    Velocity Sensor- unknown

    Computer- 486DX50 with monitor and printer- $400

    ** Used parts will be used if available.

    10.0 Plans for Next Term

    The project has reached a point where a major decision has to be made on which of the two designs will be our primary design. Both the design exhibit the proper motion and strengththat is desired. The choice will be based on the ease and cost involved with building as well as maintenance.

    The team plans to order the necessary parts for the project by the end of December. It is expected that the data acquisition unit will take the longest to arrive so provisions have beenmade to utilize current school DAQs for testing.

    The DAQ and software will have to be programmed to match the clients needs and ease of operation. The structure will have to be assembled and bolted or welded depending on thepart. The load cell will have to be properly calibrated for the system. The motor will have to be properly wired up to the system with our variable speed controller.

    After all the parts arrive and the mechanism is assembled, the structure will have to be tested for strength, vibration and functionality. This testing will help determine which areas of theproject need to be improved or addressed. The team hopes to have the working unit completed before April 1, 1999 for testing shocks at Mike MacKenzies Garage.

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  • References

    http://www.monroe.com/monroe/shockcon.htm

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  • Appendix A

    Scotch Yoke, Mathematical analysis

    The analysis of the scotch yoke mechanism extends from newtons second law, sum of the forces equals mass times acceleration, sum of the torques equals mass moment of inertiatimes angular acceleration. The following is the dynamic and force analysis of the scotch yoke. The dynamic analysis is done with using geometry and calculus.

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  • Position:

    Y = r*sinq

    Differentiate with respect to time to get velocity of the cross beam.

    V = r*w *cosq

    Differentiate with respect to time to get acceleration of the cross beam.

    A = r*(a *cosq - w ^2*sinq )Force analysis

    F32 = m3A3 + FP

    Torque = -r*F32*cosq

    Piston Crank Analysis

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  • Using geometry and Newtons second law a completedynamic and force analysis can be performed. The following is the mathematical analysis.

    Position analysis

    q 3 = -(a/b)*sinq 2 + p

    d = a*cosq 2 - b*sinq 3

    Velocity analysis

    w 3 = (a/b)* (cosq 2/sinq 3)* w 2Vb = -a*w 2* sinq 2 + b*w 3* sinq 3

    Acceleration analysis

    a 3 = (a*a 2* cosq 2 - a*w 2^2*sinq 2 + b*w 3^2* sinq 3)/(b* cosq 3)

    Ab = - a*a 2* sinq 2 - a*w 2^2*cosq 2 + b*a 3* sinq 3 + b*w 3^2* cosq 3

    Force analysis

    After a complete dynamic analysis is performed the following matrix equation can be solved to find forces in the links for a know set of initial conditions, angular position, angularvelocity, and angular acceleration.

    1 0 1 0 0 0 0 0 F12x m2aG2x

    0 1 0 1 0 0 0 0 F12y m2aG2y

    -R12y R12x -R32y R32x 0 0 0 1 F32x IG2a 2

    0 0 -1 0 1 0 0 0 X F32y = m3aG3x

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  • 0 0 0 -1 0 1 0 0 F43x m3aG3y

    0 0 R23y -R23x -R43y R43x 0 0 F43y IG3a 3

    0 0 0 0 -1 0 0 0 F14y m4aG4x+Fpx

    0 0 0 0 0 -1 1 0 T12 -Fpy

    The previous analysis ignores gravitational and frictional forces.

    See the included spreadsheet for application of these equations.

    Power Calculation

    Power = Force * Velocity

    Power = torque * angular velocity

    Using the maximum torque found from the dynamic force analysis.

    Power = (3028 * 7.5) * (1/6600) = 3.44 hp min.Because the analysis ignores gravitational and friction forces a 5 hp motor is chosen in case the extra power was needed.

    Shock Absorber Dynamometer http://poisson.me.dal.ca/~dp_98_7/report/firstreport.htm

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