[Psychology] Mechanical Assemblies Phần pot

270 10 ASSEMBLY OF COMPLIANTLY SUPPORTED RIGID PARTS FIGURE 10-15. Geometry of a Two-Point Contact. The variable c is called the clearance ratio. It is the di- mensionless clearance between peg and hole. Figure 10-16 shows that the clearance ratio describes different kinds of parts rather well. That is, knowing the name of the part and its approximate size, one can predict the clearance ratio with good accuracy. The data in this figure are de- rived from industry recommended practices and ASME standard fit classes ([Baumeister and Marks]). Equation (10-2) shows that as the peg goes deeper into the hole, angle 0 gets smaller and the peg becomes more parallel to the axis of the hole. This fact is reflected in the long curved portion of Figure 10-12. Figure 10-17 plots the exact version of Equation (10-2) for different values of clearance ratio c. Note particularly the very small values of 9 that apply to parts with small values of c. Intuitively we know that small 9 implies dif- ficult assembly. Combining Figure 10-17 with data such as that in Figure 10-16 permits us to predict which kinds of parts might present assembly difficulties. The dashed line in Figure 10-17 represents the fact that there is a maximum value for 9 above which the peg cannot even enter the hole. This value is given by (10-4) It turns out in practice that the condition in Equa- tion (10-4) is very easy to satisfy and that in fact a smaller maximum value for 9 usually governs. This is called the wedging angle 9 W . Wedging and jamming are discussed next. 10.C.4. Wedging and Jamming Wedging and jamming are conditions that arise from the interplay of forces between the parts. To unify the discus- sion, we use the definitions in Figure 10-9, Figure 10-10, and Figure 10-18. The forces applied to the peg by the compliances are represented by F x , F z , and M at or about the tip of the peg. The forces applied to the peg by its contact with the hole are represented by f\, fa, and the friction forces normal to the contacted surfaces. The co- efficient of friction is JJL. (In the case of one-point contact, there is only one contact force and its associated friction force.) The analyses that follow assume that these forces are in approximate static equilibrium. This means in prac- tice that there is always some contact—either one point or two—-and that accelerations are negligible. The analyses also assume that the support for the peg can be described as having a compliance center. FIGURE 10-16. Survey of Dimensioning Prac- tice for Rigid Parts. This figure shows that for a given type of part and a two-decade range in di- ameters, the clearance ratio varies by a decade or less, indicating that the clearance ratio can be well estimated simply by knowing the name of the part. 10.C. PART MATING THEORY FOR ROUND PARTS WITH CLEARANCE AND CHAMFERS 271 FIGURE 10-17. Wobble Angle Versus Dimensionless Insertion Depth. Parts with smaller clearance ratio are limited to very small wobble angles during two-point con- tact, even for small insertion depths. Since successful as- sembly requires alignment errors between peg and hole axes to be less than the wobble angle, and since smaller errors imply more difficult assembly, it is clear that assem- bly difficulty increases as clearance ratio (rather than clear- ance itself) decreases. FIGURE 10-18. Forces and Moments on a Peg Sup- ported by a Lateral Stiffness and an Angular Stiff- ness. Left: The peg is in one-point contact in the hole. Right: The peg is in two-point contact. and respectively. These formulas are valid for 9 <$C tan ' (//). A force-moment equilibrium analysis of the peg in one- point contact shows that the angle of the peg with respect to the hole's axis is given by where SQ and #o, the initial lateral and angular error between peg and hole, are defined in Figure 10-9, while L g , the distance from the tip of the peg to the mathematical support point, is defined in Figure 10-10. We can now state the geometric conditions for stage 1, the successful entry of the peg into the hole and the avoid- ance of wedging, in terms of the initial lateral and angular errors. To cross the chamfer and enter the hole, we need 10.C.4.a. Wedging Wedging can occur if two-point contact occurs when the peg is not very far into the hole. A wedged peg and hole are shown in Figure 10-19. The contact forces f\ and /2 are pointing directly toward the opposite