Posts Tagged ‘gear’

Equating Torques and Pitch Circle Radii Within a Gear Train

Thursday, May 29th, 2014

      Last time we developed torque equations for the driving and driven gears within a simple gear train.  They are,

T1 = D1 × F

T2 = D2 × F

where, T1 and T2 are the driving and driven gear torques, D1 and D2 are the driving and driven gear pitch radii, and F is the resultant Force vector, the common factor between the two equations.

gear train exoert

      Now we’ll combine these two equations relative to F to arrive at a single equation which equates the torques and pitch circle radii of the driving and driven gears in the gear train.   This type of computation is commonly used to design gear trains to ensure they perform at a given level.

      As a first step we’ll use algebra to rearrange terms and place the two equations equal to F.    First we’ll do it for the driving gear, dividing both sides of the equation by the pitch circle radius, D1.

T1 ÷  D1 = D1 ÷ D1 × F

T1 ÷ D1= 1 × F

F = T1 ÷ D1

      In a similar fashion, we’ll do it for the driven gear by dividing both sides of the equation by the pitch circle radius, D2.

T2 = D2 × F   →   F = T2 ÷ D2

      Since F is the common term between the two equations, we can set them up as equal to each other,

F = T1 ÷ D1 = T2 ÷ D2

which means that,

T1 ÷ D1 = T2 ÷ D2

      Next time we’ll see how to use this equation to manipulate our gear train so that it acts as a torque converter by increasing T2 with respect to T1 and the ratio of D1 to D2, thus providing a mechanical advantage to the electric motor the gear train is attached to.


Distance and Force Vectors of a Simple Gear Train

Monday, May 5th, 2014

      Last time we examined how torque and force are created upon the driving gear within a simple gear train.   Today we’ll see how they affect the driven gear.

mechanical engineering expert witness

      Looking at the gear train illustration above, we see that each gear has both distance and force vectors.   We’ll call the driving gear Distance vector, D1, and the driven gear Distance vector, D2.   Each of these Distance vectors extend from pivot points located at the centers of their respective gear shafts.   From there they extend in opposite directions until they meet at the line of action, the imaginary line which represents the geometric path along which Force vectors F1 and F2 are aligned.

      As we learned last time, the Force vector, F1, results from the torque that’s created at the pivot point located at the center of the driving gear.   This driving gear is mounted on a shaft that’s attached to an electric motor, the ultimate powering source behind the torque.  F1 follows a path along the line of action until it meets with the driven gear teeth, where it then exerts its pushing force upon them.   It’s met by Force vector F2, a resisting force, which extends along the same line of action, but in a direction opposite to that of F1.   These two Force vectors butt heads, pushing back against one another.

      F2 is essentially a negative force manifested by the dead weight of the mechanical load of the machinery components resting upon the shaft of the driving gear.   Its unmoving inertia resists being put into motion.   In order for the gears in the gear train to turn, F1 must be greater than F2, in other words, it must be great enough to overcome the resistance presented by F2.

      With the two Force vectors pushing against each other along the line of action, the angle ϴ between vectors F2 and D2, is the same as the angle ϴ between F1 and D1.   Next time we’ll use the angular relationship between these four vectors to develop torque calculations for both gears in the gear train.


Systems Engineering In Medical Device Design – Production, Part 1

Sunday, February 24th, 2013
     Done any remodeling lately?  If you have, you’ve been faced with countless choices regarding design and materials.  Even a relatively simple decision such as putting in hardwood flooring requires many considerations.  What type of wood?  What grade?  How about the stain?  Should it be factory stained and sealed, or should the flooring be installed by single board, then stained and sealed in place?  Ultimately, your decision is based on your requirements with regards to cost, durability, and personal style.

     Now imagine the decision making process that is required to produce a medical device.  We’ve been discussing this complex process during our series on medical device design utilizing the systems engineering approach, a systemized approach to product development, design, and manufacture that is used within many manufacturing arenas.  Its objective is to relate the requirements for manufacture, regulatory compliance, sale, use, and maintenance of the product to specific design criteria for functionality, durability, and safety.  By doing so, the systems engineering approach ensures that the product meets or exceeds all requirements.

     Last time we wrapped up our discussion on the Development stage of systems engineering by discussing field testing of medical devices assembled during Preproduction.  Problems encountered during this phase result in a comprehensive review of the device design and instructions.  When all issues have been resolved, things move on to the manufacturing phase and full commercial production.

     During the Production stage, engineers make continual assessments of the manufacturing process and ongoing adjustments are made to the device design and manufacturing protocol as necessary, this due primarily to changing stakeholder requirements regarding cost reduction.  In the competitive marketplace, cost reduction is a never-ending quest to maintain profitability in view of changing economic and market conditions, and this must be done without compromising the quality, safety, and effectiveness of the device.

     For example, suppose a medical diagnostic imaging machine was designed to be fitted with a machined metal gear in one of its mechanisms.  The manufacturer specifies that a $10 decrease must be made in production costs so it can continue to be sold at an acceptable profit margin.  After reviewing the design, engineers discover that substitution of a molded plastic gear would reduce manufacturing cost per machine by $12.  This is a common scenario, as plastic parts are often substituted for metal to save on cost.

     Plastic versus metal?  How can that be an acceptable swap?  In many cases, it can be.  Mechanical stressors are analyzed, and if the plastic gears meet durability requirements as well as their metal counterpart, they are substituted.  During the Preproduction phase these plastic gears are used in both lab and field testing, where they are put through the rigors of real world use.  If they perform acceptably, they are made a permanent part of the device’s design and used in commercial production.

     Next time we’ll continue our look at the Production stage to discover another way that systems engineering can facilitate cost reduction to meet stakeholder requirements.


medical device design