contact point and thus directly at each other, creating a compressive force inside the peg. The largest value of insertion depth I and angle 9 for which this can occur are given by 272 10 ASSEMBLY OF COMPLIANTLY SUPPORTED RIGID PARTS FIGURE 10-19. Geometry of Wedging Condition. Left: The peg is shown with the smallest 9 and largest i for which wedg- ing can occur, namely I = i^d. The shaded regions, enclosing angle 20, are the friction cones for the two contact forces. The contact force can be anywhere inside this cone. The two contact forces are able to point directly toward the opposite contact point and thus directly at each other. This creates a compressive force inside the peg and sets up the wedge. This can happen only if each friction cone contains the opposite contact point. Right: Once t > /j,d, this can no longer happen. Contact force f-\ is at the lower limit of its friction cone while f-2 is at the upper limit of its cone, so that they cannot point right at each other. where W is the sum of chamfer widths on the peg and hole, and If parts become wedged, there is generally no cure (if we wish to avoid potentially damaging the parts) except to withdraw the peg and try again. It is best to avoid wedging in the first place. The conditions for achieving this, Equa- tion (10-8) and Equation (10-9), can be plotted together as in Figure 10-20. This figure shows that avoiding wedging is related to success in initial entry and that both are gov- erned by control of the initial lateral and angular errors. We can see from the figure that the amount of permitted lateral error depends on the amount of angular error and vice versa. For example, we can tolerate more angular er- ror to the right when there is lateral error to the left because this combination tends to reduce the angular error during chamfer crossing. Since we cannot plan to have such op- timistic combinations occur, however, the extra tolerance does us no good, and in fact we must plan for the more pessimistic case. This forces us to consider the smallest error window. Note particularly what happens if L g = 0. In this case the parallelogram in Figure 10-20 becomes a rectangle and all interaction between lateral and angular errors disap- pears. The reason for this is discussed above in connection with Figure 10-14. This makes planning of an assembly the easiest and makes the error window the largest. FIGURE 10-20. Geometry Constraints on Allowed Lateral and Angular Error To Permit Chamfer Crossing and Avoid Wedging. Bigger W, c, and e, and smaller \JL make the par- allelogram bigger, making wedging easier to avoid. Not only must the error angle between peg and hole be less than the allowed wobble angle, as shown in Figure 10-17, but the maximum angular error is also governed by the coefficient of friction if wedging is to be avoided. If L g is not zero, then if there is also some initial lateral error, this error could be converted to angular error after chamfer crossing. So, avoid- ing wedging places conditions on both initial lateral error and initial angular error. The interaction between these con- ditions disappears if L g = 0. This fact is shown intuitively in Figure 10-14. 10.C.4.b. Jamming Jamming can occur because the wrong combination of applied forces is acting on the peg. Figure 10-21 states that any combinations of the applied forces F x , F z , and M which lie inside the parallelogram guarantee avoidance 10.C. PART MATING THEORY FOR ROUND PARTS WITH CLEARANCE AND CHAMFERS 273 of jamming. The equations that underlie this figure are derived in Section 10.J.4. To understand this figure, it is important to see the effect of the variable A. This variable is the dimensionless insertion depth and is given by As insertion proceeds, both t and X get bigger. This in turn makes the parallelogram in Figure 10-21 get taller, expanding the region of successful assembly. The region is smallest when A. is smallest, near the beginning of as- sembly. We may conclude that jamming is most likely when the region is smallest. (Since the vertical sides of the region are governed by the coefficient of friction /i, the parallelogram does not change width during insertion as long as /z is constant.) If we analyze the forces shown on the right side of Figure 10-18 to determine what F x , F z , and M are for the case where KQ is small, we find that F x = — F arising from deformation of K x M = L g F = -L g F x Dividing both sides by rF z yields (10-lla) which says that the combined forces and moments on the peg F x / F z andM/rF z must lie on a line of slope— (L g /r) passing through the origin in Figure 10-21. If L g /r is big, this line will be steep and the chances of F X /F Z and M/rF z falling inside the parallelogram will be small. Sim- ilarly, if M/rF z and F X /F Z are large, the combination of these two quantities will define a point on the line that is far from the origin and thus likely to lie outside the parallelogram. On the other hand, if L g /r is small so that the line is about parallel to the sloping sides of the parallelogram when A is small, then the chance of the applied forces falling inside the parallelogram will be as large as pos- sible and will only increase as A increases. Similarly if M/rF z and F X /F Z are small, they will define a point on the line that is close to the origin and thus be likely to lie inside the parallelogram. When A is small and jamming is most likely, the slope of sides of the parallelogram is approximately /z. Thus, if L g /r is approximately equal to JJL, then the line, and thus applied forces and moments, have the best chance to lie inside the parallelogram. Since JJL is typically 0.1 to 0.3, we see that the compliance center should be quite near, but just inside, the end of the peg to avoid jamming. Instead of considering a single lateral spring support- ing the peg at the compliance center, let us imagine that we have attached a string to the peg at this point. FIGURE 10-21. The Jamming Diagram. This dia- gram shows what combinations of applied forces and moments on the peg F x / F z and M/r F z will permit as- sembly without jamming. These combinations are rep- resented by points that lie inside or on the boundary of the parallelogram. A is the dimensionless insertion depth given in Equation (10-10). When A is small, in- sertion is just beginning, and the parallelogram is very small, making jamming hard to avoid. As insertion pro- ceeds and A gets bigger, the parallelogram expands as its upper left corner moves vertically upward and its lower right corner moves vertically downward. As the parallelogram expands, jamming becomes easier to avoid. 274 10 ASSEMBLY OF COMPLIANTLY SUPPORTED RIGID PARTS FIGURE 10-22. Peg in Two-Point Contact Pulled by Vector F. This models pulling the peg from the compliance center by means of a string. See Figure 10-22. This again represents a pure force F acting on the peg. In this case, F can be separated into components along F x and F z to yield (10-12) so that (10-13) which is similar to Equation (10-11). In this case, we can aim the string anywhere we want but we cannot indepen- dently set F x and F z . But, by aiming the force, which means choosing 0, we can make F x as small as we want, forcing the peg into the hole. As L g —>• 0, we can aim </> increasingly away from the axis of the hole and still make M and F x both very small. In Chapter 9, a particular type of compliant support called a Remote Center Compliance, or RCC, is described which succeeds in placing a compliance center outside it- self. The compliance center is far enough away that there is space to put a gripper and workpiece between the RCC and the compliance center, allowing the compliance cen- ter to be at or near the tip of the peg. Thus L g —>• 0 if an RCC is used. Figure 10-23 shows the configuration of the peg, the hole, and the supporting stiffnesses when L g = 0. In this case, K x hardly deforms at all. This removes the source of a large lateral force on the peg that would have acted at distance L g from the tip of the peg, exerting a con- siderable moment and giving rise to large contact forces during two-point contact. The product of these contact FIGURE 10-23. When L g is Almost Zero, the Lateral Support Spring Hardly De- forms Under Angular Er- ror. Compare the deformation of the springs with that in Fig- ure 10-13, which shows the case where L a » 0. forces with friction coefficient /z is the main source of insertion force. Drastically reducing these contact forces consequently drastically reduces the insertion force for a given lateral and angular error. Section 10.J derives all these forces and presents a short computer program that permits study of different part mating conditions by cal- culating insertion forces and deflections as functions of insertion depth. The next section shows example experi- mental data and compares them with these equations. 10.C.5. Typical Insertion Force Histories We can get an idea of the meaning of the above relations by looking at a few insertion force histories. These were obtained by mounting a peg and hole on a milling machine and lowering the quill to insert the peg into the hole. A 6-axis force-torque sensor recorded the forces. The peg was held by an RCC. The experimental conditions are given in Table 10-1. TABLE 10-1. Experimental Conditions for Part Mating Experiments Support: Draper Laboratory Remote Center Compliance Lateral stiffness = K x = 1 N/mm (40 Ib/in.) Angular stiffness = K® = 53,000 N-mm/rad (470 in lb/rad) Peg and hole: Steel, hardened and ground Hole diameter = 12.705 mm (0.5002 in.) Peg diameter = 12.672 mm (0.4989 in.) Clearance ratio = 0.0026 Coefficient of friction = 0.1 (determined empirically from one-point contact data) M = -F x L g 10.C. PART MATING THEORY FOR ROUND PARTS WITH CLEARANCE AND CHAMFERS 275 FIGURE 10-24. Insertion Force History. The compliance center is 4r back inside the peg from the tip. There is lateral error only, no angular error. As expected, two-point contact occurs, giving rise to the peak in the insertion force at a depth of about 18 mm. The peak at around 0 mm is due to chamfer crossing. Also shown on the plot is a theoretical estimate of insertion force based on equations given in the Section 10.J. A computer program in Section 10.J was used to create the theoretical plot. Figure 10-24 shows a typical history of F z for a case where there is only lateral error and the compliance center is about 4r away from the tip of the peg. The first peak in the force indicates chamfer crossing. Between t — \ mm and 1 = 9 mm is one-point contact, following which two- point contact occurs. The maximum force occurs at about £=18 mm or about twice the depth at which two-point contact began. For many cases, we can prove that the peak force will occur at this depth. A sketch of the proof is in Section 10.J. Figure 10-25 shows the insertion force for the case where the lateral error is larger than that in Figure 10-24, but L g is almost zero. Here, there is essentially no two- point contact, as predicted intuitively by Figure 10-14 and Figure 10-23. Also shown is the lateral force F x . These results show the merit of placing the compliance center near the tip of the peg. FIGURE 10-25. Insertion and Lateral Force History. The peg, hole, and compliant support are the same as in Fig- ure 10-24, but L g is essentially zero. As predicted, two- point contact does not occur, even though there is initially more lateral error than in Figure 10-24. This additional lat- eral error also is responsible for the larger chamfer crossing force (the large spike at t = 0) in this case compared to Figure 10-24. Figure 10-26 summarizes the conditions for successful chamfered compliantly supported rigid peg-hole mating. 10.C.6. Comment on Chamfers Chamfers play a central role in part mating. Clearly, wider chamfers make assembly easier since they lessen the re- strictions on the permissible lateral error. Chapter 17 dis- cusses the relationships among the various sources of error in an assembly workstation and describes how to calculate the width of chamfers needed. While all of the figures in this chapter show chamfers on the hole, the same conclusions can be drawn if the chamfer is on the peg. If both peg and hole have chamfers, then W in Equation (10-7) and Figure 10-20 is the sum of the widths of these chamfers. Also, it is significant that if a properly designed com- pliant support is used, with its compliance center at the tip 276 10 ASSEMBLY OF COMPLIANTLY SUPPORTED RIGID PARTS FIGURE 10-26. Pictorial Summary of Conditions for Successful Assembly of Round Pegs and Holes with Chamfers. of the peg, there will be little insertion force except that generated by chamfer crossing. As Chapter 11 shows, the magnitude of this force depends heavily on the slope and shape of the chamfers. While most chamfers are flat 45-degree bevels, some solutions to rigid part mating problems have been based on chamfers of other shapes. Figure 10-27 shows two exam- ples of designs for the ends of plug gauges. Plug gauges are measuring tools used to determine if a hole is the correct diameter. To make this determination accurately requires that the clearance between hole and gauge be very small, making it difficult and time-consuming to insert and re- move the gauge, and to avoid wedging it in the hole. The designs in Figure 10-27 specifically prevent wedging by making the ends of the gauges spheres whose radii are equal to the peg's diameter. The small undercut in the second design also helps to avoid damaging the rim of the hole. FIGURE 10-27. Two De- signs of Chamfer That Prevent Wedging. Note that the radius of the arc forming the nose of the peg is equal in length to the diameter of the peg. In order to avoid wedging, it is necessary to pivot the peg about the point where the nose becomes tangent to the straight side, as shown at the right. 10.D. CHAMFERLESS ASSEMBLY Chamferless assembly is a rare event compared to cham- fered insertion because only a few parts have to be made without chamfers. Many of these are parts of hydraulic valves, whose sharp edges are essential for obtaining the correct fluid flow patterns inside the valves. In other cases, chamfers must be very small due to lack of space; a cham- fer always adds length to a part, and sometimes there is a severe length constraint, either on a part or on the whole product. Chamferless assemblies are, of course, more dif- ficult than chamfered ones because W in Equation (10-8) is essentially zero. An attempt to assemble such parts by directly controlling the lateral error to be less than the clearance is almost certain to fail. This is especially true of hydraulic valve parts, whose clearances are only 10 or 20 fim (0.0004" to 0.0008"). In spite of their relative rarity, chamferless assemblies have attracted much research interest and some solutions that require active control, such as that in Figure 10-28. This is a multiphase method in which the peg is lowered until it strikes the surface well to one side of the hole. The 10.D. CHAMFERLESS ASSEMBLY 277 FIGURE 10-28. A Chamferless Assembly Strategy: (1) Approach, (2) Slide laterally, (3) Catch the Rim of the Hole and Tilt, (4) Lower Peg into Hole. lateral error may not be known exactly but the direction toward the hole is known well enough for the method to proceed. The peg is then slid sideways toward the hole. It is held compliantly near the top so that when it passes over the edge of the hole its tip catches the rim of the hole and it starts to tip over. A sensor detects this tilt and lateral motion is stopped and reversed slightly. Hopefully this allows the tip to fall slightly into the hole. The peg is then lowered carefully. Rocking and lowering are repeated until the peg is in. An elaboration of this strategy is employed by the Hi- Ti Hand ([Goto et al.]), a motorized fine motion device invented by Hitachi, Ltd. In this method, if the peg meets resistance during the lowering phase, it is gently rocked side to side in two perpendicular planes. The limits of this rocking are detected by sensors, and the top of the peg is then positioned midway between the limits. The peg is then pushed down some more or until resistance is again detected. This push and rock procedure is repeated as necessary until the peg is all the way in. In the case of the Hi-Ti Hand, mating time is typically 3 to 5 seconds. This method is good if the parts are delicate because it specif- ically limits the insertion force. For parts that can stand a little contact force, however, it is far too slow. Typical assembly times for chamfered parts held by an RCC are of the order of 0.2 seconds. Figure 10-29 shows an entirely passive chamferless assembly method ([Gustavson, Selvage, and Whitney]). "Passive" means that it contains no sensors or motors. Figure 10-30 is a schematic of the apparatus itself. It has several novel features, including two centers of compli- ance which operate one after the other. The operation be- gins with the peg deliberately tilted into an angular error and as little lateral error as possible. (Note that this is the opposite of the initial conditions for the Hi-Ti Hand, where initial angular error is zero and there is deliberate lateral error.) When the peg is tilted, one side of the peg FIGURE 10-29. Passive Chamferless Assembly Strategy. The inserter works by first permitting the peg to approach the hole tilted and then to turn up to an upright orientation with one edge slightly in the mouth of the hole. Insertion proceeds from that point with the aid of a conventional RCC. The de- tails of how this is accomplished are shown in Figure 10-30. FIGURE 10-30. Schematic of Passive Chamferless In- serter. Left: Arrangement of the device while the peg is ap- proaching the hole. The first compliance center is active and the part can rotate around it because of the sprung linkage attached to the gripper. The linkage is designed so that the tip of the peg does not move laterally very much while the peg is rotating up to vertical. What little tip motion there is will be in a direction away from the first compliance center so as to keep the tip pressed firmly against the rim of the hole. By this means the peg is most likely to remain in the mouth of the hole. Right: The part has engaged the mouth of the hole and is now locked into the vertical position. Insertion proceeds from here the same as if there had been chamfers and chamfer crossing were complete. Next Page 278 10 ASSEMBLY OF COMPLIANTLY SUPPORTED RIGID PARTS effectively acts as a chamfer, and it is almost certain that the tip of the peg and mouth of the hole will meet. Once they meet, the gripper continues moving down while the peg tilts up to approximately vertical under the influence of the linkage which creates the first compliance center. Upon reaching vertical, the peg locks into the gripper and comes under the influence of the compliant support above 10.E. SCREW THREAD MATING it, having the second center of compliance at the tip of the peg. The peg's tip stays in the mouth of the hole while rotating up to vertical. Insertion then proceeds as if the parts had chamfers, starting from the point where chamfer crossing is complete. Examples of the apparatus in Figure 10-30 are in use installing valves into automobile engine cylinder heads. Figure 10-4 showed normally mated screws. Assembling screws involves a chamfer mate similar to peg-hole mat- ing followed by thread engagement. The screw (or nut) is then turned several turns until it starts to tighten. The last stage comprises tightening a specified amount. Aside from missing the mouth of the hole, screw mat- ing can fail in two possible ways. One is a mismatch of threads caused by angular error normal to the insertion direction. The other is a mismatch caused by having the peaks of the screw miss the valleys of the hole due to an- gular error along the insertion direction. Both of these are interchangeably called "cross-threading." In order for the threads to mismate angularly normal to the insertion direction, the angular error must be greater than the angle a. between successive peaks or valleys, de- fined in Figure 10-31. If we define the angle between peaks as a, the diameter of the screw as d, and the thread pitch as p threads per unit length, then Values for a for different standard screw thread sizes are shown in Figure 10-32. They indicate that for very small screws, an angular error of 1.14 mrad or 0.8 degree is enough to cause a tilt mismatch. Angular control at this level is comparable to that required to mate precision pegs and holes, as indicated in Figure 10-17. For larger screws, the angles become comfortably large, indicating what is FIGURE 10-31. Schematic of Screw Thread Defining p and d. In order for threads to mismate due to tilt angle error, the tilt must be greater than a. FIGURE 10-32. Maximum Permissible Angular Error Ver- sus Screw Size for UNC Threads to Prevent Tilt Mismatch Between Threads. Since angular errors are relatively easy to keep below a few tenths of a degree, angular cross- threading is fairly easy to avoid for all but the smallest screws. found in practice, namely that this kind of error does not happen very often since angular control as good as a de- gree or so is easy to obtain, even from simple tools and fixtures. The other kind of screw mating error is illustrated in Figure 10-33. Here, the error is also angular, but the angle in question is about the insertion axis in the twist direc- tion. That is, the thread helices are out of phase. Unless the materials of either the screw or the hole are soft, this kind of error is also difficult to create. Some study of this problem may be found in Russian papers. Figure 10-34 and Figure 10-35 are from [Romanov]. The screw has a taper or chamfer of angle oc while the hole thread has a taper of angle y. The analysis in this paper is entirely geometric, with no consideration of friction. The conclusion is that a should be greater than y (see Figure 10-36). This is an interesting conclusion because the Russian standards at the time the paper was written were a = 45 degrees, y = 60. Previous Page 10.E. SCREW THREAD MATING 279 FIGURE 10-33. Mismated Screws Due to Helical Phase Error. The helices of the screw's threads and the hole's threads are out of phase and have inter- fered plastically with each other. FIGURE 10-34. Variables Involved in Predicting Screw Cross-Threading. ([Romanov]) Region 1: Adjacent Threads Crossed Region 2: Screw Tilted ~ p/d Region 3: Screw Tilted ~ 2p/d Note: The graph is drawn for p/d = 0.156, but graphs for other p/d are similar. FIGURE 10-35. Sample Diagram of Good and Bad Values of of and y. ([Romanov]) FIGURE 10-36. Screw and Threaded Hole with Screw Chamfer Steeper than Hole Chamfer. Another method of aiding the starting of screws is to drastically change the shape of the tip. Two examples are shown in Figure 10-37. These are called "dog point" and "cone point" screws. Each has two disadvantages—extra cost and extra length—but the advantages are valuable. The dog point is a short cylinder that assures that the screw is centered in the hole and parallel to it. The cone point provides the largest possible chamfer, making it easier to put the screw in a poorly toleranced or uncertainly located hole, such as in sheet metal. The above methods of assembling screws all depend on the helices mating with the correct phase without doing anything explicit to ensure that correct phase is achieved. A method that searches for the correct phase is the "turn backwards first" method, known to work well with lids of peanut butter jars. Usually this method requires sensing. To utilize it, one places screw and hole mouth-to-mouth and turns the screw backwards until one senses that the it has advanced suddenly. The magnitude of this advance is approximately one thread pitch. At this point, the threads are in a dangerous configuration, with chamfered peaks al- most exactly facing each other. So it is necessary to turn an additional amount back, perhaps 45 degrees. Then it is safe to begin turning forwards. If a full turn is made without an advance being detected, successful mating will not be possible, and the parts should be separated. This method is slow and, as stated, requires sensing, but it works well and may be necessary in the case of unusually large diameters and small thread pitches, where even small angular errors can cause mismating. FIGURE 10-37. (a) Dog Point and (b) Cone Point Screws. [...]... Compliance," Assembly Automation, August, pp 204-210, 1981 [Baumeister and Marks] Baumeister, T., and Marks, L S., Standard Handbook for Mechanical Engineers, 7th ed., New York: McGraw-Hill, 1967 [Dunne] Dunne, B J., "Precision Torque Control for Threaded Part Assembly," M.S thesis, MIT Mechanical Engineering Department, 1986 [Gustavson, Selvage, and Whitney] Gustavson, R E., Selvage, C C., and Whitney, D E.,... geometric conditions given for gears and screws are also merely necessary ones and are not sufficient, implying that the true conditions are more restrictive 10.H PROBLEMS AND THOUGHT QUESTIONS 1 Take apart a mechanical item (the stapler, a pump, toaster, light fixture, etc.) and classify the part mates as follows: Type of mate—peg/hole, press, tab/slot, screw, solder or glue, thermal shrink, bayonet, compliant... many criteria that we list only a few, involving the insertion force (force in the direction of insertion) or withdrawal force 1 Avoid sharp discontinuities in force versus insertion depth 2 Minimize mechanical work during insertion 3 Minimize the peak value attained by the insertion force during insertion 4 Achieve a specific pattern of force versus depth 5 Achieve a specific ratio of insertion force... shape becomes the focus of attention in the quest to reduce insertion force This is the topic of the next section of this chapter 11.D DESIGN OF CHAMFERS 11.D.1 Introduction The chamfer is the hero of mechanical parts assembly It guides parts together when they are laterally or angularly misaligned Since misalignment is almost inevitable, chamfers are called into play all the time Yet they are often . Handbook for Mechanical Engineers, 7th ed., New York: McGraw-Hill, 1967. [Dunne] Dunne, B. J., "Precision Torque Control for Threaded Part Assembly," M.S. thesis, MIT Mechanical. there is a severe length constraint, either on a part or on the whole product. Chamferless assemblies are, of course, more dif- ficult than chamfered ones because W in Equation (10-8) is . or 20 fim (0.0004" to 0.0008"). In spite of their relative rarity, chamferless assemblies have attracted much research interest and some solutions that require active control,